% % % % automatically generated % % bibtex2html /home/sontag/grants/publication_list.bib -sort-criterium year % Date: Sat Oct 3 12:23:34 2009 % Author: sontag % % % @INCOLLECTION{angeli_sontag_mitbook09, AUTHOR = {D. Angeli and E.D. Sontag}, BOOKTITLE = {Control Theory in Systems Biology}, PUBLISHER = {MIT Press}, TITLE = {Graphs and the Dynamics of Biochemical Networks}, YEAR = {2009}, OPTADDRESS = {}, OPTCHAPTER = {}, OPTCROSSREF = {}, OPTEDITION = {}, EDITOR = {B. Ingalls and P. Iglesias}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, PAGES = {125-142}, OPTSERIES = {}, OPTTYPE = {}, OPTVOLUME = {}, ABSTRACT = { This is an expository paper about graph-theoretical properties of biochemical networks, discussing two approaches, one based on bipartite graphs and Petri net concepts, and another based on decompositions into order-preserving subsystems. Other papers on this website contain basically the same material. } } @INCOLLECTION{delvecchio_sontag_mitbook09, AUTHOR = {Del Vecchio, D. and E.D. Sontag}, BOOKTITLE = {Control Theory in Systems Biology}, PUBLISHER = {MIT Press}, TITLE = {Synthetic Biology: A Systems Engineering Perspective}, YEAR = {2009}, OPTADDRESS = {}, OPTCHAPTER = {}, OPTCROSSREF = {}, OPTEDITION = {}, EDITOR = {B. Ingalls and P. Iglesias}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, PAGES = {101-123}, OPTSERIES = {}, OPTTYPE = {}, OPTVOLUME = {}, ABSTRACT = { This is an expository paper about certain aspects of Synthetic Biology, including a discussion of the issue of modularity (load effects from downstream components). } } @ARTICLE{angeli_hirsch_sontag_jde09, AUTHOR = {D. Angeli and M.W. Hirsch and E.D. Sontag}, JOURNAL = {J. of Differential Equations}, TITLE = {Attractors in coherent systems of differential equations}, YEAR = {2009}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, PAGES = {3058-3076}, VOLUME = {246}, KEYWORDS = {monotone systems, positive feedback systems}, PDF = {../FTP_DIR/hirsch_angeli_sontag_jde09_ps2pdf.pdf}, ABSTRACT = {Attractors of cooperative dynamical systems are particularly simple; for example, a nontrivial periodic orbit cannot be an attractor. This paper provides characterizations of attractors for the wider class of systems defined by the property that all directed feedback loops are positive. Several new results for cooperative systems are obtained in the process.} } @ARTICLE{biotechprogress08, AUTHOR = {D. Angeli and de Leenheer, P. and E.D. Sontag}, JOURNAL = {Biotechnology Progress}, TITLE = {Chemical networks with inflows and outflows: A positive linear differential inclusions approach}, YEAR = {2009}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, PAGES = {632-642}, VOLUME = {25}, KEYWORDS = {biochemical networks, fluxes, differential inclusions, positive systems, Petri nets, persistence, biochemical networks, differential inclusions, switched systems}, PDF = {../FTP_DIR/angeli_leenheer_sontag_biotech08.pdf}, ABSTRACT = {Certain mass-action kinetics models of biochemical reaction networks, although described by nonlinear differential equations, may be partially viewed as state-dependent linear time-varying systems, which in turn may be modeled by convex compact valued positive linear differential inclusions. A result is provided on asymptotic stability of such inclusions, and applied to biochemical reaction networks with inflows and outflows. Included is also a characterization of exponential stability of general homogeneous switched systems } } @ARTICLE{reaction_coordinates08, AUTHOR = {D. Angeli and de Leenheer, P. and E.D. Sontag}, JOURNAL = {J. Mathematical Biology}, TITLE = {Graph-theoretic characterizations of monotonicity of chemical networks in reaction coordinates}, YEAR = {2009}, OPTMONTH = {}, NOTE = {Accepted subject to revisions.}, OPTNUMBER = {}, OPTPAGES = {}, OPTVOLUME = {}, KEYWORDS = {biochemical networks, fluxes, monotone systems, reaction cordinates, Petri nets, persistence, futile cycles}, ABSTRACT = { This paper derives new results for certain classes of chemical reaction networks, linking structural to dynamical properties. In particular, it investigates their monotonicity and convergence without making assumptions on the form of the kinetics (e.g., mass-action) of the dynamical equations involved, and relying only on stoichiometric constraints. The key idea is to find an alternative representation under which the resulting system is monotone. As a simple example, the paper shows that a phosphorylation/dephosphorylation process, which is involved in many signaling cascades, has a global stability property. } } @ARTICLE{chaves_sengupta07, AUTHOR = {M. Chaves and A. Sengupta and E.D. Sontag}, JOURNAL = {J. of Mathematical Biology}, TITLE = {Geometry and topology of parameter space: investigating measures of robustness in regulatory networks}, YEAR = {2009}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, PAGES = {315-358}, VOLUME = {59}, PDF = {../FTP_DIR/chaves_sengupta_sontag_j_math_biology_2009.pdf}, ABSTRACT = {The concept of robustness of regulatory networks has been closely related to the nature of the interactions among genes, and the capability of pattern maintenance or reproducibility. Defining this robustness property is a challenging task, but mathematical models have often associated it to the volume of the space of admissible parameters. Not only the volume of the space but also its topology and geometry contain information on essential aspects of the network, including feasible pathways, switching between two parallel pathways or distinct/disconnected active regions of parameters. A method is presented here to characterize the space of admissible parameters, by writing it as a semi-algebraic set, and then theoretically analyzing its topology and geometry, as well as volume. This method provides a more objective and complete measure of the robustness of a developmental module. As a detailed case study, the segment polarity gene network is analyzed. } } @ARTICLE{adel, AUTHOR = {A. Dayarian and M. Chaves and E.D. Sontag and A. Sengupta}, JOURNAL = {PLoS Computational Biology}, TITLE = {Shape, Size and Robustness: Feasible Regions in the Parameter Space of Biochemical Networks}, YEAR = {2009}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, PAGES = {e10000256}, VOLUME = {5}, PDF = {../FTP_DIR/dayarian_chaves_sontag_sengupta_plos09.pdf}, ABSTRACT = {The concept of robustness of regulatory networks has received much attention in the last decade. One measure of robustness has been associated with the volume of the feasible region, namely, the region in the parameter space in which the system is functional. In recent work, we emphasized that topology and geometry matter, as well as volume. In this paper, and using the segment polarity gene network to illustrate our approach, we show that random walks in parameter space and how they exit the feasible region provide a rich perspective on the different modes of failure of a model. In particular, for the segment polarity network, we found that, between two alternative ways of activating Wingless, one is more robust. Our method provides a more complete measure of robustness to parameter variation. As a general modeling strategy, our approach is an interesting alternative to Boolean representation of biochemical networks. } } @ARTICLE{riley07hmm, AUTHOR = {T. Riley and X. Yu and E.D. Sontag and A. Levine}, JOURNAL = {BMC Bioinformatics}, TITLE = {The P53HMM algorithm: using novel profile Hidden Markov Models to detect p53-responsive genes}, YEAR = {2009}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, PAGES = {111}, VOLUME = {10}, KEYWORDS = {Hidden Markov Models, p53, transcription factors}, PDF = {../FTP_DIR/riley_yu_sontag_levine_p53hmm_bmc_bioinformatics09.pdf}, ABSTRACT = { A novel computational method (called p53HMM) is presented that utilizes Profile Hidden Markov Models (PHMM's) to estimate the relative binding affinities of putative p53 response elements (RE's), both p53 single-sites and cluster-sites. These models incorporate a novel ``Correlated Baum Welch'' training algorithm that provides increased predictive power by exploiting the redundancy of information found in the repeated, palindromic p53-binding motif. The predictive accuracy of these new models are compared against other predictive models, including position specic score matrices (PSSM's, or weight matrices). Finally, we provide experimental evidence that verifies a predicted p53-target site that regu- lates the CHMP4C gene. The P53HMM algorithm is available on-line from http://tools.csb.ias.edu. }, DOI = {10.1186/1471-2105-10-111} } @ARTICLE{russo_dibernardo_sontag09, AUTHOR = {G. Russo and di Bernardo, M. and E.D. Sontag}, JOURNAL = {}, TITLE = {Global entrainment of transcriptional systems to periodic inputs}, YEAR = {2009}, OPTMONTH = {}, NOTE = {Submitted. Preprint in http://arxiv.org/abs/0907.0017.}, OPTNUMBER = {}, OPTPAGES = {}, OPTVOLUME = {}, KEYWORDS = {contractive systems, systems biology, biochemical networks, gene and protein networks}, ABSTRACT = {This paper addresses the problem of giving conditions for transcriptional systems to be globally entrained to external periodic inputs. By using contraction theory, a powerful tool from dynamical systems theory, it is shown that certain systems driven by external periodic signals have the property that all solutions converge to a fixed limit cycle. General results are proved, and the properties are verified in the specific case of some models of transcriptional systems. } } @ARTICLE{scardovi_arcak_TAC09, AUTHOR = {L. Scardovi and M. Arcak and E.D. Sontag}, JOURNAL = {IEEE Transactions Autom. Control}, TITLE = {Synchronization of interconnected systems with applications to biochemical networks: an input-output approach}, YEAR = {2009}, OPTMONTH = {}, NOTE = {Accepted for publication.}, OPTNUMBER = {}, OPTPAGES = {}, OPTVOLUME = {}, PDF = {http://arxiv.org/pdf/0903.1882v1}, ABSTRACT = {This paper provides synchronization conditions for networks of nonlinear systems, where each component of the network itself consists of subsystems represented as operators in the extended L2 space. The synchronization conditions are provided by combining the input-output properties of the subsystems with information about the structure of network. The paper also explores results for state-space models as well as biochemical applications. The work is motivated by cellular networks where signaling occurs both internally, through interactions of species, and externally, through intercellular signaling. } } @ARTICLE{feedforward_circuits_adaptation, AUTHOR = {E.D. Sontag}, JOURNAL = {IET Systems Biology}, TITLE = {Remarks on Feedforward Circuits, Adaptation, and Pulse Memory}, YEAR = {2009}, OPTMONTH = {}, NOTE = {To appear. Preprint: http://arxiv.org/abs/0812.0622.}, OPTNUMBER = {}, OPTPAGES = {}, OPTVOLUME = {}, ABSTRACT = { This note studies feedforward circuits as models for perfect adaptation to step signals in biological systems. A global convergence theorem is proved in a general framework, which includes examples from the literature as particular cases. A notable aspect of these circuits is that they do not adapt to pulse signals, because they display a memory phenomenon. Estimates are given of the magnitude of this effect. } } @ARTICLE{sontag-wang-megretski-tac, AUTHOR = {E.D. Sontag and Y. Wang and A. Megretski}, JOURNAL = {IEEE Transactions Autom. Control}, TITLE = {Input classes for identification of bilinear systems}, YEAR = {2009}, OPTMONTH = {}, NOTE = {Also arXiv math.OC/0610633, 20 Oct 2006, and short version in ACC'07.}, OPTNUMBER = {}, PAGES = {195-207}, VOLUME = {54}, KEYWORDS = {realization theory, observability, identifiability, bilinear systems}, PDF = {../FTP_DIR/sontag_wang_megretski_inputs_tac_54_195_207.pdf}, ABSTRACT = { This paper asks what classes of input signals are sufficient in order to completely identify the input/output behavior of generic bilinear systems. The main results are that step inputs are not sufficient, nor are single pulses, but the family of all pulses (of a fixed amplitude but varying widths) do suffice for identification. } } @ARTICLE{mvp, AUTHOR = {E.D. Sontag and D. Zeilberger}, JOURNAL = {Advances in Applied Mathematics}, TITLE = {A symbolic computation approach to a problem involving multivariate Poisson distributions}, YEAR = {2009}, OPTMONTH = {}, NOTE = {To appear. See also http://arxiv.org/abs/0906.1141.}, OPTNUMBER = {}, OPTPAGES = {}, OPTVOLUME = {}, KEYWORDS = {probability theory, systems biology, biochemical networks, Chemical Master Equation}, PDF = {../FTP_DIR/sontag_zeilberger_mvp_final_version_28sep09v2.pdf}, ABSTRACT = {Multivariate Poisson random variables subject to linear integer constraints arise in several application areas, such as queuing and biomolecular networks. This note shows how to compute conditional statistics in this context, by employing WZ Theory and associated algorithms. A symbolic computation package has been developed and is made freely available. A discussion of motivating biomolecular problems is also provided. } } @ARTICLE{weinstein07, AUTHOR = {A.M. Weinstein and E.D. Sontag}, JOURNAL = {Bulletin of Mathematical Biology}, TITLE = {Modeling proximal tubule cell homeostasis: Tracking changes in luminal flow}, YEAR = {2009}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, PAGES = {1285-1322}, VOLUME = {71}, PDF = {../FTP_DIR/weinstein_sontag_bulletin_math_biology_proximal_tubule_2009.pdf}, ABSTRACT = {During normal kidney function, there are are routinely wide swings in proximal tubule fluid flow and proportional changes in Na+ reabsorption across tubule epithelial cells. This "glomerulotubular balance" occurs in the absence of any substantial change in cell volume, and is thus a challenge to coordinate luminal membrane solute entry with peritubular membrane solute exit. In this work, linear optimal control theory is applied to generate a configuration of regulated transporters that could achieve this result. A previously developed model of rat proximal tubule epithelium is linearized about a physiologic reference condition; the approximate linear system is recast as a dynamical system; and a Riccati equation is solved to yield optimal linear feedback that stabilizes Na+ flux, cell volume, and cell pH. This optimal feedback control is largely consigned to three physiologic variables, cell volume, cell electrical potential, and lateral intercellular hydrostatic pressure. Transport modulation by cell volume stabilizes cell volume; transport modulation by electrical potential or interspace pressure act to stabilize Na+ flux and cell pH. This feedback control is utilized in a tracking problem, in which reabsorptive Na+ flux varies over a factor of two. The resulting control parameters consist of two terms, an autonomous term and a feedback term, and both terms include transporters on both luminal and peritubular cell membranes. Overall, the increase in Na+ flux is achieved with upregulation of luminal Na+/H+ exchange and Na+-glucose cotransport, with increased peritubular Na+-3HCO_3- and K+-Cl- cotransport, and with increased Na+,K+-ATPase activity. The configuration of activated transporters emerges as testable hypothesis of the molecular basis for glomerulotubular balance. It is suggested that the autonomous control component at each cell membrane could represent the cytoskeletal effects of luminal flow. } } @INPROCEEDINGS{09cdc_angeli_leenheer, AUTHOR = {D. Angeli and de Leenheer, P. and E.D. Sontag}, BOOKTITLE = {Proc. IEEE Conf. Decision and Control, Shanhai, Dec. 2009}, TITLE = {On persistence of chemical reaction networks with time-dependent kinetics and no global conservation laws}, YEAR = {2009}, OPTADDRESS = {}, OPTCROSSREF = {}, OPTEDITOR = {}, OPTMONTH = {}, NOTE = {To appear. Paper 347.}, OPTNUMBER = {}, OPTORGANIZATION = {}, OPTPAGES = {}, OPTPUBLISHER = {}, OPTSERIES = {}, OPTVOLUME = {}, KEYWORDS = {biochemical networks, fluxes, Petri nets, persistence, biochemical networks with inputs}, PDF = {../FTP_DIR/09cdc_angeli_leenheer_sontag_final.pdf}, ABSTRACT = {New checkable criteria for persistence of chemical reaction networks are proposed, which extend those obtained by the authors in previous work. The new results allow the consideration of reaction rates which are time-varying, thus incorporating the effects of external signals, and also relax the assumption of existence of global conservation laws, thus allowing for inflows (production) and outflows (degradation). As an illustration, a hypoxia network is analyzed. } } @INPROCEEDINGS{ddv_ecc09, AUTHOR = {Del Vecchio, D. and E.D. Sontag}, BOOKTITLE = {Proceedings of the European Control Conference 2009, August 23-26, 2009, Budapest}, TITLE = {Engineering Principles in Bio-Molecular Systems: From Retroactivity to Modularity}, YEAR = {2009}, OPTADDRESS = {}, OPTCROSSREF = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, OPTORGANIZATION = {}, PAGES = {MoB2.2}, OPTPUBLISHER = {}, OPTSERIES = {}, OPTVOLUME = {}, KEYWORDS = {systems biology, biochemical networks, synthetic biology, futile cycles, singular perturbations, modularity} } @INPROCEEDINGS{09cdc_scardovi_arcak_part1, AUTHOR = {L. Scardovi and M. Arcak and E.D. Sontag}, BOOKTITLE = {Proc. IEEE Conf. Decision and Control, Shanhai, Dec. 2009}, TITLE = {Synchronization of interconnected systems with an input-output approach. Part I: Main results}, YEAR = {2009}, OPTADDRESS = {}, OPTCROSSREF = {}, OPTEDITOR = {}, OPTMONTH = {}, NOTE = {To appear. Paper 2847. First part of conference version of journal paper.}, OPTNUMBER = {}, OPTORGANIZATION = {}, OPTPAGES = {}, OPTPUBLISHER = {}, OPTSERIES = {}, OPTVOLUME = {}, KEYWORDS = {passive systems, secant condition, biochemical networks, systems biology}, ABSTRACT = {See abstract and link to pdf in entry for Journal paper. } } @INPROCEEDINGS{09cdc_scardovi_arcak_part2, AUTHOR = {L. Scardovi and M. Arcak and E.D. Sontag}, BOOKTITLE = {Proc. IEEE Conf. Decision and Control, Shanhai, Dec. 2009}, TITLE = {Synchronization of interconnected systems with an input-output approach. Part II: State-Space result and application to biochemical networks}, YEAR = {2009}, OPTADDRESS = {}, OPTCROSSREF = {}, OPTEDITOR = {}, OPTMONTH = {}, NOTE = {To appear. Paper 2883. Second part of conference version of journal paper.}, OPTNUMBER = {}, OPTORGANIZATION = {}, OPTPAGES = {}, OPTPUBLISHER = {}, OPTSERIES = {}, OPTVOLUME = {}, KEYWORDS = {passive systems, secant condition, biochemical networks, systems biology}, ABSTRACT = {See abstract and link to pdf in entry for Journal paper. } } @TECHREPORT{arxiv_chaos_2009, AUTHOR = {E.D. Sontag}, INSTITUTION = {arxiv 0906.2166}, TITLE = {An observation regarding systems which converge to steady states for all constant inputs, yet become chaotic with periodic inputs}, YEAR = {2009}, OPTADDRESS = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, OPTTYPE = {}, PDF = {http://arxiv.org/pdf/0906.2166} } @INCOLLECTION{SontagArcakSagarBook08, AUTHOR = {M. Arcak and E.D. Sontag}, BOOKTITLE = {Recent Advances in Learning and Control}, PUBLISHER = {Springer-Verlag, NY}, TITLE = {Passivity-based Stability of Interconnection Structures}, YEAR = {2008}, OPTADDRESS = {}, OPTCHAPTER = {}, OPTCROSSREF = {}, OPTEDITION = {}, EDITOR = {V. Blondel and S. Boyd and H. Kimura}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, PAGES = {195-204}, OPTSERIES = {}, OPTTYPE = {}, VOLUME = {Volume 371}, KEYWORDS = {passive systems, secant condition, biochemical networks}, PDF = {../FTP_DIR/sontag_arcak_vidyasagar_book.pdf}, ABSTRACT = {In this expository paper, we provide a streamlined version of the key lemma on stability of interconnections due to Vidyasagar and Moylan and Hill, and then show how it its hypotheses may be verified for network structures of great interest in biology.}, DOI = {10.1007/978-1-84800-155-8_14} } @ARTICLE{dasgupta-albert, AUTHOR = {R. Albert and B. Dasgupta and R. Dondi and E.D. Sontag}, JOURNAL = {Algorithmica}, TITLE = {Inferring (biological) signal transduction networks via transitive reductions of directed graphs}, YEAR = {2008}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, PAGES = {129-159}, VOLUME = {51}, KEYWORDS = {systems biology, biochemical networks, algorithms, signal transduction networks, graph algorithms}, PDF = {../FTP_DIR/albert_dasgupta_dondi_sontag_algorithmica.pdf}, ABSTRACT = {The transitive reduction problem is that of inferring a sparsest possible biological signal transduction network consistent with a set of experimental observations, with a goal to minimize false positive inferences even if risking false negatives. This paper provides computational complexity results as well as approximation algorithms with guaranteed performance.}, DOI = {10.1007/s00453-007-9055-0} } @ARTICLE{IEEEsysbio_AS, AUTHOR = {D. Angeli and E.D. Sontag}, JOURNAL = {IEEE Transactions on Circuits and Systems, Special Issue on Systems Biology}, TITLE = {Oscillations in I/O monotone systems}, YEAR = {2008}, OPTMONTH = {}, NOTE = {Preprint version in arXiv q-bio.QM/0701018, 14 Jan 2007}, OPTNUMBER = {}, PAGES = {166-176}, VOLUME = {55}, KEYWORDS = {monotone systems, hopf bifurcations, circadian rhythms, tridiagonal systems, nonlinear dynamics, systems biology, biochemical networks, oscillations, periodic behavior}, PDF = {../FTP_DIR/angeli_sontag_circadian_TAC_CAS_2008.pdf}, ABSTRACT = {In this note, we show how certain properties of Goldbeter's 1995 model for circadian oscillations can be proved mathematically, using techniques from the recently developed theory of monotone systems with inputs and outputs. The theory establishes global asymptotic stability, and in particular no oscillations, if the rate of transcription is somewhat smaller than that assumed by Goldbeter, based on the application of a tight small gain condition. This stability persists even under arbitrary delays in the feedback loop. On the other hand, when the condition is violated a Poincare'-Bendixson result allows to conclude existence of oscillations, for sufficiently high delays.} } @ARTICLE{translation-invariance, AUTHOR = {D. Angeli and E.D. Sontag}, JOURNAL = {Nonlinear Analysis Series B: Real World Applications}, TITLE = {Translation-invariant monotone systems, and a global convergence result for enzymatic futile cycles}, YEAR = {2008}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, PAGES = {128-140}, VOLUME = {9}, KEYWORDS = {systems biology, biochemical networks, nonlinear stability, dynamical systems, monotone systems}, PDF = {../FTP_DIR/angeli_sontag_translationinvariance_nonlinear_analysis08.pdf}, ABSTRACT = { Strongly monotone systems of ordinary differential equations which have a certain translation-invariance property are shown to have the property that all projected solutions converge to a unique equilibrium. This result may be seen as a dual of a well-known theorem of Mierczynski for systems that satisfy a conservation law. As an application, it is shown that enzymatic futile cycles have a global convergence property. }, DOI = {10.1016/j.nonrwa.2006.09.006} } @ARTICLE{arcak-sontag-MBSE07, AUTHOR = {M. Arcak and E.D. Sontag}, JOURNAL = {Mathematical Biosciences and Engineering}, TITLE = {A passivity-based stability criterion for a class of interconnected systems and applications to biochemical reaction networks}, YEAR = {2008}, OPTMONTH = {}, NOTE = {Also, preprint: arxiv0705.3188v1 [q-bio], May 2007}, OPTNUMBER = {}, PAGES = {1-19}, VOLUME = {5}, KEYWORDS = {systems biology, biochemical networks, cyclic feedback systems, secant condition, nonlinear stability, dynamical systems}, PDF = {../FTP_DIR/arcak_sontag_MBE_2008_galleys.pdf}, ABSTRACT = {This paper presents a stability test for a class of interconnected nonlinear systems motivated by biochemical reaction networks. One of the main results determines global asymptotic stability of the network from the diagonal stability of a "dissipativity matrix" which incorporates information about the passivity properties of the subsystems, the interconnection structure of the network, and the signs of the interconnection terms. This stability test encompasses the "secant criterion" for cyclic networks presented in our previous paper, and extends it to a general interconnection structure represented by a graph. A second main result allows one to accommodate state products. This extension makes the new stability criterion applicable to a broader class of models, even in the case of cyclic systems. The new stability test is illustrated on a mitogen activated protein kinase (MAPK) cascade model, and on a branched interconnection structure motivated by metabolic networks. Finally, another result addresses the robustness of stability in the presence of diffusion terms in a compartmental system made out of identical systems.} } @ARTICLE{ddv07, AUTHOR = {Del Vecchio, D. and A.J. Ninfa and E.D. Sontag}, JOURNAL = {Nature Molecular Systems Biology}, TITLE = {Modular Cell Biology: Retroactivity and Insulation}, YEAR = {2008}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, PAGES = {161}, VOLUME = {4}, KEYWORDS = {systems biology, biochemical networks, synthetic biology, futile cycles, singular perturbations, modularity}, PDF = {../FTP_DIR/delvecchio-ninfa-sontag-MSB2008-paper-and-supplement.pdf}, ABSTRACT = {Modularity plays a fundamental role in the prediction of the behavior of a system from the behavior of its components, guaranteeing that the properties of individual components do not change upon interconnection. Just as electrical, hydraulic, and other physical systems often do not display modularity, nor do many biochemical systems, and specifically, genetic networks. Here, we study the effect of interconnections on the input/output dynamic characteristics of transcriptional components, focusing on a property, which we call "retroactivity," that plays a role analogous to non-zero output impedance in electrical systems. In transcriptional networks, retroactivity is large when the amount of transcription factor is comparable to, or smaller than, the amount of promoter binding sites, or when the affinity of such binding sites is high. In order to attenuate the effect of retroactivity, we propose a feedback mechanism inspired by the design of amplifiers in electronics. We introduce, in particular, a mechanism based on a phosphorylation/dephosphorylation cycle. This mechanism enjoys a remarkable insulation property, due to the fast time scales of the phosphorylation and dephosphorylation reactions. Such a mechanism, when viewed as a signal transduction system, has thus an inherent capacity to provide insulation and hence to increase the modularity of the system in which it is placed.} } @ARTICLE{enciso_multi_submitted, AUTHOR = {G.A. Enciso and E.D. Sontag}, JOURNAL = {Journal of Biological Dynamics}, TITLE = {Monotone bifurcation graphs}, YEAR = {2008}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, PAGES = {121-139}, VOLUME = {2}, PDF = {../FTP_DIR/enciso_sontag_multicharacteristics_journal_biological_dynamics_2008.pdf}, ABSTRACT = {This paper generalizes the approach to bistability based on the existence of characteristics for open-loop monotone systems to the case when characteristics do not exist. A set-valued version is provided, instead.} } @ARTICLE{IEEEsysbio_JAS, AUTHOR = {M.R. Jovanovic and M. Arcak and E.D. Sontag}, JOURNAL = {IEEE Transactions on Circuits and Systems, Special Issue on Systems Biology}, TITLE = {A passivity-based approach to stability of spatially distributed systems with a cyclic interconnection structure}, YEAR = {2008}, OPTMONTH = {}, NOTE = {Preprint: also arXiv math.OC/0701622, 22 January 2007.}, OPTNUMBER = {}, PAGES = {75-86}, VOLUME = {55}, KEYWORDS = {MAPK cascades, systems biology, biochemical networks, nonlinear stability, nonlinear dynamics, diffusion, secant condition, cyclic feedback systems}, PDF = {../FTP_DIR/jovanovic_arcak_sontag_TAC_CAS2008.pdf}, ABSTRACT = {A class of distributed systems with a cyclic interconnection structure is considered. These systems arise in several biochemical applications and they can undergo diffusion driven instability which leads to a formation of spatially heterogeneous patterns. In this paper, a class of cyclic systems in which addition of diffusion does not have a destabilizing effect is identified. For these systems global stability results hold if the "secant" criterion is satisfied. In the linear case, it is shown that the secant condition is necessary and sufficient for the existence of a decoupled quadratic Lyapunov function, which extends a recent diagonal stability result to partial differential equations. For reaction-diffusion equations with nondecreasing coupling nonlinearities global asymptotic stability of the origin is established. All of the derived results remain true for both linear and nonlinear positive diffusion terms. Similar results are shown for compartmental systems.} } @ARTICLE{dasgupta-albert3, AUTHOR = {S. Kachalo and R. Zhang and E.D. Sontag and R. Albert and B. Dasgupta}, JOURNAL = {Bioinformatics}, TITLE = {NET-SYNTHESIS: A software for synthesis, inference and simplification of signal transduction networks}, YEAR = {2008}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, PAGES = {293 - 295}, VOLUME = {24}, KEYWORDS = {systems biology, biochemical networks, algorithms, signal transduction networks, graph algorithms}, PDF = {../FTP_DIR/kachalo_zhang_sontag_albert_dasgupta_bioinformatics08.pdf}, ABSTRACT = {This paper presents a software tool for inference and simplification of signal transduction networks. The method relies on the representation of observed indirect causal relationships as network paths, using techniques from combinatorial optimization to find the sparsest graph consistent with all experimental observations. We illustrate the biological usability of our software by applying it to a previously published signal transduction network and by using it to synthesize and simplify a novel network corresponding to activation-induced cell death in large granular lymphocyte leukemia.} } @ARTICLE{maayan07, AUTHOR = {A. Maayan and R. Iyengar and E.D. Sontag}, JOURNAL = {IET Systems Biology}, TITLE = {Intracellular Regulatory Networks are close to Monotone Systems}, YEAR = {2008}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, PAGES = {103-112}, VOLUME = {2}, PDF = {../FTP_DIR/maayan_lipshtat_iyengar_sontag_IETsystemsbio08.pdf}, ABSTRACT = {We find that three intracellular regulatory networks contain far more positive "sign-consistent" feedback and feed-forward loops than negative loops. Negative inconsistent loops can be more easily removed from real regulatory network topologies compared to removing negative loops from shuffled networks. The abundance of positive feed-forward loops and feedback loops in real networks emerges from the presence of hubs that are enriched with either negative or positive links, and from the non-uniform connectivity distribution. Boolean dynamics applied to the signaling network further support the stability of its topology. These observations suggest that the "close-to-monotone" structure of intracellular regulatory networks may contribute to the dynamical stability observed in cellular behavior.} } @ARTICLE{riley07, AUTHOR = {T. Riley and E.D. Sontag and P. Chen and A. Levine}, JOURNAL = {Nature Reviews Molecular Cell Biology}, TITLE = {The transcriptional regulation of human p53-regulated genes}, YEAR = {2008}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, PAGES = {402-412}, VOLUME = {9}, KEYWORDS = {Hidden Markov Models, p53, transcription}, PDF = {../FTP_DIR/riley_sontag_chen_levine_p53_nature_reviews_cell_bio_2008_including_supplements.pdf}, ABSTRACT = { The p53 protein regulates the transcription of many different genes in response to a wide variety of stress signals. Following DNA damage, p53 regulates key processes, including DNA repair, cell-cycle arrest, senescence and apoptosis, in order to suppress cancer. This Analysis article provides an overview of the current knowledge of p53-regulated genes in these pathways and others, and the mechanisms of their regulation. In addition, we present the most comprehensive list so far of human p53-regulated genes and their experimentally validated, functional binding sites that confer p53 regulation. } } @ARTICLE{essays_biochemistry, AUTHOR = {E.D. Sontag}, JOURNAL = {Essays in Biochemistry}, TITLE = {Network reconstruction based on steady-state data}, YEAR = {2008}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, PAGES = {161-176}, VOLUME = {45}, KEYWORDS = {systems biology, biochemical networks, gene and protein networks, reverse engineering, systems identification}, PUBLISHER = {Portland Press}, PDF = {../FTP_DIR/unravel_essays_biochem_reprint.pdf}, ABSTRACT = { The ``reverse engineering problem'' in systems biology is that of unraveling of the web of interactions among the components of protein and gene regulatory networks, so as to map out the direct or local interactions among components. These direct interactions capture the topology of the functional network. An intrinsic difficulty in capturing these direct interactions, at least in intact cells, is that any perturbation to a particular gene or signaling component may rapidly propagate throughout the network, thus causing global changes which cannot be easily distinguished from direct effects. Thus, a major goal in reverse engineering is to use these observed global responses - such as steady-state changes in concentrations of active proteins, mRNA levels, or transcription rates - in order to infer the local interactions between individual nodes. One approach to solving this global-to-local problem is the ``Modular Response Analysis'' (MRA) method proposed in work of the author with Kholodenko et. al. (PNAS, 2002) and further elaborated in other papers. The basic method deals only with steady-state data. However, recently, quasi-steady state MRA has been used by Santos et. al. (Nature Cell Biology, 2007) for quantifying positive and negative feedback effects in the Raf/Mek/Erk MAPK network in rat adrenal pheochromocytoma (PC-12) cells. This paper presents an overview of the MRA technique, as well as a generalization of the algorithm to that quasi-steady state case. } } @ARTICLE{sontag_laubenbacher_jarrah07, AUTHOR = {E.D. Sontag and A. Veliz-Cuba and R. Laubenbacher and A.S. Jarrah}, JOURNAL = {Biophysical Journal}, TITLE = {The effect of negative feedback loops on the dynamics of Boolean networks}, YEAR = {2008}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, PAGES = {518-526}, VOLUME = {95}, PDF = {../FTP_DIR/sontag_cuba_laubenbacher_jarrah_biophysical_journal_2008.pdf}, ABSTRACT = {Feedback loops play an important role in determining the dynamics of biological networks. In order to study the role of negative feedback loops, this paper introduces the notion of "distance to positive feedback (PF-distance)" which in essence captures the number of "independent" negative feedback loops in the network, a property inherent in the network topology. Through a computational study using Boolean networks it is shown that PF-distance has a strong influence on network dynamics and correlates very well with the number and length of limit cycles in the phase space of the network. To be precise, it is shown that, as the number of independent negative feedback loops increases, the number (length) of limit cycles tends to decrease (increase). These conclusions are consistent with the fact that certain natural biological networks exhibit generally regular behavior and have fewer negative feedback loops than randomized networks with the same numbers of nodes and connectivity. } } @ARTICLE{arxiv:futileequilibria, AUTHOR = {L. Wang and E.D. Sontag}, JOURNAL = {Journal of Mathematical Biology}, TITLE = {On the number of steady states in a multiple futile cycle}, YEAR = {2008}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, PAGES = {29-52}, VOLUME = {57}, KEYWORDS = {singular perturbations, futile cycles, MAPK cascades, systems biology, biochemical networks, multistability}, PDF = {../FTP_DIR/liming_wang_sontag_futile_cycles_JMB08.pdf}, ABSTRACT = {This note studies the number of positive steady states in biomolecular reactions consisting of activation/deactivation futile cycles, such as those arising from phosphorylations and dephosphorylations at each level of a MAPK cascade. It is shown that: (1) for some parameter ranges, there are at least n+1 (if n is even) or n (if n is odd) steady states; (2) there never are more than 2n-1 steady states (so, for n=2, there are no more than 3 steady states); (3) for parameters near the standard Michaelis-Menten quasi-steady state conditions, there are at most n+1 steady states; and (4) for parameters far from the standard Michaelis-Menten quasi-steady state conditions, there is at most one steady state.} } @ARTICLE{wang:JNS07, AUTHOR = {L. Wang and E.D. Sontag}, JOURNAL = {J. Nonlinear Science}, TITLE = {Singularly perturbed monotone systems and an application to double phosphorylation cycles}, YEAR = {2008}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, PAGES = {527-550}, VOLUME = {18}, KEYWORDS = {singular perturbations, futile cycles, MAPK cascades, systems biology, biochemical networks, nonlinear stability, nonlinear dynamics, multistability, monotone systems}, PDF = {../FTP_DIR/wang_sontag_JNS08.pdf}, ABSTRACT = {The theory of monotone dynamical systems has been found very useful in the modeling of some gene, protein, and signaling networks. In monotone systems, every net feedback loop is positive. On the other hand, negative feedback loops are important features of many systems, since they are required for adaptation and precision. This paper shows that, provided that these negative loops act at a comparatively fast time scale, the main dynamical property of (strongly) monotone systems, convergence to steady states, is still valid. An application is worked out to a double-phosphorylation "futile cycle" motif which plays a central role in eukaryotic cell signaling.} } @INPROCEEDINGS{iglesias_ifac08, AUTHOR = {B. Andrews and E.D. Sontag and P. Iglesias}, BOOKTITLE = {Proc. 17th IFAC World Congress, Seoul}, TITLE = {An approximate internal model principle: Applications to nonlinear models of biological systems}, YEAR = {2008}, OPTADDRESS = {}, OPTCROSSREF = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, OPTORGANIZATION = {}, PAGES = {Paper FrB25.3, 6 pages}, OPTPUBLISHER = {}, OPTSERIES = {}, OPTVOLUME = {}, KEYWORDS = {biological adaptation, internal model principle}, PDF = {../FTP_DIR/andrews_sontag_iglesias_approximate_internal_model_IFAC2008.pdf}, ABSTRACT = {The proper function of many biological systems requires that external perturbations be detected, allowing the system to adapt to these environmental changes. It is now well established that this dual detection and adaptation requires that the system have an internal model in the feedback loop. In this paper we relax the requirement that the response of the system adapt perfectly, but instead allow regulation to within a neighborhood of zero. We show, in a nonlinear setting, that systems with the ability to detect input signals and approximately adapt require an approximate model of the input. We illustrate our results by analyzing a well-studied biological system. These results generalize previous work which treats the perfectly adapting case. } } @INPROCEEDINGS{ddv_acc08, AUTHOR = {Del Vecchio, D. and A.J. Ninfa and E.D. Sontag}, BOOKTITLE = {Proceedings of the 2008 American Control Conference, Seattle, June 2008}, TITLE = {A Systems Theory with Retroactivity: Application to Transcriptional Modules}, YEAR = {2008}, OPTADDRESS = {}, OPTCROSSREF = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, OPTORGANIZATION = {}, PAGES = {Paper WeC04.1}, OPTPUBLISHER = {}, OPTSERIES = {}, OPTVOLUME = {}, KEYWORDS = {systems biology, biochemical networks, synthetic biology, futile cycles, singular perturbations, modularity} } @INPROCEEDINGS{08cdc_liming, AUTHOR = {L. Wang and de Leenheer, P. and E.D. Sontag}, BOOKTITLE = {Proc. IEEE Conf. Decision and Control, Cancun, Dec. 2008}, TITLE = {Global stability for monotone tridiagonal systems with negative feedback}, YEAR = {2008}, OPTADDRESS = {}, OPTCROSSREF = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, OPTORGANIZATION = {}, PAGES = {4091-4096}, OPTPUBLISHER = {}, OPTSERIES = {}, OPTVOLUME = {}, KEYWORDS = {systems biology, monotone systems, tridiagonal systems, global stability}, PDF = {../FTP_DIR/wang_leenheer_sontag_cdc08.pdf}, ABSTRACT = {This paper studies monotone tridiagonal systems with negative feedback. These systems possess the Poincar{\'e}-Bendixson property, which implies that, if orbits are bounded, if there is a unique steady state and this unique equilibrium is asymptotically stable, and if one can rule out periodic orbits, then the steady state is globally asymptotically stable. Different approaches are discussed to rule out period orbits. One is based on direct linearization, while the other uses the theory of second additive compound matrices. Among the examples that will illustrate our main theoretical results is the classical Goldbeter model of the circadian rhythm. } } @INCOLLECTION{dasgupta-albert2b, AUTHOR = {R. Albert and B. DasGupta and R. Dondi and S. Kachalo and E.D. Sontag and A. Zelikovsky and K. Westbrooks}, BOOKTITLE = {7th Workshop on Algorithms in Bioinformatics (WABI)}, PUBLISHER = {Springer-Verlag, Berlin}, TITLE = {A novel method for signal transduction network inference from indirect experimental evidence}, YEAR = {2007}, OPTADDRESS = {}, OPTCHAPTER = {}, OPTCROSSREF = {}, OPTEDITION = {}, EDITOR = {R. Giancarlo and S. Hannenhalli}, OPTMONTH = {}, NOTE = {Conference version of journal paper with same title}, OPTNUMBER = {}, PAGES = {407-419}, OPTSERIES = {}, OPTTYPE = {}, VOLUME = {14}, KEYWORDS = {systems biology, biochemical networks, algorithms, signal transduction networks, graph algorithms} } @INCOLLECTION{angeli_leenheer_petri_toulouse, AUTHOR = {D. Angeli and De Leenheer, P. and E.D. Sontag}, BOOKTITLE = {Biology and Control Theory: Current Challenges (Lecture Notes in Control and Information Sciences Volume 357)}, PUBLISHER = {Springer-Verlag, Berlin}, TITLE = {A Petri net approach to persistence analysis in chemical reaction networks}, YEAR = {2007}, OPTADDRESS = {}, OPTCHAPTER = {}, OPTCROSSREF = {}, OPTEDITION = {}, EDITOR = {I. Queinnec and S. Tarbouriech and G. Garcia and S-I. Niculescu}, OPTMONTH = {}, NOTE = {See abstract for A Petri net approach to the study of persistence in chemical reaction networks.}, OPTNUMBER = {}, PAGES = {181-216}, OPTSERIES = {}, OPTTYPE = {}, OPTVOLUME = {}, PDF = {../FTP_DIR/angeli_deleenheer_sontag_petri_toulouse_book07.pdf} } @INCOLLECTION{04cime, AUTHOR = {E.D. Sontag}, BOOKTITLE = {Nonlinear and Optimal Control Theory}, PUBLISHER = {Springer-Verlag, Berlin}, TITLE = {Input to state stability: Basic concepts and results}, YEAR = {2007}, OPTADDRESS = {}, OPTCHAPTER = {}, OPTCROSSREF = {}, OPTEDITION = {}, EDITOR = {P. Nistri and G. Stefani}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, PAGES = {163--220}, OPTSERIES = {}, OPTTYPE = {}, OPTVOLUME = {}, KEYWORDS = {input to state stability, stability, input to state stability, nonlinear systems, detectability, nonlinear regulation}, PDF = {../FTP_DIR/04cetraro.pdf}, ABSTRACT = { This expository presentation, prepared for a summer course, addresses the precise formulation of questions of robustness with respect to disturbances, using the paradigm of input to state stability. It provides an intuitive and informal presentation of the main concepts. } } @INCOLLECTION{almostmonotone_toulouse, AUTHOR = {E.D. Sontag}, BOOKTITLE = {Biology and Control Theory: Current Challenges (Lecture Notes in Control and Information Sciences Volume 357)}, PUBLISHER = {Springer-Verlag, Berlin}, TITLE = {Monotone and near-monotone systems}, YEAR = {2007}, OPTADDRESS = {}, OPTCHAPTER = {}, OPTCROSSREF = {}, OPTEDITION = {}, EDITOR = {I. Queinnec and S. Tarbouriech and G. Garcia and S-I. Niculescu}, OPTMONTH = {}, NOTE = {Conference version of ``Monotone and near-monotone biochemical networks,'' basically the same paper.}, OPTNUMBER = {}, PAGES = {79-122}, OPTSERIES = {}, OPTTYPE = {}, OPTVOLUME = {}, KEYWORDS = {systems biology, biochemical networks, monotone systems, Ising spin models, nonlinear stability, dynamical systems, consistent graphs, gene networks}, ABSTRACT = {See abstract and pdf for ``Monotone and near-monotone biochemical networks''.} } @INCOLLECTION{stabilization_encyclopaedia07, AUTHOR = {E.D. Sontag}, BOOKTITLE = {Encyclopedia of Complexity and Systems Science}, PUBLISHER = {Springer-Verlag, Berlin}, TITLE = {Stability and Feedback Stabilization}, YEAR = {2007}, OPTADDRESS = {}, OPTCHAPTER = {}, OPTCROSSREF = {}, OPTEDITION = {}, EDITOR = {Robert Meyers}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, OPTPAGES = {}, OPTSERIES = {}, OPTTYPE = {}, OPTVOLUME = {}, KEYWORDS = {stability, nonlinear control, feedback stabilization}, ABSTRACT = {The problem of stabilization of equilibria is one of the central issues in control. In addition to its intrinsic interest, it represents a first step towards the solution of more complicated problems, such as the stabilization of periodic orbits or general invariant sets, or the attainment of other control objectives, such as tracking, disturbance rejection, or output feedback, all of which may be interpreted as requiring the stabilization of some quantity (typically, some sort of ``error'' signal). A very special case, when there are no inputs, is that of stability. This short and informal article provides an introduction to the subject. } } @INCOLLECTION{ywang_isidori_book07, AUTHOR = {E.D. Sontag and Y. Wang}, BOOKTITLE = {Analysis and Design of Nonlinear Control Systems}, PUBLISHER = {Springer-Verlag, London}, TITLE = {Uniformly Universal Inputs}, YEAR = {2007}, OPTADDRESS = {}, OPTCHAPTER = {}, OPTCROSSREF = {}, OPTEDITION = {}, EDITOR = {Alessandro Astolfi}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, PAGES = {9-24}, OPTSERIES = {}, OPTTYPE = {}, VOLUME = {224}, KEYWORDS = {observability, identification}, PDF = {../FTP_DIR/sontag_wang_uniformly_universal08.pdf}, ABSTRACT = {A result is presented showing the existence of inputs universal for observability, uniformly with respect to the class of all continuous-time analytic systems. This represents an ultimate generalization of a 1977 theorem, for bilinear systems, due to Alberto Isidori and Osvaldo Grasselli.} } @ARTICLE{dasgupta-albert2, AUTHOR = {R. Albert and B. DasGupta and R. Dondi and S. Kachalo and E.D. Sontag and A. Zelikovsky and K. Westbrooks}, JOURNAL = {Journal of Computational Biology}, TITLE = {A novel method for signal transduction network inference from indirect experimental evidence}, YEAR = {2007}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, PAGES = {927-949}, VOLUME = {14}, KEYWORDS = {systems biology, biochemical networks, algorithms, signal transduction networks, graph algorithms}, PDF = {../FTP_DIR/albert_dasgupta_et_all_jcb07_galleys.pdf}, ABSTRACT = {This paper introduces a new method of combined synthesis and inference of biological signal transduction networks. The main idea lies in representing observed causal relationships as network paths, and using techniques from combinatorial optimization to find the sparsest graph consistent with all experimental observations. The paper formalizes the approach, studies its computational complexity, proves new results for exact and approximate solutions of the computationally hard transitive reduction substep of the approach, validates the biological applicability by applying it to a previously published signal transduction network by Li et al., and shows that the algorithm for the transitive reduction substep performs well on graphs with a structure similar to those observed in transcriptional regulatory and signal transduction networks.} } @ARTICLE{persistencePetri, AUTHOR = {D. Angeli and de Leenheer, P. and E.D. Sontag}, JOURNAL = {Mathematical Biosciences}, TITLE = {A Petri net approach to the study of persistence in chemical reaction networks}, YEAR = {2007}, OPTMONTH = {}, NOTE = {Please look at the paper A Petri net approach to persistence analysis in chemical reaction networks, which has many additional results, not included in the journal paper due to lack of space. See also the preprint: arXiv q-bio.MN/068019v2, 10 Aug 2006}, OPTNUMBER = {}, PAGES = {598-618}, VOLUME = {210}, KEYWORDS = {Petri nets, systems biology, biochemical networks, nonlinear stability, dynamical systems, futile cycles}, PDF = {../FTP_DIR/angeli_leenheer_sontag_math_biosciences_MBS-D-06-00188R1.pdf}, ABSTRACT = { Persistency is the property, for differential equations in Rn, that solutions starting in the positive orthant do not approach the boundary. For chemical reactions and population models, this translates into the non-extinction property: provided that every species is present at the start of the reaction, no species will tend to be eliminated in the course of the reaction. This paper provides checkable conditions for persistence of chemical species in reaction networks, using concepts and tools from Petri net theory, and verifies these conditions on various systems which arise in the modeling of cell signaling pathways. } } @ARTICLE{berman-dasgupta-sontag-nyacad, AUTHOR = {P. Berman and B. Dasgupta and E.D. Sontag}, JOURNAL = {Annals of the NY Academy of Sciences}, TITLE = {Algorithmic issues in reverse engineering of protein and gene networks via the modular response analysis method}, YEAR = {2007}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, PAGES = {132-141}, VOLUME = {1115}, KEYWORDS = {systems biology, biochemical networks, gene and protein networks, reverse engineering, systems identification, graph algorithms}, ABSTRACT = {This paper studies a computational problem motivated by the modular response analysis method for reverse engineering of protein and gene networks. This set-cover problem is hard to solve exactly for large networks, but efficient approximation algorithms are given and their complexity is analyzed.} } @ARTICLE{berman_dasgupta_sontag, AUTHOR = {P. Berman and B. Dasgupta and E.D. Sontag}, JOURNAL = {Discrete Applied Mathematics Special Series on Computational Molecular Biology}, TITLE = {Randomized approximation algorithms for set multicover problems with applications to reverse engineering of protein and gene networks}, YEAR = {2007}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, PAGES = {733-749}, VOLUME = {155}, KEYWORDS = {systems biology, biochemical networks, gene and protein networks, systems identification, reverse engineering}, PDF = {../FTP_DIR/dasgupta-berman-sontag-setcover-journal-final.pdf}, ABSTRACT = { This paper investigates computational complexity aspects of a combinatorial problem that arises in the reverse engineering of protein and gene networks, showing relations to an appropriate set multicover problem with large "coverage" factor, and providing a non-trivial analysis of a simple randomized polynomial-time approximation algorithm for the problem. } } @ARTICLE{biosystems06, AUTHOR = {B. DasGupta and G.A. Enciso and E.D. Sontag and Y. Zhang}, JOURNAL = {BioSystems}, TITLE = {Algorithmic and complexity aspects of decompositions of biological networks into monotone subsystems}, YEAR = {2007}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, PAGES = {161-178}, VOLUME = {90}, KEYWORDS = {monotone systems, systems biology, biochemical networks}, PDF = {../FTP_DIR/dasgupta_enciso_sontag_zhang_9sep05.pdf}, ABSTRACT = { A useful approach to the mathematical analysis of large-scale biological networks is based upon their decompositions into monotone dynamical systems. This paper deals with two computational problems associated to finding decompositions which are optimal in an appropriate sense. In graph-theoretic language, the problems can be recast in terms of maximal sign-consistent subgraphs. The theoretical results include polynomial-time approximation algorithms as well as constant-ratio inapproximability results. One of the algorithms, which has a worst-case guarantee of 87.9% from optimality, is based on the semidefinite programming relaxation approach of Goemans-Williamson. The algorithm was implemented and tested on a Drosophila segmentation network and an Epidermal Growth Factor Receptor pathway model. }, DOI = {http://dx.doi.org/10.1016/j.biosystems.2006.08.001} } @ARTICLE{gedeon05, AUTHOR = {T. Gedeon and E.D. Sontag}, JOURNAL = {J. of Differential Equations}, TITLE = {Oscillations in multi-stable monotone systems with slowly varying feedback}, YEAR = {2007}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, PAGES = {273-295}, VOLUME = {239}, KEYWORDS = {systems biology, biochemical networks, nonlinear stability, dynamical systems, monotone systems}, PDF = {../FTP_DIR/gedeon_sontag_JDE07.pdf}, ABSTRACT = {This paper gives a theorem showing that a slow feedback adaptation, acting entirely analogously to the role of negative feedback for ordinary relaxation oscillations, leads to periodic orbits for bistable monotone systems. The proof is based upon a combination of i/o monotone systems theory and Conley Index theory.} } @ARTICLE{06plos, AUTHOR = {W. Maass and P. Joshi and E.D. Sontag}, JOURNAL = {PLoS Computational Biology}, TITLE = {Computational aspects of feedback in neural circuits}, YEAR = {2007}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, PAGES = {e165 1-20}, VOLUME = {3}, KEYWORDS = {neural networks, feedback linearization, computation by cortical microcircuits}, PDF = {../FTP_DIR/maass_joshi_sontag_PLOS_CompBio_jan07.pdf}, ABSTRACT = { It had previously been shown that generic cortical microcircuit models can perform complex real-time computations on continuous input streams, provided that these computations can be carried out with a rapidly fading memory. We investigate in this article the computational capability of such circuits in the more realistic case where not only readout neurons, but in addition a few neurons within the circuit have been trained for specific tasks. This is essentially equivalent to the case where the output of trained readout neurons is fed back into the circuit. We show that this new model overcomes the limitation of a rapidly fading memory. In fact, we prove that in the idealized case without noise it can carry out any conceivable digital or analog computation on time-varying inputs. But even with noise the resulting computational model can perform a large class of biologically relevant real-time computations that require a non-fading memory. } } @ARTICLE{almostmonotone_journal, AUTHOR = {E.D. Sontag}, JOURNAL = {Systems and Synthetic Biology}, TITLE = {Monotone and near-monotone biochemical networks}, YEAR = {2007}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, PAGES = {59-87}, VOLUME = {1}, KEYWORDS = {systems biology, biochemical networks, monotone systems, Ising spin models, nonlinear stability, dynamical systems, consistent graphs, gene networks}, PDF = {http://www.springerlink.com/content/x44774083876j062/fulltext.pdf}, ABSTRACT = { This paper provides an expository introduction to monotone and near-monotone biochemical network structures. Monotone systems respond in a predictable fashion to perturbations, and have very robust dynamical characteristics. This makes them reliable components of more complex networks, and suggests that natural biological systems may have evolved to be, if not monotone, at least close to monotone. In addition, interconnections of monotone systems may be fruitfully analyzed using tools from control theory. }, DOI = {10.1007/s11693-007-9005-9} } @ARTICLE{JMathChemMonotone06, AUTHOR = {de Leenheer, P. and D. Angeli and E.D. Sontag}, JOURNAL = {J. Math Chemistry}, TITLE = {Monotone chemical reaction networks}, YEAR = {2007}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, PAGES = {295-314}, VOLUME = {41}, KEYWORDS = {systems biology, biochemical networks, nonlinear stability, dynamical systems, monotone systems}, PDF = {../FTP_DIR/leenheer-angeli-sontag-JMathChem07.pdf}, ABSTRACT = { We analyze certain chemical reaction networks and show that every solution converges to some steady state. The reaction kinetics are assumed to be monotone but otherwise arbitrary. When diffusion effects are taken into account, the conclusions remain unchanged. The main tools used in our analysis come from the theory of monotone dynamical systems. We review some of the features of this theory and provide a self-contained proof of a particular attractivity result which is used in proving our main result. }, DOI = {10.1007/s10910-006-9075-z} } @INPROCEEDINGS{07nolcos_persistence, AUTHOR = {D. Angeli and de Leenheer, P. and E.D. Sontag}, BOOKTITLE = {Proc. 7th IFAC Symposium on Nonlinear Control Systems (NOLCOS 2007), Pretoria, South Africa, 22-24 August, 2007}, TITLE = {Petri nets tools for the analysis of persistence in chemical networks}, YEAR = {2007}, OPTADDRESS = {}, OPTCROSSREF = {}, OPTEDITOR = {}, OPTMONTH = {}, NOTE = {Summarized version of journal paper with same title.}, OPTNUMBER = {}, OPTORGANIZATION = {}, OPTPAGES = {}, OPTPUBLISHER = {}, OPTSERIES = {}, OPTVOLUME = {}, KEYWORDS = {Petri nets, systems biology, biochemical networks, nonlinear stability, dynamical systems, futile cycles} } @INPROCEEDINGS{07cdc_arcak, AUTHOR = {M. Arcak and E.D. Sontag}, BOOKTITLE = {Proc. IEEE Conf. Decision and Control, New Orleans, Dec. 2007}, TITLE = {A passivity-based stability criterion for a class of interconnected systems and applications to biochemical reaction networks}, YEAR = {2007}, OPTADDRESS = {}, OPTCROSSREF = {}, OPTEDITOR = {}, OPTMONTH = {}, NOTE = {Conference version of journal paper with same title}, OPTNUMBER = {}, OPTORGANIZATION = {}, PAGES = {4477-4482}, OPTPUBLISHER = {}, OPTSERIES = {}, OPTVOLUME = {}, KEYWORDS = {systems biology, biochemical networks, cyclic feedback systems, secant condition, nonlinear stability, dynamical systems} } @INPROCEEDINGS{07acc_ddv, AUTHOR = {Del Vecchio, D. and E.D. Sontag}, BOOKTITLE = {Proceedings American Control Conf., New York, July 2007}, TITLE = {Dynamics and control of synthetic bio-molecular networks}, YEAR = {2007}, OPTADDRESS = {}, OPTCROSSREF = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, OPTORGANIZATION = {}, PAGES = {1577-1588}, OPTPUBLISHER = {}, OPTSERIES = {}, OPTVOLUME = {}, KEYWORDS = {systems biology, biochemical networks, synthetic biology}, ABSTRACT = { This tutorial paper presents an introduction to systems and synthetic molecular biology. It provides an introduction to basic biological concepts, and describes some of the techniques as well as challenges in the analysis and design of biomolecular networks. } } @INPROCEEDINGS{07acc_jovanovic_arcak_sontag, AUTHOR = {M.R. Jovanovic and M. Arcak and E.D. Sontag}, BOOKTITLE = {Proceedings American Control Conf., New York, July 2007}, TITLE = {Remarks on the stability of spatially distributed systems with a cyclic interconnection structure}, YEAR = {2007}, OPTADDRESS = {}, OPTCROSSREF = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, OPTORGANIZATION = {}, PAGES = {2696-2701}, OPTPUBLISHER = {}, OPTSERIES = {}, OPTVOLUME = {}, KEYWORDS = {systems biology, biochemical networks, cyclic feedback systems, spatially distributed systems, secant condition}, ABSTRACT = { For distributed systems with a cyclic interconnection structure, a global stability result is shown to hold if the secant criterion is satisfied. } } @INPROCEEDINGS{07acc:SontagWangMegretski, AUTHOR = {E.D. Sontag and Y. Wang and A. Megretski}, BOOKTITLE = {Proceedings American Control Conf., New York, July 2007}, TITLE = {Remarks on Input Classes for Identification of Bilinear Systems}, YEAR = {2007}, OPTADDRESS = {}, OPTCROSSREF = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, OPTORGANIZATION = {}, PAGES = {4345-4350}, OPTPUBLISHER = {}, OPTSERIES = {}, OPTVOLUME = {}, KEYWORDS = {realization theory, observability, identifiability, bilinear systems} } @INPROCEEDINGS{07cdc_WS, AUTHOR = {L. Wang and E.D. Sontag}, BOOKTITLE = {Proc. IEEE Conf. Decision and Control, New Orleans, Dec. 2007}, TITLE = {Further results on singularly perturbed monotone systems, with an application to double phosphorylation cycles}, YEAR = {2007}, OPTADDRESS = {}, OPTCROSSREF = {}, OPTEDITOR = {}, OPTMONTH = {}, NOTE = {Conference version of Singularly perturbed monotone systems and an application to double phosphorylation cycles.}, OPTNUMBER = {}, OPTORGANIZATION = {}, PAGES = {627-632}, OPTPUBLISHER = {}, OPTSERIES = {}, OPTVOLUME = {}, KEYWORDS = {singular perturbations, futile cycles, MAPK cascades, systems biology, biochemical networks, nonlinear stability, nonlinear dynamics, multistability, monotone systems} } @INCOLLECTION{dasgupta-book05, AUTHOR = {B. Dasgupta and P. Berman and E.D. Sontag}, BOOKTITLE = {Advances in Computational Intelligence: Theory & Applications}, PUBLISHER = {World Scientific, Hackensack}, TITLE = {Computational complexities of combinatorial problems with applications to reverse engineering of biological networks}, YEAR = {2006}, OPTADDRESS = {}, OPTCHAPTER = {}, OPTCROSSREF = {}, OPTEDITION = {}, EDITOR = {D. Liu and F-Y. Wan}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, PAGES = {303--316}, OPTSERIES = {}, OPTTYPE = {}, OPTVOLUME = {}, KEYWORDS = {systems biology, biochemical networks, gene and protein networks, reverse engineering, systems identification, theory of computing and complexity} } @INCOLLECTION{dasgupta_enciso05, AUTHOR = {B. Dasgupta and G.A. Enciso and E.D. Sontag and Y. Zhang}, BOOKTITLE = {Lecture Notes in Computer Science: Experimental Algorithms: 5th International Workshop, WEA 2006}, PUBLISHER = {Springer-Verlag}, TITLE = {Algorithmic and complexity results for decompositions of biological networks into monotone subsystems}, YEAR = {2006}, OPTADDRESS = {}, OPTCHAPTER = {}, OPTCROSSREF = {}, OPTEDITION = {}, EDITOR = {C. Àlvarez and M. Serna}, OPTMONTH = {}, NOTE = {(Cala Galdana, Menorca, Spain, May 24-27, 2006)}, OPTNUMBER = {}, PAGES = {253--264}, OPTSERIES = {}, OPTTYPE = {}, OPTVOLUME = {}, KEYWORDS = {systems biology, biochemical networks, monotone systems, theory of computing and complexity} } @INCOLLECTION{05nips, AUTHOR = {W. Maass and P. Joshi and E.D. Sontag}, BOOKTITLE = {Advances in Neural Information Processing Systems 18}, PUBLISHER = {MIT Press, Cambridge}, TITLE = {Principles of real-time computing with feedback applied to cortical microcircuit models}, YEAR = {2006}, OPTADDRESS = {}, OPTCHAPTER = {}, OPTCROSSREF = {}, OPTEDITION = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, OPTPAGES = {}, OPTSERIES = {}, OPTTYPE = {}, OPTVOLUME = {}, KEYWORDS = {neural networks} } @ARTICLE{arcak_secant, AUTHOR = {M. Arcak and E.D. Sontag}, JOURNAL = {Automatica}, TITLE = {Diagonal stability for a class of cyclic systems and applications}, YEAR = {2006}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, PAGES = {1531-1537}, VOLUME = {42}, KEYWORDS = {passive systems, systems biology, biochemical networks, cyclic feedback systems, secant condition, nonlinear stability, dynamical systems}, PDF = {../FTP_DIR/arcak_sontag_automatica06.pdf}, ABSTRACT = { This paper considers a class of systems with a cyclic structure that arises, among other examples, in dynamic models for certain biochemical reactions. We first show that a criterion for local stability, derived earlier in the literature, is in fact a necessary and sufficient condition for diagonal stability of the corresponding class of matrices. We then revisit a recent generalization of this criterion to output strictly passive systems, and recover the same stability condition using our diagonal stability result as a tool for constructing a Lyapunov function. Using this procedure for Lyapunov construction we exhibit classes of cyclic systems with sector nonlinearities and characterize their global stability properties. } } @ARTICLE{chaves_automatica06, AUTHOR = {M. Chaves and E.D. Sontag}, JOURNAL = {Automatica}, TITLE = {Exact computation of amplification for a class of nonlinear systems arising from cellular signaling pathways}, YEAR = {2006}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, PAGES = {1987-1992}, VOLUME = {42}, KEYWORDS = {systems biology, biochemical networks, nonlinear stability, dynamical systems}, PDF = {../FTP_DIR/chaves_gains_comparison_automatica06.pdf}, ABSTRACT = { A commonly employed measure of the signal amplification properties of an input/output system is its induced L2 norm, sometimes also known as H-infinity gain. In general, however, it is extremely difficult to compute the numerical value for this norm, or even to check that it is finite, unless the system being studied is linear. This paper describes a class of systems for which it is possible to reduce this computation to that of finding the norm of an associated linear system. In contrast to linearization approaches, a precise value, not an estimate, is obtained for the full nonlinear model. The class of systems that we study arose from the modeling of certain biological intracellular signaling cascades, but the results should be of wider applicability. } } @ARTICLE{csa06, AUTHOR = {M. Chaves and E.D. Sontag and R. Albert}, JOURNAL = {IET Systems Biology}, TITLE = {Methods of robustness analysis for Boolean models of gene control networks}, YEAR = {2006}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, PAGES = {154-167}, VOLUME = {153}, KEYWORDS = {systems biology, biochemical networks, boolean systems, gene and protein networks, hybrid systems}, PDF = {../FTP_DIR/chaves_sontag_albert_sysbio06_with_bibliography.pdf}, ABSTRACT = { As a discrete approach to genetic regulatory networks, Boolean models provide an essential qualitative description of the structure of interactions among genes and proteins. Boolean models generally assume only two possible states (expressed or not expressed) for each gene or protein in the network as well as a high level of synchronization among the various regulatory processes. In this paper, we discuss and compare two possible methods of adapting qualitative models to incorporate the continuous-time character of regulatory networks. The first method consists of introducing asynchronous updates in the Boolean model. In the second method, we adopt the approach introduced by L. Glass to obtain a set of piecewise linear differential equations which continuously describe the states of each gene or protein in the network. We apply both methods to a particular example: a Boolean model of the segment polarity gene network of Drosophila melanogaster. We analyze the dynamics of the model, and provide a theoretical characterization of the model's gene pattern prediction as a function of the timescales of the various processes. } } @ARTICLE{bdas00, AUTHOR = {B. DasGupta and J.P. Hespanha and J. Riehl and E.D. Sontag}, JOURNAL = {Nonlinear Analysis}, TITLE = {Honey-pot constrained searching with local sensory information}, YEAR = {2006}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, PAGES = {1773-1793}, VOLUME = {65}, KEYWORDS = {search problems, algorithms, computational complexity}, PDF = {../FTP_DIR/dasgupta_hespanha_riehl_sontag_nonlinearanalysis06.pdf}, ABSTRACT = { This paper investigates the problem of searching for a hidden target in a bounded region of the plane by an autonomous robot which is only able to use limited local sensory information. It proposes an aggregation-based approach to solve this problem, in which the continuous search space is partitioned into a finite collection of regions on which we define a discrete search problem and a solution to the original problem is obtained through a refinement procedure that lifts the discrete path into a continuous one. The resulting solution is in general not optimal but one can construct bounds to gauge the cost penalty incurred. The discrete version is formalized and an optimization problem is stated as a `reward-collecting' bounded-length path problem. NP-completeness and efficient approximation algorithms for various cases of this problem are discussed. } } @ARTICLE{enciso_smith_sontagJDE06, AUTHOR = {G.A. Enciso and H.L. Smith and E.D. Sontag}, JOURNAL = {J. of Differential Equations}, TITLE = {Non-monotone systems decomposable into monotone systems with negative feedback}, YEAR = {2006}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, PAGES = {205-227}, VOLUME = {224}, KEYWORDS = {nonlinear stability, dynamical systems, monotone systems}, PDF = {../FTP_DIR/enciso_smith_sontag_JDE06.pdf}, ABSTRACT = { Motivated by the theory of monotone i/o systems, this paper shows that certain finite and infinite dimensional semi-dynamical systems with negative feedback can be decomposed into a monotone open loop system with inputs and a decreasing output function. The original system is reconstituted by plugging the output into the input. By embedding the system into a larger symmetric monotone system, this paper obtains finer information on the asymptotic behavior of solutions, including existence of positively invariant sets and global convergence. An important new result is the extension of the "small gain theorem" of monotone i/o theory to reaction-diffusion partial differential equations: adding diffusion preserves the global attraction of the ODE equilibrium. } } @ARTICLE{dcds06, AUTHOR = {G.A. Enciso and E.D. Sontag}, JOURNAL = {Discrete Contin. Dyn. Syst.}, TITLE = {Global attractivity, I/O monotone small-gain theorems, and biological delay systems}, YEAR = {2006}, OPTMONTH = {}, OPTNOTE = {}, NUMBER = {3}, PAGES = {549--578}, VOLUME = {14}, KEYWORDS = {systems biology, biochemical networks, nonlinear stability, dynamical systems, monotone systems}, PDF = {../FTP_DIR/enciso_sontag_DCDS06_galleys.pdf}, ABSTRACT = { This paper further develops a method, originally introduced in a paper by Angeli and Sontag, for proving global attractivity of steady states in certain classes of dynamical systems. In this aproach, one views the given system as a negative feedback loop of a monotone controlled system. An auxiliary discrete system, whose global attractivity implies that of the original system, plays a key role in the theory, which is presented in a general Banach space setting. Applications are given to delay systems, as well as to systems with multiple inputs and outputs, and the question of expressing a given system in the required negative feedback form is addressed. } } @ARTICLE{malisoff-krichman-sontag, AUTHOR = {M. Malisoff and M. Krichman and E.D. Sontag}, JOURNAL = {Journal of Dynamical and Control Systems}, TITLE = {Global stabilization for systems evolving on manifolds}, YEAR = {2006}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, PAGES = {161--184}, VOLUME = {12}, KEYWORDS = {nonlinear stability, nonlinear control, feedback stabilization}, PDF = {../FTP_DIR/malisoff-krichman-sontag-JCDS06.pdf}, ABSTRACT = { This paper shows that any globally asymptotically controllable system on any smooth manifold can be globally stabilized by a state feedback. Since discontinuous feedbacks are allowed, solutions are understood in the ``sample and hold'' sense introduced by Clarke-Ledyaev-Sontag-Subbotin (CLSS). This work generalizes the CLSS Theorem, which is the special case of our result for systems on Euclidean space. We apply our result to the input-to-state stabilization of systems on manifolds relative to actuator errors, under small observation noise. } } @ARTICLE{ryan05, AUTHOR = {E.P. Ryan and E.D. Sontag}, JOURNAL = {Systems and Control Letters}, TITLE = {Well-defined steady-state response does not imply CICS}, YEAR = {2006}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, PAGES = {707-710}, VOLUME = {55}, KEYWORDS = {nonlinear stability, dynamical systems}, PDF = {../FTP_DIR/ryan-sontag-SCL06.pdf}, ABSTRACT = { Systems for which each constant input gives rise to a unique globally attracting equilibrium are considered. A counterexample is provided to show that inputs which are only asymptotically constant may not result in states converging to equilibria (failure of the converging-input converging state, or ``CICS'' property). }, DOI = {10.1016/j.sysconle.2006.02.001} } @ARTICLE{secant, AUTHOR = {E.D. Sontag}, JOURNAL = {Systems Control Lett.}, TITLE = {Passivity gains and the ``secant condition'' for stability}, YEAR = {2006}, OPTMONTH = {}, OPTNOTE = {}, NUMBER = {3}, PAGES = {177--183}, VOLUME = {55}, KEYWORDS = {cyclic feedback systems, systems biology, biochemical networks, nonlinear stability, dynamical systems, passive systems, secant condition, biochemical networks}, PDF = {../FTP_DIR/secant_SCL06.pdf}, ABSTRACT = { A generalization of the classical secant condition for the stability of cascades of scalar linear systems is provided for passive systems. The key is the introduction of a quantity that combines gain and phase information for each system in the cascade. For linear one-dimensional systems, the known result is recovered exactly. } } @ARTICLE{ywang_cooperative_example, AUTHOR = {E.D. Sontag and Y. Wang}, JOURNAL = {J. of Differential Equations}, TITLE = {A cooperative system which does not satisfy the limit set dichotomy}, YEAR = {2006}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, PAGES = {373-384}, VOLUME = {224}, KEYWORDS = {dynamical systems, monotone systems}, PDF = {../FTP_DIR/sontag_ywang_JDE_2006.pdf}, ABSTRACT = { The fundamental property of strongly monotone systems, and strongly cooperative systems in particular, is the limit set dichotomy due to Hirsch: if x < y, then either Omega(x) < Omega (y), or Omega(x) = Omega(y) and both sets consist of equilibria. We provide here a counterexample showing that this property need not hold for (non-strongly) cooperative systems. } } @ARTICLE{crowding, AUTHOR = {de Leenheer, P. and D. Angeli and E.D. Sontag}, JOURNAL = {Journal of Mathematical Analysis and Applications}, TITLE = {Crowding effects promote coexistence in the chemostat}, YEAR = {2006}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, PAGES = {48-60}, VOLUME = {319}, KEYWORDS = {systems biology, biochemical networks, nonlinear stability, dynamical systems, monotone systems}, PDF = {../FTP_DIR/leenheer_angeli_sontag_JMAA06.pdf}, ABSTRACT = { We provide an almost-global stability result for a particular chemostat model, in which crowding effects are taken into consideration. The model can be rewritten as a negative feedback interconnection of two monotone i/o systems with well-defined characteristics, which allows the use of a small-gain theorem for feedback interconnections of monotone systems. This leads to a sufficient condition for almost-global stability, and we show that coexistence occurs in this model if the crowding effects are large enough. } } @ARTICLE{leenheer-levin-klausmeier, AUTHOR = {de Leenheer, P. and S.A. Levin and E.D. Sontag and C.A. Klausmeier}, JOURNAL = {J. Mathematical Biology}, TITLE = {Global stability in a chemostat with multiple nutrients}, YEAR = {2006}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, PAGES = {419--438}, VOLUME = {52}, KEYWORDS = {systems biology, biochemical networks, nonlinear stability, dynamical systems, monotone systems}, PDF = {../FTP_DIR/leenheer_levin_sontag_klausmeier_JMB06.pdf}, ABSTRACT = { We study a single species in a chemostat, limited by two nutrients, and separate nutrient uptake from growth. For a broad class of uptake and growth functions it is proved that a nontrivial equilibrium may exist. Moreover, if it exists it is unique and globally stable, generalizing a previous result by Legovic and Cruzado. } } @ARTICLE{vanriel06, AUTHOR = {van Riel, N.A.W. and E.D. Sontag}, JOURNAL = {IET Systems Biology}, TITLE = {Parameter estimation in models combining signal transduction and metabolic pathways: The dependent input approach}, YEAR = {2006}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, PAGES = {263-274}, VOLUME = {153}, KEYWORDS = {systems biology, biochemical networks, parameter identification}, PDF = {../FTP_DIR/vanriel_sontag_sysbio_153_pp_263_274_2006.pdf}, ABSTRACT = { Biological complexity and limited quantitative measurements impose severe challenges to standard engineering methodologies for systems identification. This paper presents an approach, justified by the theory of universal inputs for distinguishability, based on replacing unmodeled dynamics by fictitious `dependent inputs'. The approach is particularly useful in validation experiments, because it allows one to fit model parameters to experimental data generated by a reference (wild-type) organism and then testing this model on data generated by a variation (mutant), so long as the mutations only affect the unmodeled dynamics that produce the dependent inputs. As a case study, this paper addresses the pathways that control the nitrogen uptake fluxes in baker's yeast Saccharomyces cerevisiae enabling it to optimally respond to changes in nitrogen availability. Well-defined perturbation experiments were performed on cells growing in steady-state. Time-series data of extracellular and intracellular metabolites were obtained, as well as mRNA levels. A nonlinear model was proposed, and shown to be structurally identifiable given input/output data. The identified model correctly predicted the responses of different yeast strains and different perturbations. } } @INPROCEEDINGS{06cdc_iglesias-andrews, AUTHOR = {B. Andrews and P. Iglesias and E.D. Sontag}, BOOKTITLE = {Proc. IEEE Conf. Decision and Control, San Diego, Dec. 2006}, TITLE = {Signal detection and approximate adaptation implies an approximate internal model}, YEAR = {2006}, OPTADDRESS = {}, OPTCROSSREF = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, OPTORGANIZATION = {}, PAGES = {2364-2369}, PUBLISHER = {IEEE}, OPTSERIES = {}, OPTVOLUME = {}, KEYWORDS = {biological adaptation, internal model principle}, PDF = {../FTP_DIR/06cdc_burton_iglesias_sontag_final.pdf}, ABSTRACT = { This conference paper presented a version of an approximate internal model principle, for linear systems. A subsequent paper at the IFAC 2008 conference improved on this result by extending it to a class of nonlinear systems. } } @INPROCEEDINGS{translation-inv-med06, AUTHOR = {D. Angeli and E.D. Sontag}, BOOKTITLE = {Control and Automation, 2006. MED '06. 14th Mediterranean Conference on, 28-30 June 2006}, TITLE = {A note on monotone systems with positive translation invariance}, YEAR = {2006}, OPTADDRESS = {}, OPTCROSSREF = {}, OPTEDITOR = {}, OPTMONTH = {}, NOTE = {available from ieeexplore.ieee.org}, OPTNUMBER = {}, OPTORGANIZATION = {}, PAGES = {1-6}, PUBLISHER = {IEEE}, OPTSERIES = {}, OPTVOLUME = {}, KEYWORDS = {systems biology, biochemical networks, nonlinear stability, dynamical systems, monotone systems}, PDF = {../FTP_DIR/angeli_translation_invariance_med06.pdf}, ABSTRACT = { Strongly monotone systems of ordinary differential equations which have a certain translation-invariance property are shown to have the property that all projected solutions converge to a unique equilibrium. This result may be seen as a dual of a well-known theorem of Mierczynski for systems that satisfy a conservation law. As an application, it is shown that enzymatic futile cycles have a global convergence property. }, DOI = {10.1109/MED.2006.3287822B2B2B2B2B2B} } @INPROCEEDINGS{06cdc_chemical, AUTHOR = {D. Angeli and de Leenheer, P. and E.D. Sontag}, BOOKTITLE = {Proc. IEEE Conf. Decision and Control, San Diego, Dec. 2006}, TITLE = {On the structural monotonicity of chemical reaction networks}, YEAR = {2006}, OPTADDRESS = {}, OPTCROSSREF = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, OPTORGANIZATION = {}, PAGES = {7-12}, PUBLISHER = {IEEE}, OPTSERIES = {}, OPTVOLUME = {}, KEYWORDS = {monotone systems, systems biology, biochemical networks, nonlinear stability, dynamical systems}, PDF = {../FTP_DIR/06cdc_angeli_leenheer_sontag_final.pdf}, ABSTRACT = { This paper derives new results for certain classes of chemical reaction networks, linking structural to dynamical properties. In particular, it investigates their monotonicity and convergence without making assumptions on the structure (e.g., mass-action kinetics) of the dynamical equations involved, and relying only on stoichiometric constraints. The key idea is to find a suitable set of coordinates under which the resulting system is cooperative. As a simple example, the paper shows that a phosphorylation/dephosphorylation process, which is involved in many signaling cascades, has a global stability property. } } @INPROCEEDINGS{arcak-06acc, AUTHOR = {M. Arcak and E.D. Sontag}, BOOKTITLE = {Proc. American Control Conference, Minneapolis, June 2006}, TITLE = {Connections between diagonal stability and the secant condition for cyclic systems}, YEAR = {2006}, OPTADDRESS = {}, OPTCROSSREF = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, OPTORGANIZATION = {}, PAGES = {1493-1498}, OPTPUBLISHER = {}, OPTSERIES = {}, OPTVOLUME = {}, KEYWORDS = {systems biology, biochemical networks, cyclic feedback systems, secant condition, nonlinear stability, dynamical systems} } @INPROCEEDINGS{06cdc_chaves-albert, AUTHOR = {M. Chaves and E.D. Sontag and R. Albert}, BOOKTITLE = {Proc. IEEE Conf. Decision and Control, San Diego, Dec. 2006}, TITLE = {Structure and timescale analysis in genetic regulatory networks}, YEAR = {2006}, OPTADDRESS = {}, OPTCROSSREF = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, OPTORGANIZATION = {}, PAGES = {2358-2363}, PUBLISHER = {IEEE}, OPTSERIES = {}, OPTVOLUME = {}, KEYWORDS = {genetic regulatory networks, Boolean systems, hybrid systems}, PDF = {../FTP_DIR/06cdc_chaves_albert_sontag_final.pdf}, ABSTRACT = { This work is concerned with the study of the robustness and fragility of gene regulation networks to variability in the timescales of the distinct biological processes involved. It explores and compares two methods: introducing asynchronous updates in a Boolean model, or integrating the Boolean rules in a continuous, piecewise linear model. As an example, the segment polarity network of the fruit fly is analyzed. A theoretical characterization is given of the model's ability to predict the correct development of the segmented embryo, in terms of the specific timescales of the various regulation interactions. } } @INPROCEEDINGS{06cdc_wang_sontag, AUTHOR = {L. Wang and E.D. Sontag}, BOOKTITLE = {Proc. IEEE Conf. Decision and Control, San Diego, Dec. 2006}, TITLE = {A remark on singular perturbations of strongly monotone systems}, YEAR = {2006}, OPTADDRESS = {}, OPTCROSSREF = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, OPTORGANIZATION = {}, PAGES = {989-994}, PUBLISHER = {IEEE}, OPTSERIES = {}, OPTVOLUME = {}, KEYWORDS = {systems biology, biochemical networks, nonlinear stability, dynamical systems, singular perturbations, monotone systems}, PDF = {../FTP_DIR/06cdc_limingwang_sontag_final.pdf}, ABSTRACT = { This paper deals with global convergence to equilibria, and in particular Hirsch's generic convergence theorem for strongly monotone systems, for singular perturbations of monotone systems. } } @INPROCEEDINGS{06posta_wang, AUTHOR = {L. Wang and E.D. Sontag}, BOOKTITLE = {Positive Systems}, TITLE = {Almost global convergence in singular perturbations of strongly monotone systems}, YEAR = {2006}, OPTADDRESS = {}, OPTCROSSREF = {}, EDITOR = {C. Commault and N. Marchand}, OPTMONTH = {}, NOTE = {(Lecture Notes in Control and Information Sciences Volume 341, Proceedings of the second Multidisciplinary International Symposium on Positive Systems: Theory and Applications (POSTA 06) Grenoble, France)}, OPTNUMBER = {}, OPTORGANIZATION = {}, PAGES = {415--422}, PUBLISHER = {Springer-Verlag, Berlin/Heidelberg}, OPTSERIES = {}, OPTVOLUME = {}, KEYWORDS = {systems biology, biochemical networks, nonlinear stability, dynamical systems, singular perturbations, monotone systems}, PDF = {../FTP_DIR/wang-sontag_posta06_published.pdf}, ABSTRACT = { This paper deals with global convergence to equilibria, and in particular Hirsch's generic convergence theorem for strongly monotone systems, for singular perturbations of monotone systems. }, DOI = {10.1007/3-540-34774-7} } @ARTICLE{kholodenkoJTB05, AUTHOR = {M. Andrec and B.N. Kholodenko and R.M. Levy and E.D. Sontag}, JOURNAL = {J. Theoret. Biol.}, TITLE = {Inference of signaling and gene regulatory networks by steady-state perturbation experiments: structure and accuracy}, YEAR = {2005}, OPTMONTH = {}, NOTE = {Supplementary materials are here: http://www.math.rutgers.edu/(tilde)sontag/FTPDIR/andrec-kholodenko-levy-sontag-JTB04-supplementary.pdf}, NUMBER = {3}, PAGES = {427--441}, VOLUME = {232}, KEYWORDS = {systems biology, biochemical networks, gene and protein networks, systems identification, reverse engineering}, PDF = {../FTP_DIR/andrec_kholodenko_levy_sontag_JTB04.pdf}, ABSTRACT = { One of the fundamental problems of cell biology is the understanding of complex regulatory networks. Such networks are ubiquitous in cells, and knowledge of their properties is essential for the understanding of cellular behavior. This paper studies the effect of experimental uncertainty on the accuracy of the inferred structure of the networks determined using the method in "Untangling the wires: a novel strategy to trace functional interactions in signaling and gene networks". } } @ARTICLE{chaves_albert_sontagJTB05, AUTHOR = {M. Chaves and R. Albert and E.D. Sontag}, JOURNAL = {J. Theoret. Biol.}, TITLE = {Robustness and fragility of Boolean models for genetic regulatory networks}, YEAR = {2005}, OPTMONTH = {}, OPTNOTE = {}, NUMBER = {3}, PAGES = {431--449}, VOLUME = {235}, KEYWORDS = {systems biology, biochemical networks, boolean systems, gene and protein networks}, PDF = {../FTP_DIR/chaves_albert_sontag_JTB05.pdf}, ABSTRACT = { Interactions between genes and gene products give rise to complex circuits that enable cells to process information and respond to external signals. Theoretical studies often describe these interactions using continuous, stochastic, or logical approaches. Here we propose a framework for gene regulatory networks that combines the intuitive appeal of a qualitative description of gene states with a high flexibility in incorporating stochasticity in the duration of cellular processes. We apply our methods to the regulatory network of the segment polarity genes, thus gaining novel insights into the development of gene expression patterns. For example, we show that very short synthesis and decay times can perturb the wild type pattern. On the other hand, separation of timescales between pre- and post-translational processes and a minimal prepattern ensure convergence to the wild type expression pattern regardless of fluctuations. } } @ARTICLE{enciso_sontagSCL05, AUTHOR = {G.A. Enciso and E.D. Sontag}, JOURNAL = {Systems Control Lett.}, TITLE = {Monotone systems under positive feedback: multistability and a reduction theorem}, YEAR = {2005}, OPTMONTH = {}, OPTNOTE = {}, NUMBER = {2}, PAGES = {159--168}, VOLUME = {54}, KEYWORDS = {multistability, systems biology, biochemical networks, nonlinear stability, dynamical systems, monotone systems}, PDF = {../FTP_DIR/enciso_sontag_multistability_SCL04_inpress.pdf}, ABSTRACT = { For feedback loops involving single input, single output monotone systems with well-defined I/O characteristics, a previous paper provided an approach to determining the location and stability of steady states. A result on global convergence for multistable systems followed as a consequence of the technique. The present paper extends the approach to multiple inputs and outputs. A key idea is the introduction of a reduced system which preserves local stability properties. New results characterizing strong monotonicity of feedback loops involving cascades are also presented. } } @ARTICLE{HLAS, AUTHOR = {J.P. Hespanha and D. Liberzon and D. Angeli and E.D. Sontag}, JOURNAL = {IEEE Trans. Automat. Control}, TITLE = {Nonlinear norm-observability notions and stability of switched systems}, YEAR = {2005}, OPTMONTH = {}, OPTNOTE = {}, NUMBER = {2}, PAGES = {154--168}, VOLUME = {50}, KEYWORDS = {observability, input to state stability, observability, invariance principle}, PDF = {../FTP_DIR/liberzon-hespanha-angeli-sontag-observability-TAC05.pdf}, ABSTRACT = { This paper proposes several definitions of observability for nonlinear systems and explores relationships among them. These observability properties involve the existence of a bound on the norm of the state in terms of the norms of the output and the input on some time interval. A Lyapunov-like sufficient condition for observability is also obtained. As an application, we prove several variants of LaSalle's stability theorem for switched nonlinear systems. These results are demonstrated to be useful for control design in the presence of switching as well as for developing stability results of Popov type for switched feedback systems. } } @ARTICLE{mancilla_garcia_wang_representation05, AUTHOR = {J. L. Mancilla-Aguilar and R. Garcìa and E.D. Sontag and Y. Wang}, JOURNAL = {Nonlinear Anal.}, TITLE = {On the representation of switched systems with inputs by perturbed control systems}, YEAR = {2005}, OPTMONTH = {}, OPTNOTE = {}, NUMBER = {6}, PAGES = {1111--1150}, VOLUME = {60}, PDF = {../FTP_DIR/mancilla-garcia-wang-sontag-switched-representations-NA05.pdf}, ABSTRACT = { This paper provides representations of switched systems described by controlled differential inclusions, in terms of perturbed control systems. The control systems have dynamics given by differential equations, and their inputs consist of the original controls together with disturbances that evolve in compact sets; their sets of maximal trajectories contain, as a dense subset, the set of maximal trajectories of the original system. Several applications to control theory, dealing with properties of stability with respect to inputs and of detectability, are derived as a consequence of the representation theorem. } } @ARTICLE{mancilla-garcia-wang-representation-switches, AUTHOR = {J. L. Mancilla-Aguilar and R. Garcìa and E.D. Sontag and Y. Wang}, JOURNAL = {Nonlinear Anal.}, TITLE = {Uniform stability properties of switched systems with switchings governed by digraphs}, YEAR = {2005}, OPTMONTH = {}, OPTNOTE = {}, NUMBER = {3}, PAGES = {472--490}, VOLUME = {63}, PDF = {../FTP_DIR/mancilla_garcia_sontag_wang_switching-diagraph_NA05.pdf}, ABSTRACT = { This paper develops characterizations of various uniform stability properties of switched systems described by differential inclusions, and whose switchings are governed by a digraph. These characterizations are given in terms of stability properties of the system with restricted switchings and also in terms of Lyapunov functions. } } @ARTICLE{ejc05es, AUTHOR = {E.D. Sontag}, JOURNAL = {Eur. J. Control}, TITLE = {Molecular systems biology and control}, YEAR = {2005}, OPTMONTH = {}, OPTNOTE = {}, NUMBER = {4-5}, PAGES = {396--435}, VOLUME = {11}, KEYWORDS = {cell biology, systems biology, biochemical networks, nonlinear stability, dynamical systems, monotone systems, molecular biology, systems biology, cellular signaling}, PDF = {../FTP_DIR/05cdc_ejc_oct05.pdf}, ABSTRACT = { This paper, prepared for a tutorial at the 2005 IEEE Conference on Decision and Control, presents an introduction to molecular systems biology and some associated problems in control theory. It provides an introduction to basic biological concepts, describes several questions in dynamics and control that arise in the field, and argues that new theoretical problems arise naturally in this context. A final section focuses on the combined use of graph-theoretic, qualitative knowledge about monotone building-blocks and steady-state step responses for components. } } @ARTICLE{predatorpreysgt05, AUTHOR = {de Leenheer, P. and D. Angeli and E.D. Sontag}, JOURNAL = {Math. Biosci. Eng.}, TITLE = {On predator-prey systems and small-gain theorems}, YEAR = {2005}, OPTMONTH = {}, OPTNOTE = {}, NUMBER = {1}, PAGES = {25--42}, VOLUME = {2}, KEYWORDS = {systems biology, biochemical networks, nonlinear stability, dynamical systems, monotone systems}, PDF = {../FTP_DIR/angeli-leenheer-sontag-MBE04.pdf}, ABSTRACT = { This paper deals with an almost global attractivity result for Lotka-Volterra systems with predator-prey interactions. These systems can be written as (negative) feedback systems. The subsystems of the feedback loop are monotone control systems, possessing particular input-output properties. We use a small-gain theorem, adapted to a context of systems with multiple equilibrium points to obtain the desired almost global attractivity result. It provides sufficient conditions to rule out oscillatory or more complicated behavior which is often observed in predator-prey systems. } } @INPROCEEDINGS{05cdc_enciso_sontag, AUTHOR = {G.A. Enciso and E.D. Sontag}, BOOKTITLE = {Proc. IEEE Conf. Decision and Control, Seville, Dec. 2005, IEEE Publications}, TITLE = {A remark on multistability for monotone systems II}, YEAR = {2005}, OPTADDRESS = {}, OPTCROSSREF = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, OPTORGANIZATION = {}, PAGES = {2957--2962}, OPTPUBLISHER = {}, OPTSERIES = {}, OPTVOLUME = {}, KEYWORDS = {multistability, systems biology, biochemical networks, nonlinear stability, dynamical systems, monotone systems} } @INPROCEEDINGS{05cdc-secant, AUTHOR = {E.D. Sontag}, BOOKTITLE = {Proc. IEEE Conf. Decision and Control, Seville, Dec. 2005, IEEE Publications}, TITLE = {A notion of passivity gain and a generalization of the `secant condition' for stability}, YEAR = {2005}, OPTADDRESS = {}, OPTCROSSREF = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, OPTORGANIZATION = {}, PAGES = {5645--5649}, OPTPUBLISHER = {}, OPTSERIES = {}, OPTVOLUME = {}, KEYWORDS = {nonlinear stability, dynamical systems} } @INPROCEEDINGS{05ifac, AUTHOR = {E.D. Sontag and M. Chaves}, BOOKTITLE = {Proc. 16th IFAC World Congress, Prague, July 2005}, TITLE = {Computation of amplification for systems arising from cellular signaling pathways}, YEAR = {2005}, OPTADDRESS = {}, OPTCROSSREF = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, OPTORGANIZATION = {}, OPTPAGES = {}, OPTPUBLISHER = {}, OPTSERIES = {}, OPTVOLUME = {}, KEYWORDS = {systems biology, biochemical networks, dynamical systems} } @INCOLLECTION{monotoneLSU, AUTHOR = {D. Angeli and E.D. Sontag}, BOOKTITLE = {Optimal control, stabilization and nonsmooth analysis}, PUBLISHER = {Springer}, TITLE = {Interconnections of monotone systems with steady-state characteristics}, YEAR = {2004}, ADDRESS = {Berlin}, OPTCHAPTER = {}, OPTCROSSREF = {}, OPTEDITION = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, PAGES = {135--154}, SERIES = {Lecture Notes in Control and Inform. Sci.}, OPTTYPE = {}, VOLUME = {301}, KEYWORDS = {systems biology, biochemical networks, nonlinear stability, dynamical systems, monotone systems}, PDF = {../FTP_DIR/monotone-lsu-book-final.pdf}, ABSTRACT = { One of the key ideas in control theory is that of viewing a complex dynamical system as an interconnection of simpler subsystems, thus deriving conclusions regarding the complete system from properties of its building blocks. Following this paradigm, and motivated by questions in molecular biology modeling, the authors have recently developed an approach based on components which are monotone systems with respect to partial orders in state and signal spaces. This paper presents a brief exposition of recent results, with an emphasis on small gain theorems for negative feedback, and the emergence of multi-stability and associated hysteresis effects under positive feedback. } } @INCOLLECTION{MalisoffSontag04, AUTHOR = {M. Malisoff and E.D. Sontag}, BOOKTITLE = {Optimal control, stabilization and nonsmooth analysis}, PUBLISHER = {Springer}, TITLE = {Asymptotic controllability and input-to-state stabilization: the effect of actuator errors}, YEAR = {2004}, ADDRESS = {Berlin}, OPTCHAPTER = {}, OPTCROSSREF = {}, OPTEDITION = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, PAGES = {155--171}, SERIES = {Lecture Notes in Control and Inform. Sci.}, OPTTYPE = {}, VOLUME = {301}, KEYWORDS = {input to state stability, control-Lyapunov functions, nonlinear control, feedback stabilization}, PDF = {../FTP_DIR/malisoff-sontag-lsu03.pdf}, ABSTRACT = { We discuss several issues related to the stabilizability of nonlinear systems. First, for continuously stabilizable systems, we review constructions of feedbacks that render the system input-to-state stable with respect to actuator errors. Then, we discuss a recent paper which provides a new feedback design that makes globally asymptotically controllable systems input-to-state stable to actuator errors and small observation noise. We illustrate our constructions using the nonholonomic integrator, and discuss a related feedback design for systems with disturbances. } } @ARTICLE{pnasangeliferrellsontag04, AUTHOR = {D. Angeli and J. E. Ferrell and E.D. Sontag}, JOURNAL = {Proc Natl Acad Sci USA}, TITLE = {Detection of multistability, bifurcations, and hysteresis in a large class of biological positive-feedback systems.}, YEAR = {2004}, OPTMONTH = {}, NOTE = {A revision of Suppl. Fig. 7(b) is here: http://www.math.rutgers.edu/(tilde)sontag/FTPDIR/nullclines-f-g-REV.jpg; and typos can be found here: http://www.math.rutgers.edu/(tilde)sontag/FTPDIR/angeli-ferrell-sontag-pnas04-errata.txt}, NUMBER = {7}, PAGES = {1822--1827}, VOLUME = {101}, KEYWORDS = {multistability, systems biology, biochemical networks, nonlinear stability, dynamical systems, monotone systems}, URL = {http://dx.doi.org/10.1073/pnas.0308265100}, PDF = {../FTP_DIR/angeli_ferrell_sontag_pnas04_paper_and_supplementary.pdf}, ABSTRACT = { Multistability is an important recurring theme in cell signaling, of particular relevance to biological systems that switch between discrete states, generate oscillatory responses, or "remember" transitory stimuli. Standard mathematical methods allow the detection of bistability in some very simple feedback systems (systems with one or two proteins or genes that either activate each other or inhibit each other), but realistic depictions of signal transduction networks are invariably much more complex than this. Here we show that for a class of feedback systems of arbitrary order, the stability properties of the system can be deduced mathematically from how the system behaves when feedback is blocked. Provided that this "open loop," feedback-blocked system is monotone and possesses a sigmoidal characteristic, the system is guaranteed to be bistable for some range of feedback strengths. We present a simple graphical method for deducing the stability behavior and bifurcation diagrams for such systems, and illustrate the method with two examples taken from recent experimental studies of bistable systems: a two-variable Cdc2/Wee1 system and a more complicated five-variable MAPK cascade. }, DOI = {10.1073/pnas.0308265100} } @ARTICLE{angeli_ingalls_sontag_wang_separation_SICOPT04, AUTHOR = {D. Angeli and B. Ingalls and E.D. Sontag and Y. Wang}, JOURNAL = {SIAM J. Control Optim.}, TITLE = {Separation principles for input-output and integral-input-to-state stability}, YEAR = {2004}, OPTMONTH = {}, OPTNOTE = {}, NUMBER = {1}, PAGES = {256--276}, VOLUME = {43}, ADDRESS = {Philadelphia, PA, USA}, KEYWORDS = {input to state stability}, PUBLISHER = {Society for Industrial and Applied Mathematics}, PDF = {../FTP_DIR/separation_principles_ios_iiss_angeli_ingalls_sontag_wang_SICON04.pdf}, ABSTRACT = { We present new characterizations of input-output-to-state stability. This is a notion of detectability formulated in the ISS framework. Equivalent properties are presented in terms of asymptotic estimates of the state trajectories based on the magnitudes of the external input and output signals. These results provide a set of "separation principles" for input-output-to-state stability , characterizations of the property in terms of weaker stability notions. When applied to the closely related notion of integral ISS, these characterizations yield analogous results. }, DOI = {http://dx.doi.org/10.1137/S0363012902419047} } @ARTICLE{angeli_ingalls_sontag_wang_UGAS_DE_DynCtrSys04, AUTHOR = {D. Angeli and B. Ingalls and E.D. Sontag and Y. Wang}, JOURNAL = {J. Dynam. Control Systems}, TITLE = {Uniform global asymptotic stability of differential inclusions}, YEAR = {2004}, OPTMONTH = {}, OPTNOTE = {}, NUMBER = {3}, PAGES = {391--412}, VOLUME = {10}, ADDRESS = {Hingham, MA, USA}, KEYWORDS = {differential inclusions}, PUBLISHER = {Kluwer Academic Publishers}, PDF = {../FTP_DIR/ingalls-ywang-angeli-sontag-gas-ugas-di-JDCS04.pdf}, ABSTRACT = { The stability of differential inclusions defined by locally Lipschitz compact valued maps is addressed. It is shown that if such a differential inclusion is globally asymptotically stable, then in fact it is uniformly globally asymptotically stable (with respect to initial states in compacts). This statement is trivial for differential equations, but here we provide the extension to compact (not necessarily convex) valued differential inclusions. The main result is presented in a context which is useful for control-theoretic applications: a differential inclusion with two outputs is considered, and the result applies to the property of global error detectability. }, DOI = {http://dx.doi.org/10.1023/B:JODS.0000034437.54937.7f} } @ARTICLE{monotoneMulti, AUTHOR = {D. Angeli and E.D. Sontag}, JOURNAL = {Systems Control Lett.}, TITLE = {Multi-stability in monotone input/output systems}, YEAR = {2004}, OPTMONTH = {}, OPTNOTE = {}, NUMBER = {3-4}, PAGES = {185--202}, VOLUME = {51}, KEYWORDS = {multistability, systems biology, biochemical networks, nonlinear stability, dynamical systems, monotone systems}, PDF = {../FTP_DIR/angeli_sontag_multistability_SCL04.pdf}, ABSTRACT = { This paper studies the emergence of multi-stability and hysteresis in those systems that arise, under positive feedback, from monotone systems with well-defined steady-state responses. Such feedback configurations appear routinely in several fields of application, and especially in biology. The results are stated in terms of directly checkable conditions which do not involve explicit knowledge of basins of attractions of each equilibria. } } @ARTICLE{angelileenheersontagSCL04, AUTHOR = {D. Angeli and de Leenheer, P. and E.D. Sontag}, JOURNAL = {Systems Control Lett.}, TITLE = {A small-gain theorem for almost global convergence of monotone systems}, YEAR = {2004}, OPTMONTH = {}, OPTNOTE = {}, NUMBER = {5}, PAGES = {407--414}, VOLUME = {52}, KEYWORDS = {systems biology, biochemical networks, nonlinear stability, dynamical systems, monotone systems}, PDF = {../FTP_DIR/angeli_leenheer_sontag_SCL04.pdf}, ABSTRACT = { A small-gain theorem is presented for almost global stability of monotone control systems which are open-loop almost globally stable, when constant inputs are applied. The theorem assumes "negative feedback" interconnections. This typically destroys the monotonicity of the original flow and potentially destabilizes the resulting closed-loop system. } } @ARTICLE{signaling_gains04, AUTHOR = {M. Chaves and R.J. Dinerstein and E.D. Sontag}, JOURNAL = {J. Physical Chemistry}, TITLE = {Optimal length and signal amplification in weakly activated signal transduction cascades}, YEAR = {2004}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, PAGES = {15311--15320}, VOLUME = {108}, KEYWORDS = {systems biology, biochemical networks, dynamical systems}, PDF = {../FTP_DIR/chaves-sontag-dinerstein-signaling-gains-JPC-with-supplement.pdf}, ABSTRACT = { Weakly activated signaling cascades can be modeled as linear systems. The input-to-output transfer function and the internal gain of a linear system, provide natural measures for the propagation of the input signal down the cascade and for the characterization of the final outcome. The most efficient design of a cascade for generating sharp signals, is obtained by choosing all the off rates equal, and a "universal" finite optimal length. } } @ARTICLE{receptorligandJTB04, AUTHOR = {M. Chaves and E.D. Sontag and R. J. Dinerstein}, JOURNAL = {J. Theoret. Biol.}, TITLE = {Steady-states of receptor-ligand dynamics: A theoretical framework}, YEAR = {2004}, OPTMONTH = {}, OPTNOTE = {}, NUMBER = {3}, PAGES = {413--428}, VOLUME = {227}, KEYWORDS = {zero-deficiency networks, systems biology, biochemical networks, receptor-ligand models, dynamical systems}, PDF = {../FTP_DIR/chaves-sontag-dinerstein-JTB04.pdf}, ABSTRACT = { This paper studies aspects of the dynamics of a conventional mechanism of ligand-receptor interactions, with a focus on the stability and location of steady-states. A theoretical framework is developed, and, as an application, a minimal parametrization is provided for models for two- or multi-state receptor interaction with ligand. In addition, an "affinity quotient" is introduced, which allows an elegant classification of ligands into agonists, neutral agonists, and inverse agonists. } } @ARTICLE{testosterone, AUTHOR = {G.A. Enciso and E.D. Sontag}, JOURNAL = {J. Math. Biol.}, TITLE = {On the stability of a model of testosterone dynamics}, YEAR = {2004}, OPTMONTH = {}, OPTNOTE = {}, NUMBER = {6}, PAGES = {627--634}, VOLUME = {49}, KEYWORDS = {systems biology, biochemical networks, nonlinear stability, dynamical systems, monotone systems}, PDF = {../FTP_DIR/enciso-sontag-testosterone-JMB.pdf}, ABSTRACT = { We prove the global asymptotic stability of a well-known delayed negative-feedback model of testosterone dynamics, which has been proposed as a model of oscillatory behavior. We establish stability (and hence the impossibility of oscillations) even in the presence of delays of arbitrary length. } } @ARTICLE{kuusela_ocone_sontag04, AUTHOR = {P. Kuusela and D. Ocone and E.D. Sontag}, JOURNAL = {SIAM J. Control Optim.}, TITLE = {Learning Complexity Dimensions for a Continuous-Time Control System}, YEAR = {2004}, OPTMONTH = {}, OPTNOTE = {}, NUMBER = {3}, PAGES = {872--898}, VOLUME = {43}, ADDRESS = {Philadelphia, PA, USA}, KEYWORDS = {theory of computing and complexity, VC dimension}, PUBLISHER = {Society for Industrial and Applied Mathematics}, PDF = {../FTP_DIR/kuusela-ocone-sontag-as-published-SIAM04.pdf}, ABSTRACT = { This paper takes a computational learning theory approach to a problem of linear systems identification. It is assumed that input signals have only a finite number k of frequency components, and systems to be identified have dimension no greater than n. The main result establishes that the sample complexity needed for identification scales polynomially with n and logarithmically with k. }, DOI = {http://dx.doi.org/10.1137/S0363012901384302} } @ARTICLE{MalisoffRiffordSontag04, AUTHOR = {M. Malisoff and L. Rifford and E.D. Sontag}, JOURNAL = {SIAM J. Control Optim.}, TITLE = {Global Asymptotic Controllability Implies Input-to-State Stabilization}, YEAR = {2004}, OPTMONTH = {}, OPTNOTE = {}, NUMBER = {6}, PAGES = {2221--2238}, VOLUME = {42}, ADDRESS = {Philadelphia, PA, USA}, KEYWORDS = {input to state stability, control-Lyapunov functions, nonlinear control, feedback stabilization}, PUBLISHER = {Society for Industrial and Applied Mathematics}, PDF = {../FTP_DIR/malisoff-rifford-sontag-SIAM04.pdf}, ABSTRACT = { The main problem addressed in this paper is the design of feedbacks for globally asymptotically controllable (GAC) control affine systems that render the closed loop systems input to state stable with respect to actuator errors. Extensions for fully nonlinear GAC systems with actuator errors are also discussed. Our controllers have the property that they tolerate small observation noise as well. }, DOI = {http://dx.doi.org/10.1137/S0363012903422333} } @ARTICLE{sysbio04, AUTHOR = {E.D. Sontag}, JOURNAL = {IET Systems Biology}, TITLE = {Some new directions in control theory inspired by systems biology}, YEAR = {2004}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, PAGES = {9-18}, VOLUME = {1}, KEYWORDS = {systems biology, biochemical networks, nonlinear stability, dynamical systems, monotone systems, cellular signaling}, PDF = {../FTP_DIR/sysbio_sontag04.pdf}, ABSTRACT = { This paper, addressed primarily to engineers and mathematicians with an interest in control theory, argues that entirely new theoretical problems arise naturally when addressing questions in the field of systems biology. Examples from the author's recent work are used to illustrate this point. } } @ARTICLE{SontagKiyatinKholodenko04, AUTHOR = {E.D. Sontag and A. Kiyatkin and B.N. Kholodenko}, JOURNAL = {Bioinformatics}, TITLE = {Inferring dynamic architecture of cellular networks using time series of gene expression, protein and metabolite data}, YEAR = {2004}, OPTMONTH = {}, NOTE = {Supplementary materials are here: http://www.math.rutgers.edu/(tilde)sontag/FTPDIR/sontag-kiyatkin-kholodenko-informatics04-supplement.pdf}, NUMBER = {12}, PAGES = {1877--1886}, VOLUME = {20}, ADDRESS = {Oxford, UK}, KEYWORDS = {systems biology, biochemical networks, systems identification, gene and protein networks, reverse engineering}, PUBLISHER = {Oxford University Press}, PDF = {../FTP_DIR/sontag_kiyatkin_kholodenko_informatics04.pdf}, ABSTRACT = { High-throughput technologies have facilitated the acquisition of large genomics and proteomics data sets. However, these data provide snapshots of cellular behavior, rather than help us reveal causal relations. Here, we propose how these technologies can be utilized to infer the topology and strengths of connections among genes, proteins, and metabolites by monitoring time-dependent responses of cellular networks to experimental interventions. We show that all connections leading to a given network node, e.g., to a particular gene, can be deduced from responses to perturbations none of which directly influences that node, e.g., using strains with knock-outs to other genes. To infer all interactions from stationary data, each node should be perturbed separately or in combination with other nodes. Monitoring time series provides richer information and does not require perturbations to all nodes. }, DOI = {http://dx.doi.org/10.1093/bioinformatics/bth173} } @INPROCEEDINGS{04cdc-circadian, AUTHOR = {D. Angeli and E.D. Sontag}, BOOKTITLE = {Proc. IEEE Conf. Decision and Control, Paradise Island, Bahamas, Dec. 2004, IEEE Publications}, TITLE = {An analysis of a circadian model using the small-gain approach to monotone systems}, YEAR = {2004}, OPTADDRESS = {}, OPTCROSSREF = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, OPTORGANIZATION = {}, PAGES = {575--578}, OPTPUBLISHER = {}, OPTSERIES = {}, OPTVOLUME = {}, KEYWORDS = {circadian rhythms, tridiagonal systems, nonlinear dynamics, systems biology, biochemical networks, oscillations, periodic behavior, monotone systems}, PDF = {../FTP_DIR/04cdc-circadian-final.pdf}, ABSTRACT = { We show how certain properties of Goldbeter's original 1995 model for circadian oscillations can be proved mathematically. We establish global asymptotic stability, and in particular no oscillations, if the rate of transcription is somewhat smaller than that assumed by Goldbeter, but, on the other hand, this stability persists even under arbitrary delays in the feedback loop. We are mainly interested in illustrating certain mathematical techniques, including the use of theorems concerning tridiagonal cooperative systems and the recently developed theory of monotone systems with inputs and outputs. } } @INPROCEEDINGS{04mtns-angeli-leenheer-monotone, AUTHOR = {D. Angeli and de Leenheer, P. and E.D. Sontag}, BOOKTITLE = {Proc. 16th Int. Symp. Mathematical Theory of Networks and Systems (MTNS 2004), CD-ROM, WP9.1, Katholieke Universiteit Leuven}, TITLE = {A tutorial on monotone systems- with an application to chemical reaction networks}, YEAR = {2004}, OPTADDRESS = {}, OPTCROSSREF = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, OPTORGANIZATION = {}, OPTPAGES = {}, OPTPUBLISHER = {}, OPTSERIES = {}, OPTVOLUME = {}, KEYWORDS = {systems biology, biochemical networks, nonlinear stability, dynamical systems, monotone systems}, PDF = {../FTP_DIR/04mtns-leenheer-angeli-monotone.pdf}, ABSTRACT = { Monotone systems are dynamical systems for which the flow preserves a partial order. Some applications will be briefly reviewed in this paper. Much of the appeal of the class of monotone systems stems from the fact that roughly, most solutions converge to the set of equilibria. However, this usually requires a stronger monotonicity property which is not always satisfied or easy to check in applications. Following work of J.F. Jiang, we show that monotonicity is enough to conclude global attractivity if there is a unique equilibrium and if the state space satisfies a particular condition. The proof given here is self-contained and does not require the use of any of the results from the theory of monotone systems. We will illustrate it on a class of chemical reaction networks with monotone, but otherwise arbitrary, reaction kinetics. } } @INPROCEEDINGS{04cdc-angeli-leenheer-monotone, AUTHOR = {D. Angeli and de Leenheer, P. and E.D. Sontag}, BOOKTITLE = {Proc. IEEE Conf. Decision and Control, Paradise Island, Bahamas, Dec. 2004, IEEE Publications}, TITLE = {Remarks on monotonicity and convergence in chemical reaction networks}, YEAR = {2004}, OPTADDRESS = {}, OPTCROSSREF = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, OPTORGANIZATION = {}, PAGES = {243--248}, OPTPUBLISHER = {}, OPTSERIES = {}, OPTVOLUME = {}, KEYWORDS = {systems biology, biochemical networks, nonlinear stability, dynamical systems, monotone systems} } @INPROCEEDINGS{04cdc-chaves-dinerstein, AUTHOR = {M. Chaves and E.D. Sontag and R.J. Dinerstein}, BOOKTITLE = {Proc. IEEE Conf. Decision and Control, Paradise Island, Bahamas, Dec. 2004, IEEE Publications}, TITLE = {Gains and optimal design in signaling pathways}, YEAR = {2004}, OPTADDRESS = {}, OPTCROSSREF = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, OPTORGANIZATION = {}, PAGES = {596--601}, OPTPUBLISHER = {}, OPTSERIES = {}, OPTVOLUME = {}, KEYWORDS = {systems biology, biochemical networks, dynamical systems} } @INPROCEEDINGS{04acc1, AUTHOR = {B. DasGupta and J.P. Hespanha and E.D. Sontag}, BOOKTITLE = {Proceedings American Control Conf., Boston, June 2004}, TITLE = {Aggregation-based approaches to honey-pot searching with local sensory information}, YEAR = {2004}, OPTADDRESS = {}, OPTCROSSREF = {}, OPTEDITOR = {}, OPTMONTH = {}, NOTE = {(CD-ROM WeM17.4, IEEE Publications, Piscataway)}, OPTNUMBER = {}, OPTORGANIZATION = {}, OPTPAGES = {}, OPTPUBLISHER = {}, OPTSERIES = {}, OPTVOLUME = {}, PDF = {../FTP_DIR/04acc-dasgupta-hespanha-sontag-aggregation-search.pdf}, ABSTRACT = { We investigate the problem of searching for a hidden target in a bounded region by an autonomous agent that is only able to use limited local sensory information. We propose an aggregation-based approach to solve this problem, in which the continuous search space is partitioned into a finite collection of regions on which we define a discrete search problem. A solution to the original problem is then obtained through a refinement procedure that lifts the discrete path into a continuous one. The resulting solution is in general not optimal but one can construct bounds to gauge the cost penalty incurred. } } @INPROCEEDINGS{04acc2, AUTHOR = {B. DasGupta and J.P. Hespanha and E.D. Sontag}, BOOKTITLE = {Proceedings American Control Conf., Boston, June 2004, CD-ROM, ThA06.1, IEEE Publications, Piscataway}, TITLE = {Computational complexities of honey-pot searching with local sensory information}, YEAR = {2004}, OPTADDRESS = {}, OPTCROSSREF = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, OPTORGANIZATION = {}, OPTPAGES = {}, OPTPUBLISHER = {}, OPTSERIES = {}, OPTVOLUME = {}, PDF = {../FTP_DIR/04acc-dasgupta-hespanha-sontag-computational-search.pdf}, ABSTRACT = { In this paper we investigate the problem of searching for a hidden target in a bounded region of the plane, by an autonomous robot which is only able to use limited local sensory information. We formalize a discrete version of the problem as a "reward-collecting" path problem and provide efficient approximation algorithms for various cases. } } @INPROCEEDINGS{04cdc-enciso-multi, AUTHOR = {G.A. Enciso and E.D. Sontag}, BOOKTITLE = {Proc. IEEE Conf. Decision and Control, Paradise Island, Bahamas, Dec. 2004, IEEE Publications}, TITLE = {A remark on multistability for monotone systems}, YEAR = {2004}, OPTADDRESS = {}, OPTCROSSREF = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, OPTORGANIZATION = {}, PAGES = {249--254}, OPTPUBLISHER = {}, OPTSERIES = {}, OPTVOLUME = {}, KEYWORDS = {multistability, systems biology, biochemical networks, nonlinear stability, dynamical systems, monotone systems} } @INPROCEEDINGS{04cdc-mancilla-wang-representation, AUTHOR = {J.L. Mancilla-Aguilar and R. Garcìa and E.D. Sontag and Y. Wang}, BOOKTITLE = {Proc. IEEE Conf. Decision and Control, Paradise Island, Bahamas, Dec. 2004, IEEE Publications}, TITLE = {Representation of switched systems by perturbed control systems}, YEAR = {2004}, OPTADDRESS = {}, OPTCROSSREF = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, OPTORGANIZATION = {}, PAGES = {3259--3264}, OPTPUBLISHER = {}, OPTSERIES = {}, OPTVOLUME = {} } @INCOLLECTION{posta03chemostat, AUTHOR = {de Leenheer, P. and D. Angeli and E.D. Sontag}, BOOKTITLE = {Positive systems (Rome, 2003)}, PUBLISHER = {Springer}, TITLE = {A feedback perspective for chemostat models with crowding effects}, YEAR = {2003}, ADDRESS = {Berlin}, OPTCHAPTER = {}, OPTCROSSREF = {}, OPTEDITION = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, PAGES = {167--174}, SERIES = {Lecture Notes in Control and Inform. Sci.}, OPTTYPE = {}, VOLUME = {294}, KEYWORDS = {systems biology, biochemical networks, nonlinear stability, dynamical systems, monotone systems} } @INCOLLECTION{MR2019317, AUTHOR = {de Leenheer, P. and D. Angeli and E.D. Sontag}, BOOKTITLE = {Positive systems (Rome, 2003)}, PUBLISHER = {Springer}, TITLE = {Small-gain theorems for predator-prey systems}, YEAR = {2003}, ADDRESS = {Berlin}, OPTCHAPTER = {}, OPTCROSSREF = {}, OPTEDITION = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, PAGES = {191--198}, SERIES = {Lecture Notes in Control and Inform. Sci.}, OPTTYPE = {}, VOLUME = {294}, KEYWORDS = {systems biology, biochemical networks, nonlinear stability, dynamical systems, monotone systems} } @ARTICLE{monotoneTAC, AUTHOR = {D. Angeli and E.D. Sontag}, JOURNAL = {IEEE Trans. Automat. Control}, TITLE = {Monotone control systems}, YEAR = {2003}, OPTMONTH = {}, NOTE = {Errata are here: http://www.math.rutgers.edu/(tilde)sontag/FTPDIR/angeli-sontag-monotone-TAC03-typos.txt}, NUMBER = {10}, PAGES = {1684--1698}, VOLUME = {48}, KEYWORDS = {systems biology, biochemical networks, nonlinear stability, dynamical systems, monotone systems}, PDF = {../FTP_DIR/angeli-sontag-monotone-TAC03.pdf}, ABSTRACT = { Monotone systems constitute one of the most important classes of dynamical systems used in mathematical biology modeling. The objective of this paper is to extend the notion of monotonicity to systems with inputs and outputs, a necessary first step in trying to understand interconnections, especially including feedback loops, built up out of monotone components. Basic definitions and theorems are provided, as well as an application to the study of a model of one of the cell's most important subsystems. } } @ARTICLE{DiffISS_IJRNC03, AUTHOR = {D. Angeli and E.D. Sontag and Y. Wang}, JOURNAL = {Internat. J. Robust Nonlinear Control}, TITLE = {Input-to-state stability with respect to inputs and their derivatives}, YEAR = {2003}, OPTMONTH = {}, OPTNOTE = {}, NUMBER = {11}, PAGES = {1035--1056}, VOLUME = {13}, KEYWORDS = {input to state stability, input to state stability}, PDF = {../FTP_DIR/diss-ijrac03.pdf}, ABSTRACT = { A new notion of input-to-state stability involving infinity norms of input derivatives up to a finite order k is introduced and characterized. An example shows that this notion of stability is indeed weaker than the usual ISS. Applications to the study of global asymptotic stability of cascaded nonlinear systems are discussed. } } @ARTICLE{chyba03, AUTHOR = {M. Chyba and N. E. Leonard and E.D. Sontag}, JOURNAL = {Journal of Dynamical and Control Systems}, TITLE = {Singular trajectories in multi-input time-optimal problems: Application to controlled mechanical systems}, YEAR = {2003}, OPTMONTH = {}, OPTNOTE = {}, NUMBER = {1}, PAGES = {103--129}, VOLUME = {9}, ADDRESS = {Hingham, MA, USA}, KEYWORDS = {optimal control}, PUBLISHER = {Kluwer Academic Publishers}, PDF = {../FTP_DIR/underwater.pdf}, ABSTRACT = { This paper addresses the time-optimal control problem for a class of control systems which includes controlled mechanical systems with possible dissipation terms. The Lie algebras associated with such mechanical systems enjoy certain special properties. These properties are explored and are used in conjunction with the Pontryagin maximum principle to determine the structure of singular extremals and, in particular, time-optimal trajectories. The theory is illustrated with an application to a time-optimal problem for a class of underwater vehicles. }, DOI = {http://dx.doi.org/10.1023/A:1022159318457} } @ARTICLE{relaxation-DE-PAMS03, AUTHOR = {B. Ingalls and E.D. Sontag and Y. Wang}, JOURNAL = {Proc. Amer. Math. Soc.}, TITLE = {An infinite-time relaxation theorem for differential inclusions}, YEAR = {2003}, OPTMONTH = {}, OPTNOTE = {}, NUMBER = {2}, PAGES = {487--499}, VOLUME = {131}, PDF = {../FTP_DIR/relaxation-di-as-appeared.pdf}, ABSTRACT = { The fundamental relaxation result for Lipschitz differential inclusions is the Filippov-Wazewski Relaxation Theorem, which provides approximations of trajectories of a relaxed inclusion on finite intervals. A complementary result is presented, which provides approximations on infinite intervals, but does not guarantee that the approximation and the reference trajectory satisfy the same initial condition. } } @ARTICLE{moreau_sontagPRE03, AUTHOR = {L. Moreau and E.D. Sontag}, JOURNAL = {Phys. Rev. E (3)}, TITLE = {Balancing at the border of instability}, YEAR = {2003}, OPTMONTH = {}, OPTNOTE = {}, NUMBER = {2}, PAGES = {020901, 4}, VOLUME = {68}, KEYWORDS = {bifurcations, adaptive control}, PDF = {../FTP_DIR/moreau-sontag-physrevE03.pdf}, ABSTRACT = { Some biological systems operate at the critical point between stability and instability and this requires a fine-tuning of parameters. We bring together two examples from the literature that illustrate this: neural integration in the nervous system and hair cell oscillations in the auditory system. In both examples the question arises as to how the required fine-tuning may be achieved and maintained in a robust and reliable way. We study this question using tools from nonlinear and adaptive control theory. We illustrate our approach on a simple model which captures some of the essential features of neural integration. As a result, we propose a large class of feedback adaptation rules that may be responsible for the experimentally observed robustness of neural integration. We mention extensions of our approach to the case of hair cell oscillations in the ear. } } @ARTICLE{moreau_sontag_arcak03, AUTHOR = {L. Moreau and E.D. Sontag and M. Arcak}, JOURNAL = {Systems Control Lett.}, TITLE = {Feedback tuning of bifurcations}, YEAR = {2003}, OPTMONTH = {}, OPTNOTE = {}, NUMBER = {3}, PAGES = {229--239}, VOLUME = {50}, KEYWORDS = {bifurcations, adaptive control}, PDF = {../FTP_DIR/moreau-sontag-arcak-bifurcations.pdf}, ABSTRACT = { This paper studies a feedback regulation problem that arises in at least two different biological applications. The feedback regulation problem under consideration may be interpreted as an adaptive control problem for tuning bifurcation parameters, and it has not been studied in the control literature. The goal of the paper is to formulate this problem and to present some preliminary results. } } @ARTICLE{pomerening-ferrell, AUTHOR = {J. R. Pomerening and E.D. Sontag and J. E. Ferrell}, JOURNAL = {Nature Cell Biology}, TITLE = {Building a cell cycle oscillator: hysteresis and bistability in the activation of Cdc2}, YEAR = {2003}, OPTMONTH = {}, NOTE = {Supplementary materials 2-4 are here: http://www.math.rutgers.edu/(tilde)sontag/FTPDIR/pomerening-sontag-ferrell-additional.pdf}, NUMBER = {4}, PAGES = {346--351}, VOLUME = {5}, ADDRESS = {Department of Molecular Pharmacology, Stanford University School of Medicine, Stanford, CA 94305-5174, USA.}, KEYWORDS = {systems biology, biochemical networks, oscillations, nonlinear stability, dynamical systems, monotone systems}, URL = {http://dx.doi.org/10.1038/ncb954}, PDF = {../FTP_DIR/pomerening-sontag-ferrell-naturecell03.pdf}, ABSTRACT = { In the early embryonic cell cycle, Cdc2-cyclin B functions like an autonomous oscillator, at whose core is a negative feedback loop: cyclins accumulate and produce active mitotic Cdc2-cyclin B Cdc2 activates the anaphase-promoting complex (APC); the APC then promotes cyclin degradation and resets Cdc2 to its inactive, interphase state. Cdc2 regulation also involves positive feedback4, with active Cdc2-cyclin B stimulating its activator Cdc25 and inactivating its inhibitors Wee1 and Myt1. Under the correct circumstances, these positive feedback loops could function as a bistable trigger for mitosis, and oscillators with bistable triggers may be particularly relevant to biological applications such as cell cycle regulation. This paper examined whether Cdc2 activation is bistable, confirming that the response of Cdc2 to non-degradable cyclin B is temporally abrupt and switchlike, as would be expected if Cdc2 activation were bistable. It is also shown that Cdc2 activation exhibits hysteresis, a property of bistable systems with particular relevance to biochemical oscillators. These findings help establish the basic systems-level logic of the mitotic oscillator. }, DOI = {10.1038/ncb954} } @ARTICLE{CICS_TAC03, AUTHOR = {E.D. Sontag}, JOURNAL = {IEEE Trans. Automat. Control}, TITLE = {A remark on the converging-input converging-state property}, YEAR = {2003}, OPTMONTH = {}, OPTNOTE = {}, NUMBER = {2}, PAGES = {313--314}, VOLUME = {48}, PDF = {../FTP_DIR/cics-TAC03-as-appeared.pdf}, ABSTRACT = { Suppose that an equilibrium is asymptotically stable when external inputs vanish. Then, every bounded trajectory which corresponds to a control which approaches zero and which lies in the domain of attraction of the unforced system, must also converge to the equilibrium. This "well-known" but hard-to-cite fact is proved and slightly generalized here. } } @ARTICLE{imp03, AUTHOR = {E.D. Sontag}, JOURNAL = {Systems Control Lett.}, TITLE = {Adaptation and regulation with signal detection implies internal model}, YEAR = {2003}, OPTMONTH = {}, OPTNOTE = {}, NUMBER = {2}, PAGES = {119--126}, VOLUME = {50}, KEYWORDS = {biological adaptation, internal model principle}, PDF = {../FTP_DIR/imp-scl03.pdf}, ABSTRACT = { This note provides a simple result showing, under suitable technical assumptions, that if a system S adapts to a class of external signals U, then S must necessarily contain a subsystem which is capable of generating all the signals in U. It is not assumed that regulation is robust, nor is there a prior requirement for the system to be partitioned into separate plant and controller components. Instead, a "signal detection" capability is imposed. These weaker assumptions make the result better applicable to cellular phenomena such as the adaptation of E-coli chemotactic tumbling rate to constant concentrations. } } @ARTICLE{sontag_krichman_integrable_perturb_TAC03, AUTHOR = {E.D. Sontag and M. Krichman}, JOURNAL = {IEEE Trans. Automat. Control}, TITLE = {An example of a GAS system which can be destabilized by an integrable perturbation}, YEAR = {2003}, OPTMONTH = {}, OPTNOTE = {}, NUMBER = {6}, PAGES = {1046--1049}, VOLUME = {48}, KEYWORDS = {nonlinear stability}, PDF = {../FTP_DIR/L1-perturb-GAS.pdf}, ABSTRACT = { A construction is given of a globally asymptotically stable time-invariant system which can be destabilized by some integrable perturbation. Besides its intrinsic interest, this serves to provide counterexamples to an open question regarding Lyapunov functions. } } @INPROCEEDINGS{angeli-03cdc-multistability, AUTHOR = {D. Angeli and E.D. Sontag}, BOOKTITLE = {Proc. IEEE Conf. Decision and Control, Maui, Dec. 2003, IEEE Publications, 2003}, TITLE = {A note on multistability and monotone I/O systems}, YEAR = {2003}, OPTADDRESS = {}, OPTCROSSREF = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, OPTORGANIZATION = {}, PAGES = {67--72}, OPTPUBLISHER = {}, OPTSERIES = {}, OPTVOLUME = {}, KEYWORDS = {systems biology, biochemical networks, nonlinear stability, dynamical systems, monotone systems} } @INPROCEEDINGS{malisoff-rifford-03cdc, AUTHOR = {M. Malisoff and L. Rifford and E.D. Sontag}, BOOKTITLE = {Proc. IEEE Conf. Decision and Control, Maui, Dec. 2003, IEEE Publications, 2003}, TITLE = {Remarks on input to state stabilization}, YEAR = {2003}, OPTADDRESS = {}, OPTCROSSREF = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, OPTORGANIZATION = {}, PAGES = {1053--1058}, OPTPUBLISHER = {}, OPTSERIES = {}, OPTVOLUME = {}, KEYWORDS = {nonlinear control, feedback stabilization} } @INPROCEEDINGS{moreau-arcak-03cdc, AUTHOR = {L. Moreau and E.D. Sontag and M. Arcak}, BOOKTITLE = {Proc. IEEE Conf. Decision and Control, Maui, Dec. 2003, IEEE Publications, 2003}, TITLE = {How feedback can tune a bifurcation parameter towards its unknown critical bifurcation value}, YEAR = {2003}, OPTADDRESS = {}, OPTCROSSREF = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, OPTORGANIZATION = {}, PAGES = {2401--2406}, OPTPUBLISHER = {}, OPTSERIES = {}, OPTVOLUME = {} } @ARTICLE{arcak_angeli_sontag_cascades_SICOPT02, AUTHOR = {M. Arcak and D. Angeli and E.D. Sontag}, JOURNAL = {SIAM J. Control Optim.}, TITLE = {A unifying integral ISS framework for stability of nonlinear cascades}, YEAR = {2002}, OPTMONTH = {}, OPTNOTE = {}, NUMBER = {6}, PAGES = {1888--1904}, VOLUME = {40}, ADDRESS = {Philadelphia, PA, USA}, KEYWORDS = {input to state stability}, PUBLISHER = {Society for Industrial and Applied Mathematics}, PDF = {../FTP_DIR/iiss-cascades.pdf}, ABSTRACT = { We analyze nonlinear cascades in which the driven subsystem is integral ISS, and characterize the admissible integral ISS gains for stability. This characterization makes use of the convergence speed of the driving subsystem, and allows a larger class of gain functions when the convergence is faster. We show that our integral ISS gain characterization unifies different approaches in the literature which restrict the nonlinear growth of the driven subsystem and the convergence speed of the driving subsystem. }, DOI = {http://dx.doi.org/10.1137/S0363012901387987} } @ARTICLE{chem-obs-journal, AUTHOR = {M. Chaves and E.D. Sontag}, JOURNAL = {European J. Control}, TITLE = {State-Estimators for chemical reaction networks of Feinberg-Horn-Jackson zero deficiency type}, YEAR = {2002}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, PAGES = {343--359}, VOLUME = {8}, KEYWORDS = {observability, zero-deficiency networks, systems biology, biochemical networks, observers, nonlinear stability, dynamical systems}, PDF = {../FTP_DIR/chem-observers.pdf}, ABSTRACT = { This paper provides a necessary and sufficient condition for detectability, and an explicit construction of observers when this condition is satisfied, for chemical reaction networks of the Feinberg-Horn-Jackson zero deficiency type. } } @ARTICLE{kholodenkoPNAS02, AUTHOR = {B.N. Kholodenko and A. Kiyatkin and F. Bruggeman and E.D. Sontag and H. Westerhoff and J. Hoek}, JOURNAL = {Proceedings of the National Academy of Sciences USA}, TITLE = {Untangling the wires: a novel strategy to trace functional interactions in signaling and gene networks}, YEAR = {2002}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, PAGES = {12841--12846}, VOLUME = {99}, KEYWORDS = {systems biology, biochemical networks, reverse engineering, gene and protein networks, protein networks, gene networks, systems identification}, PDF = {../FTP_DIR/unravel_pnas02_including_supporting.pdf}, ABSTRACT = { Emerging technologies have enabled the acquisition of large genomics and proteomics data sets. This paper proposes a novel quantitative method for determining functional interactions in cellular signaling and gene networks. It can be used to explore cell systems at a mechanistic level, or applied within a modular framework, which dramatically decreases the number of variables to be assayed. The topology and strength of network connections are retrieved from experimentally measured network responses to successive perturbations of all modules. In addition, the method can reveal functional interactions even when the components of the system are not all known, in which casesome connections retrieved by the analysis will not be direct but correspond to the interaction routes through unidentified elements. The method is tested and illustrated using computer-generated responses of a modeled MAPK cascade and gene network. } } @ARTICLE{IOSS_discontinuous_IJC02, AUTHOR = {M. Krichman and E.D. Sontag}, JOURNAL = {Internat. J. Control}, TITLE = {Characterizations of detectability notions in terms of discontinuous dissipation functions}, YEAR = {2002}, OPTMONTH = {}, OPTNOTE = {}, NUMBER = {12}, PAGES = {882--900}, VOLUME = {75}, KEYWORDS = {input to state stability, detectability}, PDF = {../FTP_DIR/ioss-nonsmooth.pdf}, ABSTRACT = { We consider a new Lyapunov-type characterization of detectability for nonlinear systems without controls, in terms of lower-semicontinuous (not necessarily smooth, or even continuous) dissipation functions, and prove its equivalence to the GASMO (global asymptotic stability modulo outputs) and UOSS (uniform output-to-state stability) properties studied in previous work. The result is then extended to provide a construction of a discontinuous dissipation function characterization of the IOSS (input-to-state stability) property for systems with controls. This paper complements a recent result on smooth Lyapunov characterizations of IOSS. The utility of non-smooth Lyapunov characterizations is illustrated by application to a well-known transistor network example. } } @ARTICLE{liberzon_morse_sontag_minphase_TAC02, AUTHOR = {D. Liberzon and A. S. Morse and E.D. Sontag}, JOURNAL = {IEEE Trans. Automat. Control}, TITLE = {Output-input stability and minimum-phase nonlinear systems}, YEAR = {2002}, OPTMONTH = {}, OPTNOTE = {}, NUMBER = {3}, PAGES = {422--436}, VOLUME = {47}, KEYWORDS = {input to state stability, nonlinear control, minimum phase, adaptive control}, PDF = {../FTP_DIR/minphase.pdf}, ABSTRACT = { This paper introduces and studies a new definition of the minimum-phase property for general smooth nonlinear control systems. The definition does not rely on a particular choice of coordinates in which the system takes a normal form or on the computation of zero dynamics. In the spirit of the ``input-to-state stability'' philosophy, it requires the state and the input of the system to be bounded by a suitable function of the output and derivatives of the output, modulo a decaying term depending on initial conditions. The class of minimum-phase systems thus defined includes all affine systems in global normal form whose internal dynamics are input-to-state stable and also all left-invertible linear systems whose transmission zeros have negative real parts. As an application, we explain how the new concept enables one to develop a natural extension to nonlinear systems of a basic result from linear adaptive control. } } @ARTICLE{liberzon_sontag_wang_universalISS_SCL02, AUTHOR = {D. Liberzon and E.D. Sontag and Y. Wang}, JOURNAL = {Systems Control Lett.}, TITLE = {Universal construction of feedback laws achieving ISS and integral-ISS disturbance attenuation}, YEAR = {2002}, OPTMONTH = {}, NOTE = {Errata here: http://www.math.rutgers.edu/(tilde)sontag/FTPDIR/iiss-clf-errata.pdf}, NUMBER = {2}, PAGES = {111--127}, VOLUME = {46}, KEYWORDS = {input to state stability, nonlinear control, feedback stabilization}, PDF = {../FTP_DIR/iISS-CLFs.pdf}, ABSTRACT = { We study nonlinear systems with both control and disturbance inputs. The main problem addressed in the paper is design of state feedback control laws that render the closed-loop system integral-input-to-state stable (iISS) with respect to the disturbances. We introduce an appropriate concept of control Lyapunov function (iISS-CLF), whose existence leads to an explicit construction of such a control law. The same method applies to the problem of input-to-state stabilization. Converse results and techniques for generating iISS-CLFs are also discussed. } } @ARTICLE{cauchySCL02, AUTHOR = {E.D. Sontag}, JOURNAL = {Systems Control Lett.}, TITLE = {Asymptotic amplitudes and Cauchy gains: A small-gain principle and an application to inhibitory biological feedback}, YEAR = {2002}, OPTMONTH = {}, OPTNOTE = {}, NUMBER = {2}, PAGES = {167--179}, VOLUME = {47}, KEYWORDS = {cyclic feedback systems, small-gain}, PDF = {../FTP_DIR/cauchy-gains-scl-as-published.pdf}, ABSTRACT = { The notions of asymptotic amplitude for signals, and Cauchy gain for input/output systems, and an associated small-gain principle, are introduced. These concepts allow the consideration of systems with multiple, and possibly feedback-dependent, steady states. A Lyapunov-like characterization allows the computation of gains for state-space systems, and the formulation of sufficient conditions insuring the lack of oscillations and chaotic behaviors in a wide variety of cascades and feedback loops. An application in biology (MAPK signaling) is worked out in detail. } } @ARTICLE{MR1893535, AUTHOR = {E.D. Sontag}, JOURNAL = {IEEE Trans. Automat. Control}, TITLE = {Correction to: ``Structure and stability of certain chemical networks and applications to the kinetic proofreading model of T-cell receptor signal transduction'' [IEEE Trans. Automat. Control 46 (2001), no. 7, 1028--1047; MR1842137 (2002e:92006)]}, YEAR = {2002}, OPTMONTH = {}, OPTNOTE = {}, NUMBER = {4}, PAGES = {705}, VOLUME = {47}, KEYWORDS = {zero-deficiency networks, systems biology, biochemical networks, nonlinear stability, dynamical systems}, PDF = {../FTP_DIR/chem-errata.pdf}, ABSTRACT = { errata for Structure and stability of certain chemical networks and applications to the kinetic proofreading model of T-cell receptor signal transduction } } @ARTICLE{ident_experiments02, AUTHOR = {E.D. Sontag}, JOURNAL = {J. Nonlinear Sci.}, TITLE = {For differential equations with r parameters, 2r+1 experiments are enough for identification}, YEAR = {2002}, OPTMONTH = {}, OPTNOTE = {}, NUMBER = {6}, PAGES = {553--583}, VOLUME = {12}, KEYWORDS = {systems biology, biochemical networks, parameter identification}, PDF = {../FTP_DIR/ident-experiments.pdf}, ABSTRACT = { Given a set of differential equations whose description involves unknown parameters, such as reaction constants in chemical kinetics, and supposing that one may at any time measure the values of some of the variables and possibly apply external inputs to help excite the system, how many experiments are sufficient in order to obtain all the information that is potentially available about the parameters? This paper shows that the best possible answer (assuming exact measurements) is 2r+1 experiments, where r is the number of parameters. } } @ARTICLE{sontag_ingalls_small_gain_JFI02, AUTHOR = {E.D. Sontag and B. Ingalls}, JOURNAL = {J. Franklin Inst.}, TITLE = {A small-gain theorem with applications to input/output systems, incremental stability, detectability, and interconnections}, YEAR = {2002}, OPTMONTH = {}, OPTNOTE = {}, NUMBER = {2}, PAGES = {211--229}, VOLUME = {339}, KEYWORDS = {input to state stability}, PDF = {../FTP_DIR/small-gain-as-published.pdf}, ABSTRACT = { A general ISS-type small-gain result is presented. It specializes to a small-gain theorem for ISS operators, and it also recovers the classical statement for ISS systems in state-space form. In addition, we highlight applications to incrementally stable systems, detectable systems, and to interconnections of stable systems. } } @INPROCEEDINGS{02cdc-monotone, AUTHOR = {D. Angeli and E.D. Sontag}, BOOKTITLE = {Proc. IEEE Conf. Decision and Control, Las Vegas, Dec. 2002, IEEE Publications}, TITLE = {A remark on monotone control systems}, YEAR = {2002}, OPTADDRESS = {}, OPTCROSSREF = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, OPTORGANIZATION = {}, PAGES = {1876--1881}, OPTPUBLISHER = {}, OPTSERIES = {}, OPTVOLUME = {} } @INPROCEEDINGS{02cdc-liberzon-hespanha, AUTHOR = {J.P. Hespanha and D. Liberzon and E.D. Sontag}, BOOKTITLE = {Proc. IEEE Conf. Decision and Control, Las Vegas, Dec. 2002, IEEE Publications}, TITLE = {Nonlinear observability and an invariance principle for switched systems}, YEAR = {2002}, OPTADDRESS = {}, OPTCROSSREF = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, OPTORGANIZATION = {}, PAGES = {4300--4305}, OPTPUBLISHER = {}, OPTSERIES = {}, OPTVOLUME = {}, KEYWORDS = {observability}, PDF = {../FTP_DIR/02cdc-liberzon-hespanha-as-sent.pdf} } @INPROCEEDINGS{02mtns-relaxation, AUTHOR = {B. Ingalls and E.D. Sontag and Y. Wang}, BOOKTITLE = {Mathematical Theory of Networks and Systems, Electronic Proceedings of MTNS-2002 Symposium held at the University of Notre Dame, August 2002}, TITLE = {A relaxation theorem for differential inclusions with applications to stability properties}, YEAR = {2002}, OPTADDRESS = {}, OPTCROSSREF = {}, EDITOR = {D. Gilliam and J. Rosenthal}, OPTMONTH = {}, NOTE = {(12 pages)}, OPTNUMBER = {}, OPTORGANIZATION = {}, OPTPAGES = {}, OPTPUBLISHER = {}, OPTSERIES = {}, OPTVOLUME = {}, PDF = {../FTP_DIR/02mtns-ingalls-sontag-wang.pdf}, ABSTRACT = { The fundamental Filippov--Wazwski Relaxation Theorem states that the solution set of an initial value problem for a locally Lipschitz inclusion is dense in the solution set of the same initial value problem for the corresponding relaxation inclusion on compact intervals. In a recent paper of ours, a complementary result was provided for inclusions with finite dimensional state spaces which says that the approximation can be carried out over non-compact or infinite intervals provided one does not insist on the same initial values. This note extends the infinite-time relaxation theorem to the inclusions whose state spaces are Banach spaces. To illustrate the motivations for studying such approximation results, we briefly discuss a quick application of the result to output stability and uniform output stability properties. } } @INPROCEEDINGS{02cdc-mes, AUTHOR = {B. Ingalls and E.D. Sontag and Y. Wang}, BOOKTITLE = {Proc. IEEE Conf. Decision and Control, Las Vegas, Dec. 2002, IEEE Publications}, TITLE = {Measurement to error stability: a notion of partial detectability for nonlinear systems}, YEAR = {2002}, OPTADDRESS = {}, OPTCROSSREF = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, OPTORGANIZATION = {}, PAGES = {3946--3951}, OPTPUBLISHER = {}, OPTSERIES = {}, OPTVOLUME = {}, KEYWORDS = {input to state stability}, PDF = {../FTP_DIR/02cdc-ingalls-sontag-wang-published.pdf}, ABSTRACT = { For systems whose output is to be kept small (thought of as an error output), the notion of input to output stability (IOS) arises. Alternatively, when considering a system whose output is meant to provide information about the state (i.e. a measurement output), one arrives at the detectability notion of output to state stability (OSS). Combining these concepts, one may consider a system with two types of outputs, an error and a measurement. This leads naturally to a notion of partial detectability which we call measurement to error stability (MES). This property characterizes systems in which the error signal is detectable through the measurement signal. This paper provides a partial Lyapunov characterization of the MES property. A closely related property of stability in three measures (SIT) is introduced, which characterizes systems for which the error decays whenever it dominates the measurement. The SIT property is shown to imply MES, and the two are shown to be equivalent under an additional boundedness assumption. A nonsmooth Lyapunov characterization of the SIT property is provided, which yields the partial characterization of MES. The analysis is carried out on systems described by differential inclusions -- implicitly incorporating a disturbance input with compact value-set. } } @INPROCEEDINGS{02cdc-cauchy-gains, AUTHOR = {E.D. Sontag}, BOOKTITLE = {Proc. IEEE Conf. Decision and Control, Las Vegas, Dec. 2002, IEEE Publications}, TITLE = {Asymptotic amplitudes, Cauchy gains, an associated small-gain principle, and an application to inhibitory biological feedback}, YEAR = {2002}, OPTADDRESS = {}, OPTCROSSREF = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, OPTORGANIZATION = {}, PAGES = {4318--4323}, OPTPUBLISHER = {}, OPTSERIES = {}, OPTVOLUME = {}, KEYWORDS = {cyclic feedback systems, small-gain} } @INCOLLECTION{MR1806191, AUTHOR = {E.D. Sontag}, BOOKTITLE = {Nonlinear control in the year 2000, Vol. 2 (Paris)}, PUBLISHER = {Springer}, TITLE = {The ISS philosophy as a unifying framework for stability-like behavior}, YEAR = {2001}, ADDRESS = {London}, OPTCHAPTER = {}, OPTCROSSREF = {}, OPTEDITION = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, PAGES = {443--467}, SERIES = {Lecture Notes in Control and Inform. Sci.}, OPTTYPE = {}, VOLUME = {259}, KEYWORDS = {input to state stability}, PDF = {../FTP_DIR/00paris.pdf}, ABSTRACT = { (This is an expository paper prepared for a plenary talk given at the Second Nonlinear Control Network Workshop, Paris, June 9, 2000.) The input to state stability (ISS) paradigm is motivated as a generalization of classical linear systems concepts under coordinate changes. A summary is provided of the main theoretical results concerning ISS and related notions of input/output stability and detectability. A bibliography is also included, listing extensions, applications, and other current work. } } @ARTICLE{TCShybrid01, AUTHOR = {B. DasGupta and E.D. Sontag}, JOURNAL = {Theor. Comput. Sci.}, TITLE = {A polynomial-time algorithm for checking equivalence under certain semiring congruences motivated by the state-space isomorphism problem for hybrid systems}, YEAR = {2001}, OPTMONTH = {}, OPTNOTE = {}, NUMBER = {1-2}, PAGES = {161--189}, VOLUME = {262}, ADDRESS = {Essex, UK}, KEYWORDS = {hybrid systems, computational complexity}, PUBLISHER = {Elsevier Science Publishers Ltd.}, PDF = {../FTP_DIR/pl-decide.pdf}, ABSTRACT = { The area of hybrid systems concerns issues of modeling, computation, and control for systems which combine discrete and continuous components. The subclass of piecewise linear (PL) systems provides one systematic approach to discrete-time hybrid systems, naturally blending switching mechanisms with classical linear components. PL systems model arbitrary interconnections of finite automata and linear systems. Tools from automata theory, logic, and related areas of computer science and finite mathematics are used in the study of PL systems, in conjunction with linear algebra techniques, all in the context of a "PL algebra" formalism. PL systems are of interest as controllers as well as identification models. Basic questions for any class of systems are those of equivalence, and, in particular, if state spaces are equivalent under a change of variables. This paper studies this state-space equivalence problem for PL systems. The problem was known to be decidable, but its computational complexity was potentially exponential; here it is shown to be solvable in polynomial-time. }, DOI = {http://dx.doi.org/10.1016/S0304-3975(00)00188-2} } @ARTICLE{desch_logemann_ryan_sontag_meagre_NA01, AUTHOR = {W. Desch and H. Logemann and E. P. Ryan and E.D. Sontag}, JOURNAL = {Nonlinear Anal.}, TITLE = {Meagre functions and asymptotic behaviour of dynamical systems}, YEAR = {2001}, OPTMONTH = {}, OPTNOTE = {}, NUMBER = {8, Ser. A: Theory Methods}, PAGES = {1087--1109}, VOLUME = {44}, ADDRESS = {Oxford, UK, UK}, KEYWORDS = {invariance principle}, PUBLISHER = {Elsevier Science Ltd.}, PDF = {../FTP_DIR/ryan-logeman.pdf}, ABSTRACT = { A measurable function x from a subset J of R into a metric space X is said to be C-meagre if C is non-empty subset of X and, for every closed subset K of X disjoint from C, the preimage of K under x has finite Lebesgue measure. This concept of meagreness, applied to trajectories, is shown to provide a unifying framework which facilitates a variety of characterizations, extensions or generalizations of diverse facts pertaining to asymptotic behaviour of dynamical systems. }, DOI = {http://dx.doi.org/10.1016/S0362-546X(99)00323-5} } @ARTICLE{krichman_sontag_wang_IOSS_01, AUTHOR = {M. Krichman and E.D. Sontag and Y. Wang}, JOURNAL = {SIAM J. Control Optim.}, TITLE = {Input-output-to-state stability}, YEAR = {2001}, OPTMONTH = {}, OPTNOTE = {}, NUMBER = {6}, PAGES = {1874--1928}, VOLUME = {39}, ADDRESS = {Philadelphia, PA, USA}, KEYWORDS = {input to state stability}, PUBLISHER = {Society for Industrial and Applied Mathematics}, PDF = {../FTP_DIR/ioss.pdf}, ABSTRACT = { This work explores Lyapunov characterizations of the input-output-to-state stability (IOSS) property for nonlinear systems. The notion of IOSS is a natural generalization of the standard zero-detectability property used in the linear case. The main contribution of this work is to establish a complete equivalence between the input-output-to-state stability property and the existence of a certain type of smooth Lyapunov function. As corollaries, one shows the existence of "norm-estimators", and obtains characterizations of nonlinear detectability in terms of relative stability and of finite-energy estimates. }, DOI = {http://dx.doi.org/10.1137/S0363012999365352} } @ARTICLE{Tcell01, AUTHOR = {E.D. Sontag}, JOURNAL = {IEEE Trans. Automat. Control}, TITLE = {Structure and stability of certain chemical networks and applications to the kinetic proofreading model of T-cell receptor signal transduction}, YEAR = {2001}, OPTMONTH = {}, OPTNOTE = {}, NUMBER = {7}, PAGES = {1028--1047}, VOLUME = {46}, KEYWORDS = {zero-deficiency networks, systems biology, biochemical networks, nonlinear stability, dynamical systems}, PDF = {../FTP_DIR/chem.pdf}, ABSTRACT = { This paper deals with the theory of structure, stability, robustness, and stabilization for an appealing class of nonlinear systems which arises in the analysis of chemical networks. The results given here extend, but are also heavily based upon, certain previous work by Feinberg, Horn, and Jackson, of which a self-contained and streamlined exposition is included. The theoretical conclusions are illustrated through an application to the kinetic proofreading model proposed by McKeithan for T-cell receptor signal transduction. } } @INPROCEEDINGS{01nolcos-diss, AUTHOR = {D. Angeli and E.D. Sontag and Y. Wang}, BOOKTITLE = {Proc. Nonlinear Control System Design Symposium, St. Petersburg, July 2001}, TITLE = {A note on input-to-state stability with input derivatives}, YEAR = {2001}, OPTADDRESS = {}, OPTCROSSREF = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, OPTORGANIZATION = {}, PAGES = {720--725}, OPTPUBLISHER = {}, OPTSERIES = {}, OPTVOLUME = {}, KEYWORDS = {input to state stability} } @INPROCEEDINGS{01cdc-arcak, AUTHOR = {M. Arcak and D. Angeli and E.D. Sontag}, BOOKTITLE = {Proc. IEEE Conf. Decision and Control, Orlando, Dec. 2001, IEEE Publications, 2001}, TITLE = {Stabilization of cascades using integral input-to-state stability}, YEAR = {2001}, OPTADDRESS = {}, OPTCROSSREF = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, OPTORGANIZATION = {}, PAGES = {3814--3819}, OPTPUBLISHER = {}, OPTSERIES = {}, OPTVOLUME = {}, KEYWORDS = {nonlinear control, feedback stabilization, input to state stability} } @INPROCEEDINGS{01nolcos-chaves, AUTHOR = {M. Chaves and E.D. Sontag}, BOOKTITLE = {Proc. Nonlinear Control System Design Symposium, St. Petersburg, July 2001}, TITLE = {An alternative observer for zero deficiency chemical networks}, YEAR = {2001}, OPTADDRESS = {}, OPTCROSSREF = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, OPTORGANIZATION = {}, PAGES = {575--578}, OPTPUBLISHER = {}, OPTSERIES = {}, OPTVOLUME = {}, KEYWORDS = {observability, observers, zero-deficiency networks, systems biology, biochemical networks, nonlinear stability, dynamical systems} } @INPROCEEDINGS{01ecc-chaves, AUTHOR = {M. Chaves and E.D. Sontag}, BOOKTITLE = {Proc. 2001 European Control Conf., Sep. 2001}, TITLE = {Observers for certain chemical reaction networks}, YEAR = {2001}, OPTADDRESS = {}, OPTCROSSREF = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, OPTORGANIZATION = {}, PAGES = {3715--3720}, OPTPUBLISHER = {}, OPTSERIES = {}, OPTVOLUME = {}, KEYWORDS = {zero-deficiency networks, systems biology, biochemical networks, nonlinear stability, dynamical systems, observability, observers} } @INPROCEEDINGS{01cdc-chyba, AUTHOR = {M. Chyba and N.E. Leonard and E.D. Sontag}, BOOKTITLE = {Proc. IEEE Conf. Decision and Control, Orlando, Dec. 2001,IEEE Publications, 2001}, TITLE = {Optimality for underwater vehicles}, YEAR = {2001}, OPTADDRESS = {}, OPTCROSSREF = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, OPTORGANIZATION = {}, PAGES = {4204--4210}, OPTPUBLISHER = {}, OPTSERIES = {}, OPTVOLUME = {}, KEYWORDS = {optimal control} } @INPROCEEDINGS{01cdc-angeli-ingalls-wang, AUTHOR = {B. Ingalls and D. Angeli and E.D. Sontag and Y. Wang}, BOOKTITLE = {Proc. IEEE Conf. Decision and Control, Orlando, Dec. 2001, IEEE Publications, 2001}, TITLE = {Asymptotic characterizations of IOSS}, YEAR = {2001}, OPTADDRESS = {}, OPTCROSSREF = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, OPTORGANIZATION = {}, PAGES = {881--886}, OPTPUBLISHER = {}, OPTSERIES = {}, OPTVOLUME = {}, KEYWORDS = {nonlinear control, feedback stabilization, input to state stability} } @INPROCEEDINGS{01ifac-kuusela, AUTHOR = {P. Kuusela and D. Ocone and E.D. Sontag}, BOOKTITLE = {IFAC Workshop on Adaptation and Learning in Control and Signal Processing, ALCOSP2001, Cernobbio-Como, Italy, 29-31 August, 2001}, TITLE = {Remarks on the sample complexity for linear control systems identification}, YEAR = {2001}, OPTADDRESS = {}, OPTCROSSREF = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, OPTORGANIZATION = {}, PAGES = {431--436}, OPTPUBLISHER = {}, OPTSERIES = {}, OPTVOLUME = {} } @INPROCEEDINGS{01nolcos-minphase, AUTHOR = {D. Liberzon and A.S. Morse and E.D. Sontag}, BOOKTITLE = {Proc. Nonlinear Control System Design Symposium, St. Petersburg, July 2001}, TITLE = {Output-input stability: a new variant of the minimum-phase property for nonlinear systems}, YEAR = {2001}, OPTADDRESS = {}, OPTCROSSREF = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, OPTORGANIZATION = {}, PAGES = {743--748}, OPTPUBLISHER = {}, OPTSERIES = {}, OPTVOLUME = {}, KEYWORDS = {input to state stability} } @INPROCEEDINGS{01acc-ingalls, AUTHOR = {E.D. Sontag and B. Ingalls and Y. Wang}, BOOKTITLE = {Proc. American Control Conf., Arlington, June 2001}, TITLE = {Generalizations of asymptotic gain characterizations of ISS to input-to-output stability}, YEAR = {2001}, OPTADDRESS = {}, OPTCROSSREF = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, OPTORGANIZATION = {}, PAGES = {2279--2284}, OPTPUBLISHER = {}, OPTSERIES = {}, OPTVOLUME = {}, KEYWORDS = {input to state stability} } @INCOLLECTION{MR1870247, AUTHOR = {L. Grüne and E.D. Sontag and F.R. Wirth}, BOOKTITLE = {International Conference on Differential Equations, Vol. 1, 2 (Berlin, 1999)}, PUBLISHER = {World Sci. Publishing}, TITLE = {On equivalence of exponential and asymptotic stability under changes of variables}, YEAR = {2000}, ADDRESS = {River Edge, NJ}, OPTCHAPTER = {}, OPTCROSSREF = {}, OPTEDITION = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, PAGES = {850--852}, OPTSERIES = {}, OPTTYPE = {}, OPTVOLUME = {}, KEYWORDS = {input to state stability} } @ARTICLE{angeli_sontag_wang_iISS_TAC00, AUTHOR = {D. Angeli and E.D. Sontag and Y. Wang}, JOURNAL = {IEEE Trans. Automat. Control}, TITLE = {A characterization of integral input-to-state stability}, YEAR = {2000}, OPTMONTH = {}, OPTNOTE = {}, NUMBER = {6}, PAGES = {1082--1097}, VOLUME = {45}, KEYWORDS = {input to state stability}, PDF = {../FTP_DIR/iiss-asw.pdf}, ABSTRACT = { Just as input to state stability (ISS) generalizes the idea of finite gains with respect to supremum norms, the new notion of integral input to state stability (IISS) generalizes the concept of finite gain when using an integral norm on inputs. In this paper, we obtain a necessary and sufficient characterization of the IISS property, expressed in terms of dissipation inequalities. } } @ARTICLE{angeli_sontag_wang_further_equiv_DYNA00, AUTHOR = {D. Angeli and E.D. Sontag and Y. Wang}, JOURNAL = {Dynam. Control}, TITLE = {Further equivalences and semiglobal versions of integral input to state stability}, YEAR = {2000}, OPTMONTH = {}, OPTNOTE = {}, NUMBER = {2}, PAGES = {127--149}, VOLUME = {10}, ADDRESS = {Hingham, MA, USA}, KEYWORDS = {input to state stability}, PUBLISHER = {Kluwer Academic Publishers}, PDF = {../FTP_DIR/iiss-new.pdf}, ABSTRACT = { This paper continues the study of the integral input-to-state stability (IISS) property. It is shown that the IISS property is equivalent to one which arises from the consideration of mixed norms on states and inputs, as well as to the superposition of a ``bounded energy bounded state'' requirement and the global asymptotic stability of the unforced system. A semiglobal version of IISS is shown to imply the global version, though a counterexample shows that the analogous fact fails for input to state stability (ISS). The results in this note complete the basic theoretical picture regarding IISS and ISS. }, DOI = {http://dx.doi.org/10.1023/A:1008356223747} } @ARTICLE{bao_lin_sontag_dt_saturation_automatica00, AUTHOR = {X. Bao and Z. Lin and E.D. Sontag}, JOURNAL = {Automatica}, TITLE = {Finite gain stabilization of discrete-time linear systems subject to actuator saturation}, YEAR = {2000}, OPTMONTH = {}, OPTNOTE = {}, NUMBER = {2}, PAGES = {269--277}, VOLUME = {36}, KEYWORDS = {discrete-time, saturation, input-to-state stability}, PDF = {../FTP_DIR/sat-dt-iss.pdf}, ABSTRACT = { It is shown that, for neutrally stable discrete-time linear systems subject to actuator saturation, finite gain lp stabilization can be achieved by linear output feedback, for all p>1. An explicit construction of the corresponding feedback laws is given. The feedback laws constructed also result in a closed-loop system that is globally asymptotically stable, and in an input-to-state estimate. } } @ARTICLE{maass_sontag_filters_NC00, AUTHOR = {W. Maass and E.D. Sontag}, JOURNAL = {Neural Comput.}, TITLE = {Neural Systems as Nonlinear Filters}, YEAR = {2000}, OPTMONTH = {}, OPTNOTE = {}, NUMBER = {8}, PAGES = {1743--1772}, VOLUME = {12}, ADDRESS = {Cambridge, MA, USA}, KEYWORDS = {neural networks, neural networks, Volterra series}, PUBLISHER = {MIT Press}, PDF = {../FTP_DIR/spiking.pdf}, ABSTRACT = { We analyze computations on temporal patterns and spatio-temporal patterns in formal network models whose temporal dynamics arises from empirically established quantitative models for short term dynamics at biological synapses. We give a complete characterization of all linear and nonlinear filters that can be approximated by such dynamic network models: it is the class of all filters that can be approximated by Volterra series. This characterization is shown to be rather stable with regard to changes in the model. For example it is shown that synaptic facilitation and one layer of neurons suffices for approximating arbitrary filters from this class. Our results provide a new complexity hierarchy for all filters that are approximable by Volterra series, which appears to be closer related to the actual cost of implementing such filters in neural hardware than preceding complexity measures. Our results also provide a new parameterization for approximations to such filters in terms of parameters that are arguable related to those that are tunable in biological neural systems. }, DOI = {http://dx.doi.org/10.1162/089976600300015123} } @ARTICLE{MR1828059, AUTHOR = {M. Malisoff and E.D. Sontag}, JOURNAL = {Systems Control Lett.}, TITLE = {Universal formulas for feedback stabilization with respect to Minkowski balls}, YEAR = {2000}, OPTMONTH = {}, OPTNOTE = {}, NUMBER = {4}, PAGES = {247--260}, VOLUME = {40}, KEYWORDS = {nonlinear control, feedback stabilization, saturation, control-Lyapunov functions}, PDF = {../FTP_DIR/minkowski.pdf}, ABSTRACT = { This note provides explicit algebraic stabilizing formulas for clf's when controls are restricted to certain Minkowski balls in Euclidean space. Feedbacks of this kind are known to exist by a theorem of Artstein, but the proof of Artstein's theorem is nonconstructive. The formulas are obtained from a general feedback stabilization technique and are used to construct approximation solutions to some stabilization problems. } } @ARTICLE{rosier_sontag_gap_SCL00, AUTHOR = {L. Rosier and E.D. Sontag}, JOURNAL = {Systems Control Lett.}, TITLE = {Remarks regarding the gap between continuous, Lipschitz, and differentiable storage functions for dissipation inequalities appearing in $H\sb \infty$ control}, YEAR = {2000}, OPTMONTH = {}, OPTNOTE = {}, NUMBER = {4}, PAGES = {237--249}, VOLUME = {41}, KEYWORDS = {viscosity solutions, H-infinity control}, PDF = {../FTP_DIR/hoo.pdf}, ABSTRACT = { This paper deals with the regularity of solutions of the Hamilton-Jacobi Inequality which arises in H-infinity control. It shows by explicit counterexamples that there are gaps between existence of continuous and locally Lipschitz (positive definite and proper) solutions, and between Lipschitz and continuously differentiable ones. On the other hand, it is shown that it is always possible to smooth-out solutions, provided that an infinitesimal increase in gain is allowed. } } @ARTICLE{sontag_wang_Lyapunov_IOS_SICOPT00, AUTHOR = {E.D. Sontag and Y. Wang}, JOURNAL = {SIAM J. Control Optim.}, TITLE = {Lyapunov characterizations of input to output stability}, YEAR = {2000}, OPTMONTH = {}, OPTNOTE = {}, NUMBER = {1}, PAGES = {226--249}, VOLUME = {39}, ADDRESS = {Philadelphia, PA, USA}, KEYWORDS = {input to state stability}, PUBLISHER = {Society for Industrial and Applied Mathematics}, PDF = {../FTP_DIR/lios.pdf}, ABSTRACT = { This paper presents necessary and sufficient characterizations of several notions of input to output stability. Similar Lyapunov characterizations have been found to play a key role in the analysis of the input to state stability property, and the results given here extend their validity to the case when the output, but not necessarily the entire internal state, is being regulated. }, DOI = {http://dx.doi.org/10.1137/S0363012999350213} } @INPROCEEDINGS{chyba-IFAC, AUTHOR = {M. Chyba and N.E. Leonard and E.D. Sontag}, BOOKTITLE = {Lagrangian and Hamiltonian Methods for Nonlinear Control}, TITLE = {Time-optimal control for underwater vehicles}, YEAR = {2000}, OPTADDRESS = {}, OPTCROSSREF = {}, EDITOR = {N.E. Leonard and R. Ortega}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, OPTORGANIZATION = {}, PAGES = {117--122}, PUBLISHER = {Pergamon Press, Oxford}, OPTSERIES = {}, OPTVOLUME = {} } @INPROCEEDINGS{00cdc-minphase, AUTHOR = {D. Liberzon and A.S. Morse and E.D. Sontag}, BOOKTITLE = {Proc. IEEE Conf. Decision and Control, Sydney, Dec. 2000, IEEE Publications, 2000}, TITLE = {A new definition of the minimum-phase property for nonlinear systems, with an application to adaptive control}, YEAR = {2000}, OPTADDRESS = {}, OPTCROSSREF = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, OPTORGANIZATION = {}, PAGES = {2106--2111}, OPTPUBLISHER = {}, OPTSERIES = {}, OPTVOLUME = {} } @INPROCEEDINGS{00nips, AUTHOR = {T. Natschläger and W. Maass and E.D. Sontag and A. Zador}, BOOKTITLE = {Advances in Neural Information Processing Systems 13 (NIPS2000)}, TITLE = {Processing of time series by neural circuits with biologically realistic synaptic dynamics}, YEAR = {2000}, OPTADDRESS = {}, OPTCROSSREF = {}, EDITOR = {Todd K. Leen and Thomas G. Dietterich and Volker Tresp}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, OPTORGANIZATION = {}, PAGES = {145--151}, PUBLISHER = {MIT Press, Cambridge}, OPTSERIES = {}, OPTVOLUME = {}, KEYWORDS = {neural networks, neural networks, Volterra series}, PDF = {../FTP_DIR/2000nips.pdf}, ABSTRACT = { Experimental data show that biological synapses are dynamic, i.e., their weight changes on a short time scale by several hundred percent in dependence of the past input to the synapse. In this article we explore the consequences that this synaptic dynamics entails for the computational power of feedforward neural networks. It turns out that even with just a single hidden layer such networks can approximate a surprisingly large large class of nonlinear filters: all filters that can be characterized by Volterra series. This result is robust with regard to various changes in the model for synaptic dynamics. Furthermore we show that simple gradient descent suffices to approximate a given quadratic filter by a rather small neural system with dynamic synapses. } } @BOOK{openprob, PUBLISHER = {Springer Verlag}, TITLE = {Open Problems in Mathematical Systems and Control Theory (edited book)}, YEAR = {1999}, AUTHOR = {V.D. Blondel and E.D Sontag and M. Vidyasagar and J.C. Willems}, ALTEDITOR = {}, OPTADDRESS = {}, OPTEDITION = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, OPTSERIES = {}, OPTVOLUME = {} } @INCOLLECTION{MR1727964, AUTHOR = {E.D. Sontag}, BOOKTITLE = {Open problems in mathematical systems and control theory}, PUBLISHER = {Springer}, TITLE = {Control-Lyapunov functions}, YEAR = {1999}, ADDRESS = {London}, OPTCHAPTER = {}, OPTCROSSREF = {}, OPTEDITION = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, PAGES = {211--216}, SERIES = {Comm. Control Engrg. Ser.}, OPTTYPE = {}, OPTVOLUME = {}, KEYWORDS = {control-Lyapunov functions} } @INCOLLECTION{MR1684843, AUTHOR = {E.D. Sontag}, BOOKTITLE = {Dynamical systems, control, coding, computer vision (Padova, 1998)}, PUBLISHER = {Birkhäuser}, TITLE = {Nonlinear feedback stabilization revisited}, YEAR = {1999}, ADDRESS = {Basel}, OPTCHAPTER = {}, OPTCROSSREF = {}, OPTEDITION = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, PAGES = {223--262}, SERIES = {Progr. Systems Control Theory}, OPTTYPE = {}, VOLUME = {25} } @INCOLLECTION{montreal98, AUTHOR = {E.D. Sontag}, BOOKTITLE = {Nonlinear analysis, differential equations and control (Montreal, QC, 1998)}, PUBLISHER = {Kluwer Acad. Publ.}, TITLE = {Stability and stabilization: discontinuities and the effect of disturbances}, YEAR = {1999}, ADDRESS = {Dordrecht}, OPTCHAPTER = {}, OPTCROSSREF = {}, OPTEDITION = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, PAGES = {551--598}, SERIES = {NATO Sci. Ser. C Math. Phys. Sci.}, OPTTYPE = {}, VOLUME = {528}, KEYWORDS = {feedback stabilization, nonlinear control, input to state stability}, PDF = {../FTP_DIR/stab-survey98.pdf}, ABSTRACT = { In this expository paper, we deal with several questions related to stability and stabilization of nonlinear finite-dimensional continuous-time systems. We review the basic problem of feedback stabilization, placing an emphasis upon relatively new areas of research which concern stability with respect to "noise" (such as errors introduced by actuators or sensors). The table of contents is as follows: Review of Stability and Asymptotic Controllability, The Problem of Stabilization, Obstructions to Continuous Stabilization, Control-Lyapunov Functions and Artstein's Theorem, Discontinuous Feedback, Nonsmooth CLF's, Insensitivity to Small Measurement and Actuator Errors, Effect of Large Disturbances: Input-to-State Stability, Comments on Notions Related to ISS. } } @ARTICLE{MR1733874, AUTHOR = {F. Albertini and E.D. Sontag}, JOURNAL = {Internat. J. Control}, TITLE = {Continuous control-Lyapunov functions for asymptotically controllable time-varying systems}, YEAR = {1999}, OPTMONTH = {}, OPTNOTE = {}, NUMBER = {18}, PAGES = {1630--1641}, VOLUME = {72}, KEYWORDS = {control-Lyapunov functions}, PDF = {../FTP_DIR/albertini-clf.pdf}, ABSTRACT = { This paper shows that, for time varying systems, global asymptotic controllability to a given closed subset of the state space is equivalent to the existence of a continuous control-Lyapunov function with respect to the set. } } @ARTICLE{MR1754903, AUTHOR = {D. Angeli and E.D. Sontag}, JOURNAL = {Systems Control Lett.}, TITLE = {Forward completeness, unboundedness observability, and their Lyapunov characterizations}, YEAR = {1999}, OPTMONTH = {}, OPTNOTE = {}, NUMBER = {4-5}, PAGES = {209--217}, VOLUME = {38}, KEYWORDS = {observability, input to state stability, dynamical systems}, PDF = {../FTP_DIR/uo.pdf}, ABSTRACT = { A finite-dimensional continuous-time system is forward complete if solutions exist globally, for positive time. This paper shows that forward completeness can be characterized in a necessary and sufficient manner by means of smooth scalar growth inequalities. Moreover, a version of this fact is also proved for systems with inputs, and a generalization is also provided for systems with outputs and a notion (unboundedness observability) of relative completeness. We apply these results to obtain a bound on reachable states in terms of energy-like estimates of inputs. } } @ARTICLE{MR1751688, AUTHOR = {L. Grüne and E.D. Sontag and F.R. Wirth}, JOURNAL = {Systems Control Lett.}, TITLE = {Asymptotic stability equals exponential stability, and ISS equals finite energy gain---if you twist your eyes}, YEAR = {1999}, OPTMONTH = {}, OPTNOTE = {}, NUMBER = {2}, PAGES = {127--134}, VOLUME = {38}, KEYWORDS = {input to state stability}, PDF = {../FTP_DIR/gas2ges.pdf}, ABSTRACT = { This paper shows that uniformly global asymptotic stability for a family of ordinary differential equations is equivalent to uniformly global exponential stability under a suitable nonlinear change of variables. The same is shown respectively for input-to-state stability, input-to-state exponential stability, and the property of finite square-norm gain ("nonlinear H-infty"). The results are shown for systems of any dimension not equal to 4 or 5. } } @ARTICLE{MR1695080, AUTHOR = {Y.S. Ledyaev and E.D. Sontag}, JOURNAL = {Nonlinear Anal.}, TITLE = {A Lyapunov characterization of robust stabilization}, YEAR = {1999}, OPTMONTH = {}, OPTNOTE = {}, NUMBER = {7, Ser. A: Theory Methods}, PAGES = {813--840}, VOLUME = {37}, KEYWORDS = {nonlinear control, feedback stabilization}, PDF = {../FTP_DIR/yuri-clf.pdf}, ABSTRACT = { One of the fundamental facts in control theory (Artstein's theorem) is the equivalence, for systems affine in controls, between continuous feedback stabilizability to an equilibrium and the existence of smooth control Lyapunov functions. This equivalence breaks down for general nonlinear systems, not affine in controls. One of the main results in this paper establishes that the existence of smooth Lyapunov functions implies the existence of (in general, discontinuous) feedback stabilizers which are insensitive to small errors in state measurements. Conversely, it is shown that the existence of such stabilizers in turn implies the existence of smooth control Lyapunov functions. Moreover, it is established that, for general nonlinear control systems under persistently acting disturbances, the existence of smooth Lyapunov functions is equivalent to the existence of (possibly) discontinuous) feedback stabilizers which are robust with respect to small measurement errors and small additive external disturbances. } } @ARTICLE{316387, AUTHOR = {W. Maass and E.D. Sontag}, JOURNAL = {Neural Comput.}, TITLE = {Analog neural nets with Gaussian or other common noise distributions cannot recognize arbitary regular languages}, YEAR = {1999}, OPTMONTH = {}, OPTNOTE = {}, NUMBER = {3}, PAGES = {771--782}, VOLUME = {11}, ADDRESS = {Cambridge, MA, USA}, KEYWORDS = {neural networks}, PUBLISHER = {MIT Press}, PDF = {../FTP_DIR/noisy-nets.pdf}, ABSTRACT = { We consider recurrent analog neural nets where the output of each gate is subject to Gaussian noise, or any other common noise distribution that is nonzero on a large set. We show that many regular languages cannot be recognized by networks of this type, and we give a precise characterization of those languages which can be recognized. This result implies severe constraints on possibilities for constructing recurrent analog neural nets that are robust against realistic types of analog noise. On the other hand we present a method for constructing feedforward analog neural nets that are robust with regard to analog noise of this type. }, DOI = {http://dx.doi.org/10.1162/089976699300016656} } @ARTICLE{MR1753276, AUTHOR = {D. Nesic and A.R. Teel and E.D. Sontag}, JOURNAL = {Systems Control Lett.}, TITLE = {Formulas relating KL stability estimates of discrete-time and sampled-data nonlinear systems}, YEAR = {1999}, OPTMONTH = {}, OPTNOTE = {}, NUMBER = {1}, PAGES = {49--60}, VOLUME = {38}, KEYWORDS = {input to state stability}, PDF = {../FTP_DIR/klsampling.pdf}, ABSTRACT = { We provide an explicit KL stability or input-to-state stability (ISS) estimate for a sampled-data nonlinear system in terms of the KL estimate for the corresponding discrete-time system and a K function describing inter-sample growth. It is quite obvious that a uniform inter-sample growth condition, plus an ISS property for the exact discrete-time model of a closed-loop system, implies uniform ISS of the sampled-data nonlinear system; our results serve to quantify these facts by means of comparison functions. Our results can be used as an alternative to prove and extend results of Aeyels et al and extend some results by Chen et al to a class of nonlinear systems. Finally, the formulas we establish can be used as a tool for some other problems which we indicate. } } @ARTICLE{clocks99, AUTHOR = {E.D. Sontag}, JOURNAL = {ESAIM Control Optim. Calc. Var.}, TITLE = {Clocks and insensitivity to small measurement errors}, YEAR = {1999}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, PAGES = {537--557}, VOLUME = {4}, KEYWORDS = {nonlinear control, feedback stabilization, hybrid systems, discontinuous feedback, measurement noise}, PDF = {../FTP_DIR/clocks-sampling.pdf}, ABSTRACT = { This paper provides a precise result which shows that insensitivity to small measurement errors in closed-loop stabilization can be attained provided that the feedback controller ignores observations during small time intervals. } } @ARTICLE{MR1750806, AUTHOR = {E.D. Sontag and Y. Qiao}, JOURNAL = {Systems Control Lett.}, TITLE = {Further results on controllability of recurrent neural networks}, YEAR = {1999}, OPTMONTH = {}, OPTNOTE = {}, NUMBER = {2}, PAGES = {121--129}, VOLUME = {36}, KEYWORDS = {neural networks, controllability}, PDF = {../FTP_DIR/qiao-scl.pdf}, ABSTRACT = { This paper studies controllability properties of recurrent neural networks. The new contributions are: (1) an extension of the result in "Complete controllability of continuous-time recurrent neural networks" to a slightly different model, where inputs appear in an affine form, (2) a formulation and proof of a necessary and sufficient condition, in terms of local-local controllability, and (3) a complete analysis of the 2-dimensional case for which the hypotheses made in previous work do not apply. } } @ARTICLE{MR1754906, AUTHOR = {E.D. Sontag and Y. Wang}, JOURNAL = {Systems Control Lett.}, TITLE = {Notions of input to output stability}, YEAR = {1999}, OPTMONTH = {}, OPTNOTE = {}, NUMBER = {4-5}, PAGES = {235--248}, VOLUME = {38}, KEYWORDS = {input to state stability}, PDF = {../FTP_DIR/ios.pdf}, ABSTRACT = { This paper deals with several related notions of output stability with respect to inputs (which may be thought of as disturbances). The main such notion is called input to output stability (IOS), and it reduces to input to state stability (ISS) when the output equals the complete state. For systems with no inputs, IOS provides a generalization of the classical concept of partial stability. Several variants, which formalize in different manners the transient behavior, are introduced. The main results provide a comparison among these notions } } @INPROCEEDINGS{99cdc-uo, AUTHOR = {D. Angeli and E.D. Sontag}, BOOKTITLE = {Proc. IEEE Conf. Decision and Control, Phoenix, Dec. 1999, IEEE Publications, 1999}, TITLE = {Characterizations of forward completeness}, YEAR = {1999}, OPTADDRESS = {}, OPTCROSSREF = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, OPTORGANIZATION = {}, PAGES = {2551--2556}, OPTPUBLISHER = {}, OPTSERIES = {}, OPTVOLUME = {} } @INPROCEEDINGS{99cdc-gesgas, AUTHOR = {L. Grune and E.D. Sontag and F.R. Wirth}, BOOKTITLE = {Proc. IEEE Conf. Decision and Control, Phoenix, Dec. 1999, IEEE Publications, 1999}, TITLE = {On the equivalence between asymptotic and exponential stability, and between ISS and finite $H_\infty$ gain}, YEAR = {1999}, OPTADDRESS = {}, OPTCROSSREF = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, OPTORGANIZATION = {}, PAGES = {1220--1225}, OPTPUBLISHER = {}, OPTSERIES = {}, OPTVOLUME = {}, KEYWORDS = {input to state stability} } @INPROCEEDINGS{99cdc-ios, AUTHOR = {B. Ingalls and E.D. Sontag and Y. Wang}, BOOKTITLE = {Proc. IEEE Conf. Decision and Control, Phoenix, Dec. 1999, IEEE Publications, 1999}, TITLE = {Remarks on input to output stability}, YEAR = {1999}, OPTADDRESS = {}, OPTCROSSREF = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, OPTORGANIZATION = {}, PAGES = {1226--1231}, OPTPUBLISHER = {}, OPTSERIES = {}, OPTVOLUME = {}, KEYWORDS = {input to state stability} } @INPROCEEDINGS{99ifac, AUTHOR = {Z-P. Jiang and E.D. Sontag and Y. Wang}, BOOKTITLE = {Proc. 14th IFAC World Congress, Vol E (Beijing)}, TITLE = {Input-to-state stability for discrete-time nonlinear systems}, YEAR = {1999}, OPTADDRESS = {}, OPTCROSSREF = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, OPTORGANIZATION = {}, PAGES = {277--282}, OPTPUBLISHER = {}, OPTSERIES = {}, OPTVOLUME = {}, KEYWORDS = {input to state stability, input to state stability, discrete-time}, PDF = {../FTP_DIR/dt-iss-ifac.pdf}, ABSTRACT = { This paper studies the input-to-state stability (ISS) property for discrete-time nonlinear systems. We show that many standard ISS results may be extended to the discrete-time case. More precisely, we provide a Lyapunov-like sufficient condition for ISS, and we show the equivalence between the ISS property and various other properties, as well as provide a small gain theorem. } } @INPROCEEDINGS{99cdc-ioss, AUTHOR = {M. Krichman and E.D. Sontag and Y. Wang}, BOOKTITLE = {Proc. IEEE Conf. Decision and Control, Phoenix, Dec. 1999, IEEE Publications, 1999}, TITLE = {Lyapunov characterizations of input-ouput-to-state stability}, YEAR = {1999}, OPTADDRESS = {}, OPTCROSSREF = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, OPTORGANIZATION = {}, PAGES = {2070--2075}, OPTPUBLISHER = {}, OPTSERIES = {}, OPTVOLUME = {}, KEYWORDS = {input to state stability} } @INPROCEEDINGS{99acc-liberzon, AUTHOR = {D. Liberzon and E.D. Sontag and Y. Wang}, BOOKTITLE = {Proc. American Control Conf., San Diego, June 1999}, TITLE = {On integral-input-to-state stabilization}, YEAR = {1999}, OPTADDRESS = {}, OPTCROSSREF = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, OPTORGANIZATION = {}, PAGES = {1598--1602}, OPTPUBLISHER = {}, OPTSERIES = {}, OPTVOLUME = {}, KEYWORDS = {input to state stability, control-Lyapunov functions}, PDF = {../FTP_DIR/99acc-liberzon-wang.pdf}, ABSTRACT = { This paper continues the investigation of the recently introduced integral version of input-to-state stability (iISS). We study the problem of designing control laws that achieve iISS disturbance attenuation. The main contribution is an appropriate concept of control Lyapunov function (iISS-CLF), whose existence leads to an explicit construction of such a control law. The results are compared and contrasted with the ones available for the ISS case. } } @INPROCEEDINGS{340649, AUTHOR = {W. Maass and E.D. Sontag}, BOOKTITLE = {Proceedings of the 1998 conference on Advances in neural information processing systems II}, TITLE = {A precise characterization of the class of languages recognized by neural nets under Gaussian and other common noise distributions}, YEAR = {1999}, ADDRESS = {Cambridge, MA, USA}, OPTCROSSREF = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, OPTORGANIZATION = {}, PAGES = {281--287}, PUBLISHER = {MIT Press}, OPTSERIES = {}, OPTVOLUME = {}, KEYWORDS = {neural networks} } @INPROCEEDINGS{99acc-malissoff, AUTHOR = {M. Malisoff and E.D. Sontag}, BOOKTITLE = {Proc. American Control Conf., San Diego, June 1999}, TITLE = {Universal formulas for CLF's with respect to Minkowski balls}, YEAR = {1999}, OPTADDRESS = {}, OPTCROSSREF = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, OPTORGANIZATION = {}, PAGES = {3033--3037}, OPTPUBLISHER = {}, OPTSERIES = {}, OPTVOLUME = {} } @INPROCEEDINGS{99acc-nesic-teel, AUTHOR = {D. Nesic and A.R. Teel and E.D. Sontag}, BOOKTITLE = {Proc. American Control Conf., San Diego, June 1999}, TITLE = {On stability and input-to-state stability ${\cal K}{\cal L}$ estimates of discrete-time and sampled-data nonlinear systems}, YEAR = {1999}, OPTADDRESS = {}, OPTCROSSREF = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, OPTORGANIZATION = {}, PAGES = {3990--3994}, OPTPUBLISHER = {}, OPTSERIES = {}, OPTVOLUME = {}, KEYWORDS = {input to state stability} } @INPROCEEDINGS{99cdc-clocks, AUTHOR = {E.D. Sontag}, BOOKTITLE = {Proc. IEEE Conf. Decision and Control, Phoenix, Dec. 1999, IEEE Publications, 1999}, TITLE = {Feedback insensitive to small measurement errors}, YEAR = {1999}, OPTADDRESS = {}, OPTCROSSREF = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, OPTORGANIZATION = {}, PAGES = {2661--2666}, OPTPUBLISHER = {}, OPTSERIES = {}, OPTVOLUME = {} } @BOOK{mct, PUBLISHER = {Springer-Verlag}, TITLE = {Mathematical Control Theory. Deterministic Finite-Dimensional Systems}, YEAR = {1998}, AUTHOR = {E.D. Sontag}, ALTEDITOR = {}, ADDRESS = {New York}, EDITION = {Second}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, SERIES = {Texts in Applied Mathematics}, VOLUME = {6}, PAGES = {xvi+531}, PDF = {../FTP_DIR/sontag_mathematical_control_theory_springer98.pdf}, ABSTRACT = { This book is copyrighted by Springer-Verlag. Springer has kindly allowed me to place a copy on the web, as a reference and for ease of web searches. Please consider buying your own hardcopy. } } @INCOLLECTION{MR1655025, AUTHOR = {E.D. Sontag}, BOOKTITLE = {Essays on mathematical robotics (Minneapolis, MN, 1993)}, PUBLISHER = {Springer}, TITLE = {A general approach to path planning for systems without drift}, YEAR = {1998}, ADDRESS = {New York}, OPTCHAPTER = {}, OPTCROSSREF = {}, OPTEDITION = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, PAGES = {151--168}, SERIES = {IMA Vol. Math. Appl.}, OPTTYPE = {}, VOLUME = {104} } @INCOLLECTION{303613, AUTHOR = {E.D. Sontag}, BOOKTITLE = {The handbook of brain theory and neural networks}, PUBLISHER = {MIT Press}, TITLE = {Automata and neural networks}, YEAR = {1998}, ADDRESS = {Cambridge, MA, USA}, OPTCHAPTER = {}, OPTCROSSREF = {}, OPTEDITION = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, PAGES = {119--122}, OPTSERIES = {}, OPTTYPE = {}, OPTVOLUME = {}, KEYWORDS = {neural networks} } @INCOLLECTION{newtonVC, AUTHOR = {E.D. Sontag}, BOOKTITLE = {Neural Networks and Machine Learning}, PUBLISHER = {Springer, Berlin}, TITLE = {VC dimension of neural networks}, YEAR = {1998}, OPTADDRESS = {}, OPTCHAPTER = {}, OPTCROSSREF = {}, OPTEDITION = {}, EDITOR = {C.M. Bishop}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, PAGES = {69-95}, OPTSERIES = {}, OPTTYPE = {}, OPTVOLUME = {}, KEYWORDS = {neural networks, VC dimension, learning, neural networks, shattering}, PDF = {../FTP_DIR/vc-expo.pdf}, ABSTRACT = { The Vapnik-Chervonenkis (VC) dimension is an integer which helps to characterize distribution-independent learning of binary concepts from positive and negative samples. This paper, based on lectures delivered at the Isaac Newton Institute in August of 1997, presents a brief introduction, establishes various elementary results, and discusses how to estimate the VC dimension in several examples of interest in neural network theory. (It does not address the learning and estimation-theoretic applications of VC dimension, and the applications to uniform convergence theorems for empirical probabilities, for which many suitable references are available.) } } @ARTICLE{MR1634875, AUTHOR = {P. Koiran and E.D. Sontag}, JOURNAL = {Discrete Appl. Math.}, TITLE = {Vapnik-Chervonenkis dimension of recurrent neural networks}, YEAR = {1998}, OPTMONTH = {}, OPTNOTE = {}, NUMBER = {1}, PAGES = {63--79}, VOLUME = {86}, ADDRESS = {Amsterdam, The Netherlands, The Netherlands}, KEYWORDS = {neural networks}, PUBLISHER = {Elsevier Science Publishers B. V.}, PDF = {../FTP_DIR/koiran-dam.pdf}, ABSTRACT = { This paper provides lower and upper bounds for the VC dimension of recurrent networks. Several types of activation functions are discussed, including threshold, polynomial, piecewise-polynomial and sigmoidal functions. The bounds depend on two independent parameters: the number w of weights in the network, and the length k of the input sequence. Ignoring multiplicative constants, the main results say roughly the following: 1. For architectures whose activation is any fixed nonlinear polynomial, the VC dimension is proportional to wk. 2. For architectures whose activation is any fixed piecewise polynomial, the VC dimension is between wk and w**2k. 3. For architectures with threshold activations, the VC dimension is between wlog(k/w) and the smallest of wklog(wk) and w**2+wlog(wk). 4. For the standard sigmoid tanh(x), the VC dimension is between wk and w**4 k**2. }, DOI = {http://dx.doi.org/10.1016/S0166-218X(98)00014-6} } @ARTICLE{MR1749163, AUTHOR = {D. Nesic and E.D. Sontag}, JOURNAL = {Systems Control Lett.}, TITLE = {Input-to-state stabilization of linear systems with positive outputs}, YEAR = {1998}, OPTMONTH = {}, OPTNOTE = {}, NUMBER = {4}, PAGES = {245--255}, VOLUME = {35}, PDF = {../FTP_DIR/iss-sign-output.pdf}, ABSTRACT = { This paper considers the problem of stabilization of linear systems for which only the magnitudes of outputs are measured. It is shown that, if a system is controllable and observable, then one can find a stabilizing controller, which is robust with respect to observation noise (in the ISS sense). } } @ARTICLE{MR1632338, AUTHOR = {E.D. Sontag}, JOURNAL = {Systems Control Lett.}, TITLE = {A learning result for continuous-time recurrent neural networks}, YEAR = {1998}, OPTMONTH = {}, OPTNOTE = {}, NUMBER = {3}, PAGES = {151--158}, VOLUME = {34}, ADDRESS = {Amsterdam, The Netherlands, The Netherlands}, KEYWORDS = {neural networks, VC dimension}, PUBLISHER = {Elsevier Science Publishers B. V.}, PDF = {../FTP_DIR/recur-learn.pdf}, ABSTRACT = { The following learning problem is considered, for continuous-time recurrent neural networks having sigmoidal activation functions. Given a ``black box'' representing an unknown system, measurements of output derivatives are collected, for a set of randomly generated inputs, and a network is used to approximate the observed behavior. It is shown that the number of inputs needed for reliable generalization (the sample complexity of the learning problem) is upper bounded by an expression that grows polynomially with the dimension of the network and logarithmically with the number of output derivatives being matched. }, DOI = {http://dx.doi.org/10.1016/S0167-6911(98)00006-1} } @ARTICLE{MR1629012, AUTHOR = {E.D. Sontag}, JOURNAL = {Systems Control Lett.}, TITLE = {Comments on integral variants of ISS}, YEAR = {1998}, OPTMONTH = {}, OPTNOTE = {}, NUMBER = {1-2}, PAGES = {93--100}, VOLUME = {34}, ADDRESS = {Amsterdam, The Netherlands, The Netherlands}, KEYWORDS = {input-to-state stability}, PUBLISHER = {Elsevier Science Publishers B. V.}, PDF = {../FTP_DIR/iiss.pdf}, ABSTRACT = { This note discusses two integral variants of the input-to-state stability (ISS) property, which represent nonlinear generalizations of L2 stability, in much the same way that ISS generalizes L-infinity stability. Both variants are equivalent to ISS for linear systems. For general nonlinear systems, it is shown that one of the new properties is strictly weaker than ISS, while the other one is equivalent to it. For bilinear systems, a complete characterization is provided of the weaker property. An interesting fact about functions of type KL is proved as well. }, DOI = {http://dx.doi.org/10.1016/S0167-6911(98)00003-6} } @ARTICLE{MR1607810, AUTHOR = {E.D. Sontag and F.R. Wirth}, JOURNAL = {Systems Control Lett.}, TITLE = {Remarks on universal nonsingular controls for discrete-time systems}, YEAR = {1998}, OPTMONTH = {}, OPTNOTE = {}, NUMBER = {2}, PAGES = {81--88}, VOLUME = {33}, ADDRESS = {Amsterdam, The Netherlands, The Netherlands}, KEYWORDS = {discrete time, controllability}, PUBLISHER = {Elsevier Science Publishers B. V.}, PDF = {../FTP_DIR/wirth-scl.pdf}, ABSTRACT = { For analytic discrete-time systems, it is shown that uniform forward accessibility implies the generic existence of universal nonsingular control sequences. A particular application is given by considering forward accessible systems on compact manifolds. For general systems, it is proved that the complement of the set of universal sequences of infinite length is of the first category. For classes of systems satisfying a descending chain condition, and in particular for systems defined by polynomial dynamics, forward accessibility implies uniform forward accessibility. }, DOI = {http://dx.doi.org/10.1016/S0167-6911(97)00117-5} } @INPROCEEDINGS{98cdc-angeli-wang98, AUTHOR = {D. Angeli and E.D. Sontag and Y. Wang}, BOOKTITLE = {Proc. IEEE Conf. Decision and Control, Tampa, Dec. 1998, IEEE Publications, 1998}, TITLE = {A remark on integral input to state stability}, YEAR = {1998}, OPTADDRESS = {}, OPTCROSSREF = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, OPTORGANIZATION = {}, PAGES = {2491--2496}, OPTPUBLISHER = {}, OPTSERIES = {}, OPTVOLUME = {}, KEYWORDS = {input to state stability} } @INPROCEEDINGS{98cdc-lin, AUTHOR = {X. Bao and Z. Lin and E.D. Sontag}, BOOKTITLE = {Proc. IEEE Conf. Decision and Control, Tampa, Dec. 1998, IEEE Publications, 1998}, TITLE = {Some new results on finite gain $l_p$ stabilization of discrete-time linear systems subject to actuator saturation}, YEAR = {1998}, OPTADDRESS = {}, OPTCROSSREF = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, OPTORGANIZATION = {}, PAGES = {4628--4629}, OPTPUBLISHER = {}, OPTSERIES = {}, OPTVOLUME = {} } @INPROCEEDINGS{98cdc-dasgupta, AUTHOR = {B. Dasgupta and E.D. Sontag}, BOOKTITLE = {Proc. IEEE Conf. Decision and Control, Tampa, Dec. 1998, IEEE Publications, 1998}, TITLE = {A polynomial-time algorithm for an equivalence problem which arises in hybrid systems theory}, YEAR = {1998}, OPTADDRESS = {}, OPTCROSSREF = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, OPTORGANIZATION = {}, PAGES = {1629--1634}, OPTPUBLISHER = {}, OPTSERIES = {}, OPTVOLUME = {} } @INPROCEEDINGS{98cdc-krichman, AUTHOR = {M. Krichman and E.D. Sontag}, BOOKTITLE = {Proc. IEEE Conf. Decision and Control, Tampa, Dec. 1998, IEEE Publications, 1998}, TITLE = {A version of a converse Lyapunov theorem for input-output to state stability}, YEAR = {1998}, OPTADDRESS = {}, OPTCROSSREF = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, OPTORGANIZATION = {}, PAGES = {4121--4126}, OPTPUBLISHER = {}, OPTSERIES = {}, OPTVOLUME = {}, KEYWORDS = {input to state stability} } @INPROCEEDINGS{98ciss-kuusela, AUTHOR = {P. Kuusela and D. Ocone and E.D. Sontag}, BOOKTITLE = {Proc. 32nd Annual Conf. on Information Sciences and Systems (CISS 98), Princeton, NJ}, TITLE = {On the VC dimension of continuous-time linear control systems}, YEAR = {1998}, OPTADDRESS = {}, OPTCROSSREF = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, OPTORGANIZATION = {}, PAGES = {795--800}, OPTPUBLISHER = {}, OPTSERIES = {}, OPTVOLUME = {} } @INPROCEEDINGS{98acc-yuri, AUTHOR = {Y.S. Ledyaev and E.D. Sontag}, BOOKTITLE = {Proc. American Control Conf., Philadelphia, June 1998}, TITLE = {Stabilization under measurement noise: Lyapunov characterization}, YEAR = {1998}, OPTADDRESS = {}, OPTCROSSREF = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, OPTORGANIZATION = {}, PAGES = {1658--166}, OPTPUBLISHER = {}, OPTSERIES = {}, OPTVOLUME = {} } @INPROCEEDINGS{98cdc-nesic, AUTHOR = {D. Nesic and E.D. Sontag}, BOOKTITLE = {Proc. IEEE Conf. Decision and Control, Tampa, Dec. 1998, IEEE Publications, 1998}, TITLE = {Output stabilization of nonlinear systems: Linear systems with positive outputs as a case study}, YEAR = {1998}, OPTADDRESS = {}, OPTCROSSREF = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, OPTORGANIZATION = {}, PAGES = {885--890}, OPTPUBLISHER = {}, OPTSERIES = {}, OPTVOLUME = {} } @INPROCEEDINGS{98acc-iiss, AUTHOR = {E.D. Sontag}, BOOKTITLE = {Proc. American Control Conf., Philadelphia, June 1998}, TITLE = {Notions of integral input-to-state stability}, YEAR = {1998}, OPTADDRESS = {}, OPTCROSSREF = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, OPTORGANIZATION = {}, PAGES = {3215--321}, OPTPUBLISHER = {}, OPTSERIES = {}, OPTVOLUME = {}, KEYWORDS = {input to state stability} } @INPROCEEDINGS{98london, AUTHOR = {E.D. Sontag}, BOOKTITLE = {Proc. Workshop on Control of Nonlinear and Uncertain Systems, London, Feb. 1998}, TITLE = {Recent results on discontinuous stabilization and control-Lyapunov functions}, YEAR = {1998}, OPTADDRESS = {}, OPTCROSSREF = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, OPTORGANIZATION = {}, OPTPAGES = {}, OPTPUBLISHER = {}, OPTSERIES = {}, OPTVOLUME = {}, KEYWORDS = {control-Lyapunov functions} } @INPROCEEDINGS{98cdc-qiao, AUTHOR = {E.D. Sontag and Y. Qiao}, BOOKTITLE = {Proc. IEEE Conf. Decision and Control, Tampa, Dec. 1998, IEEE Publications, 1998}, TITLE = {Remarks on controllability of recurrent neural networks}, YEAR = {1998}, OPTADDRESS = {}, OPTCROSSREF = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, OPTORGANIZATION = {}, PAGES = {501--506}, OPTPUBLISHER = {}, OPTSERIES = {}, OPTVOLUME = {}, KEYWORDS = {neural networks} } @INCOLLECTION{MR1476934, AUTHOR = {P. Koiran and E.D. Sontag}, BOOKTITLE = {Computational learning theory (Jerusalem, 1997)}, PUBLISHER = {Springer-Verlag}, TITLE = {Vapnik-Chervonenkis dimension of recurrent neural networks}, YEAR = {1997}, ADDRESS = {London, UK}, OPTCHAPTER = {}, OPTCROSSREF = {}, OPTEDITION = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, PAGES = {223--237}, SERIES = {Lecture Notes in Comput. Sci.}, OPTTYPE = {}, VOLUME = {1208}, KEYWORDS = {neural networks, VC dimension} } @INCOLLECTION{MR1430107, AUTHOR = {Y.S. Ledyaev and E.D. Sontag}, BOOKTITLE = {Control using logic-based switching (Block Island, RI, 1995)}, PUBLISHER = {Springer}, TITLE = {A notion of discontinuous feedback}, YEAR = {1997}, ADDRESS = {London}, OPTCHAPTER = {}, OPTCROSSREF = {}, OPTEDITION = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, PAGES = {97--103}, SERIES = {Lecture Notes in Control and Inform. Sci.}, OPTTYPE = {}, VOLUME = {222} } @INCOLLECTION{recur-book-survey, AUTHOR = {E.D. Sontag}, BOOKTITLE = {Dealing with Complexity: a Neural Network Approach}, PUBLISHER = {Springer-Verlag, London}, TITLE = {Recurrent neural networks: Some systems-theoretic aspects}, YEAR = {1997}, OPTADDRESS = {}, OPTCHAPTER = {}, OPTCROSSREF = {}, OPTEDITION = {}, EDITOR = {M. Karny and K. Warwick and V. Kurkova}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, PAGES = {1--12}, OPTSERIES = {}, OPTTYPE = {}, OPTVOLUME = {}, KEYWORDS = {neural networks}, PDF = {../FTP_DIR/recur-survey-book.pdf}, ABSTRACT = { This paper provides an exposition of some recent results regarding system-theoretic aspects of continuous-time recurrent (dynamic) neural networks with sigmoidal activation functions. The class of systems is introduced and discussed, and a result is cited regarding their universal approximation properties. Known characterizations of controllability, observability, and parameter identifiability are reviewed, as well as a result on minimality. Facts regarding the computational power of recurrent nets are also mentioned. } } @ARTICLE{clss97, AUTHOR = {F. H. Clarke and Y.S. Ledyaev and E.D. Sontag and A.I. Subbotin}, JOURNAL = {IEEE Trans. Automat. Control}, TITLE = {Asymptotic controllability implies feedback stabilization}, YEAR = {1997}, OPTMONTH = {}, OPTNOTE = {}, NUMBER = {10}, PAGES = {1394--1407}, VOLUME = {42}, PDF = {../FTP_DIR/nonsmooth-feedback.pdf}, ABSTRACT = { It is shown that every asymptotically controllable system can be stabilized by means of some (discontinuous) feedback law. One of the contributions of the paper is in defining precisely the meaning of stabilization when the feedback rule is not continuous. The main ingredients in our construction are: (a) the notion of control-Lyapunov function, (b) methods of nonsmooth analysis, and (c) techniques from positional differential games. } } @ARTICLE{MR1437210, AUTHOR = {M. J. Donahue and L. Gurvits and C. Darken and E.D. Sontag}, JOURNAL = {Constr. Approx.}, TITLE = {Rates of convex approximation in non-Hilbert spaces}, YEAR = {1997}, OPTMONTH = {}, OPTNOTE = {}, NUMBER = {2}, PAGES = {187--220}, VOLUME = {13}, KEYWORDS = {neural networks, optimization, approximation theory}, PDF = {../FTP_DIR/ddgs.pdf}, ABSTRACT = { This paper deals with sparse approximations by means of convex combinations of elements from a predetermined "basis" subset S of a function space. Specifically, the focus is on the rate at which the lowest achievable error can be reduced as larger subsets of S are allowed when constructing an approximant. The new results extend those given for Hilbert spaces by Jones and Barron, including in particular a computationally attractive incremental approximation scheme. Bounds are derived for broad classes of Banach spaces. The techniques used borrow from results regarding moduli of smoothness in functional analysis as well as from the theory of stochastic processes on function spaces. } } @ARTICLE{MR1463259, AUTHOR = {P. Koiran and E.D. Sontag}, JOURNAL = {J. Comput. System Sci.}, TITLE = {Neural networks with quadratic VC dimension}, YEAR = {1997}, OPTMONTH = {}, NOTE = {(1st Annual Dagstuhl Seminar on Neural Computing, 1994)}, NUMBER = {1, part 2}, PAGES = {190--198}, VOLUME = {54}, ADDRESS = {Orlando, FL, USA}, KEYWORDS = {neural networks, VC dimension}, PUBLISHER = {Academic Press, Inc.}, PDF = {../FTP_DIR/quadratic-vc.pdf}, ABSTRACT = { This paper shows that neural networks which use continuous activation functions have VC dimension at least as large as the square of the number of weights w. This result settles the open question of whether whether the well-known O(w log w) bound, known for hard-threshold nets, also held for more general sigmoidal nets. Implications for the number of samples needed for valid generalization are discussed. }, DOI = {http://dx.doi.org/10.1006/jcss.1997.1479} } @ARTICLE{fourier-renee, AUTHOR = {R. Koplon and E.D. Sontag}, JOURNAL = {Neurocomputing}, TITLE = {Using Fourier-neural recurrent networks to fit sequential input/output data}, YEAR = {1997}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, PAGES = {225--248}, VOLUME = {15}, KEYWORDS = {neural networks}, PDF = {../FTP_DIR/fouriernet.pdf}, ABSTRACT = { This paper suggests the use of Fourier-type activation functions in fully recurrent neural networks. The main theoretical advantage is that, in principle, the problem of recovering internal coefficients from input/output data is solvable in closed form. } } @ARTICLE{250973, AUTHOR = {E.D. Sontag}, JOURNAL = {Neural Comput.}, TITLE = {Shattering all sets of k points in `general position' requires (k-1)/2 parameters}, YEAR = {1997}, OPTMONTH = {}, OPTNOTE = {}, NUMBER = {2}, PAGES = {337--348}, VOLUME = {9}, ADDRESS = {Cambridge, MA, USA}, KEYWORDS = {neural networks, VC dimension}, PUBLISHER = {MIT Press}, PDF = {../FTP_DIR/generic.pdf}, ABSTRACT = { For classes of concepts defined by certain classes of analytic functions depending on k parameters, there are nonempty open sets of samples of length 2k+2 which cannot be shattered. A slighly weaker result is also proved for piecewise-analytic functions. The special case of neural networks is discussed. } } @ARTICLE{MR1455876, AUTHOR = {E.D. Sontag and H.J. Sussmann}, JOURNAL = {Systems Control Lett.}, TITLE = {Complete controllability of continuous-time recurrent neural networks}, YEAR = {1997}, OPTMONTH = {}, OPTNOTE = {}, NUMBER = {4}, PAGES = {177--183}, VOLUME = {30}, ADDRESS = {Amsterdam, The Netherlands, The Netherlands}, KEYWORDS = {neural networks}, PUBLISHER = {Elsevier Science Publishers B. V.}, PDF = {../FTP_DIR/reach-sigmoid.pdf}, ABSTRACT = { This paper presents a characterization of controllability for the class of control systems commonly called (continuous-time) recurrent neural networks. The characterization involves a simple condition on the input matrix, and is proved when the activation function is the hyperbolic tangent. }, DOI = {http://dx.doi.org/10.1016/S0167-6911(97)00002-9} } @ARTICLE{MR1432653, AUTHOR = {E.D. Sontag and Y. Wang}, JOURNAL = {Systems Control Lett.}, TITLE = {Output-to-state stability and detectability of nonlinear systems}, YEAR = {1997}, OPTMONTH = {}, OPTNOTE = {}, NUMBER = {5}, PAGES = {279--290}, VOLUME = {29}, ADDRESS = {Amsterdam, The Netherlands, The Netherlands}, KEYWORDS = {input to state stability, detectability, input to state stability}, PUBLISHER = {Elsevier Science Publishers B. V.}, PDF = {../FTP_DIR/oss_scl97.pdf}, ABSTRACT = { The notion of input-to-state stability (ISS) has proved to be useful in nonlinear systems analysis. This paper discusses a dual notion, output-to-state stability (OSS). A characterization is provided in terms of a dissipation inequality involving storage (Lyapunov) functions. Combining ISS and OSS there results the notion of input/output-to-state stability (IOSS), which is also studied and related to the notion of detectability, the existence of observers, and output injection. }, DOI = {http://dx.doi.org/10.1016/S0167-6911(97)90013-X} } @ARTICLE{MR1453841, AUTHOR = {Y. Yang and E.D. Sontag and H.J. Sussmann}, JOURNAL = {Systems Control Lett.}, TITLE = {Global stabilization of linear discrete-time systems with bounded feedback}, YEAR = {1997}, OPTMONTH = {}, OPTNOTE = {}, NUMBER = {5}, PAGES = {273--281}, VOLUME = {30}, ADDRESS = {Amsterdam, The Netherlands, The Netherlands}, KEYWORDS = {discrete-time, saturation}, PUBLISHER = {Elsevier Science Publishers B. V.}, PDF = {../FTP_DIR/saturated-dt.pdf}, ABSTRACT = { This paper deals with the problem of global stabilization of linear discrete time systems by means of bounded feedback laws. The main result proved is an analog of one proved for the continuous time case by the authors, and shows that such stabilization is possible if and only if the system is stabilizable with arbitrary controls and the transition matrix has spectral radius less or equal to one. The proof provides in principle an algorithm for the construction of such feedback laws, which can be implemented either as cascades or as parallel connections (``single hidden layer neural networks'') of simple saturation functions. }, DOI = {http://dx.doi.org/10.1016/S0167-6911(97)00021-2} } @INPROCEEDINGS{fa-clf, AUTHOR = {F. Albertini and E.D. Sontag}, BOOKTITLE = {Proc. European Control Conf., Brussels, July 1997}, TITLE = {Control-Lyapunov functions for time-varying set stabilization}, YEAR = {1997}, OPTADDRESS = {}, OPTCROSSREF = {}, OPTEDITOR = {}, OPTMONTH = {}, NOTE = {(Paper WE-E A5, CD-ROM file ECC515.pdf, 6 pages)}, OPTNUMBER = {}, OPTORGANIZATION = {}, OPTPAGES = {}, OPTPUBLISHER = {}, OPTSERIES = {}, OPTVOLUME = {}, KEYWORDS = {control-Lyapunov functions} } @INPROCEEDINGS{97ciss-yuri, AUTHOR = {Y.S. Ledyaev and E.D. Sontag}, BOOKTITLE = {Proc. Conf. on Information Sciences and Systems (CISS 97), Johns Hopkins, Baltimore, MD, March 1997}, TITLE = {A remark on robust stabilization of general asymptotically controllable systems}, YEAR = {1997}, OPTADDRESS = {}, OPTCROSSREF = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, OPTORGANIZATION = {}, PAGES = {246--251}, OPTPUBLISHER = {}, OPTSERIES = {}, OPTVOLUME = {}, PDF = {../FTP_DIR/97ciss-robust.pdf}, ABSTRACT = { We showned in another recent paper that any asymptotically controllable system can be stabilized by means of a certain type of discontinuous feedback. The feedback laws constructed in that work are robust with respect to actuator errors as well as to perturbations of the system dynamics. A drawback, however, is that they may be highly sensitive to errors in the measurement of the state vector. This paper addresses this shortcoming, and shows how to design a dynamic hybrid stabilizing controller which, while preserving robustness to external perturbations and actuator error, is also robust with respect to measurement error. This new design relies upon a controller which incorporates an internal model of the system driven by the previously constructed feedback. } } @INPROCEEDINGS{97ciss-nn, AUTHOR = {E.D. Sontag}, BOOKTITLE = {Proc. Conf. on Information Sciences and Systems (CISS 97), Johns Hopkins, Baltimore, MD, March 1997}, TITLE = {Some learning and systems-theoretic questions regarding recurrent neural networks}, YEAR = {1997}, OPTADDRESS = {}, OPTCROSSREF = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, OPTORGANIZATION = {}, PAGES = {630--635}, OPTPUBLISHER = {}, OPTSERIES = {}, OPTVOLUME = {}, KEYWORDS = {neural networks, VC dimension} } @INPROCEEDINGS{ios-ecc, AUTHOR = {E.D. Sontag and Y. Wang}, BOOKTITLE = {Proc. European Control Conf., Brussels, July 1997}, TITLE = {A notion of input to output stability}, YEAR = {1997}, OPTADDRESS = {}, OPTCROSSREF = {}, OPTEDITOR = {}, OPTMONTH = {}, NOTE = {(Paper WE-E A2, CD-ROM file ECC958.pdf, 6 pages)}, OPTNUMBER = {}, OPTORGANIZATION = {}, OPTPAGES = {}, OPTPUBLISHER = {}, OPTSERIES = {}, OPTVOLUME = {}, KEYWORDS = {input to state stability, input to state stability}, PDF = {../FTP_DIR/97ecc-ios.pdf}, ABSTRACT = { This paper deals with a notion of "input to output stability (IOS)", which formalizes the idea that outputs depend in an "aymptotically stable" manner on inputs, while internal signals remain bounded. When the output equals the complete state, one recovers the property of input to state stability (ISS). When there are no inputs, one has a generalization of the classical concept of partial stability. The main results provide Lyapunov-function characterizations of IOS. } } @BOOK{AHS, PUBLISHER = {Springer Verlag, Berlin}, TITLE = {Hybrid Systems III. Verification and Control (edited book)}, YEAR = {1996}, AUTHOR = {R. Alur and T.A. Henzinger and E.D. Sontag}, ALTEDITOR = {}, OPTADDRESS = {}, OPTEDITION = {}, OPTMONTH = {}, NOTE = {(LNCS 1066)}, OPTNUMBER = {}, OPTSERIES = {}, OPTVOLUME = {} } @INCOLLECTION{PLS96dimacs, AUTHOR = {E.D. Sontag}, BOOKTITLE = {Proceedings of the DIMACS/SYCON workshop on Hybrid systems III : verification and control}, PUBLISHER = {Springer-Verlag New York, Inc.}, TITLE = {Interconnected automata and linear systems: a theoretical framework in discrete-time}, YEAR = {1996}, ADDRESS = {Secaucus, NJ, USA}, OPTCHAPTER = {}, OPTCROSSREF = {}, OPTEDITION = {}, EDITOR = {R. Alur and T.A. Henzinger and E.D. Sontag}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, PAGES = {436--448}, OPTSERIES = {}, OPTTYPE = {}, OPTVOLUME = {}, KEYWORDS = {hybrid systems}, PDF = {../FTP_DIR/pls-expo.pdf}, ABSTRACT = { This paper summarizes the definitions and several of the main results of an approach to hybrid systems, which combines finite automata and linear systems, developed by the author in the early 1980s. Some related more recent results are briefly mentioned as well. } } @INCOLLECTION{MR1416368, AUTHOR = {E.D. Sontag and H.J. Sussmann}, BOOKTITLE = {Stability theory (Ascona, 1995)}, PUBLISHER = {Birkhäuser}, TITLE = {General classes of control-Lyapunov functions}, YEAR = {1996}, ADDRESS = {Basel}, OPTCHAPTER = {}, OPTCROSSREF = {}, OPTEDITION = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, PAGES = {87--96}, SERIES = {Internat. Ser. Numer. Math.}, OPTTYPE = {}, VOLUME = {121}, KEYWORDS = {control-Lyapunov functions}, PDF = {../FTP_DIR/95hurwitzconf.pdf}, ABSTRACT = { Shorter and more expository version of "Nonsmooth control-Lyapunov functions" } } @ARTICLE{TransInfoTheoVCperceptrons96, AUTHOR = {B. DasGupta and E.D. Sontag}, JOURNAL = {IEEE Trans. Inform. Theory}, TITLE = {Sample complexity for learning recurrent perceptron mappings}, YEAR = {1996}, OPTMONTH = {}, OPTNOTE = {}, NUMBER = {5}, PAGES = {1479--1487}, VOLUME = {42}, KEYWORDS = {neural networks, VC dimension}, PDF = {../FTP_DIR/vcdim-signlinear.pdf}, ABSTRACT = { Recurrent perceptron classifiers generalize the usual perceptron model. They correspond to linear transformations of input vectors obtained by means of "autoregressive moving-average schemes", or infinite impulse response filters, and allow taking into account those correlations and dependences among input coordinates which arise from linear digital filtering. This paper provides tight bounds on sample complexity associated to the fitting of such models to experimental data. The results are expressed in the context of the theory of probably approximately correct (PAC) learning. } } @ARTICLE{MR1372908, AUTHOR = {Y. Lin and E.D. Sontag and Y. Wang}, JOURNAL = {SIAM J. Control Optim.}, TITLE = {A smooth converse Lyapunov theorem for robust stability}, YEAR = {1996}, OPTMONTH = {}, OPTNOTE = {}, NUMBER = {1}, PAGES = {124--160}, VOLUME = {34}, ADDRESS = {Philadelphia, PA, USA}, KEYWORDS = {input to state stability}, PUBLISHER = {Society for Industrial and Applied Mathematics}, PDF = {../FTP_DIR/converse-siam.pdf}, ABSTRACT = { This paper presents a Converse Lyapunov Function Theorem motivated by robust control analysis and design. Our result is based upon, but generalizes, various aspects of well-known classical theorems. In a unified and natural manner, it (1) allows arbitrary bounded time-varying parameters in the system description, (2) deals with global asymptotic stability, (3) results in smooth (infinitely differentiable) Lyapunov functions, and (4) applies to stability with respect to not necessarily compact invariant sets. }, DOI = {http://dx.doi.org/10.1137/S0363012993259981} } @ARTICLE{MR1395830, AUTHOR = {W. Liu and Y. Chitour and E.D. Sontag}, JOURNAL = {SIAM J. Control Optim.}, TITLE = {On finite-gain stabilizability of linear systems subject to input saturation}, YEAR = {1996}, OPTMONTH = {}, OPTNOTE = {}, NUMBER = {4}, PAGES = {1190--1219}, VOLUME = {34}, ADDRESS = {Philadelphia, PA, USA}, KEYWORDS = {saturation}, PUBLISHER = {Society for Industrial and Applied Mathematics}, PDF = {../FTP_DIR/saturated-gains.pdf}, ABSTRACT = { This paper deals with (global) finite-gain input/output stabilization of linear systems with saturated controls. For neutrally stable systems, it is shown that the linear feedback law suggested by the passivity approach indeed provides stability, with respect to every Lp-norm. Explicit bounds on closed-loop gains are obtained, and they are related to the norms for the respective systems without saturation. These results do not extend to the class of systems for which the state matrix has eigenvalues on the imaginary axis with nonsimple (size >1) Jordan blocks, contradicting what may be expected from the fact that such systems are globally asymptotically stabilizable in the state-space sense; this is shown in particular for the double integrator. }, DOI = {http://dx.doi.org/10.1137/S0363012994263469} } @ARTICLE{MR1399383, AUTHOR = {E.D. Sontag}, JOURNAL = {Adv. Comput. Math.}, TITLE = {Critical points for least-squares problems involving certain analytic functions, with applications to sigmoidal nets}, YEAR = {1996}, OPTMONTH = {}, OPTNOTE = {}, NUMBER = {2-3}, PAGES = {245--268}, VOLUME = {5}, KEYWORDS = {subanalytic sets, semianalytic sets, analytic geometry, critical points, approximation theory, neural networks}, PDF = {../FTP_DIR/crit-sigmoid.pdf}, ABSTRACT = { This paper deals with nonlinear least-squares problems involving the fitting to data of parameterized analytic functions. For generic regression data, a general result establishes the countability, and under stronger assumptions finiteness, of the set of functions giving rise to critical points of the quadratic loss function. In the special case of what are usually called "single-hidden layer neural networks", which are built upon the standard sigmoidal activation tanh(x) or equivalently 1/(1+exp(-x)), a rough upper bound for this cardinality is provided as well. } } @ARTICLE{MR1409473, AUTHOR = {E.D. Sontag and Y. Wang}, JOURNAL = {IEEE Trans. Automat. Control}, TITLE = {New characterizations of input-to-state stability}, YEAR = {1996}, OPTMONTH = {}, OPTNOTE = {}, NUMBER = {9}, PAGES = {1283--1294}, VOLUME = {41}, KEYWORDS = {input to state stability}, PDF = {../FTP_DIR/new-iss.pdf}, ABSTRACT = { We present new characterizations of the Input to State Stability property. As a consequence of these results, we show the equivalence between the ISS property and several (apparent) variations proposed in the literature. } } @INPROCEEDINGS{ciss96cls, AUTHOR = {F.H. Clarke and Y.S. Ledyaev and E.D. Sontag and A.I. Subbotin}, BOOKTITLE = {Proc. Conf. on Information Sciences and Systems (CISS 96)Princeton, NJ}, TITLE = {Asymptotic controllability and feedback stabilization}, YEAR = {1996}, OPTADDRESS = {}, OPTCROSSREF = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, OPTORGANIZATION = {}, PAGES = {1232--1237}, OPTPUBLISHER = {}, OPTSERIES = {}, OPTVOLUME = {}, KEYWORDS = {control-Lyapunov functions, feedback stabilization} } @INPROCEEDINGS{dasgupta-nips, AUTHOR = {B. Dasgupta and E.D. Sontag}, BOOKTITLE = {Advances in Neural Information Processing Systems 8}, TITLE = {Sample complexity for learning recurrent perceptron mappings}, YEAR = {1996}, OPTADDRESS = {}, OPTCROSSREF = {}, EDITOR = {D.S. Touretzky and M.C. Moser and M.E. Hasselmo}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, OPTORGANIZATION = {}, PAGES = {204--210}, PUBLISHER = {MIT Press, Cambridge, MA}, OPTSERIES = {}, OPTVOLUME = {}, KEYWORDS = {neural networks, VC dimension} } @INPROCEEDINGS{koiran-nips, AUTHOR = {P. Koiran and E.D. Sontag}, BOOKTITLE = {Advances in Neural Information Processing Systems 8}, TITLE = {Neural networks with quadratic VC dimension}, YEAR = {1996}, OPTADDRESS = {}, OPTCROSSREF = {}, EDITOR = {D.S. Touretzky and M.C. Moser and M.E. Hasselmo}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, OPTORGANIZATION = {}, PAGES = {197--203}, PUBLISHER = {MIT Press, Cambridge, MA}, OPTSERIES = {}, OPTVOLUME = {}, KEYWORDS = {neural networks, VC dimension} } @INPROCEEDINGS{ciss96, AUTHOR = {E.D. Sontag and Y. Wang}, BOOKTITLE = {Proc. Conf. on Information Sciences and Systems (CISS 96), Princeton, NJ}, TITLE = {Detectability of nonlinear systems}, YEAR = {1996}, OPTADDRESS = {}, OPTCROSSREF = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, OPTORGANIZATION = {}, PAGES = {1031--1036}, OPTPUBLISHER = {}, OPTSERIES = {}, OPTVOLUME = {}, KEYWORDS = {detectability, input to state stability}, PDF = {../FTP_DIR/oss.pdf}, ABSTRACT = { Contains a proof of a technical step, which was omitted from the journal paper due to space constraints } } @TECHREPORT{bremen96, AUTHOR = {E.D. Sontag and F.R. Wirth}, INSTITUTION = {Institute for Dynamical Systems, University of Bremen}, TITLE = {Remarks on universal nonsingular controls for discrete-time systems}, YEAR = {1996}, OPTADDRESS = {}, OPTMONTH = {}, OPTNOTE = {}, NUMBER = {381}, OPTTYPE = {} } @INCOLLECTION{MR1326162, AUTHOR = {E.D. Sontag}, BOOKTITLE = {Feedback control, nonlinear systems, and complexity (Montreal, PQ, 1994)}, PUBLISHER = {Springer}, TITLE = {State-space and i/o stability for nonlinear systems}, YEAR = {1995}, ADDRESS = {London}, OPTCHAPTER = {}, OPTCROSSREF = {}, OPTEDITION = {}, OPTEDITOR = {}, OPTMONTH = {}, NOTE = {(Expository paper, placed online per request. The paper ``Input to state stability: Basic concepts and results'' is far more up to date and should be downloaded instead of this one!)}, OPTNUMBER = {}, PAGES = {215--235}, SERIES = {Lecture Notes in Control and Inform. Sci.}, OPTTYPE = {}, VOLUME = {202}, KEYWORDS = {input to state stability}, PDF = {../FTP_DIR/94montreal.pdf} } @INCOLLECTION{ControlHandbook, AUTHOR = {A.R. Teel and T.T. Georgiou and L. Praly and E.D. Sontag}, BOOKTITLE = {The Control Handbook}, PUBLISHER = {CRC Press, Boca Raton}, TITLE = {Input-Output Stability}, YEAR = {1995}, OPTADDRESS = {}, OPTCHAPTER = {}, OPTCROSSREF = {}, OPTEDITION = {}, EDITOR = {W. S. Levine}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, PAGES = {895--908}, OPTSERIES = {}, OPTTYPE = {}, OPTVOLUME = {}, PDF = {../FTP_DIR/crc.pdf}, ABSTRACT = { An encyclopedia-type article on foundations of input/output stability. } } @ARTICLE{MR1346408, AUTHOR = {Y. Chitour and W. Liu and E.D. Sontag}, JOURNAL = {Internat. J. Robust Nonlinear Control}, TITLE = {On the continuity and incremental-gain properties of certain saturated linear feedback loops}, YEAR = {1995}, OPTMONTH = {}, OPTNOTE = {}, NUMBER = {5}, PAGES = {413--440}, VOLUME = {5}, KEYWORDS = {saturation}, PDF = {../FTP_DIR/saturated-incr-gains.pdf}, ABSTRACT = { This paper discusses various continuity and incremental-gain properties for neutrally stable linear systems under linear feedback subject to actuator saturation. The results complement our previous ones, which applied to the same class of problems and provided finite-gain stability. } } @ARTICLE{MR1321019, AUTHOR = {M. A. Dahleh and E.D. Sontag and D. N. C. Tse and J. N. Tsitsiklis}, JOURNAL = {Automatica}, TITLE = {Worst-case identification of nonlinear fading memory systems}, YEAR = {1995}, OPTMONTH = {}, OPTNOTE = {}, NUMBER = {3}, PAGES = {503--508}, VOLUME = {31}, ADDRESS = {Tarrytown, NY, USA}, PUBLISHER = {Pergamon Press, Inc.}, PDF = {../FTP_DIR/ibc-fading-mem.pdf}, ABSTRACT = { We consider the problem of characterizing possible supply functions for a given dissipative nonlinear system, and provide a result that allows some freedom in the modification of such functions. }, DOI = {http://dx.doi.org/10.1016/0005-1098(94)00131-2} } @ARTICLE{DasGupta-TNN, AUTHOR = {B. DasGupta and H.T. Siegelmann and E.D. Sontag}, JOURNAL = {IEEE Trans. Neural Networks}, TITLE = {On the complexity of training neural networks with continuous activation functions}, YEAR = {1995}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, PAGES = {1490--1504}, VOLUME = {6}, KEYWORDS = {neural networks, theory of computing and complexity}, PDF = {../FTP_DIR/complexity-training.pdf}, ABSTRACT = { Blum and Rivest showed that any possible neural net learning algorithm based on fixed architectures faces severe computational barriers. This paper extends their NP-completeness result, which applied only to nets based on hard threshold activations, to nets that employ a particular continuous activation. In view of neural network practice, this is a more relevant result to understanding the limitations of backpropagation and related techniques. } } @ARTICLE{MR1424371, AUTHOR = {Y. Lin and E.D. Sontag}, JOURNAL = {Control Theory Adv. Tech.}, TITLE = {Control-Lyapunov universal formulas for restricted inputs}, YEAR = {1995}, OPTMONTH = {}, OPTNOTE = {}, NUMBER = {4, part 5}, PAGES = {1981--2004}, VOLUME = {10}, KEYWORDS = {control-Lyapunov functions, saturation}, PDF = {../FTP_DIR/clf-bounded-ctat.pdf}, ABSTRACT = { We deal with the question of obtaining explicit feedback control laws that stabilize a nonlinear system, under the assumption that a "control Lyapunov function" is known. In previous work, the case of unbounded controls was considered. Here we obtain results for bounded and/or positive controls. We also provide some simple preliminary remarks regarding a set stability version of the problem and a version for systems subject to disturbances. } } @ARTICLE{MR1329624, AUTHOR = {Y. Lin and E.D. Sontag and Y. Wang}, JOURNAL = {Internat. J. Robust Nonlinear Control}, TITLE = {Input to state stabilizability for parametrized families of systems}, YEAR = {1995}, OPTMONTH = {}, OPTNOTE = {}, NUMBER = {3}, PAGES = {187--205}, VOLUME = {5}, PDF = {../FTP_DIR/issparametric.pdf}, ABSTRACT = { This paper studies various stability issues for parameterized families of systems, including problems of stabilization with respect to sets. The study of such families is motivated by robust control applications. A Lyapunov-theoretic necessary and sufficient characterization is obtained for a natural notion of robust uniform set stability; this characterization allows replacing ad hoc conditions found in the literature by more conceptual stability notions. We then use these techniques to establish a result linking state space stability to ``input to state'' (bounded-input bounded-state) stability. In addition, the preservation of stabilizability under certain types of cascade interconnections is analyzed. } } @ARTICLE{MR1322637, AUTHOR = {H. T. Siegelmann and E.D. Sontag}, JOURNAL = {J. Comput. System Sci.}, TITLE = {On the computational power of neural nets}, YEAR = {1995}, OPTMONTH = {}, OPTNOTE = {}, NUMBER = {1}, PAGES = {132--150}, VOLUME = {50}, ADDRESS = {Orlando, FL, USA}, KEYWORDS = {neural networks, neural networks, computational complexity}, PUBLISHER = {Academic Press, Inc.}, PDF = {../FTP_DIR/nets-rational.pdf}, ABSTRACT = { This paper deals with finite size networks which consist of interconnections of synchronously evolving processors. Each processor updates its state by applying a "sigmoidal" function to a rational-coefficient linear combination of the previous states of all units. We prove that one may simulate all Turing Machines by such nets. In particular, one can simulate any multi-stack Turing Machine in real time, and there is a net made up of 886 processors which computes a universal partial-recursive function. Products (high order nets) are not required, contrary to what had been stated in the literature. Non-deterministic Turing Machines can be simulated by non-deterministic rational nets, also in real time. The simulation result has many consequences regarding the decidability, or more generally the complexity, of questions about recursive nets. }, DOI = {http://dx.doi.org/10.1006/jcss.1995.1013} } @ARTICLE{MR1344033, AUTHOR = {E.D. Sontag}, JOURNAL = {IEEE Trans. Automat. Control}, TITLE = {Control of systems without drift via generic loops}, YEAR = {1995}, OPTMONTH = {}, OPTNOTE = {}, NUMBER = {7}, PAGES = {1210--1219}, VOLUME = {40}, KEYWORDS = {controllability}, PDF = {../FTP_DIR/nonsing-loop.pdf}, ABSTRACT = { This paper proposes a simple numerical technique for the steering of arbitrary analytic systems with no drift. It is based on the generation of "nonsingular loops" which allow linearized controllability along suitable trajetories. Once such loops are available, it is possible to employ standard Newton or steepest descent methods, as classically done in numerical control. The theoretical justification of the approach relies on recent results establishing the genericity of nonsingular controls, as well as a simple convergence lemma. } } @ARTICLE{iss-ejc, AUTHOR = {E.D. Sontag}, JOURNAL = {European J. Control}, TITLE = {On the input-to-state stability property}, YEAR = {1995}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, PAGES = {24--36}, VOLUME = {1}, KEYWORDS = {input to state stability}, PDF = {../FTP_DIR/iss-ejc.pdf}, ABSTRACT = { The "input to state stability" (ISS) property provides a natural framework in which to formulate notions of stability with respect to input perturbations. In this expository paper, we review various equivalent definitions expressed in stability, Lyapunov-theoretic, and dissipation terms. We sketch some applications to the stabilization of cascades of systems and of linear systems subject to control saturation. } } @ARTICLE{MR1343820, AUTHOR = {E.D. Sontag and A.R. Teel}, JOURNAL = {IEEE Trans. Automat. Control}, TITLE = {Changing supply functions in input/state stable systems}, YEAR = {1995}, OPTMONTH = {}, OPTNOTE = {}, NUMBER = {8}, PAGES = {1476--1478}, VOLUME = {40}, KEYWORDS = {input to state stability, Lyapunov functions}, PDF = {../FTP_DIR/tn950112.pdf}, ABSTRACT = {We consider the problem of characterizing possible supply functions for a given dissipative nonlinear system, and provide a result that allows some freedom in the modification of such functions. } } @ARTICLE{MR1325675, AUTHOR = {E.D. Sontag and Y. Wang}, JOURNAL = {Systems Control Lett.}, TITLE = {On characterizations of the input-to-state stability property}, YEAR = {1995}, OPTMONTH = {}, OPTNOTE = {}, NUMBER = {5}, PAGES = {351--359}, VOLUME = {24}, ADDRESS = {Amsterdam, The Netherlands, The Netherlands}, KEYWORDS = {input to state stability}, PUBLISHER = {Elsevier Science Publishers B. V.}, PDF = {../FTP_DIR/converse-iss.pdf}, ABSTRACT = { We show that the well-known Lyapunov sufficient condition for input-to-state stability is also necessary, settling positively an open question raised by several authors during the past few years. Additional characterizations of the ISS property, including one in terms of nonlinear stability margins, are also provided. }, DOI = {http://dx.doi.org/10.1016/0167-6911(94)00050-6} } @ARTICLE{MR1339057, AUTHOR = {Y. Wang and E.D. Sontag}, JOURNAL = {SIAM J. Control Optim.}, TITLE = {Orders of input/output differential equations and state-space dimensions}, YEAR = {1995}, OPTMONTH = {}, OPTNOTE = {}, NUMBER = {4}, PAGES = {1102--1126}, VOLUME = {33}, ADDRESS = {Philadelphia, PA, USA}, KEYWORDS = {realization theory, observability}, PUBLISHER = {Society for Industrial and Applied Mathematics}, PDF = {../FTP_DIR/orders-yw-siam2.pdf}, ABSTRACT = { This paper deals with the orders of input/output equations satisfied by nonlinear systems. Such equations represent differential (or difference, in the discrete-time case) relations between high-order derivatives (or shifts, respectively) of input and output signals. It is shown that, under analyticity assumptions, there cannot exist equations of order less than the minimal dimension of any observable realization; this generalizes the known situation in the classical linear case. The results depend on new facts, themselves of considerable interest in control theory, regarding universal inputs for observability in the discrete case, and observation spaces in both the discrete and continuous cases. Included in the paper is also a new and simple self-contained proof of Sussmann's universal input theorem for continuous-time analytic systems. }, DOI = {http://dx.doi.org/10.1137/S0363012993246828} } @INPROCEEDINGS{95cdc-diss, AUTHOR = {E.D. Sontag}, BOOKTITLE = {Proc. IEEE Conf. Decision and Control, New Orleans, Dec. 1995, IEEE Publications, 1995}, TITLE = {An abstract approach to dissipation}, YEAR = {1995}, OPTADDRESS = {}, OPTCROSSREF = {}, OPTEDITOR = {}, OPTMONTH = {}, NOTE = {Full version, never submitted, is here: http://www.math.rutgers.edu/(tilde)sontag/FTPDIR/dissipation.pdf}, OPTNUMBER = {}, OPTORGANIZATION = {}, PAGES = {2702--2703}, OPTPUBLISHER = {}, OPTSERIES = {}, OPTVOLUME = {}, PDF = {../FTP_DIR/95cdc-diss.pdf}, ABSTRACT = { We suggest that a very natural mathematical framework for the study of dissipation -in the sense of Willems, Moylan and Hill, and others- is that of indefinite quasimetric spaces. Several basic facts about dissipative systems are seen to be simple consequences of the properties of such spaces. Quasimetric spaces provide also one natural context for optimal control problems, and even for "gap" formulations of robustness. } } @INPROCEEDINGS{95icnn, AUTHOR = {E.D. Sontag}, BOOKTITLE = {Proc. 1995 IEEE Internat. Conf. Neural Networks, IEEE Publications, 1995}, TITLE = {Critical points for neural net least-squares problems}, YEAR = {1995}, OPTADDRESS = {}, OPTCROSSREF = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, OPTORGANIZATION = {}, PAGES = {2949--2954}, OPTPUBLISHER = {}, OPTSERIES = {}, OPTVOLUME = {}, KEYWORDS = {neural networks} } @INPROCEEDINGS{95cdc-complexity, AUTHOR = {E.D. Sontag}, BOOKTITLE = {Proc. IEEE Conf. Decision and Control, New Orleans, Dec. 1995, IEEE Publications, 1995}, TITLE = {From linear to nonlinear: some complexity comparisons}, YEAR = {1995}, OPTADDRESS = {}, OPTCROSSREF = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, OPTORGANIZATION = {}, PAGES = {2916--2920}, OPTPUBLISHER = {}, OPTSERIES = {}, OPTVOLUME = {}, KEYWORDS = {theory of computing and complexity, computational complexity, controllability, observability}, PDF = {../FTP_DIR/95cdc-complexity.pdf}, ABSTRACT = { This paper deals with the computational complexity, and in some cases undecidability, of several problems in nonlinear control. The objective is to compare the theoretical difficulty of solving such problems to the corresponding problems for linear systems. In particular, the problem of null-controllability for systems with saturations (of a "neural network" type) is mentioned, as well as problems regarding piecewise linear (hybrid) systems. A comparison of accessibility, which can be checked fairly simply by Lie-algebraic methods, and controllability, which is at least NP-hard for bilinear systems, is carried out. Finally, some remarks are given on analog computation in this context. } } @INPROCEEDINGS{icm94, AUTHOR = {E.D. Sontag}, BOOKTITLE = {Proceedings of the International Congress of Mathematicians, Vol. 1, 2 (Zürich, 1994)}, TITLE = {Spaces of observables in nonlinear control}, YEAR = {1995}, ADDRESS = {Basel}, OPTCROSSREF = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, OPTORGANIZATION = {}, PAGES = {1532--1545}, PUBLISHER = {Birkhäuser}, OPTSERIES = {}, OPTVOLUME = {}, KEYWORDS = {observability, dynamical systems}, PDF = {../FTP_DIR/icm.pdf}, ABSTRACT = { Invited talk at the 1994 ICM. Paper deals with the notion of observables for nonlinear systems, and their role in realization theory, minimality, and several control and path planning questions. } } @INPROCEEDINGS{95cdc-hs, AUTHOR = {E.D. Sontag and H.J. Sussmann}, BOOKTITLE = {Proc. IEEE Conf. Decision and Control, New Orleans, Dec. 1995, IEEE Publications, 1995}, TITLE = {Nonsmooth control-Lyapunov functions}, YEAR = {1995}, OPTADDRESS = {}, OPTCROSSREF = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, OPTORGANIZATION = {}, PAGES = {2799--2805}, OPTPUBLISHER = {}, OPTSERIES = {}, OPTVOLUME = {}, KEYWORDS = {control-Lyapunov functions}, PDF = {../FTP_DIR/95cdc-clf.pdf}, ABSTRACT = { It is shown that the existence of a continuous control-Lyapunov function (CLF) is necessary and sufficient for null asymptotic controllability of nonlinear finite-dimensional control systems. The CLF condition is expressed in terms of a concept of generalized derivative (upper contingent derivative). This result generalizes to the non-smooth case the theorem of Artstein relating closed-loop feedback stabilization to smooth CLF's. It relies on viability theory as well as optimal control techniques. A "non-strict" version of the results, analogous to the LaSalle Invariance Principle, is also provided. } } @INPROCEEDINGS{95nolcos, AUTHOR = {E.D. Sontag and Y. Wang}, BOOKTITLE = {Proceedings of IFAC Non-Linear Control Systems Design Symposium, (NOLCOS '95), Tahoe City, CA, June 1995}, TITLE = {On characterizations of input-to-state stability with respect to compact sets}, YEAR = {1995}, OPTADDRESS = {}, OPTCROSSREF = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, OPTORGANIZATION = {}, PAGES = {226--231}, OPTPUBLISHER = {}, OPTSERIES = {}, OPTVOLUME = {}, KEYWORDS = {input to state stability}, PDF = {../FTP_DIR/95nolcos.pdf}, ABSTRACT = { Previous characterizations of ISS-stability are shown to generalize without change to the case of stability with respect to sets. Some results on ISS-stabilizability are mentioned as well. } } @INPROCEEDINGS{95cdc-yw, AUTHOR = {E.D. Sontag and Y. Wang}, BOOKTITLE = {Proc. IEEE Conf. Decision and Control, New Orleans, Dec. 1995, IEEE Publications, 1995}, TITLE = {Various results concerning set input-to-state stability}, YEAR = {1995}, OPTADDRESS = {}, OPTCROSSREF = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, OPTORGANIZATION = {}, PAGES = {1330--1335}, OPTPUBLISHER = {}, OPTSERIES = {}, OPTVOLUME = {}, KEYWORDS = {input to state stability} } @INCOLLECTION{DasGupta-book, AUTHOR = {B. DasGupta and H.T. Siegelmann and E.D. Sontag}, BOOKTITLE = {Theoretical Advances in Neural Computation and Learning}, PUBLISHER = {Kluwer Academic Publishers}, TITLE = {On the Intractability of Loading Neural Networks}, YEAR = {1994}, OPTADDRESS = {}, OPTCHAPTER = {}, OPTCROSSREF = {}, OPTEDITION = {}, EDITOR = {V. P. Roychowdhury and Siu K. Y. and Orlitsky A.}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, PAGES = {357--389}, OPTSERIES = {}, OPTTYPE = {}, OPTVOLUME = {}, KEYWORDS = {neural networks} } @INCOLLECTION{maass-schnitger-book, AUTHOR = {W. Maass and G. Schnitger and E.D. Sontag}, BOOKTITLE = {Theoretical Advances in Neural Computation and Learning}, PUBLISHER = {Kluwer Academic Publishers}, TITLE = {A comparison of the computational power of sigmoid and Boolean threshold circuits}, YEAR = {1994}, OPTADDRESS = {}, OPTCHAPTER = {}, OPTCROSSREF = {}, OPTEDITION = {}, EDITOR = {V. P. Roychowdhury and Siu K. Y. and Orlitsky A.}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, PAGES = {127--151}, OPTSERIES = {}, OPTTYPE = {}, OPTVOLUME = {}, KEYWORDS = {neural networks, boolean systems, neural networks}, PDF = {../FTP_DIR/maass-schnitger-eds.pdf}, ABSTRACT = { We examine the power of constant depth circuits with sigmoid threshold gates for computing boolean functions. It is shown that, for depth 2, constant size circuits of this type are strictly more powerful than constant size boolean threshold circuits (i.e. circuits with linear threshold gates). On the other hand it turns out that, for any constant depth d, polynomial size sigmoid threshold circuits with polynomially bounded weights compute exactly the same boolean functions as the corresponding circuits with linear threshold gates. } } @ARTICLE{MR1298518, AUTHOR = {F. Albertini and E.D. Sontag}, JOURNAL = {Dynam. Control}, TITLE = {Further results on controllability properties of discrete-time nonlinear systems}, YEAR = {1994}, OPTMONTH = {}, OPTNOTE = {}, NUMBER = {3}, PAGES = {235--253}, VOLUME = {4}, ADDRESS = {Hingham, MA, USA}, KEYWORDS = {discrete-time, nonlinear control}, PUBLISHER = {Kluwer Academic Publishers}, PDF = {../FTP_DIR/dt-further-albertini.pdf}, ABSTRACT = { Controllability questions for discrete-time nonlinear systems are addressed in this paper. In particular, we continue the search for conditions under which the group-like notion of transitivity implies the stronger and semigroup-like property of forward accessibility. We show that this implication holds, pointwise, for states which have a weak Poisson stability property, and globally, if there exists a global "attractor" for the system. }, DOI = {http://dx.doi.org/10.1007/BF01985073} } @ARTICLE{MR1270887, AUTHOR = {F. Albertini and E.D. Sontag}, JOURNAL = {Systems Control Lett.}, TITLE = {State observability in recurrent neural networks}, YEAR = {1994}, OPTMONTH = {}, OPTNOTE = {}, NUMBER = {4}, PAGES = {235--244}, VOLUME = {22}, ADDRESS = {Amsterdam, The Netherlands, The Netherlands}, KEYWORDS = {neural networks, observability}, PUBLISHER = {Elsevier Science Publishers B. V.}, PDF = {../FTP_DIR/obs-sigma.pdf}, ABSTRACT = { This paper concerns recurrent networks x'=s(Ax+Bu), y=Cx, where s is a sigmoid, in both discrete time and continuous time. Our main result is that observability can be characterized, if one assumes certain conditions on the nonlinearity and on the system, in a manner very analogous to that of the linear case. Recall that for the latter, observability is equivalent to the requirement that there not be any nontrivial A-invariant subspace included in the kernel of C. We show that the result generalizes in a natural manner, except that one now needs to restrict attention to certain special "coordinate" subspaces. }, DOI = {http://dx.doi.org/10.1016/0167-6911(94)90054-X} } @ARTICLE{MR1276846, AUTHOR = {R. Koplon and E.D. Sontag and M. L. J. Hautus}, JOURNAL = {Linear Algebra Appl.}, TITLE = {Observability of linear systems with saturated outputs}, YEAR = {1994}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, PAGES = {909--936}, VOLUME = {205/206}, KEYWORDS = {observability, saturation}, PDF = {../FTP_DIR/outputsat.pdf}, ABSTRACT = { In this paper, we present necessary and sufficient conditions for observability of the class of output-saturated systems. These are linear systems whose output passes through a saturation function before it can be measured. } } @ARTICLE{MR1288945, AUTHOR = {H. T. Siegelmann and E.D. Sontag}, JOURNAL = {Theoret. Comput. Sci.}, TITLE = {Analog computation via neural networks}, YEAR = {1994}, OPTMONTH = {}, OPTNOTE = {}, NUMBER = {2}, PAGES = {331--360}, VOLUME = {131}, ADDRESS = {Essex, UK}, KEYWORDS = {neural networks, neural networks, computational complexity}, PUBLISHER = {Elsevier Science Publishers Ltd.}, PDF = {../FTP_DIR/nets-real.pdf}, ABSTRACT = { We consider recurrent networks with real-valued weights. If allowed exponential time for computation, they turn out to have unbounded power. However, under polynomial-time constraints there are limits on their capabilities, though being more powerful than Turing Machines. Moreover, there is a precise correspondence between nets and standard non-uniform circuits with equivalent resources, and as a consequence one has lower bound constraints on what they can compute. We note that these networks are not likely to solve polynomially NP-hard problems, as the equality "P=NP" in our model implies the almost complete collapse of the standard polynomial hierarchy. We show that a large class of different networks and dynamical system models have no more computational power than this neural (first-order) model with real weights. The results suggest the following Church-like Thesis of Time-bounded Analog Computing: "Any reasonable analog computer will have no more power (up to polynomial time) than first-order recurrent networks." }, DOI = {http://dx.doi.org/10.1016/0304-3975(94)90178-3} } @ARTICLE{MR1337566, AUTHOR = {H.J. Sussmann and E.D. Sontag and Y. Yang}, JOURNAL = {IEEE Trans. Automat. Control}, TITLE = {A general result on the stabilization of linear systems using bounded controls}, YEAR = {1994}, OPTMONTH = {}, OPTNOTE = {}, NUMBER = {12}, PAGES = {2411--2425}, VOLUME = {39}, KEYWORDS = {saturation}, PDF = {../FTP_DIR/saturated-stab.pdf}, ABSTRACT = { We present two constructions of controllers that globally stabilize linear systems subject to control saturation. We allow essentially arbitrary saturation functions. The only conditions imposed on the system are the obvious necessary ones, namely that no eigenvalues of the uncontrolled system have positive real part and that the standard stabilizability rank condition hold. One of the constructions is in terms of a "neural-network type" one-hidden layer architecture, while the other one is in terms of cascades of linear maps and saturations. } } @INPROCEEDINGS{94cdc-saturated, AUTHOR = {Y. Chitour and W. Liu and E.D. Sontag}, BOOKTITLE = {Proc. IEEE Conf. Decision and Control, Orlando, Dec. 1994, IEEE Publications, 1994}, TITLE = {On the continuity and incremental gain properties of certain saturated linear feedback loops}, YEAR = {1994}, OPTADDRESS = {}, OPTCROSSREF = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, OPTORGANIZATION = {}, PAGES = {127--132}, OPTPUBLISHER = {}, OPTSERIES = {}, OPTVOLUME = {} } @INPROCEEDINGS{181009, AUTHOR = {B. DasGupta and H. T. Siegelmann and E.D. Sontag}, BOOKTITLE = {COLT '94: Proceedings of the seventh annual conference on Computational learning theory}, TITLE = {On a learnability question associated to neural networks with continuous activations (extended abstract)}, YEAR = {1994}, ADDRESS = {New York, NY, USA}, OPTCROSSREF = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, OPTORGANIZATION = {}, PAGES = {47--56}, PUBLISHER = {ACM Press}, OPTSERIES = {}, OPTVOLUME = {}, KEYWORDS = {neural networks}, DOI = {http://doi.acm.org/10.1145/180139.181009} } @INPROCEEDINGS{94cdc-renee, AUTHOR = {R. Koplon and E.D. Sontag}, BOOKTITLE = {Proc. IEEE Conf. Decision and Control, Orlando, Dec. 1994, IEEE Publications, 1994}, TITLE = {Techniques for parameter reconstruction in Fourier-Neural recurrent networks}, YEAR = {1994}, OPTADDRESS = {}, OPTCROSSREF = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, OPTORGANIZATION = {}, PAGES = {213--218}, OPTPUBLISHER = {}, OPTSERIES = {}, OPTVOLUME = {}, KEYWORDS = {neural networks} } @INPROCEEDINGS{94cdc-clf, AUTHOR = {Y. Lin and E.D. Sontag}, BOOKTITLE = {Proc. IEEE Conf. Decision and Control, Orlando, Dec. 1994, IEEE Publications, 1994}, TITLE = {On control-Lyapunov functions under input constraints}, YEAR = {1994}, OPTADDRESS = {}, OPTCROSSREF = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, OPTORGANIZATION = {}, PAGES = {640--645}, OPTPUBLISHER = {}, OPTSERIES = {}, OPTVOLUME = {}, KEYWORDS = {control-Lyapunov functions} } @INPROCEEDINGS{94acc, AUTHOR = {Y. Lin and E.D. Sontag and Y. Wang}, BOOKTITLE = {Proc. Amer. Automatic Control Conf., Baltimore, June 1994}, TITLE = {Recent results on Lyapunov-theoretic techniques for nonlinear stability}, YEAR = {1994}, OPTADDRESS = {}, OPTCROSSREF = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, OPTORGANIZATION = {}, PAGES = {1771--1775}, OPTPUBLISHER = {}, OPTSERIES = {}, OPTVOLUME = {} } @INPROCEEDINGS{94cdc-iss, AUTHOR = {E.D. Sontag and Y. Wang}, BOOKTITLE = {Proc. IEEE Conf. Decision and Control, Orlando, Dec. 1994, IEEE Publications, 1994}, TITLE = {Notions equivalent to input-to-state stability}, YEAR = {1994}, OPTADDRESS = {}, OPTCROSSREF = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, OPTORGANIZATION = {}, PAGES = {3438--3443}, OPTPUBLISHER = {}, OPTSERIES = {}, OPTVOLUME = {}, KEYWORDS = {input to state stability} } @INPROCEEDINGS{94cdc-univ, AUTHOR = {E.D. Sontag and Y. Wang}, BOOKTITLE = {Proc. IEEE Conf. Decision and Control, Orlando, Dec. 1994, IEEE Publications, 1994}, TITLE = {Orders of I/O equations and uniformly universal inputs}, YEAR = {1994}, OPTADDRESS = {}, OPTCROSSREF = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, OPTORGANIZATION = {}, PAGES = {1270--1275}, OPTPUBLISHER = {}, OPTSERIES = {}, OPTVOLUME = {} } @INCOLLECTION{92caip, AUTHOR = {F. Albertini and E.D. Sontag and V. Maillot}, BOOKTITLE = {Artificial Neural Networks for Speech and Vision}, PUBLISHER = {Chapman and Hall, London}, TITLE = {Uniqueness of weights for neural networks}, YEAR = {1993}, OPTADDRESS = {}, OPTCHAPTER = {}, OPTCROSSREF = {}, OPTEDITION = {}, EDITOR = {R. Mammone}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, PAGES = {115--125}, OPTSERIES = {}, OPTTYPE = {}, OPTVOLUME = {}, KEYWORDS = {neural networks}, PDF = {../FTP_DIR/92caip.pdf}, ABSTRACT = { In this short expository survey, we sketch various known facts about uniqueness of weights in neural networks, including results about recurrent nets, and we provide a new and elementary complex-variable proof of a uniqueness result that applies in the single hidden layer case. } } @INCOLLECTION{MR1247275, AUTHOR = {E.D. Sontag}, BOOKTITLE = {Essays on control: perspectives in the theory and its applications (Groningen, 1993)}, PUBLISHER = {Birkhäuser Boston}, TITLE = {Neural networks for control}, YEAR = {1993}, ADDRESS = {Boston, MA}, OPTCHAPTER = {}, OPTCROSSREF = {}, OPTEDITION = {}, EDITOR = {H. L. Trentelman and J. C. Willems}, OPTMONTH = {}, NOTE = {A longer version (tech report with more details) is here: http://www.math.rutgers.edu/(tilde)sontag/FTPDIR/neural-nets-siemens.pdf}, OPTNUMBER = {}, PAGES = {339--380}, SERIES = {Progr. Systems Control Theory}, OPTTYPE = {}, VOLUME = {14}, KEYWORDS = {neural networks, neural networks}, PDF = {../FTP_DIR/93ecc-nn.pdf}, ABSTRACT = { This paper has an expository introduction to two related topics: (a) Some mathematical results regarding "neural networks", and (b) so-called "neurocontrol" and "learning control" (each part can be read independently of the other). It was prepared for a short course given at the 1993 European Control Conference. } } @INCOLLECTION{robot86reprint, AUTHOR = {E.D. Sontag and H.J. Sussmann}, BOOKTITLE = {Robot Control}, PUBLISHER = {IEEE Press, New York}, TITLE = {Time-optimal control of manipulators (reprint of 1986 IEEE Int Conf on Robotics and Automation paper}, YEAR = {1993}, OPTADDRESS = {}, OPTCHAPTER = {}, OPTCROSSREF = {}, OPTEDITION = {}, EDITOR = {M.W. Spong and F.L. Lewis and C.T. Abdallah}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, PAGES = {266--271}, OPTSERIES = {}, OPTTYPE = {}, OPTVOLUME = {} } @ARTICLE{MR1242218, AUTHOR = {F. Albertini and E.D. Sontag}, JOURNAL = {SIAM J. Control Optim.}, TITLE = {Discrete-time transitivity and accessibility: analytic systems}, YEAR = {1993}, OPTMONTH = {}, OPTNOTE = {}, NUMBER = {6}, PAGES = {1599--1622}, VOLUME = {31}, ADDRESS = {Philadelphia, PA, USA}, PUBLISHER = {Society for Industrial and Applied Mathematics}, PDF = {../FTP_DIR/dt-analytic-albertini.pdf}, ABSTRACT = { A basic open question for discrete-time nonlinear systems is that of determining when, in analogy with the classical continuous-time "positive form of Chow's Lemma", accessibility follows from transitivity of a natural group action. This paper studies the problem, and establishes the desired implication for analytic systems in several cases: (i) compact state space, (ii) under a Poisson stability condition, and (iii) in a generic sense. In addition, the paper studies accessibility properties of the "control sets" recently introduced in the context of dynamical systems studies. Finally, various examples and counterexamples are provided relating the various Lie algebras introduced in past work. }, DOI = {http://dx.doi.org/10.1137/0331075} } @ARTICLE{165043, AUTHOR = {F. Albertini and E.D. Sontag}, JOURNAL = {Neural Netw.}, TITLE = {For neural networks, function determines form}, YEAR = {1993}, OPTMONTH = {}, OPTNOTE = {}, NUMBER = {7}, PAGES = {975--990}, VOLUME = {6}, ADDRESS = {Oxford, UK, UK}, KEYWORDS = {neural networks, realization theory, observability, neural networks}, PUBLISHER = {Elsevier Science Ltd.}, PDF = {../FTP_DIR/net-ident.pdf}, ABSTRACT = { This paper shows that the weights of continuous-time feedback neural networks x'=s(Ax+Bu), y=Cx (where s is a sigmoid) are uniquely identifiable from input/output measurements. Under very weak genericity assumptions, the following is true: Assume given two nets, whose neurons all have the same nonlinear activation function s; if the two nets have equal behaviors as "black boxes" then necessarily they must have the same number of neurons and -except at most for sign reversals at each node- the same weights. Moreover, even if the activations are not a priori known to coincide, they are shown to be also essentially determined from the external measurements. } } @ARTICLE{MR1234002, AUTHOR = {R. Koplon and E.D. Sontag}, JOURNAL = {SIAM J. Control Optim.}, TITLE = {Linear systems with sign-observations}, YEAR = {1993}, OPTMONTH = {}, OPTNOTE = {}, NUMBER = {5}, PAGES = {1245--1266}, VOLUME = {31}, ADDRESS = {Philadelphia, PA, USA}, KEYWORDS = {observability}, PUBLISHER = {Society for Industrial and Applied Mathematics}, PDF = {../FTP_DIR/signlinear.pdf}, ABSTRACT = { This paper deals with systems that are obtained from linear time-invariant continuous- or discrete-time devices followed by a function that just provides the sign of each output. Such systems appear naturally in the study of quantized observations as well as in signal processing and neural network theory. Results are given on observability, minimal realizations, and other system-theoretic concepts. Certain major differences exist with the linear case, and other results generalize in a surprisingly straightforward manner. }, DOI = {http://dx.doi.org/10.1137/0331059} } @ARTICLE{MR1198475, AUTHOR = {E.D. Sontag}, JOURNAL = {Systems Control Lett.}, TITLE = {Errata: ``Universal nonsingular controls'' [Systems Control Lett. 19 (1992), no. 3, 221--224; MR1180510 (93f:93024)]}, YEAR = {1993}, OPTMONTH = {}, OPTNOTE = {}, NUMBER = {1}, PAGES = {77}, VOLUME = {20}, PDF = {../FTP_DIR/univctr-errata.pdf}, ABSTRACT = { Errata for Universal nonsingular controls } } @INPROCEEDINGS{fa-93mtns1, AUTHOR = {F. Albertini and E.D. Sontag}, BOOKTITLE = {Systems and Networks: Mathematical Theory and Applications, Proc. MTNS '93, Vol. 2, Akad. Verlag, Regensburg}, TITLE = {Controllability of discrete-time nonlinear systems}, YEAR = {1993}, OPTADDRESS = {}, OPTCROSSREF = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, OPTORGANIZATION = {}, PAGES = {35--38}, OPTPUBLISHER = {}, OPTSERIES = {}, OPTVOLUME = {} } @INPROCEEDINGS{fa-93ecc, AUTHOR = {F. Albertini and E.D. Sontag}, BOOKTITLE = {Proc. European Control Conf., Groningen, June 1993}, TITLE = {Identifiability of discrete-time neural networks}, YEAR = {1993}, OPTADDRESS = {}, OPTCROSSREF = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, OPTORGANIZATION = {}, PAGES = {460--465}, OPTPUBLISHER = {}, OPTSERIES = {}, OPTVOLUME = {}, KEYWORDS = {neural networks} } @INPROCEEDINGS{93cdc-obs-sigma, AUTHOR = {F. Albertini and E.D. Sontag}, BOOKTITLE = {Proc. IEEE Conf. Decision and Control, San Antonio, Dec. 1993, IEEE Publications, 1993}, TITLE = {State observability in recurrent neural networks}, YEAR = {1993}, OPTADDRESS = {}, OPTCROSSREF = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, OPTORGANIZATION = {}, PAGES = {3706--3707}, OPTPUBLISHER = {}, OPTSERIES = {}, OPTVOLUME = {}, KEYWORDS = {neural networks, observability} } @INPROCEEDINGS{fa-93mtns2, AUTHOR = {F. Albertini and E.D. Sontag}, BOOKTITLE = {Systems and Networks: Mathematical Theory and Applications, Proc. MTNS '93, Vol. 2, Akad. Verlag, Regensburg}, TITLE = {Uniqueness of weights for recurrent nets}, YEAR = {1993}, OPTADDRESS = {}, OPTCROSSREF = {}, OPTEDITOR = {}, OPTMONTH = {}, NOTE = {Full version, never submitted for publication, is here: http://www.math.rutgers.edu/(tilde)sontag/FTPDIR/93mtns-nn-extended.pdf}, OPTNUMBER = {}, OPTORGANIZATION = {}, PAGES = {599--602}, OPTPUBLISHER = {}, OPTSERIES = {}, OPTVOLUME = {}, KEYWORDS = {neural networks}, PDF = {../FTP_DIR/93mtns-nn.pdf}, ABSTRACT = { This paper concerns recurrent networks x'=s(Ax+Bu), y=Cx, where s is a sigmoid, in both discrete time and continuous time. The paper establishes parameter identifiability under stronger assumptions on the activation than in "For neural networks, function determines form", but on the other hand deals with arbitrary (nonzero) initial states. } } @INPROCEEDINGS{MR1310805, AUTHOR = {J. L. Balcázar and R. Gavaldà and H. T. Siegelmann and E.D. Sontag}, BOOKTITLE = {Proceedings of the Eighth Annual Structure in Complexity Theory Conference (San Diego, CA, 1993)}, TITLE = {Some structural complexity aspects of neural computation}, YEAR = {1993}, ADDRESS = {Los Alamitos, CA}, OPTCROSSREF = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, OPTORGANIZATION = {}, PAGES = {253--265}, PUBLISHER = {IEEE Comput. Soc. Press}, OPTSERIES = {}, OPTVOLUME = {}, KEYWORDS = {neural networks, theory of computing and complexity} } @INPROCEEDINGS{168357, AUTHOR = {C. Darken and M.J. Donahue and L. Gurvits and E.D. Sontag}, BOOKTITLE = {COLT '93: Proceedings of the sixth annual conference on Computational learning theory}, TITLE = {Rate of approximation results motivated by robust neural network learning}, YEAR = {1993}, ADDRESS = {New York, NY, USA}, OPTCROSSREF = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, OPTORGANIZATION = {}, PAGES = {303--309}, PUBLISHER = {ACM Press}, OPTSERIES = {}, OPTVOLUME = {}, KEYWORDS = {neural networks, optimization problems, approximation theory}, DOI = {http://doi.acm.org/10.1145/168304.168357} } @INPROCEEDINGS{93cdc-renee, AUTHOR = {R. Koplon and E.D. Sontag}, BOOKTITLE = {Proc. IEEE Conf. Decision and Control, San Antonio, Dec. 1993, IEEE Publications, 1993}, TITLE = {Sign-linear systems as cascades of automata and continuous variable systems}, YEAR = {1993}, OPTADDRESS = {}, OPTCROSSREF = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, OPTORGANIZATION = {}, PAGES = {2290--2291}, OPTPUBLISHER = {}, OPTSERIES = {}, OPTVOLUME = {} } @INPROCEEDINGS{93cdc-gerardo, AUTHOR = {G.A. Lafferriere and E.D. Sontag}, BOOKTITLE = {Proc. IEEE Conf. Decision and Control, San Antonio, Dec. 1993, IEEE Publications, 1993}, TITLE = {Remarks on control Lyapunov functions for discontinuous stabilizing feedback}, YEAR = {1993}, OPTADDRESS = {}, OPTCROSSREF = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, OPTORGANIZATION = {}, PAGES = {306--308}, OPTPUBLISHER = {}, OPTSERIES = {}, OPTVOLUME = {}, KEYWORDS = {feedback stabilization}, PDF = {../FTP_DIR/93cdc-clf.pdf}, ABSTRACT = { We present a formula for a stabilizing feedback law under the assumption that a piecewise smooth control-Lyapunov function exists. The resulting feedback is continuous at the origin and smooth everywhere except on a hypersurface of codimension 1, assuming that certain transversality conditions are imposed there. } } @INPROCEEDINGS{93cdc-yuandan, AUTHOR = {Y. Lin and E.D. Sontag and Y. Wang}, BOOKTITLE = {Proc. IEEE Conf. Decision and Control, San Antonio, Dec. 1993, IEEE Publications, 1993}, TITLE = {Lyapunov-function characterizations of stability and stabilization for parameterized families of systems}, YEAR = {1993}, OPTADDRESS = {}, OPTCROSSREF = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, OPTORGANIZATION = {}, PAGES = {1978--1983}, OPTPUBLISHER = {}, OPTSERIES = {}, OPTVOLUME = {} } @INPROCEEDINGS{93cdc-liu, AUTHOR = {W. Liu and Y. Chitour and E.D. Sontag}, BOOKTITLE = {Proc. IEEE Conf. Decision and Control, San Antonio, Dec. 1993, IEEE Publications, 1993}, TITLE = {Remarks on finite gain stabilizability of linear systems subject to input saturation,}, YEAR = {1993}, OPTADDRESS = {}, OPTCROSSREF = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, OPTORGANIZATION = {}, PAGES = {1808--1813}, OPTPUBLISHER = {}, OPTSERIES = {}, OPTVOLUME = {} } @INPROCEEDINGS{167192, AUTHOR = {A. Macintyre and E.D. Sontag}, BOOKTITLE = {STOC '93: Proceedings of the twenty-fifth annual ACM symposium on Theory of computing}, TITLE = {Finiteness results for sigmoidal neural networks}, YEAR = {1993}, ADDRESS = {New York, NY, USA}, OPTCROSSREF = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, OPTORGANIZATION = {}, PAGES = {325--334}, PUBLISHER = {ACM Press}, OPTSERIES = {}, OPTVOLUME = {}, KEYWORDS = {neural networks, theory of computing and complexity}, PDF = {../FTP_DIR/ajm.pdf}, ABSTRACT = { This paper deals with analog circuits. It establishes the finiteness of VC dimension, teaching dimension, and several other measures of sample complexity which arise in learning theory. It also shows that the equivalence of behaviors, and the loading problem, are effectively decidable, modulo a widely believed conjecture in number theory. The results, the first ones that are independent of weight size, apply when the gate function is the "standard sigmoid" commonly used in neural networks research. The proofs rely on very recent developments in the elementary theory of real numbers with exponentiation. (Some weaker conclusions are also given for more general analytic gate functions.) Applications to learnability of sparse polynomials are also mentioned. }, DOI = {http://doi.acm.org/10.1145/167088.167192} } @INPROCEEDINGS{93israel-hava, AUTHOR = {H.T. Siegelmann and E.D. Sontag}, BOOKTITLE = {Proc. 2nd Israel Symposium on Theory of Computing and Systems (ISTCS93), IEEE Computer Society Press, 1993}, TITLE = {Analog computation via neural networks}, YEAR = {1993}, OPTADDRESS = {}, OPTCROSSREF = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, OPTORGANIZATION = {}, OPTPAGES = {}, OPTPUBLISHER = {}, OPTSERIES = {}, OPTVOLUME = {}, KEYWORDS = {neural networks} } @INPROCEEDINGS{93cdc-pathplanning, AUTHOR = {E.D. Sontag}, BOOKTITLE = {Proc. IEEE Conf. Decision and Control, San Antonio, Dec. 1993, IEEE Publications, 1993}, TITLE = {Numerical path planning based on nonsingular controls}, YEAR = {1993}, OPTADDRESS = {}, OPTCROSSREF = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, OPTORGANIZATION = {}, PAGES = {2706--2711}, OPTPUBLISHER = {}, OPTSERIES = {}, OPTVOLUME = {} } @INPROCEEDINGS{93cdc-sus-yang, AUTHOR = {H.J. Sussmann and E.D. Sontag and Y. Yang}, BOOKTITLE = {Proc. IEEE Conf. Decision and Control, San Antonio, Dec. 1993, IEEE Publications, 1993}, TITLE = {A general result on the stabilization of linear systems using bounded controls}, YEAR = {1993}, OPTADDRESS = {}, OPTCROSSREF = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, OPTORGANIZATION = {}, PAGES = {1802--1807}, OPTPUBLISHER = {}, OPTSERIES = {}, OPTVOLUME = {}, KEYWORDS = {saturation} } @INPROCEEDINGS{f8-conf, AUTHOR = {Y. Yang and E.D. Sontag}, BOOKTITLE = {Proc. 1993 IEEE Conf. on Aerospace Control Systems, Thousand Oaks, CA, May 1993}, TITLE = {Stabilization with saturated actuators, a worked example: F-8 longitudinal flight control}, YEAR = {1993}, OPTADDRESS = {}, OPTCROSSREF = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, OPTORGANIZATION = {}, PAGES = {289--293}, OPTPUBLISHER = {}, OPTSERIES = {}, OPTVOLUME = {}, KEYWORDS = {saturation}, PDF = {../FTP_DIR/f8.pdf}, ABSTRACT = { This paper develops in detail an explicit design for control under saturation limits for the linearized equations of longitudinal flight control for an F-8 aircraft, and tests the obtained controller on the original nonlinear model. } } @ARTICLE{two-layer, AUTHOR = {E.D. Sontag}, JOURNAL = {IEEE Trans. Neural Networks}, TITLE = {Feedback stabilization using two-hidden-layer nets}, YEAR = {1992}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, PAGES = {981--990}, VOLUME = {3}, KEYWORDS = {neural networks, feedback stabilization, neural networks}, PDF = {../FTP_DIR/two-layer.pdf}, ABSTRACT = { This paper compares the representational capabilities of one hidden layer and two hidden layer nets consisting of feedforward interconnections of linear threshold units. It is remarked that for certain problems two hidden layers are required, contrary to what might be in principle expected from the known approximation theorems. The differences are not based on numerical accuracy or number of units needed, nor on capabilities for feature extraction, but rather on a much more basic classification into "direct" and "inverse" problems. The former correspond to the approximation of continuous functions, while the latter are concerned with approximating one-sided inverses of continuous functions - and are often encountered in the context of inverse kinematics determination or in control questions. A general result is given showing that nonlinear control systems can be stabilized using two hidden layers, but not in general using just one. } } @ARTICLE{MR1170916, AUTHOR = {E.D. Sontag}, JOURNAL = {J. Comput. System Sci.}, TITLE = {Feedforward nets for interpolation and classification}, YEAR = {1992}, OPTMONTH = {}, OPTNOTE = {}, NUMBER = {1}, PAGES = {20--48}, VOLUME = {45}, ADDRESS = {Orlando, FL, USA}, KEYWORDS = {neural networks, VC dimension, boolean systems}, PUBLISHER = {Academic Press, Inc.}, PDF = {../FTP_DIR/jcss-sigmoids.pdf}, ABSTRACT = { This paper deals with single-hidden-layer feedforward nets, studying various aspects of classification power and interpolation capability. In particular, a worst-case analysis shows that direct input to output connections in threshold nets double the recognition but not the interpolation power, while using sigmoids rather than thresholds allows doubling both. For other measures of classification, including the Vapnik-Chervonenkis dimension, the effect of direct connections or sigmoidal activations is studied in the special case of two-dimensional inputs. }, DOI = {http://dx.doi.org/10.1016/0022-0000(92)90039-L} } @ARTICLE{MR1180510, AUTHOR = {E.D. Sontag}, JOURNAL = {Systems Control Lett.}, TITLE = {Universal nonsingular controls}, YEAR = {1992}, OPTMONTH = {}, OPTNOTE = {}, NUMBER = {3}, PAGES = {221--224}, VOLUME = {19}, ADDRESS = {Amsterdam, The Netherlands, The Netherlands}, KEYWORDS = {controllability}, PUBLISHER = {Elsevier Science Publishers B. V.}, PDF = {../FTP_DIR/univctr.pdf}, ABSTRACT = { For analytic systems satisfying the strong accessibility rank condition, generic inputs produce trajectories along which the linearized system is controllable. Applications to the steering of systems without drift are briefly mentioned. }, DOI = {http://dx.doi.org/10.1016/0167-6911(92)90116-A} } @ARTICLE{MR1178655, AUTHOR = {Y. Wang and E.D. Sontag}, JOURNAL = {SIAM J. Control Optim.}, TITLE = {Algebraic differential equations and rational control systems}, YEAR = {1992}, OPTMONTH = {}, OPTNOTE = {}, NUMBER = {5}, PAGES = {1126--1149}, VOLUME = {30}, KEYWORDS = {input/output system representations, realization theory}, PDF = {../FTP_DIR/yw-siam-rational.pdf}, ABSTRACT = { It is shown that realizability of an input/output operators by a finite-dimensional continuous-time rational control system is equivalent to the existence of a high-order algebraic differential equation satisfied by the corresponding input/output pairs ("behavior"). This generalizes, to nonlinear systems, the classical equivalence between autoregressive representations and finite dimensional linear realizability. } } @ARTICLE{MR1164098, AUTHOR = {Y. Wang and E.D. Sontag}, JOURNAL = {Forum Math.}, TITLE = {Generating series and nonlinear systems: analytic aspects, local realizability, and i/o representations}, YEAR = {1992}, OPTMONTH = {}, OPTNOTE = {}, NUMBER = {3}, PAGES = {299--322}, VOLUME = {4}, KEYWORDS = {input/output system representations, realization theory}, PDF = {../FTP_DIR/yw2.pdf}, ABSTRACT = { This paper studies fundamental analytic properties of generating series for nonlinear control systems, and of the operators they define. It then applies the results obtained to the extension of facts, which relate realizability and algebraic input/output equations, to local realizability and analytic equations. } } @INPROCEEDINGS{92cdc-fa, AUTHOR = {F. Albertini and E.D. Sontag}, BOOKTITLE = {Proc. IEEE Conf. Decision and Control, Tucson, Dec. 1992, IEEE Publications, 1992}, TITLE = {For neural networks, function determines form}, YEAR = {1992}, OPTADDRESS = {}, OPTCROSSREF = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, OPTORGANIZATION = {}, PAGES = {26--31}, OPTPUBLISHER = {}, OPTSERIES = {}, OPTVOLUME = {}, KEYWORDS = {neural networks} } @INPROCEEDINGS{dahleh-92acc, AUTHOR = {M.A. Dahleh and E.D. Sontag and D.N.C. Tse and J.N. Tsitsiklis}, BOOKTITLE = {Proc. Amer. Automatic Control Conf., Chicago, June 1992}, TITLE = {Worst-case identification of nonlinear fading memory systems}, YEAR = {1992}, OPTADDRESS = {}, OPTCROSSREF = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, OPTORGANIZATION = {}, PAGES = {241--245}, OPTPUBLISHER = {}, OPTSERIES = {}, OPTVOLUME = {} } @INPROCEEDINGS{92ciss, AUTHOR = {Y. Lin and E.D. Sontag}, BOOKTITLE = {Proc. Conf. Inform. Sci. and Systems, Princeton University, March 1992}, TITLE = {Gradient techniques for steering systems with no drift}, YEAR = {1992}, OPTADDRESS = {}, OPTCROSSREF = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, OPTORGANIZATION = {}, PAGES = {1003--1008}, OPTPUBLISHER = {}, OPTSERIES = {}, OPTVOLUME = {} } @INPROCEEDINGS{92acc, AUTHOR = {R. Schwarzschild and E.D. Sontag and M.L.J. Hautus}, BOOKTITLE = {Proc. Amer. Automatic Control Conf. , Chicago, June 1992}, TITLE = {Output-Saturated Systems}, YEAR = {1992}, OPTADDRESS = {}, OPTCROSSREF = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, OPTORGANIZATION = {}, PAGES = {2504--2509}, OPTPUBLISHER = {}, OPTSERIES = {}, OPTVOLUME = {} } @INPROCEEDINGS{130432, AUTHOR = {H.T. Siegelmann and E.D. Sontag}, BOOKTITLE = {COLT '92: Proceedings of the fifth annual workshop on Computational learning theory}, TITLE = {On the computational power of neural nets}, YEAR = {1992}, ADDRESS = {New York, NY, USA}, OPTCROSSREF = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, OPTORGANIZATION = {}, PAGES = {440--449}, PUBLISHER = {ACM Press}, OPTSERIES = {}, OPTVOLUME = {}, KEYWORDS = {neural networks}, DOI = {http://doi.acm.org/10.1145/130385.130432} } @INPROCEEDINGS{92cdc-wong, AUTHOR = {H.T. Siegelmann and E.D. Sontag}, BOOKTITLE = {Proc. IEEE Conf. Decision and Control, Tucson, Dec. 1992, IEEE Publications, 1992}, TITLE = {Some results on computing with neural nets}, YEAR = {1992}, OPTADDRESS = {}, OPTCROSSREF = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, OPTORGANIZATION = {}, PAGES = {1476--1481}, OPTPUBLISHER = {}, OPTSERIES = {}, OPTVOLUME = {}, KEYWORDS = {neural networks} } @INPROCEEDINGS{659746, AUTHOR = {H.T. Siegelmann and E.D. Sontag and C.L. Giles}, BOOKTITLE = {Proceedings of the IFIP 12th World Computer Congress on Algorithms, Software, Architecture - Information Processing '92, Volume 1}, TITLE = {The Complexity of Language Recognition by Neural Networks}, YEAR = {1992}, OPTADDRESS = {}, OPTCROSSREF = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, OPTORGANIZATION = {}, PAGES = {329--335}, PUBLISHER = {North-Holland}, OPTSERIES = {}, OPTVOLUME = {}, KEYWORDS = {neural networks, theory of computing and complexity} } @INPROCEEDINGS{92yale, AUTHOR = {E.D. Sontag}, BOOKTITLE = {Proc. Seventh Yale Workshop on Adaptive and Learning Systems, Yale University, 1992}, TITLE = {Neural nets as systems models and controllers}, YEAR = {1992}, OPTADDRESS = {}, OPTCROSSREF = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, OPTORGANIZATION = {}, PAGES = {73--79}, OPTPUBLISHER = {}, OPTSERIES = {}, OPTVOLUME = {}, KEYWORDS = {neural networks, neural networks}, PDF = {../FTP_DIR/yale.pdf}, ABSTRACT = { A conference paper. Placed here because it was requested, but contains little that is not also contained in the survey on neural nets mentioned above. } } @INPROCEEDINGS{92nolcos-es, AUTHOR = {E.D. Sontag}, BOOKTITLE = {Nonlinear Control Systems Design 1992, IFAC Symposia Series, 1993, M. Fliess Ed., Pergamon Press, Oxford, 1993}, TITLE = {Systems combining linearity and saturations, and relations to neural nets}, YEAR = {1992}, OPTADDRESS = {}, OPTCROSSREF = {}, OPTEDITOR = {}, OPTMONTH = {}, NOTE = {(Also in Proc. Nonlinear Control Systems Design Symp., Bordeaux, June 1992, M. Fliess, Ed., IFAC Publications, pp. 242-247)}, OPTNUMBER = {}, OPTORGANIZATION = {}, PAGES = {15--21}, OPTPUBLISHER = {}, OPTSERIES = {}, OPTVOLUME = {}, KEYWORDS = {neural networks} } @INPROCEEDINGS{92nolcos-yuandan, AUTHOR = {E.D. Sontag and Y. Lin}, BOOKTITLE = {Nonlinear Control Systems Design 1992, IFAC Symposia Series, M. Fliess Ed., Pergamon Press, Oxford, 1993}, TITLE = {Stabilization with respect to noncompact sets: Lyapunov characterizations and effect of bounded inputs}, YEAR = {1992}, OPTADDRESS = {}, OPTCROSSREF = {}, OPTEDITOR = {}, OPTMONTH = {}, NOTE = {Also in Proc. Nonlinear Control Systems Design Symp., Bordeaux, June 1992,(M. Fliess, Ed.), IFAC Publications, pp. 9--14}, OPTNUMBER = {}, OPTORGANIZATION = {}, PAGES = {43--49}, OPTPUBLISHER = {}, OPTSERIES = {}, OPTVOLUME = {}, KEYWORDS = {saturation} } @INPROCEEDINGS{92cdc-yw, AUTHOR = {E.D. Sontag and Y. Wang}, BOOKTITLE = {Proc. IEEE Conf. Decision and Control, Tucson, Dec. 1992, IEEE Publications, 1992}, TITLE = {I/O equations in discrete and continuous time}, YEAR = {1992}, OPTADDRESS = {}, OPTCROSSREF = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, OPTORGANIZATION = {}, PAGES = {3661--3662}, OPTPUBLISHER = {}, OPTSERIES = {}, OPTVOLUME = {} } @INPROCEEDINGS{92nolcos-yss, AUTHOR = {Y. Yang and H.J. Sussmann and E.D. Sontag}, BOOKTITLE = {Nonlinear Control Systems Design 1992, IFAC Symposia Series, 1993, M. Fliess Ed., Pergamon Press, Oxford, 1993}, TITLE = {Stabilization of linear systems with bounded controls}, YEAR = {1992}, OPTADDRESS = {}, OPTCROSSREF = {}, OPTEDITOR = {}, OPTMONTH = {}, NOTE = {Also in Proc. Nonlinear Control Systems Design Symp., Bordeaux, June 1992,(M. Fliess, Ed.), IFAC Publications, pp. 15-20.}, OPTNUMBER = {}, OPTORGANIZATION = {}, PAGES = {51--56}, OPTPUBLISHER = {}, OPTSERIES = {}, OPTVOLUME = {}, KEYWORDS = {saturation} } @INCOLLECTION{MR1131981, AUTHOR = {F. Albertini and E.D. Sontag}, BOOKTITLE = {Analysis of controlled dynamical systems (Lyon, 1990)}, PUBLISHER = {Birkhäuser Boston}, TITLE = {Transitivity and forward accessibility of discrete-time nonlinear systems}, YEAR = {1991}, ADDRESS = {Boston, MA}, OPTCHAPTER = {}, OPTCROSSREF = {}, OPTEDITION = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, PAGES = {21--34}, SERIES = {Progr. Systems Control Theory}, OPTTYPE = {}, VOLUME = {8} } @INCOLLECTION{MR1114761, AUTHOR = {E.D. Sontag}, BOOKTITLE = {Neural networks (New Brunswick, NJ, 1990)}, PUBLISHER = {Academic Press}, TITLE = {Capabilities and training of feedforward nets}, YEAR = {1991}, ADDRESS = {Boston, MA}, OPTCHAPTER = {}, OPTCROSSREF = {}, OPTEDITION = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, PAGES = {303--321}, OPTSERIES = {}, OPTTYPE = {}, OPTVOLUME = {}, KEYWORDS = {neural networks, neural networks}, PDF = {../FTP_DIR/90caip.pdf}, ABSTRACT = { This paper surveys recent work by the author on learning and representational capabilities of feedforward nets. The learning results show that, among two possible variants of the so-called backpropagation training method for sigmoidal nets, both of which variants are used in practice, one is a better generalization of the older perceptron training algorithm than the other. The representation results show that nets consisting of sigmoidal neurons have at least twice the representational capabilities of nets that use classical threshold neurons, at least when this increase is quantified in terms of classification power. On the other hand, threshold nets are shown to be more useful when approximating implicit functions, as illustrated with an application to a typical control problem. } } @INCOLLECTION{MR1125161, AUTHOR = {E.D. Sontag}, BOOKTITLE = {New trends in systems theory (Genoa, 1990)}, PUBLISHER = {Birkhäuser Boston}, TITLE = {Input/output and state-space stability}, YEAR = {1991}, ADDRESS = {Boston, MA}, OPTCHAPTER = {}, OPTCROSSREF = {}, OPTEDITION = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, PAGES = {684--691}, SERIES = {Progr. Systems Control Theory}, OPTTYPE = {}, VOLUME = {7}, KEYWORDS = {input to state stability, input to state stability}, PDF = {../FTP_DIR/90genoa.pdf}, ABSTRACT = { This conference paper reviews various results relating state-space (Lyapunov) stabilization and exponential stabilization to several notions of input/output or bounded-input bounded-output stabilization. It also provides generalizations of some of these results to systems with saturating controls. Some of these latter results were not included in journal papers. } } @INCOLLECTION{MR1296059, AUTHOR = {E.D. Sontag}, BOOKTITLE = {Mathematical system theory}, PUBLISHER = {Springer}, TITLE = {Kalman's controllability rank condition: from linear to nonlinear}, YEAR = {1991}, ADDRESS = {Berlin}, OPTCHAPTER = {}, OPTCROSSREF = {}, OPTEDITION = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, PAGES = {453--462}, OPTSERIES = {}, OPTTYPE = {}, OPTVOLUME = {}, KEYWORDS = {controllability}, PDF = {../FTP_DIR/rek-volume.pdf}, ABSTRACT = { The notion of controllability was identified by Kalman as one of the central properties determining system behavior. His simple rank condition is ubiquitous in linear systems analysis. This article presents an elementary and expository overview of the generalizations of this test to a condition for testing accessibility of discrete and continuous time nonlinear systems. } } @ARTICLE{MR1112756, AUTHOR = {Y. Lin and E.D. Sontag}, JOURNAL = {Systems Control Lett.}, TITLE = {A universal formula for stabilization with bounded controls}, YEAR = {1991}, OPTMONTH = {}, OPTNOTE = {}, NUMBER = {6}, PAGES = {393--397}, VOLUME = {16}, ADDRESS = {Amsterdam, The Netherlands, The Netherlands}, KEYWORDS = {saturation}, PUBLISHER = {Elsevier Science Publishers B. V.}, PDF = {../FTP_DIR/boundedart.pdf}, ABSTRACT = { We provide a formula for a stabilizing feedback law using a bounded control, under the assumption that an appropriate control-Lyapunov function is known. Such a feedback, smooth away from the origin and continuous everywhere, is known to exist via Artstein's Theorem. As in the unbounded-control case treated in a previous note, we provide an explicit and ``universal'' formula given by an algebraic function of Lie derivatives. In particular, we extend to the bounded case the result that the feedback can be chosen analytic if the Lyapunov function and the vector fields defining the system are analytic. }, DOI = {http://dx.doi.org/10.1016/0167-6911(91)90111-Q} } @ARTICLE{MR1136617, AUTHOR = {H. T. Siegelmann and E.D. Sontag}, JOURNAL = {Appl. Math. Lett.}, TITLE = {Turing computability with neural nets}, YEAR = {1991}, OPTMONTH = {}, OPTNOTE = {}, NUMBER = {6}, PAGES = {77--80}, VOLUME = {4}, KEYWORDS = {neural networks}, PDF = {../FTP_DIR/aml-turing.pdf}, ABSTRACT = { This paper shows the existence of a finite neural network, made up of sigmoidal neurons, which simulates a universal Turing machine. It is composed of less than 100,000 synchronously evolving processors, interconnected linearly. High-order connections are not required. (Note: this paper was placed here by special request. The results in this paper have been by now improved considerably: see the JCSS pape which among other aspects provides a polynomial time simulation. This paper, based on a unary encoding, results in an exponential slowdown). } } @ARTICLE{109699, AUTHOR = {E.D. Sontag and H.J. Sussmann}, JOURNAL = {Neural Networks}, TITLE = {Back propagation separates where perceptrons do}, YEAR = {1991}, OPTMONTH = {}, OPTNOTE = {}, NUMBER = {2}, PAGES = {243--249}, VOLUME = {4}, ADDRESS = {Oxford, UK, UK}, KEYWORDS = {neural networks, neural networks}, PUBLISHER = {Elsevier Science Ltd.}, PDF = {../FTP_DIR/converge-nn.pdf}, ABSTRACT = { Feedforward nets with sigmoidal activation functions are often designed by minimizing a cost criterion. It has been pointed out before that this technique may be outperformed by the classical perceptron learning rule, at least on some problems. In this paper, we show that no such pathologies can arise if the error criterion is of a threshold LMS type, i.e., is zero for values ``beyond'' the desired target values. More precisely, we show that if the data are linearly separable, and one considers nets with no hidden neurons, then an error function as above cannot have any local minima that are not global. In addition, the proof gives the following stronger result, under the stated hypotheses: the continuous gradient adjustment procedure is such that from any initial weight configuration a separating set of weights is obtained in finite time. This is a precise analogue of the Perceptron Learning Theorem. The results are then compared with the more classical pattern recognition problem of threshold LMS with linear activations, where no spurious local minima exist even for nonseparable data: here it is shown that even if using the threshold criterion, such bad local minima may occur, if the data are not separable and sigmoids are used. keywords = { neural networks , feedforward neural nets }, }, DOI = {http://dx.doi.org/10.1016/0893-6080(91)90008-S} } @INPROCEEDINGS{91ciss-francesca, AUTHOR = {F. Albertini and E.D. Sontag}, BOOKTITLE = {Proc. Conf. Inform. Sci. and Systems, John Hopkins University, March 1991}, TITLE = {Accessibility of discrete-time nonlinear systems, and some relations to chaotic dynamics}, YEAR = {1991}, OPTADDRESS = {}, OPTCROSSREF = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, OPTORGANIZATION = {}, PAGES = {731--736}, OPTPUBLISHER = {}, OPTSERIES = {}, OPTVOLUME = {} } @INPROCEEDINGS{91ecc, AUTHOR = {F. Albertini and E.D. Sontag}, BOOKTITLE = {Proc. European Control Conf. , Vol 1, Grenoble, July 1991}, TITLE = {Some connections between chaotic dynamical systems and control systems}, YEAR = {1991}, OPTADDRESS = {}, OPTCROSSREF = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, OPTORGANIZATION = {}, PAGES = {58--163}, OPTPUBLISHER = {}, OPTSERIES = {}, OPTVOLUME = {}, KEYWORDS = {chaotic systems, controllability}, PDF = {../FTP_DIR/91ecc.pdf}, ABSTRACT = { This paper shows how to extend recent results of Colonius and Kliemann, regarding connections between chaos and controllability, from continuous to discrete time. The extension is nontrivial because the results all rely on basic properties of the accessibility Lie algebra which fail to hold in discrete time. Thus, this paper first develops further results in nonlinear accessibility, and then shows how a theorem can be proved, which while analogous to the one given in the work by Colonius and Klieman, also exhibits some important differences. A counterexample is used to show that the theorem given in continuous time cannot be generalized in a straightforward manner. } } @INPROCEEDINGS{91ciss-yuandan, AUTHOR = {Y. Lin and E.D. Sontag}, BOOKTITLE = {Proc. Conf. Inform. Sci. and Systems, John Hopkins University, March 1991}, TITLE = {Further universal formulas for Lyapunov approaches to nonlinear stabilization}, YEAR = {1991}, OPTADDRESS = {}, OPTCROSSREF = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, OPTORGANIZATION = {}, PAGES = {541--546}, OPTPUBLISHER = {}, OPTSERIES = {}, OPTVOLUME = {} } @INPROCEEDINGS{123410, AUTHOR = {W. Maass and G. Schnitger and E.D. Sontag}, BOOKTITLE = {Proceedings of the 32nd annual symposium on Foundations of computer science}, TITLE = {On the computational power of sigmoid versus Boolean threshold circuits (extended abstract)}, YEAR = {1991}, ADDRESS = {Los Alamitos, CA, USA}, OPTCROSSREF = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, OPTORGANIZATION = {}, PAGES = {767--776}, PUBLISHER = {IEEE Computer Society Press}, OPTSERIES = {}, OPTVOLUME = {}, KEYWORDS = {neural networks, theory of computing and complexity} } @INPROCEEDINGS{91acc-renee, AUTHOR = {R. Schwarzschild and E.D. Sontag}, BOOKTITLE = {Proc. Amer. Automatic Control Conf., Boston, June 1991}, TITLE = {Algebraic theory of sign-linear systems}, YEAR = {1991}, OPTADDRESS = {}, OPTCROSSREF = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, OPTORGANIZATION = {}, PAGES = {799--804}, OPTPUBLISHER = {}, OPTSERIES = {}, OPTVOLUME = {} } @INPROCEEDINGS{91ciss-renee, AUTHOR = {R. Schwarzschild and E.D. Sontag}, BOOKTITLE = {Proc. Conf. Inform. Sci. and Systems, John Hopkins University, March 1991}, TITLE = {Quantized systems, saturated measurements, and sign-linear systems}, YEAR = {1991}, OPTADDRESS = {}, OPTCROSSREF = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, OPTORGANIZATION = {}, PAGES = {134--139}, OPTPUBLISHER = {}, OPTSERIES = {}, OPTVOLUME = {}, KEYWORDS = {observability} } @INPROCEEDINGS{91ciss-twolayer, AUTHOR = {E.D. Sontag}, BOOKTITLE = {Proc. Conf. Inform. Sci. and Systems, John Hopkins University, March 1991}, TITLE = {Capabilities of four- vs three-layer nets, and control applications}, YEAR = {1991}, OPTADDRESS = {}, OPTCROSSREF = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, OPTORGANIZATION = {}, PAGES = {558--563}, OPTPUBLISHER = {}, OPTSERIES = {}, OPTVOLUME = {} } @INPROCEEDINGS{91acc-twolayer, AUTHOR = {E.D. Sontag}, BOOKTITLE = {Proc. Amer. Automatic Control Conf. , Boston, June 1991}, TITLE = {Feedback Stabilization Using Two-Hidden-Layer Nets}, YEAR = {1991}, OPTADDRESS = {}, OPTCROSSREF = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, OPTORGANIZATION = {}, PAGES = {815--820}, OPTPUBLISHER = {}, OPTSERIES = {}, OPTVOLUME = {} } @INPROCEEDINGS{91cdc-wang, AUTHOR = {E.D. Sontag and Y. Wang}, BOOKTITLE = {Proc. IEEE Conf. Decision and Control, Brighton, UK, Dec. 1991, IEEE Publications, 1991}, TITLE = {I/O equations for nonlinear systems and observation spaces}, YEAR = {1991}, OPTADDRESS = {}, OPTCROSSREF = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, OPTORGANIZATION = {}, PAGES = {720--725}, OPTPUBLISHER = {}, OPTSERIES = {}, OPTVOLUME = {}, KEYWORDS = {observability}, PDF = {../FTP_DIR/91cdc-ywang.pdf}, ABSTRACT = {This paper studies various types of input/output representations for nonlinear continuous time systems. The algebraic and analytic i/o equations studied in previous papers by the authors are generalized to integral and integro-differential equations, and an abstract notion is also considered. New results are given on generic observability, and these results are then applied to give conditions under which that the minimal order of an equation equals the minimal possible dimension of a realization, just as with linear systems but in contrast to the discrete time nonlinear theory. } } @BOOK{MR1070569, PUBLISHER = {Springer-Verlag}, TITLE = {Mathematical Control Theory. Deterministic Finite-Dimensional Systems}, YEAR = {1990}, AUTHOR = {E.D. Sontag}, ALTEDITOR = {}, ADDRESS = {New York}, OPTEDITION = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, SERIES = {Texts in Applied Mathematics}, VOLUME = {6}, PAGES = {xiv+396}, ABSTRACT = { The second edition (1998) is now online; please follow that link. } } @INCOLLECTION{MR1206692, AUTHOR = {E.D. Sontag}, BOOKTITLE = {Control of uncertain systems (Bremen, 1989)}, PUBLISHER = {Birkhäuser Boston}, TITLE = {Constant McMillan degree and the continuous stabilization of families of transfer matrices}, YEAR = {1990}, ADDRESS = {Boston, MA}, OPTCHAPTER = {}, OPTCROSSREF = {}, OPTEDITION = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, PAGES = {289--295}, SERIES = {Progr. Systems Control Theory}, OPTTYPE = {}, VOLUME = {6}, KEYWORDS = {systems over rings} } @INCOLLECTION{MR1115377, AUTHOR = {E.D. Sontag}, BOOKTITLE = {Robust control of linear systems and nonlinear control (Amsterdam, 1989)}, PUBLISHER = {Birkhäuser Boston}, TITLE = {Feedback stabilization of nonlinear systems}, YEAR = {1990}, ADDRESS = {Boston, MA}, OPTCHAPTER = {}, OPTCROSSREF = {}, OPTEDITION = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, PAGES = {61--81}, SERIES = {Progr. Systems Control Theory}, OPTTYPE = {}, VOLUME = {4}, PDF = {../FTP_DIR/89mtns-feed.pdf}, ABSTRACT = { This paper surveys some well-known facts as well as some recent developments on the topic of stabilization of nonlinear systems. (NOTE: figures are not included in file; they were pasted-in.) } } @INCOLLECTION{MR1061384, AUTHOR = {E.D. Sontag}, BOOKTITLE = {Nonlinear controllability and optimal control}, PUBLISHER = {Dekker}, TITLE = {Integrability of certain distributions associated with actions on manifolds and applications to control problems}, YEAR = {1990}, ADDRESS = {New York}, OPTCHAPTER = {}, OPTCROSSREF = {}, OPTEDITION = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, PAGES = {81--131}, SERIES = {Monogr. Textbooks Pure Appl. Math.}, OPTTYPE = {}, VOLUME = {133}, KEYWORDS = {controllability}, PDF = {../FTP_DIR/actions-report.pdf}, ABSTRACT = { Results are given on the integrability of certain distributions which arise from smoothly parametrized families of diffeomorphisms acting on manifolds. Applications to control problems and in particular to the problem of sampling are discussed. Pages 42-50 apply the results to the control of continuous time systems; this is an exposition of some of the basic results of the Lie algebraic accessibility theory. } } @INCOLLECTION{MR1115322, AUTHOR = {E.D. Sontag and Y. Wang}, BOOKTITLE = {Realization and modelling in system theory (Amsterdam, 1989)}, PUBLISHER = {Birkhäuser Boston}, TITLE = {Input/output equations and realizability}, YEAR = {1990}, ADDRESS = {Boston, MA}, OPTCHAPTER = {}, OPTCROSSREF = {}, OPTEDITION = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, PAGES = {125--132}, SERIES = {Progr. Systems Control Theory}, OPTTYPE = {}, VOLUME = {3} } @ARTICLE{Jakubczyk_sicopt90, AUTHOR = {B. Jakubczyk and E.D. Sontag}, JOURNAL = {SIAM J. Control Optim.}, TITLE = {Controllability of nonlinear discrete-time systems: a Lie-algebraic approach}, YEAR = {1990}, OPTMONTH = {}, OPTNOTE = {}, NUMBER = {1}, PAGES = {1--33}, VOLUME = {28}, ADDRESS = {Philadelphia, PA, USA}, KEYWORDS = {discrete-time}, PUBLISHER = {Society for Industrial and Applied Mathematics}, PDF = {../FTP_DIR/dt-controllability.pdf}, ABSTRACT = { This paper presents a geometric study of controllability for discrete-time nonlinear systems. Various accessibility properties are characterized in terms of Lie algebras of vector fields. Some of the results obtained are parallel to analogous ones in continuous-time, but in many respects the theory is substantially different and many new phenomena appear. }, DOI = {http://dx.doi.org/10.1137/0328001} } @ARTICLE{MR1048003, AUTHOR = {E.D. Sontag}, JOURNAL = {IEEE Trans. Automat. Control}, TITLE = {Further facts about input to state stabilization}, YEAR = {1990}, OPTMONTH = {}, OPTNOTE = {}, NUMBER = {4}, PAGES = {473--476}, VOLUME = {35}, PDF = {../FTP_DIR/further-iss90.pdf}, ABSTRACT = { Previous results about input to state stabilizability are shown to hold even for systems which are not linear in controls, provided that a more general type of feedback be allowed. Applications to certain stabilization problems and coprime factorizations, as well as comparisons to other results on input to state stability, are also briefly discussed.d local minima may occur, if the data are not separable and sigmoids are used. } } @ARTICLE{MR1067673, AUTHOR = {E.D. Sontag and Y. Wang}, JOURNAL = {Linear Algebra Appl.}, TITLE = {Pole shifting for families of linear systems depending on at most three parameters}, YEAR = {1990}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, PAGES = {3--38}, VOLUME = {137/138}, KEYWORDS = {systems over rings, systems over rings}, PDF = {../FTP_DIR/quaternions.pdf}, ABSTRACT = { We prove that for any family of n-dimensional controllable linear systems, continuously parameterized by up to three parameters, and for any continuous selection of n eigenvalues (in complex conjugate pairs), there is some dynamic controller of dimension 3n which is itself continuously parameterized and for which the closed-loop eigenvalues are these same eigenvalues, each counted 4 times. An analogous result holds also for smooth parameterizations. } } @INPROCEEDINGS{Souvaine, AUTHOR = {T. Asano and J. Hershberger and J. Pach and E.D. Sontag and D. Souivaine and S. Suri}, BOOKTITLE = {Proceedings of the Second Canadian Conf. on Computational Geometry, Ottawa, Canada, 1990}, TITLE = {Separating bi-chromatic points by parallel lines}, YEAR = {1990}, OPTADDRESS = {}, OPTCROSSREF = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, OPTORGANIZATION = {}, PAGES = {46--49}, OPTPUBLISHER = {}, OPTSERIES = {}, OPTVOLUME = {}, KEYWORDS = {computational geometry}, PDF = {../FTP_DIR/dls.pdf}, ABSTRACT = { Given a 2-coloring of the vertices of a regular n-gon P, how many parallel lines are needed to separate the vertices into monochromatic subsets? We prove that floor(n/2) is a tight upper bound, and also provide an O(n log n) time algorithm to determine the direction that gives the minimum number of lines. If the polygon is a non-regular convex polygon, then n-3 lines may be necessary, while n-2 lines always suffice. This problem arises in machine learning and has implications about the representational capabilities of some neural networks. } } @INPROCEEDINGS{dewan, AUTHOR = {H. Dewan and E.D. Sontag}, BOOKTITLE = {Proc. Int. Joint Conf. on Neural Networks, Washington, DC, Jan. 1990, IEEE Publications, 1990}, TITLE = {Extrapolatory methods for speeding up the BP algorithm}, YEAR = {1990}, OPTADDRESS = {}, OPTCROSSREF = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, OPTORGANIZATION = {}, PAGES = {I.613--616}, OPTPUBLISHER = {}, OPTSERIES = {}, OPTVOLUME = {}, KEYWORDS = {neural networks} } @INPROCEEDINGS{90ciss, AUTHOR = {E.D. Sontag}, BOOKTITLE = {Proc. Conf. Info. Sci. and Systems, Princeton, 1990}, TITLE = {Comparing sigmoids and heavisides}, YEAR = {1990}, OPTADDRESS = {}, OPTCROSSREF = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, OPTORGANIZATION = {}, PAGES = {654--659}, OPTPUBLISHER = {}, OPTSERIES = {}, OPTVOLUME = {}, KEYWORDS = {neural networks, boolean systems} } @INPROCEEDINGS{119971, AUTHOR = {E.D. Sontag}, BOOKTITLE = {NIPS-3: Proceedings of the 1990 conference on Advances in neural information processing systems 3}, TITLE = {Remarks on interpolation and recognition using neural nets}, YEAR = {1990}, ADDRESS = {San Francisco, CA, USA}, OPTCROSSREF = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, OPTORGANIZATION = {}, PAGES = {939--945}, PUBLISHER = {Morgan Kaufmann Publishers Inc.}, OPTSERIES = {}, OPTVOLUME = {}, KEYWORDS = {neural networks} } @INPROCEEDINGS{90cdc, AUTHOR = {E.D. Sontag and H.J. Sussmann}, BOOKTITLE = {Proc. IEEE Conf. Decision and Control, Honolulu, Dec. 1990, IEEE Publications, 1990}, TITLE = {Nonlinear output feedback design for linear systems with saturating controls}, YEAR = {1990}, OPTADDRESS = {}, OPTCROSSREF = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, OPTORGANIZATION = {}, PAGES = {3414--3416}, OPTPUBLISHER = {}, OPTSERIES = {}, OPTVOLUME = {}, KEYWORDS = {saturation}, PDF = {../FTP_DIR/90cdc.pdf}, ABSTRACT = { This paper shows the existence of (nonlinear) smooth dynamic feedback stabilizers for linear time invariant systems under input constraints, assuming only that open-loop asymptotic controllability and detectability hold. } } @INPROCEEDINGS{90IFAC, AUTHOR = {Y. Wang and E.D. Sontag}, BOOKTITLE = {Proc. 11th IFAC World Congress, Tallinn, former USSR, 1990}, TITLE = {Realization of families of generating series: differential algebraic and state space equations}, YEAR = {1990}, OPTADDRESS = {}, OPTCROSSREF = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, OPTORGANIZATION = {}, PAGES = {62--66}, OPTPUBLISHER = {}, OPTSERIES = {}, OPTVOLUME = {} } @TECHREPORT{SYCON-90-13, AUTHOR = {F. Albertini and E.D. Sontag}, INSTITUTION = {Rutgers Center for Systems and Control}, TITLE = {Some connections between chaotic dynamical systems and control systems}, YEAR = {1990}, OPTADDRESS = {}, OPTMONTH = {}, OPTNOTE = {}, NUMBER = {SYCON-90-13}, OPTTYPE = {} } @INCOLLECTION{MR1013210, AUTHOR = {B. Jakubczyk and E.D. Sontag}, BOOKTITLE = {Modern optimal control}, PUBLISHER = {Dekker}, TITLE = {Nonlinear discrete-time systems. Accessibility conditions}, YEAR = {1989}, ADDRESS = {New York}, OPTCHAPTER = {}, OPTCROSSREF = {}, OPTEDITION = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, PAGES = {173--185}, SERIES = {Lecture Notes in Pure and Appl. Math.}, OPTTYPE = {}, VOLUME = {119} } @ARTICLE{MR1029482, AUTHOR = {A. Arapostathis and B. Jakubczyk and H.-G. Lee and S. I. Marcus and E.D. Sontag}, JOURNAL = {Systems Control Lett.}, TITLE = {The effect of sampling on linear equivalence and feedback linearization}, YEAR = {1989}, OPTMONTH = {}, OPTNOTE = {}, NUMBER = {5}, PAGES = {373--381}, VOLUME = {13}, ADDRESS = {Amsterdam, The Netherlands, The Netherlands}, KEYWORDS = {discrete-time}, PUBLISHER = {Elsevier Science Publishers B. V.}, PDF = {../FTP_DIR/gri.pdf}, ABSTRACT = { We investigate the effect of sampling on linearization for continuous time systems. It is shown that the discretized system is linearizable by state coordinate change for an open set of sampling times if and only if the continuous time system is linearizable by state coordinate change. Also, it is shown that linearizability via digital feedback imposes highly nongeneric constraints on the structure of the plant, even if this is known to be linearizable with continuous-time feedback. }, DOI = {http://dx.doi.org/10.1016/0167-6911(89)90103-5} } @ARTICLE{MR1014237, AUTHOR = {E.D. Sontag}, JOURNAL = {Systems Control Lett.}, TITLE = {A ``universal'' construction of Artstein's theorem on nonlinear stabilization}, YEAR = {1989}, OPTMONTH = {}, OPTNOTE = {}, NUMBER = {2}, PAGES = {117--123}, VOLUME = {13}, ADDRESS = {Amsterdam, The Netherlands, The Netherlands}, KEYWORDS = {control-Lyapunov functions}, PUBLISHER = {Elsevier Science Publishers B. V.}, PDF = {../FTP_DIR/art-sycon8903.pdf}, ABSTRACT = { This note presents an explicit proof of the theorem - due to Artstein - which states that the existence of a smooth control-Lyapunov function implies smooth stabilizability. Moreover, the result is extended to the real-analytic and rational cases as well. The proof uses a "universal" formula given by an algebraic function of Lie derivatives; this formula originates in the solution of a simple Riccati equation. } } @ARTICLE{sigmoids-nc, AUTHOR = {E.D. Sontag}, JOURNAL = {Neural Computation}, TITLE = {Sigmoids distinguish better than Heavisides}, YEAR = {1989}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, PAGES = {470--472}, VOLUME = {1}, KEYWORDS = {neural networks, boolean systems} } @ARTICLE{ISS89, AUTHOR = {E.D. Sontag}, JOURNAL = {IEEE Trans. Automat. Control}, TITLE = {Smooth stabilization implies coprime factorization}, YEAR = {1989}, OPTMONTH = {}, OPTNOTE = {}, NUMBER = {4}, PAGES = {435--443}, VOLUME = {34}, KEYWORDS = {input to state stability, input to state stability}, PDF = {../FTP_DIR/coprime-factorizations.pdf}, ABSTRACT = { This paper shows that coprime right factorizations exist for the input to state mapping of a continuous time nonlinear system provided that the smooth feedback stabilization problem be solvable for this system. In particular, it follows that feedback linearizable systems admit such factorizations. In order to establish the result a Lyapunov-theoretic definition is proposed for bounded input bounded output stability. The main technical fact proved relates the notion of stabilizability studied in the state space nonlinear control literature to a notion of stability under bounded control perturbations analogous to those studied in operator theoretic approaches to systems; it states that smooth stabilization implies smooth input-to-state stabilization. (Note: This is the original ISS paper, but the ISS results have been much improved in later papers. The material on coprime factorizations is still of interest, but the 89 CDC paper has some improvements and should be read too.) } } @ARTICLE{MR1102346, AUTHOR = {E.D. Sontag and H.J. Sussmann}, JOURNAL = {Complex Systems}, TITLE = {Backpropagation can give rise to spurious local minima even for networks without hidden layers}, YEAR = {1989}, OPTMONTH = {}, OPTNOTE = {}, NUMBER = {1}, PAGES = {91--106}, VOLUME = {3}, KEYWORDS = {neural networks, neural networks}, PDF = {../FTP_DIR/complex_systems.pdf}, ABSTRACT = { We give an example of a neural net without hidden layers and with a sigmoid transfer function, together with a training set of binary vectors, for which the sum of the squared errors, regarded as a function of the weights, has a local minimum which is not a global minimum. The example consists of a set of 125 training instances, with four weights and a threshold to be learnt. We do not know if substantially smaller binary examples exist. } } @ARTICLE{MR993944, AUTHOR = {E.D. Sontag and H.J. Sussmann}, JOURNAL = {Systems Control Lett.}, TITLE = {Further comments on the stabilizability of the angular velocity of a rigid body}, YEAR = {1989}, OPTMONTH = {}, OPTNOTE = {}, NUMBER = {3}, PAGES = {213--217}, VOLUME = {12}, ADDRESS = {Amsterdam, The Netherlands, The Netherlands}, KEYWORDS = {satellite control, feedback stabilization}, PUBLISHER = {Elsevier Science Publishers B. V.}, PDF = {../FTP_DIR/satel.pdf}, ABSTRACT = { We prove that the angular velocity equations can be smoothly stabilized with a single torque controller for bodies having an axis of symmetry. This complements a recent result of Aeyels and Szafranski. }, DOI = {http://dx.doi.org/10.1016/0167-6911(89)90052-2} } @ARTICLE{MR1006847, AUTHOR = {E.D. Sontag and Y. Yamamoto}, JOURNAL = {Systems Control Lett.}, TITLE = {On the existence of approximately coprime factorizations for retarded systems}, YEAR = {1989}, OPTMONTH = {}, OPTNOTE = {}, NUMBER = {1}, PAGES = {53--58}, VOLUME = {13}, ADDRESS = {Amsterdam, The Netherlands, The Netherlands}, KEYWORDS = {delay-differential systems}, PUBLISHER = {Elsevier Science Publishers B. V.}, PDF = {../FTP_DIR/yy-coprime.pdf}, ABSTRACT = { This note establishes a result linking algebraically coprime factorizations of transfer matrices of delay systems to approximately coprime factorizations in the sense of distributions. The latter have been employed by the second author in the study of function-space controllability for such systems. }, DOI = {http://dx.doi.org/10.1016/0167-6911(89)90020-0} } @ARTICLE{MR1025981, AUTHOR = {Y. Wang and E.D. Sontag}, JOURNAL = {Systems Control Lett.}, TITLE = {On two definitions of observation spaces}, YEAR = {1989}, OPTMONTH = {}, OPTNOTE = {}, NUMBER = {4}, PAGES = {279--289}, VOLUME = {13}, ADDRESS = {Amsterdam, The Netherlands, The Netherlands}, KEYWORDS = {observability, realization theory}, PUBLISHER = {Elsevier Science Publishers B. V.}, PDF = {../FTP_DIR/yw-obs.pdf}, ABSTRACT = { This paper establishes the equality of the observation spaces defined by means of piecewise constant controls with those defined in terms of differentiable controls. }, DOI = {http://dx.doi.org/10.1016/0167-6911(89)90116-3} } @INPROCEEDINGS{MR1039005, AUTHOR = {E.D. Sontag}, BOOKTITLE = {Proceedings of the 28th IEEE Conference on Decision and Control, Vol. 1--3 (Tampa, FL, 1989)}, TITLE = {Remarks on stabilization and input-to-state stability}, YEAR = {1989}, ADDRESS = {New York}, OPTCROSSREF = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, OPTORGANIZATION = {}, PAGES = {1376--1378}, PUBLISHER = {IEEE}, OPTSERIES = {}, OPTVOLUME = {}, KEYWORDS = {input to state stability}, PDF = {../FTP_DIR/89cdc-stab.pdf}, ABSTRACT = { This paper describes how notions of input-to-state stabilization are useful when stabilizing cascades of systems. The simplest result along these lines is local, and it states that a cascade of two locally asymptotically stable systems is again asystable. A global result is obtained if both systems have the origin as a globally asymptotically stable state and the "converging input bounded state" property holds for the second system. } } @INPROCEEDINGS{MR1038933, AUTHOR = {E.D. Sontag}, BOOKTITLE = {Proceedings of the 28th IEEE Conference on Decision and Control, Vol. 1--3 (Tampa, FL, 1989)}, TITLE = {Remarks on the time-optimal control of a class of Hamiltonian systems}, YEAR = {1989}, ADDRESS = {New York}, OPTCROSSREF = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, OPTORGANIZATION = {}, PAGES = {217--221}, PUBLISHER = {IEEE}, OPTSERIES = {}, OPTVOLUME = {}, KEYWORDS = {robotics, optimal control}, PDF = {../FTP_DIR/89cdc-ham.pdf}, ABSTRACT = { This paper introduces a subclass of Hamiltonian control systems motivated by mechanical models. It deals with time-optimal control problems. The main results characterize regions of the state space where singular trajectories cannot exist, and provide high-order conditions for optimality. } } @INPROCEEDINGS{MR1038986, AUTHOR = {E.D. Sontag}, BOOKTITLE = {Proceedings of the 28th IEEE Conference on Decision and Control, Vol. 1--3 (Tampa, FL, 1989)}, TITLE = {Some connections between stabilization and factorization}, YEAR = {1989}, ADDRESS = {New York}, OPTCROSSREF = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, OPTORGANIZATION = {}, PAGES = {990--995}, PUBLISHER = {IEEE}, OPTSERIES = {}, OPTVOLUME = {}, PDF = {../FTP_DIR/89cdccopr-reformat.pdf}, ABSTRACT = { Coprime right fraction representations are obtained for nonlinear systems defined by differential equations, under assumptions of stabilizability and detectability. A result is also given on left (not necessarily coprime) factorizations. } } @INPROCEEDINGS{feedback-CISS89, AUTHOR = {E.D. Sontag}, BOOKTITLE = {Proc. Conf. Info. Sciences and Systems, Johns Hopkins University Press, 1989}, TITLE = {Some recent results on nonlinear feedback}, YEAR = {1989}, OPTADDRESS = {}, OPTCROSSREF = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, OPTORGANIZATION = {}, PAGES = {151--156}, OPTPUBLISHER = {}, OPTSERIES = {}, OPTVOLUME = {} } @INPROCEEDINGS{SYCON12, AUTHOR = {E.D. Sontag and H.J. Sussmann}, BOOKTITLE = {Proc. IEEE Int. Conf. Neural Networks, Washington, DC, June 1989}, TITLE = {Backpropagation Separates when Perceptrons Do}, YEAR = {1989}, OPTADDRESS = {}, OPTCROSSREF = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, OPTORGANIZATION = {}, PAGES = {639--642}, OPTPUBLISHER = {}, OPTSERIES = {}, OPTVOLUME = {} } @INPROCEEDINGS{neural-CISS89, AUTHOR = {E.D. Sontag and H.J. Sussmann}, BOOKTITLE = {Proc. Conf. Info. Sciences and Systems, Johns Hopkins University Press, 1989}, TITLE = {Remarks on local minima in backpropagation}, YEAR = {1989}, OPTADDRESS = {}, OPTCROSSREF = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, OPTORGANIZATION = {}, PAGES = {432--435}, OPTPUBLISHER = {}, OPTSERIES = {}, OPTVOLUME = {}, KEYWORDS = {neural networks} } @INPROCEEDINGS{YW-CISS, AUTHOR = {Y. Wang and E.D. Sontag}, BOOKTITLE = {Proc. Conf. Info. Sciences and Systems, Johns Hopkins University Press, 1989}, TITLE = {A new result on the relation between differential-algebraic realizability and state space realizations}, YEAR = {1989}, OPTADDRESS = {}, OPTCROSSREF = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, OPTORGANIZATION = {}, PAGES = {143--147}, OPTPUBLISHER = {}, OPTSERIES = {}, OPTVOLUME = {} } @INPROCEEDINGS{MR1039048, AUTHOR = {Y. Wang and E.D. Sontag}, BOOKTITLE = {Proceedings of the 28th IEEE Conference on Decision and Control, Vol. 1--3 (Tampa, FL, 1989)}, TITLE = {Realization and input/output relations: the analytic case}, YEAR = {1989}, ADDRESS = {New York}, OPTCROSSREF = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, OPTORGANIZATION = {}, PAGES = {1975--1980}, PUBLISHER = {IEEE}, OPTSERIES = {}, OPTVOLUME = {} } @TECHREPORT{SYCON-89-12, AUTHOR = {E.D. Sontag}, INSTITUTION = {Rutgers Center for Systems and Control}, TITLE = {Sigmoids distinguish more efficiently than Heavisides}, YEAR = {1989}, OPTADDRESS = {}, OPTMONTH = {}, OPTNOTE = {}, NUMBER = {SYCON-89-12}, OPTTYPE = {}, KEYWORDS = {neural networks} } @BOOK{siam88book, PUBLISHER = {SIAM}, TITLE = {Linear Algebra in Signals, Systems, and Control (edited book)}, YEAR = {1988}, AUTHOR = {B.N. Datta and C.R. Johnson and M.A. Kaashoek and R.J. Plemmons and E.D. Sontag}, ALTEDITOR = {}, OPTADDRESS = {}, OPTEDITION = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, OPTSERIES = {}, OPTVOLUME = {} } @INCOLLECTION{CHOW, AUTHOR = {E.D. Sontag}, BOOKTITLE = {Analysis and Control of Nonlinear Systems}, PUBLISHER = {North Holland, Amsterdam}, TITLE = {A Chow property for sampled bilinear systems}, YEAR = {1988}, OPTADDRESS = {}, OPTCHAPTER = {}, OPTCROSSREF = {}, OPTEDITION = {}, EDITOR = {C.I. Byrnes and C.F. Martin and R. Saeks}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, PAGES = {205--211}, OPTSERIES = {}, OPTTYPE = {}, OPTVOLUME = {}, KEYWORDS = {discrete-time, bilinear systems}, PDF = {../FTP_DIR/bilin2.pdf}, ABSTRACT = { This paper studies accessibility (weak controllability) of bilinear systems under constant sampling rates. It is shown that the property is preserved provided that the sampling period satisfies a condition related to the eigenvalues of the autonomous dynamics matrix. This condition generalizes the classical Kalman-Ho-Narendra criterion which is well known in the linear case, and which, for observability, results in the classical Nyquist theorem. } } @INCOLLECTION{EQUI-MTNS87, AUTHOR = {E.D. Sontag}, BOOKTITLE = {Analysis and Control of Nonlinear Systems}, PUBLISHER = {North Holland, Amsterdam}, TITLE = {An explicit construction of the equilinearization controller}, YEAR = {1988}, OPTADDRESS = {}, OPTCHAPTER = {}, OPTCROSSREF = {}, OPTEDITION = {}, EDITOR = {C.I. Byrnes and C.F. Martin and R. Saek}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, PAGES = {483--492}, OPTSERIES = {}, OPTTYPE = {}, OPTVOLUME = {}, PDF = {../FTP_DIR/87mtnslin.pdf}, ABSTRACT = { This paper provides further results about the equilinearization method of control design recently introduced by the author. A simplified derivation of the controller is provided, as well as a theorem on local stabilization along reference trajectories. } } @ARTICLE{MR960665, AUTHOR = {E.D. Sontag}, JOURNAL = {Systems Control Lett.}, TITLE = {Bilinear realizability is equivalent to existence of a singular affine differential i/o equation}, YEAR = {1988}, OPTMONTH = {}, OPTNOTE = {}, NUMBER = {3}, PAGES = {181--187}, VOLUME = {11}, ADDRESS = {Amsterdam, The Netherlands, The Netherlands}, PUBLISHER = {Elsevier Science Publishers B. V.}, PDF = {../FTP_DIR/bilinrealiz.pdf}, ABSTRACT = { For continuous time analytic input/output maps, the existence of a singular differential equation relating derivatives of controls and outputs is shown to be equivalent to bilinear realizability. A similar result holds for the problem of immersion into bilinear systems. The proof is very analogous to that of the corresponding, and previously known, result for discrete time. }, DOI = {http://dx.doi.org/10.1016/0167-6911(88)90057-6} } @ARTICLE{MR957656, AUTHOR = {E.D. Sontag}, JOURNAL = {SIAM J. Control Optim.}, TITLE = {Controllability is harder to decide than accessibility}, YEAR = {1988}, OPTMONTH = {}, OPTNOTE = {}, NUMBER = {5}, PAGES = {1106--1118}, VOLUME = {26}, ADDRESS = {Philadelphia, PA, USA}, KEYWORDS = {computational complexity, controllability, computational complexity}, PUBLISHER = {Society for Industrial and Applied Mathematics}, PDF = {../FTP_DIR/decide.pdf}, ABSTRACT = { The present article compares the difficulties of deciding controllability and accessibility. These are standard properties of control systems, but complete algebraic characterizations of controllability have proved elusive. We show in particular that for subsystems of bilinear systems, accessibility can be decided in polynomial time, but controllability is NP-hard. }, DOI = {http://dx.doi.org/10.1137/0326061} } @ARTICLE{MR929174, AUTHOR = {E.D. Sontag}, JOURNAL = {Internat. J. Control}, TITLE = {Finite-dimensional open-loop control generators for nonlinear systems}, YEAR = {1988}, OPTMONTH = {}, OPTNOTE = {}, NUMBER = {2}, PAGES = {537--556}, VOLUME = {47}, PDF = {../FTP_DIR/fdg.pdf}, ABSTRACT = { This paper concerns itself with the existence of open-loop control generators for nonlinear (continuous-time) systems. The main result is that, under relatively mild assumptions on the original system, and for each fixed compact subset of the state space, there always exists one such generator. This is a new system with the property that the controls it produces are sufficiently rich to preserve complete controllability along nonsingular trajectories. General results are also given on the continuity and differentiability of the input to state mapping for various p-norms on controls, as well as a comparison of various nonlinear controllability notions. } } @INPROCEEDINGS{88cdc-dec, AUTHOR = {E.D. Sontag}, BOOKTITLE = {Proc. IEEE Conf. Decision and Control, Austin, Dec. 1988}, TITLE = {Some complexity questions regarding controllability}, YEAR = {1988}, OPTADDRESS = {}, OPTCROSSREF = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, OPTORGANIZATION = {}, PAGES = {1326--1329}, OPTPUBLISHER = {}, OPTSERIES = {}, OPTVOLUME = {}, KEYWORDS = {theory of computing and complexity, computational complexity, controllability, computational complexity}, PDF = {../FTP_DIR/88cdcdec.pdf}, ABSTRACT = { It has been known for a long time that certain controllability properties are more difficult to verify than others. This article makes this fact precise, comparing controllability with accessibility, for a wide class of nonlinear continuous time systems. The original contribution is in formalizing this comparison in the context of computational complexity. (This paper placed here by special request.) } } @INPROCEEDINGS{88cdc-copr, AUTHOR = {E.D. Sontag}, BOOKTITLE = {Proc. IEEE Conf. Decision and Control, Austin, Dec. 1988}, TITLE = {Stabilizability, i/o stability, and coprime factorizations}, YEAR = {1988}, OPTADDRESS = {}, OPTCROSSREF = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, OPTORGANIZATION = {}, PAGES = {457--458}, OPTPUBLISHER = {}, OPTSERIES = {}, OPTVOLUME = {}, KEYWORDS = {input to state stability} } @TECHREPORT{SYCON4, AUTHOR = {E.D. Sontag}, INSTITUTION = {Rutgers Center for Systems and Control}, TITLE = {Integrability of certain distributions associated to actions on manifolds and an introduction to Lie-algebraic control}, YEAR = {1988}, OPTADDRESS = {}, OPTMONTH = {}, OPTNOTE = {}, NUMBER = {SYCON-88-04}, OPTTYPE = {} } @TECHREPORT{SYCON2, AUTHOR = {E.D. Sontag}, INSTITUTION = {Rutgers Center for Systems and Control}, TITLE = {Some remarks on the backpropagation algorithm for neural net learning}, YEAR = {1988}, OPTADDRESS = {}, OPTMONTH = {}, OPTNOTE = {}, NUMBER = {SYCON-88-02}, OPTTYPE = {}, KEYWORDS = {neural networks, neural networks}, PDF = {../FTP_DIR/sycon88-02.pdf}, ABSTRACT = { This is a very old informal report that discusses the study of local minima of quadratic loss functions for fitting errors in sigmoidal neural net learning. It also includes several remarks concerning the growth of weights during gradient descent. There is nothing very interesting here - far better knowledge is now available - but the report was placed here by request. } } @INCOLLECTION{ENCYC1, AUTHOR = {E.D. Sontag}, BOOKTITLE = {Encycl. of Systems and Control}, PUBLISHER = {Pergamon Press}, TITLE = {Reachability, observability, and realization of a class of discrete-time nonlinear systems}, YEAR = {1987}, OPTADDRESS = {}, OPTCHAPTER = {}, OPTCROSSREF = {}, OPTEDITION = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, PAGES = {3288--3293}, OPTSERIES = {}, OPTTYPE = {}, OPTVOLUME = {}, KEYWORDS = {observability} } @ARTICLE{MR917700, AUTHOR = {E.D. Sontag}, JOURNAL = {Systems Control Lett.}, TITLE = {A remark on bilinear systems and moduli spaces of instantons}, YEAR = {1987}, OPTMONTH = {}, OPTNOTE = {}, NUMBER = {5}, PAGES = {361--367}, VOLUME = {9}, ADDRESS = {Amsterdam, The Netherlands, The Netherlands}, PUBLISHER = {Elsevier Science Publishers B. V.}, PDF = {../FTP_DIR/instantons.pdf}, ABSTRACT = { Explicit equations are given for the moduli space of framed instantons as a quasi-affine variety, based on the representation theory of noncommutative power series, or equivalently, the minimal realization theory of bilinear systems. }, DOI = {http://dx.doi.org/10.1016/0167-6911(87)90064-8} } @ARTICLE{MR907356, AUTHOR = {E.D. Sontag}, JOURNAL = {IEEE Trans. Automat. Control}, TITLE = {Controllability and linearized regulation}, YEAR = {1987}, OPTMONTH = {}, OPTNOTE = {}, NUMBER = {10}, PAGES = {877--888}, VOLUME = {32}, PDF = {../FTP_DIR/lin.pdf}, ABSTRACT = { A nonlinear controllable plant, under mild technical conditions, admits a precompensator with the following property: along control trajectories joining pairs of states, the composite system (precompensator plus plant) is, up to first order, isomorphic to a parallel connection of integrators. } } @ARTICLE{BOSE, AUTHOR = {E.D. Sontag}, JOURNAL = {Linear Alg. and Applications}, TITLE = {Review of Multidimensional Systems Theory}, YEAR = {1987}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, PAGES = {273--278}, VOLUME = {87}, PDF = {../FTP_DIR/bose.pdf}, ABSTRACT = { A book review which also provides a quick introduction to questions of stability and positivity of multivariable polynomials for 2D and spatially-distributed systems. } } @INPROCEEDINGS{GRI, AUTHOR = {B. Jakubczyk and E.D. Sontag}, BOOKTITLE = {Proc. IEEE Conf. Decision and Control, Los Angeles, Dec.1987}, TITLE = {The effect of sampling on feedback linearization}, YEAR = {1987}, OPTADDRESS = {}, OPTCROSSREF = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, OPTORGANIZATION = {}, PAGES = {1374--1379}, OPTPUBLISHER = {}, OPTSERIES = {}, OPTVOLUME = {} } @INPROCEEDINGS{EQUI-CDC87, AUTHOR = {E.D. Sontag}, BOOKTITLE = {Proc. IEEE Conf. Decision and Control, Los Angeles, Dec.1987}, TITLE = {An approach to the automatic design of first-order controllers along reference trajectories}, YEAR = {1987}, OPTADDRESS = {}, OPTCROSSREF = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, OPTORGANIZATION = {}, PAGES = {363--1367}, OPTPUBLISHER = {}, OPTSERIES = {}, OPTVOLUME = {} } @INPROCEEDINGS{JHU87, AUTHOR = {E.D. Sontag}, BOOKTITLE = {Proc. Conf. Info. Sciences and Systems, Johns Hopkins University Press}, TITLE = {Equilinearization: A simplified derivation and experimental results}, YEAR = {1987}, OPTADDRESS = {}, OPTCROSSREF = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, OPTORGANIZATION = {}, PAGES = {490--495}, OPTPUBLISHER = {}, OPTSERIES = {}, OPTVOLUME = {} } @TECHREPORT{CAIP1, AUTHOR = {E.D. Sontag and H.J. Sussmann}, INSTITUTION = {Rutgers Center for Computer Aids for Industrial Productivity}, TITLE = {Optimization algorithms for image restoration and segmentation}, YEAR = {1987}, OPTADDRESS = {}, OPTMONTH = {}, OPTNOTE = {}, NUMBER = {34}, OPTTYPE = {} } @INCOLLECTION{MR862338, AUTHOR = {E.D. Sontag}, BOOKTITLE = {Algebraic and geometric methods in nonlinear control theory}, PUBLISHER = {Reidel}, TITLE = {Orbit theorems and sampling}, YEAR = {1986}, ADDRESS = {Dordrecht}, OPTCHAPTER = {}, OPTCROSSREF = {}, OPTEDITION = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, PAGES = {441--483}, SERIES = {Math. Appl.}, OPTTYPE = {}, VOLUME = {29}, PDF = {../FTP_DIR/85paris.pdf}, ABSTRACT = { This paper proposes a notion of smooth action on a manifold, and establishes a general integrability result for certain associated distributions. As corollaries, various classical and new results on manifold structures of orbits are established, and the main theorem on preservation of transitivity under sampling is shown to be a simple consequence. } } @ARTICLE{MR836650, AUTHOR = {M. L. J. Hautus and E.D. Sontag}, JOURNAL = {J. Pure Appl. Algebra}, TITLE = {New results on pole-shifting for parametrized families of systems}, YEAR = {1986}, OPTMONTH = {}, OPTNOTE = {}, NUMBER = {3}, PAGES = {229--244}, VOLUME = {40}, KEYWORDS = {systems over rings}, PDF = {../FTP_DIR/mh2.pdf}, ABSTRACT = { New results are given on the pole-shifting problem for commutative rings, and these are then applied to conclude that rings of continuous, smooth, or real-analytic functions on a manifold X are PA rings if and only if X is one-dimensional. } } @ARTICLE{MR850445, AUTHOR = {E.D. Sontag}, JOURNAL = {Systems Control Lett.}, TITLE = {An eigenvalue condition for sample weak controllability of bilinear systems}, YEAR = {1986}, OPTMONTH = {}, OPTNOTE = {}, NUMBER = {4}, PAGES = {313--315}, VOLUME = {7}, ADDRESS = {Amsterdam, The Netherlands, The Netherlands}, KEYWORDS = {discrete-time}, PUBLISHER = {Elsevier Science Publishers B. V.}, PDF = {../FTP_DIR/bilin-scl.pdf}, ABSTRACT = { Weak controllability of bilinear systems is preserved under sampling provided that the sampling period satisfies a condition related to the eigenvalues of the autonomous dynamics matrix. This condition generalizes the classical Kalman-Ho-Narendra criterion which is well known in the linear case. }, DOI = {http://dx.doi.org/10.1016/0167-6911(86)90045-9} } @ARTICLE{MR863279, AUTHOR = {E.D. Sontag}, JOURNAL = {Systems Control Lett.}, TITLE = {Comments on: ``Some results on pole-placement and reachability'' [Systems Control Lett. 6 (1986), no. 5, 325--328; MR0821927 (87c:93032)] by P. K. Sharma}, YEAR = {1986}, OPTMONTH = {}, OPTNOTE = {}, NUMBER = {1}, PAGES = {79--83}, VOLUME = {8}, ADDRESS = {Amsterdam, The Netherlands, The Netherlands}, PUBLISHER = {Elsevier Science Publishers B. V.}, PDF = {../FTP_DIR/comments-sharma.pdf}, ABSTRACT = { We present various comments on a question about systems over rings posed in a recent note by Sharma, proving that a ring R is pole-assignable if and only if, for every reachable system (F,G), G contains a rank-one summand of the state space. We also provide a generalization to deal with dynamic feedback. }, DOI = {http://dx.doi.org/10.1016/0167-6911(86)90034-4} } @ARTICLE{HG, AUTHOR = {E.D. Sontag}, JOURNAL = {IMA Journal of Mathematical Control and Information}, TITLE = {Continuous stabilizers and high-gain feedback,}, YEAR = {1986}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, PAGES = {237--253}, VOLUME = {3}, KEYWORDS = {adaptive control, systems over rings}, PDF = {../FTP_DIR/high-gain.pdf}, ABSTRACT = { A controller is shown to exist, universal for the family of all systems of fixed dimension n, and m controls, which stabilizes those systems that are stabilizable, if certain gains are large enough. The controller parameters are continuous, in fact polynomial, functions of the entries of the plant. As a consequence, a result is proved on polynomial stabilization of families of systems. } } @INPROCEEDINGS{PU86, AUTHOR = {E.D. Sontag}, BOOKTITLE = {Proc. Conf. Info. Sci. and Systems, Princeton, 1986}, TITLE = {Controllability and linearized regulation}, YEAR = {1986}, OPTADDRESS = {}, OPTCROSSREF = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, OPTORGANIZATION = {}, PAGES = {67--671}, OPTPUBLISHER = {}, OPTSERIES = {}, OPTVOLUME = {} } @INPROCEEDINGS{ROB2, AUTHOR = {E.D. Sontag and H.J. Sussmann}, BOOKTITLE = {Proc. IEEE Int.Conf.on Robotics and Automation, San Francisco, April 1986}, TITLE = {Time-optimal control of manipulators}, YEAR = {1986}, OPTADDRESS = {}, OPTCROSSREF = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, OPTORGANIZATION = {}, PAGES = {1692--1697}, OPTPUBLISHER = {}, OPTSERIES = {}, OPTVOLUME = {}, KEYWORDS = {robotics, optimal control}, PDF = {../FTP_DIR/sf86.pdf}, ABSTRACT = { This paper studies time-optimal control questions for a certain class of nonlinear systems. This class includes a large number of mechanical systems, in particular, rigid robotic manipulators with torque constraints. As nonlinear systems, these systems have many properties that are false for generic systems of the same dimensions. } } @INCOLLECTION{MR828315, AUTHOR = {E.D. Sontag}, BOOKTITLE = {Linear algebra and its role in systems theory (Brunswick, Maine, 1984)}, PUBLISHER = {Amer. Math. Soc.}, TITLE = {An introduction to the stabilization problem for parametrized families of linear systems}, YEAR = {1985}, ADDRESS = {Providence, RI}, OPTCHAPTER = {}, OPTCROSSREF = {}, OPTEDITION = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, PAGES = {369--400}, SERIES = {Contemp. Math.}, OPTTYPE = {}, VOLUME = {47}, KEYWORDS = {systems over rings}, PDF = {../FTP_DIR/ams85.pdf}, ABSTRACT = { This paper provides an introduction to definitions and known facts relating to the stabilization of parametrized families of linear systems using static and dynamic controllers. New results are given in the rational and polynomial cases. } } @ARTICLE{MR808240, AUTHOR = {B.W. Dickinson and E.D. Sontag}, JOURNAL = {IEEE Trans. Inform. Theory}, TITLE = {Dynamic realizations of sufficient sequences}, YEAR = {1985}, OPTMONTH = {}, OPTNOTE = {}, NUMBER = {5}, PAGES = {670--676}, VOLUME = {31}, KEYWORDS = {realization theory, statistics}, PDF = {../FTP_DIR/bd-suft-seq.pdf}, ABSTRACT = { Let Ul, U2, ... be a sequence of observed random variables and (T1(U1),T2(Ul,U2),...) be a corresponding sequence of sufficient statistics (a sufficient sequence). Under certain regularity conditions, the sufficient sequence defines the input/output map of a time-varying, discrete-time nonlinear system. This system provides a recursive way of updating the sufficient statistic as new observations are made. Conditions are provided assuring that such a system evolves in a state space of minimal dimension. Several examples are provided to illustrate how this notion of dimensional minimality is related to other properties of sufficient sequences. The results can be used to verify the form of the minimum dimension (discrete-time) nonlinear filter associated with the autoregres- sive parameter estimation problem. } } @ARTICLE{MR801975, AUTHOR = {E.D. Sontag}, JOURNAL = {Inform. Process. Lett.}, TITLE = {Real addition and the polynomial hierarchy}, YEAR = {1985}, OPTMONTH = {}, OPTNOTE = {}, NUMBER = {3}, PAGES = {115--120}, VOLUME = {20}, PDF = {../FTP_DIR/ra.pdf}, ABSTRACT = { The k-th alternation level of the theory of real numbers under addition and order is log-complete for the k-th level of the polynomial hierarchy. } } @INPROCEEDINGS{JHU85, AUTHOR = {E.D. Sontag}, BOOKTITLE = {Proc.Conf. Info. Sci. and Systems, Johns Hopkins University, March 1985}, TITLE = {Further results on accessibility under sampling}, YEAR = {1985}, OPTADDRESS = {}, OPTCROSSREF = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, OPTORGANIZATION = {}, OPTPAGES = {}, OPTPUBLISHER = {}, OPTSERIES = {}, OPTVOLUME = {} } @INPROCEEDINGS{IM1, AUTHOR = {E.D. Sontag and H.J. Sussmann}, BOOKTITLE = {Proc. IEEE Conf. Dec. and Control, 1985}, TITLE = {Image restoration and segmentation using the annealing algorithm}, YEAR = {1985}, OPTADDRESS = {}, OPTCROSSREF = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, OPTORGANIZATION = {}, PAGES = {768--773}, OPTPUBLISHER = {}, OPTSERIES = {}, OPTVOLUME = {}, KEYWORDS = {image processing, optimization}, PDF = {../FTP_DIR/annealing.pdf}, ABSTRACT = { We consider the problem of estimating a signal, which is known -- or assumed -- to be constant on each of the members of a partition of a square lattice into m unknown regions, from the observation of the signal plus Gaussian noise. This is a nonlinear estimation problem, for which it is not appropriate to use the conditional expectation as the estimate. We show that, at least in principle, the "maximum iikelihood estimator" (MLE) proposed by Geman and Geman lends itself to numerical computation using the annealing algorithm. We argue that the MLE by itself can be, under certain conditions (low signal to noise ratio), a very unsatisfactory estimator, in that it does worse than just deciding that the signal was zero. However, if combined with a rule which we propose, for deciding when to use and when to ignore it, the MLE can provide a reasonable suboptimal estimator. We then discuss preliminary numerical data obtained using the annealing method. These results indicate that: (a) the annealing algorithm performs remarkably well, and (b) a criterion can be formulated in terms of quantities computed from the observed image (without using a priori knowledge of the signal-to-noise ratio) for deciding when to keep the MLE. } } @INPROCEEDINGS{ROB1, AUTHOR = {E.D. Sontag and H.J. Sussmann}, BOOKTITLE = {Proc. IEEE Conf. Dec. and Control, 1985}, TITLE = {Remarks on the time-optimal control of two-link manipulators}, YEAR = {1985}, OPTADDRESS = {}, OPTCROSSREF = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, OPTORGANIZATION = {}, PAGES = {1646--1652}, OPTPUBLISHER = {}, OPTSERIES = {}, OPTVOLUME = {} } @INCOLLECTION{MR792151, AUTHOR = {E.D. Sontag}, BOOKTITLE = {Mathematical theory of networks and systems (Beer Sheva, 1983)}, PUBLISHER = {Springer}, TITLE = {An approximation theorem in nonlinear sampling}, YEAR = {1984}, ADDRESS = {London}, OPTCHAPTER = {}, OPTCROSSREF = {}, OPTEDITION = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, PAGES = {806--812}, SERIES = {Lecture Notes in Control and Inform. Sci.}, OPTTYPE = {}, VOLUME = {58}, PDF = {../FTP_DIR/83mtns.pdf}, ABSTRACT = { We continue here our investigation into the preservation of structural properties under the sampling of nonlinear systems. The main new result is that, under minimal hypothesis, a controllable system always satisfies a strong type of approximate sampled controllability. } } @ARTICLE{MR735384, AUTHOR = {C.A. Schwartz and B.W. Dickinson and E.D. Sontag}, JOURNAL = {Stochastics}, TITLE = {Characterizing innovations realizations for random processes}, YEAR = {1984}, OPTMONTH = {}, OPTNOTE = {}, NUMBER = {3-4}, PAGES = {159--172}, VOLUME = {11}, KEYWORDS = {statistics}, PDF = {../FTP_DIR/innovations.pdf}, ABSTRACT = { In this paper we are concerned with the theory of second order (linear) innovations for discrete random processes. We show that of existence of a finite dimensional linear filter realizing the mapping from a discrete random process to its innovations is equivalent to a certain semiiseparable structure of the covariance sequence of the process. We also show that existence of a finite dimensional realization (linear or nonlinear) of the mapping from a process to its innovations implies that the process have this serniseparable covariance sequence property. In particular, for a stationary random process, the spectral density function must be rational. } } @ARTICLE{MR768713, AUTHOR = {E.D. Sontag}, JOURNAL = {Systems Control Lett.}, TITLE = {A concept of local observability}, YEAR = {1984}, OPTMONTH = {}, OPTNOTE = {}, NUMBER = {1}, PAGES = {41--47}, VOLUME = {5}, KEYWORDS = {observability}, PDF = {../FTP_DIR/localobs.pdf}, ABSTRACT = { A notion of local observability, which is natural in the context of nonlinear input/output regulation. is introduced. A simple characterization is provided, a comparison is made with other local nonlinear observability definitions. and its behavior under constant-rate sampling is analyzed. } } @ARTICLE{MR730505, AUTHOR = {E.D. Sontag}, JOURNAL = {Internat. J. Control}, TITLE = {An algebraic approach to bounded controllability of linear systems}, YEAR = {1984}, OPTMONTH = {}, OPTNOTE = {}, NUMBER = {1}, PAGES = {181--188}, VOLUME = {39}, KEYWORDS = {saturation}, PDF = {../FTP_DIR/sic.pdf}, ABSTRACT = { In this note we present an algebraic approach to the proof that a linear system with matrices (A,B) is null-controllable using bounded inputs iff it is null-controllable (with unbounded inputs) and all eigenvalues of A have nonpositive real parts (continuous time) or magnitude not greater than one (discrete time). We also give the analogous results for the asymptotic case. Finally, we give an interpretation of these results in the context of local nonlinear controllability. } } @ARTICLE{MR748279, AUTHOR = {E.D. Sontag}, JOURNAL = {Systems Control Lett.}, TITLE = {Parametric stabilization is easy}, YEAR = {1984}, OPTMONTH = {}, OPTNOTE = {}, NUMBER = {4}, PAGES = {181--188}, VOLUME = {4}, KEYWORDS = {systems over rings}, PDF = {../FTP_DIR/psis.pdf}, ABSTRACT = { A polynomially parametrized family of continuous-time controllable linear systems is always stabilizable by polynomially parametrized feedback. (Note: appendix had a MACSYMA computation. I cannot find the source file for that. Please look at journal if interested, but this is not very important. Also, two figures involving root loci are not in the web version.) } } @INPROCEEDINGS{IMMER, AUTHOR = {E.D. Sontag}, BOOKTITLE = {Proc. IEEE Conf. Dec. and Control, Las Vegas, Dec. 1984}, TITLE = {Remarks on input/output linearization}, YEAR = {1984}, OPTADDRESS = {}, OPTCROSSREF = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, OPTORGANIZATION = {}, PAGES = {409--412}, OPTPUBLISHER = {}, OPTSERIES = {}, OPTVOLUME = {}, PDF = {../FTP_DIR/84cdc-immer.pdf}, ABSTRACT = { In the context of realization theory, conditions are given for the possibility of simulating a given discrete time system, using immersion and/or feedback, by linear or state-affine systems. } } @INCOLLECTION{MR783866, AUTHOR = {E.D. Sontag}, BOOKTITLE = {Mathematical tools and models for control, systems analysis and signal processing, Vol. 3 (Toulouse/Paris, 1981/1982)}, PUBLISHER = {CNRS}, TITLE = {Remarks on the preservation of various controllability properties under sampling}, YEAR = {1983}, ADDRESS = {Paris}, OPTCHAPTER = {}, OPTCROSSREF = {}, OPTEDITION = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, PAGES = {623--637}, SERIES = {Travaux Rech. Coop. Programme 567}, OPTTYPE = {}, OPTVOLUME = {}, PDF = {../FTP_DIR/83belle-ille-sampling.pdf}, ABSTRACT = { This note studies the preservation of controllability (and other properties) under sampling of a nonlinear system. More detailed results are obtained in the cases of analytic systems and of systems with finite dimensional Lie algebras. } } @ARTICLE{MR722954, AUTHOR = {R.T. Bumby and E.D. Sontag}, JOURNAL = {Systems Control Lett.}, TITLE = {Stabilization of polynomially parametrized families of linear systems. The single-input case}, YEAR = {1983}, OPTMONTH = {}, OPTNOTE = {}, NUMBER = {5}, PAGES = {251--254}, VOLUME = {3}, KEYWORDS = {systems over rings}, PDF = {../FTP_DIR/bum.pdf}, ABSTRACT = { Given a continuous-time family of finite dimensional single input linear systems, parametrized polynomially, such that each of the systems in the family is controllable, there exists a polynomially parametrized control law making each of the systems in the family stable. } } @ARTICLE{MR696908, AUTHOR = {E.D. Sontag}, JOURNAL = {SIAM J. Control Optim.}, TITLE = {A Lyapunov-like characterization of asymptotic controllability}, YEAR = {1983}, OPTMONTH = {}, OPTNOTE = {}, NUMBER = {3}, PAGES = {462--471}, VOLUME = {21}, KEYWORDS = {control-Lyapunov functions}, PDF = {../FTP_DIR/clf83.pdf}, ABSTRACT = { It is shown that a control system in Rn is asymptotically controllable to the origin if and only if there exists a positive definite continuous functional of the states whose derivative can be made negative by appropriate choices of controls. } } @INPROCEEDINGS{JHU83, AUTHOR = {E.D. Sontag}, BOOKTITLE = {Proc. Johns Hopkins Conf. on Info. Sci. and Systems, 1983}, TITLE = {Further remarks preservation of accessibility under sampling}, YEAR = {1983}, OPTADDRESS = {}, OPTCROSSREF = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, OPTORGANIZATION = {}, PAGES = {326--332}, OPTPUBLISHER = {}, OPTSERIES = {}, OPTVOLUME = {} } @INCOLLECTION{GNV2, AUTHOR = {E.D. Sontag}, BOOKTITLE = {Dynamical Systems II}, PUBLISHER = {Academic Press, NY}, TITLE = {A characterization of asymptotic controllability}, YEAR = {1982}, OPTADDRESS = {}, OPTCHAPTER = {}, OPTCROSSREF = {}, OPTEDITION = {}, EDITOR = {A. Bednarek and L. Cesari}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, PAGES = {645--648}, OPTSERIES = {}, OPTTYPE = {}, OPTVOLUME = {}, KEYWORDS = {control-Lyapunov functions} } @INCOLLECTION{MR837462, AUTHOR = {E.D. Sontag}, BOOKTITLE = {Feedback control of linear and nonlinear systems (Bielefeld/Rome, 1981)}, PUBLISHER = {Springer}, TITLE = {Abstract regulation of nonlinear systems: stabilization}, YEAR = {1982}, ADDRESS = {Berlin}, OPTCHAPTER = {}, OPTCROSSREF = {}, OPTEDITION = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, PAGES = {227--243}, SERIES = {Lecture Notes in Control and Inform. Sci.}, OPTTYPE = {}, VOLUME = {39} } @INCOLLECTION{MR735820, AUTHOR = {E.D. Sontag}, BOOKTITLE = {Control science and technology for the progress of society, Vol. 1 (Kyoto, 1981)}, PUBLISHER = {IFAC}, TITLE = {Linear systems over commutative rings: a (partial) updated survey}, YEAR = {1982}, ADDRESS = {Laxenburg}, OPTCHAPTER = {}, OPTCROSSREF = {}, OPTEDITION = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, PAGES = {325--330}, OPTSERIES = {}, OPTTYPE = {}, OPTVOLUME = {}, KEYWORDS = {systems over rings} } @ARTICLE{MR680321, AUTHOR = {P.P. Khargonekar and E.D. Sontag}, JOURNAL = {IEEE Trans. Automat. Control}, TITLE = {On the relation between stable matrix fraction factorizations and regulable realizations of linear systems over rings}, YEAR = {1982}, OPTMONTH = {}, OPTNOTE = {}, NUMBER = {3}, PAGES = {627--638}, VOLUME = {27}, KEYWORDS = {systems over rings}, PDF = {../FTP_DIR/pk.pdf}, ABSTRACT = { Various types of transfer matrix factorizations are of interest when designing regulators for generalized types of linear systems (delay differential. 2-D, and families of systems). This paper studies the existence of stable and of stable proper factorizations, in the context of the thery of systems over rings. Factorability is related to stabilizability and detectability properties of realizations of the transfer matrix. The original formulas for coprime factorizations (which are valid, in particular, over the field of reals) were given in this paper. } } @ARTICLE{MR644949, AUTHOR = {E.D. Sontag}, JOURNAL = {Pacific J. Math.}, TITLE = {Remarks on piecewise-linear algebra}, YEAR = {1982}, OPTMONTH = {}, OPTNOTE = {}, NUMBER = {1}, PAGES = {183--201}, VOLUME = {98}, KEYWORDS = {hybrid systems, piecewise linear systems}, PDF = {../FTP_DIR/pla.pdf}, ABSTRACT = { Algebraic study of functions defined by piecewise linear (generally discontinuous) equations. File obtained by scanning a reprint. } } @INPROCEEDINGS{82ciss, AUTHOR = {E.D. Sontag}, BOOKTITLE = {Proc.Princeton Conf.on Information Sciences and Systems, Princeton, March 1982}, TITLE = {Abstract regulation of nonlinear systems: Stabilization, Part II}, YEAR = {1982}, OPTADDRESS = {}, OPTCROSSREF = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, OPTORGANIZATION = {}, PAGES = {431-435}, OPTPUBLISHER = {}, OPTSERIES = {}, OPTVOLUME = {}, KEYWORDS = {feedback stabilization} } @INPROCEEDINGS{SIC-CDC82, AUTHOR = {E.D. Sontag}, BOOKTITLE = {Proc. IEEE Conf. Dec. and Control, Orlando, Dec. 1982}, TITLE = {Small-input controllability}, YEAR = {1982}, OPTADDRESS = {}, OPTCROSSREF = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, OPTORGANIZATION = {}, OPTPAGES = {}, OPTPUBLISHER = {}, OPTSERIES = {}, OPTVOLUME = {} } @INPROCEEDINGS{ACC, AUTHOR = {E.D. Sontag and H.J. Sussmann}, BOOKTITLE = {Proc. IEEE Conf. Dec. and Control, Orlando, Dec. 1982}, TITLE = {Accessibility under sampling}, YEAR = {1982}, OPTADDRESS = {}, OPTCROSSREF = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, OPTORGANIZATION = {}, OPTPAGES = {}, OPTPUBLISHER = {}, OPTSERIES = {}, OPTVOLUME = {}, KEYWORDS = {discrete-time}, PDF = {../FTP_DIR/82cdc.pdf}, ABSTRACT = { This note addresses the following problem: Find conditions under which a continuous-time (nonlinear) system gives rise, under constant rate sampling, to a discrete-time system which satisfies the accessibility property. } } @ARTICLE{MR601679, AUTHOR = {R. Bumby and E.D. Sontag and H.J. Sussmann and W. Vasconcelos}, JOURNAL = {J. Pure Appl. Algebra}, TITLE = {Remarks on the pole-shifting problem over rings}, YEAR = {1981}, OPTMONTH = {}, OPTNOTE = {}, NUMBER = {2}, PAGES = {113--127}, VOLUME = {20}, KEYWORDS = {systems over rings, systems over rings}, PDF = {../FTP_DIR/bssv.pdf}, ABSTRACT = { Problems that appear in trying to extend linear control results to systems over rings R have attracted considerable attention lately. This interest has been due mainly to applications-oriented motivations (in particular, dealing with delay-differential equations), and partly to a purely algebraic interest. Given a square n-matrix F and an n-row matrix G. pole-shifting problems consist in obtaining more or less arbitrary characteristic polynomials for F+GK, for suitable ("feedback") matrices K. A review of known facts is given, various partial results are proved, and the case n=2 is studied in some detail. } } @ARTICLE{MR686833, AUTHOR = {E.D. Sontag}, JOURNAL = {Inform. and Control}, TITLE = {Conditions for abstract nonlinear regulation}, YEAR = {1981}, OPTMONTH = {}, OPTNOTE = {}, NUMBER = {2}, PAGES = {105--127}, VOLUME = {51}, KEYWORDS = {feedback stabilization}, PDF = {../FTP_DIR/reg.pdf}, ABSTRACT = { A paper that introduces a separation principle for general finite dimensional analytic continuous-time systems, proving the equivalence between existence of an output regulator (which is an abstract dynamical system) and certain "0-detectability" and asymptotic controllability assumptions. } } @ARTICLE{PLS, AUTHOR = {E.D. Sontag}, JOURNAL = {IEEE Trans. Automat. Control}, TITLE = {Nonlinear regulation: the piecewise linear approach}, YEAR = {1981}, OPTMONTH = {}, OPTNOTE = {}, NUMBER = {2}, PAGES = {346--358}, VOLUME = {26}, KEYWORDS = {hybrid systems}, PDF = {../FTP_DIR/pls.pdf}, ABSTRACT = { Development of an approach to nonlinear control based on mixtures of linear systems and finite automata. File obtained by scanning. } } @INPROCEEDINGS{PK-CDC81, AUTHOR = {P.P. Khargonekar and E.D. Sontag}, BOOKTITLE = {Proc. IEEE Conf.Dec. and Control, San Diego, Dec. 1981}, TITLE = {On the relation between stable matrix fraction decompositions and regulable realizations of systems over rings}, YEAR = {1981}, OPTADDRESS = {}, OPTCROSSREF = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, OPTORGANIZATION = {}, PAGES = {1006--1011}, OPTPUBLISHER = {}, OPTSERIES = {}, OPTVOLUME = {}, KEYWORDS = {systems over rings} } @TECHREPORT{BTL1, AUTHOR = {E.D. Sontag and D.E. Stevenson}, INSTITUTION = {Bell Telephone Labs.}, TITLE = {Remarks on multi-server, multi-priority queuing models related to MVS job scheduling}, YEAR = {1981}, OPTADDRESS = {}, OPTMONTH = {}, OPTNOTE = {}, NUMBER = {TM-81-45281-1}, OPTTYPE = {} } @INCOLLECTION{MR605868, AUTHOR = {M. L. J. Hautus and E.D. Sontag}, BOOKTITLE = {Algebraic and geometric methods in linear systems theory (AMS-NASA-NATO Summer Sem., Harvard Univ., Cambridge, Mass., 1979)}, PUBLISHER = {Amer. Math. Soc.}, TITLE = {An approach to detectability and observers}, YEAR = {1980}, ADDRESS = {Providence, R.I.}, OPTCHAPTER = {}, OPTCROSSREF = {}, OPTEDITION = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, PAGES = {99--135}, SERIES = {Lectures in Appl. Math.}, OPTTYPE = {}, VOLUME = {18}, KEYWORDS = {observability}, PDF = {../FTP_DIR/mh-observers.pdf}, ABSTRACT = { This paper proposes an approach to the problem of establishing the existence of observers for deterministic dynamical systems. This approach differs from the standard one based on Luenberger observers in that the observation error is not required to be Markovian given the past input and output data. A general abstract result is given, which special- izes to new results for parametrized families of linear systems, delay systems and other classes of systems. Related problems of feedback control and regulation are also studied. } } @INCOLLECTION{MR581716, AUTHOR = {E.D. Sontag}, BOOKTITLE = {Systems analysis (Conf., Bordeaux, 1978)}, PUBLISHER = {Soc. Math. France}, TITLE = {On quasireachable realizations of a polynomial response}, YEAR = {1980}, ADDRESS = {Paris}, OPTCHAPTER = {}, OPTCROSSREF = {}, OPTEDITION = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, PAGES = {207--217}, SERIES = {Astérisque}, OPTTYPE = {}, VOLUME = {75} } @ARTICLE{MR571759, AUTHOR = {E.D. Sontag}, JOURNAL = {IEEE Trans. Automat. Control}, TITLE = {On generalized inverses of polynomial and other matrices}, YEAR = {1980}, OPTMONTH = {}, OPTNOTE = {}, NUMBER = {3}, PAGES = {514--517}, VOLUME = {25}, PDF = {../FTP_DIR/wgi.pdf}, ABSTRACT = { Necessary and sufficient conditions are given for a matrix over a ring to admit a Moore-Penrose generalized inverse in a weak sense. (Attached is also a Math Review with additional comments on strong inverses.) } } @ARTICLE{MR561358, AUTHOR = {E.D. Sontag}, JOURNAL = {IEEE Trans. Automat. Control}, TITLE = {On the length of inputs necessary in order to identify a deterministic linear system}, YEAR = {1980}, OPTMONTH = {}, OPTNOTE = {}, NUMBER = {1}, PAGES = {120--121}, VOLUME = {25}, PDF = {../FTP_DIR/80tac-number-inputs.pdf}, ABSTRACT = { The family of m-input, n-dimensional linear systems can be globally Identified with a generic input sequence of length 2mn. This bound is the best possible. A best bound is proved also for a corresponding local identification problem. } } @INPROCEEDINGS{PLS-PU81, AUTHOR = {E.D. Sontag}, BOOKTITLE = {Proc.Princeton Conf.on Information Sciences and Systems, Princeton, March 1980}, TITLE = {Nonlinear regulation, the piecewise linear approach}, YEAR = {1980}, OPTADDRESS = {}, OPTCROSSREF = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, OPTORGANIZATION = {}, OPTPAGES = {}, OPTPUBLISHER = {}, OPTSERIES = {}, OPTVOLUME = {}, KEYWORDS = {piecewise linear systems} } @INPROCEEDINGS{CF, AUTHOR = {E.D. Sontag and H.J. Sussmann}, BOOKTITLE = {Proc. IEEE Conf. Decision and Control, Albuquerque, Dec.1980}, TITLE = {Remarks on continuous feedback}, YEAR = {1980}, OPTADDRESS = {}, OPTCROSSREF = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, OPTORGANIZATION = {}, PAGES = {916--921}, OPTPUBLISHER = {}, OPTSERIES = {}, OPTVOLUME = {}, KEYWORDS = {feedback stabilization}, PDF = {../FTP_DIR/80cdc.pdf}, ABSTRACT = { We show that, in general, it is impossible to stabilize a controllable system by means of a continuous feedback, even if memory is allowed. No optimality considerations are involved. All state spaces are Euclidean spaces, so no obstructions arising from the state space topology are involved either. For one dimensional state and input, we prove that continuous stabilization with memory is always possible. (This is an old conference paper, never published in journal form but widely cited nonetheless. Warning: file is very large, since it was scanned.) } } @BOOK{Springer79, PUBLISHER = {Springer-Verlag}, TITLE = {Polynomial Response Maps}, YEAR = {1979}, AUTHOR = {E.D. Sontag}, ALTEDITOR = {}, ADDRESS = {Berlin}, OPTEDITION = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, SERIES = {Lecture Notes in Control and Information Sciences}, VOLUME = {13}, KEYWORDS = {realization theory, discrete-time, real algebraic geometry}, PAGES = {viii+168}, PDF = {../FTP_DIR/polynomial_response_maps.pdf}, ABSTRACT = { (This is a monograph based upon Eduardo Sontag's Ph.D. thesis. The contents are basically the same as the thesis, except for a very few revisions and extensions.) This work deals the realization theory of discrete-time systems (with inputs and outputs, in the sense of control theory) defined by polynomial update equations. It is based upon the premise that the natural tools for the study of the structural-algebraic properties (in particular, realization theory) of polynomial input/output maps are provided by algebraic geometry and commutative algebra, perhaps as much as linear algebra provides the natural tools for studying linear systems. Basic ideas from algebraic geometry are used throughout in system-theoretic applications (Hilbert's basis theorem to finite-time observability, dimension theory to minimal realizations, Zariski's Main Theorem to uniqueness of canonical realizations, etc). In order to keep the level elementary (in particular, not utilizing sheaf-theoretic concepts), certain ideas like nonaffine varieties are used only implicitly (eg., quasi-affine as open sets in affine varieties) or in technical parts of a few proofs, and the terminology is similarly simplified (e.g., "polynomial map" instead of "scheme morphism restricted to k-points", or "k-space" instead of "k-points of an affine k-scheme"). } } @ARTICLE{MR525830, AUTHOR = {Y. Rouchaleau and E.D. Sontag}, JOURNAL = {J. Comput. System Sci.}, TITLE = {On the existence of minimal realizations of linear dynamical systems over Noetherian integral domains}, YEAR = {1979}, OPTMONTH = {}, OPTNOTE = {}, NUMBER = {1}, PAGES = {65--75}, VOLUME = {18}, PDF = {../FTP_DIR/noether-realiz.pdf}, ABSTRACT = { This paper studies the problem of obtaining minimal realizations of linear input/output maps defined over rings. In particular, it is shown that, contrary to the case of systems over fields, it is in general impossible to obtain realizations whose dimiension equals the rank of the Hankel matrix. A characterization is given of those (Noetherian) rings over which realizations of such dimensions can he always obtained, and the result is applied to delay-differential systems. } } @ARTICLE{MR554018, AUTHOR = {E.D. Sontag}, JOURNAL = {Kybernetika (Prague)}, TITLE = {On finitary linear systems}, YEAR = {1979}, OPTMONTH = {}, OPTNOTE = {}, NUMBER = {5}, PAGES = {349--358}, VOLUME = {15}, KEYWORDS = {systems over rings}, PDF = {../FTP_DIR/finitary.pdf}, ABSTRACT = { An abstract operator approach is introduced, permitting a unified study of discrete- and continuous-time linear control systems. As an application, an algorithm is given for deciding if a linear system can be built from any fixed set of linear components. Finally, a criterion is given for reachability of the abstract systems introduced, giving thus a unified proof of known reachability results for discrete-time, continuous-time, and delay-differential systems. } } @ARTICLE{MR516861, AUTHOR = {E.D. Sontag}, JOURNAL = {SIAM J. Control Optim.}, TITLE = {On the observability of polynomial systems. I. Finite-time problems}, YEAR = {1979}, OPTMONTH = {}, OPTNOTE = {}, NUMBER = {1}, PAGES = {139--151}, VOLUME = {17}, KEYWORDS = {observability}, PDF = {../FTP_DIR/obs.pdf}, ABSTRACT = { Different notions of observability are compared for systems defined by polynomial difference equations. The main result states that, for systems having the standard property of (multiple-experiment initial-state) observability, the response to a generic input sequence is sufficient for final-state determination. Some remarks are made on results for nonpolynomial and/or continuous-time systems. An identifiability result is derived from the above. } } @ARTICLE{MR529666, AUTHOR = {E.D. Sontag}, JOURNAL = {IEEE Trans. Circuits and Systems}, TITLE = {Realization theory of discrete-time nonlinear systems. I. The bounded case}, YEAR = {1979}, OPTMONTH = {}, OPTNOTE = {}, NUMBER = {5}, PAGES = {342--356}, VOLUME = {26}, PDF = {../FTP_DIR/state-affine-realiz.pdf}, ABSTRACT = { A state-space realization theory is presented for a wide class of discrete time input/output behaviors. Although In many ways restricted, this class does include as particular cases those treated in the literature (linear, multilinear, internally bilinear, homogeneous), as well ss certain nonanalytic nonlinearities. The theory is conceptually simple, and matrix-theoretic algorithms are straightforward. Finite-realizability of these behaviors by state-affine systems is shown to be equivalent both to the existence of high-order input/output equadons and to realizability by more general types of systems. } } @ARTICLE{MR509164, AUTHOR = {W. Dicks and E.D. Sontag}, JOURNAL = {J. Pure Appl. Algebra}, TITLE = {Sylvester domains}, YEAR = {1978}, OPTMONTH = {}, OPTNOTE = {}, NUMBER = {3}, PAGES = {243--275}, VOLUME = {13}, PDF = {../FTP_DIR/wdicks.pdf}, ABSTRACT = { The inner rank of an m x n matrix A over a ring is defined as the least integer r such that A can be expressed as the product of an m x r and an r x n matrix. For example, over a (skew) field this concept coincides with the usual notion of rank. This notion is studied in this paper, and is related to Sylvester's law of nullity and work by P.M. Cohn. } } @ARTICLE{2D, AUTHOR = {E.D. Sontag}, JOURNAL = {IEEE Trans. Acoustics, Speech, and Signal Processing}, TITLE = {On first-order equations for multidimensional filters}, YEAR = {1978}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, PAGES = {480--482}, VOLUME = {26}, PDF = {../FTP_DIR/2D.pdf}, ABSTRACT = { A construction is given to obtain first-order equation representations of a multidimensional filter, whose dimension is of the order of the degree of the transfer function. } } @ARTICLE{MR0490149, AUTHOR = {E.D. Sontag}, JOURNAL = {Information and Control}, TITLE = {On split realizations of response maps over rings}, YEAR = {1978}, OPTMONTH = {}, OPTNOTE = {}, NUMBER = {1}, PAGES = {23--33}, VOLUME = {37}, KEYWORDS = {systems over rings}, PDF = {../FTP_DIR/split.pdf}, ABSTRACT = { This paper deals with observability properties of realizations of linear response maps defined over commutative rings. A characterization is given for those maps which admit realizations which are simultaneously reachable and observable in a strong sense. Applications are given to delay-differential systems. } } @INPROCEEDINGS{JHU78, AUTHOR = {E.D. Sontag}, BOOKTITLE = {Proc. Conf. Inform. Sci. and Systems, John Hopkins Univ. (1978)}, TITLE = {Algebraic-geometric methods in the realization of discrete-time systems}, YEAR = {1978}, OPTADDRESS = {}, OPTCROSSREF = {}, OPTEDITOR = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, OPTORGANIZATION = {}, PAGES = {158--162}, OPTPUBLISHER = {}, OPTSERIES = {}, OPTVOLUME = {} } @INCOLLECTION{GNV1, AUTHOR = {E.D. Sontag}, BOOKTITLE = {Dynamical Systems}, PUBLISHER = {Academic Press, New York}, TITLE = {On the internal realization of nonlinear behaviors}, YEAR = {1977}, OPTADDRESS = {}, OPTCHAPTER = {}, OPTCROSSREF = {}, OPTEDITION = {}, EDITOR = {A. Bednarek and L. Cesari}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, PAGES = {93--497}, OPTSERIES = {}, OPTTYPE = {}, OPTVOLUME = {} } @ARTICLE{MR0472151, AUTHOR = {E.D. Sontag}, JOURNAL = {Math. Systems Theory}, TITLE = {The lattice of minimal realizations of response maps over rings}, YEAR = {1977}, OPTMONTH = {}, OPTNOTE = {}, NUMBER = {2}, PAGES = {169--175}, VOLUME = {11}, KEYWORDS = {systems over rings}, PDF = {../FTP_DIR/lat.pdf}, ABSTRACT = { A lattice characterization is given for the class of minimal-rank realizations of a linear response map defined over a (commutative) Noetherian integral domain. As a corollary, it is proved that there are only finitely many nonisomorphic minimal-rank realizations of a response map over the integers, while for delay -differential systems these are classified by a lattice of subspaces of a finite-dimensional real vector space. } } @ARTICLE{MR0427298, AUTHOR = {E.D. Sontag and Y. Rouchaleau}, JOURNAL = {C. R. Acad. Sci. Paris Sér. A-B}, TITLE = {Sur les anneaux de Fatou forts}, YEAR = {1977}, OPTMONTH = {}, OPTNOTE = {}, NUMBER = {5}, PAGES = {A331--A333}, VOLUME = {284}, KEYWORDS = {systems over rings}, PDF = {../FTP_DIR/fatou.pdf}, ABSTRACT = { It is well known that principal rings are strong Fatou rings. We construct here a more general type of strong Fatou rings. We also prove that the monoid of divisor classes of a noetherian strong Fatou ring contains only the zero element, and that the dimension of such a ring is at most two. } } @PHDTHESIS{thesis, AUTHOR = {E.D. Sontag}, SCHOOL = {Univ. of Florida, Advisor: R.E. Kalman}, TITLE = {On the internal realization of polynomial response maps}, YEAR = {1976}, OPTADDRESS = {}, OPTMONTH = {}, OPTNOTE = {}, OPTTYPE = {} } @ARTICLE{SSR, AUTHOR = {E.D. Sontag}, JOURNAL = {Ricerche di Automatica}, TITLE = {Linear systems over commutative rings: A survey}, YEAR = {1976}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, PAGES = {1--34}, VOLUME = {7}, KEYWORDS = {systems over rings}, PDF = {../FTP_DIR/ssr.pdf}, ABSTRACT = { An elementary presentation is given of some of the main motivations and known results on linear systems over rings, including questions of realization and control. The analogies and differences with the more standard case of systems over fields are emphasized throughout. } } @ARTICLE{MR0417241, AUTHOR = {E.D. Sontag}, JOURNAL = {J. Pure Appl. Algebra}, TITLE = {On finitely accessible and finitely observable rings}, YEAR = {1976}, OPTMONTH = {}, OPTNOTE = {}, NUMBER = {1}, PAGES = {97--104}, VOLUME = {8}, KEYWORDS = {systems over rings, observability, noncommutative rings}, PDF = {../FTP_DIR/ncr.pdf}, ABSTRACT = { Two classes of rings which occur in linear system theory are introduced and compared. Characterizations of one of them are given in terms, of integral extensions (every finite extension of R is integral) and Cayley--Hamilton type matrix condition. A comparison is made in the case of no zero-divisors with Ore domains. } } @ARTICLE{MR0479498, AUTHOR = {E.D. Sontag and Y. Rouchaleau}, JOURNAL = {Nonlinear Anal.}, TITLE = {On discrete-time polynomial systems}, YEAR = {1976}, OPTMONTH = {}, OPTNOTE = {}, NUMBER = {1}, PAGES = {55--64}, VOLUME = {1}, KEYWORDS = {discrete-time}, PDF = {../FTP_DIR/polynomialsystems76.pdf}, ABSTRACT = { Considered here are a type of discrete-time systems which have algebraic constraints on their state set and for which the state transitions are given by (arbitrary) polynomial functions of the inputs and state variables. The paper studies reachability in bounded time, the problem of deciding whether two systems have the same external behavior by applying finitely many inputs, the fact that finitely many inputs (which can be chosen quite arbitrarily) are sufficient to separate those states of a system which are distinguishable, and introduces the subject of realization theory for this class of systems. } } @ARTICLE{MR0452844, AUTHOR = {E.D. Sontag}, JOURNAL = {Math. Systems Theory}, TITLE = {On linear systems and noncommutative rings}, YEAR = {1975}, OPTMONTH = {}, OPTNOTE = {}, NUMBER = {4}, PAGES = {327--344}, VOLUME = {9}, KEYWORDS = {systems over rings}, PDF = {../FTP_DIR/ls-ncr.pdf}, ABSTRACT = { This paper studies some problems appearing in the extension of the theory of linear dynamical systems to the case in which parameters are taken from noncommutative rings. Purely algebraic statements of some of the problems are also obtained. Through systems defined by operator rings, the theory of linear systems over rings may be applied to other areas of automata and control theory; several such applications are outlined. } } @ARTICLE{jcss75rat, AUTHOR = {E.D. Sontag}, JOURNAL = {J. Comput. System Sci.}, TITLE = {On some questions of rationality and decidability}, YEAR = {1975}, OPTMONTH = {}, OPTNOTE = {}, NUMBER = {3}, PAGES = {375--381}, VOLUME = {11}, KEYWORDS = {theory of computing and complexity}, PDF = {../FTP_DIR/rat-dec.pdf}, ABSTRACT = { Some results are given in the theory of rational power series over a broad class of semirings. In particular, it is shown that for unambiguous sets the notion of rationality is independent of the semiring over which representations are defined. The undecidability of the rationality of probabilistic word functions is also established. } } @BOOK{AI, PUBLISHER = {PROLAM, Buenos Aires}, TITLE = {Temas de Inteligencia Artificial}, YEAR = {1972}, AUTHOR = {E.D. Sontag}, ALTEDITOR = {}, OPTADDRESS = {}, OPTEDITION = {}, OPTMONTH = {}, OPTNOTE = {}, OPTNUMBER = {}, OPTSERIES = {}, OPTVOLUME = {}, KEYWORDS = {artificial intelligence}, PDF = {../FTP_DIR/temas_intel_artif.pdf}, ABSTRACT = { Textbook on Artificial Intelligence. Scanned 2005. The complete pdf file is 16 Megabytes. (Libro de texto con introduccion a la inteligencia artificial. El pdf file completo tiene 16 Megabytes.) } }