Possible topics for (applied) papers for Math 577

IEEE Transactions on Control Systems Technology:

For example, just the November 2006 issue (click to access) has papers on inverted pendulum stabilization (recall that we briefly talked about this; one model can be found in page 91 of the textbook), robotics, car parking (very close to what we did in class with Lie brackets), flight control, turbine control, welding processes, heating systems, formation control of unmanned aerial vehicles (UAVs), hybrid fuel cells, etc.,

and the September 2006 issue (click to access) has articles on cooperative control of networked autonomous air vehicles, air traffic control, diesel engines, chemical plants, steel manufacturing, etc.

Some other topics, randomly picked just from tables of contents of previous 2006 issues, deal with control applications in magnetic levitation, freeway traffic surveillance, water distribution networks, fiber optics, telephone call centers, car suspensions, teleoperated laparoscopic surgery, racing motorcycle engines, wheeled mobile robots, light rail vehicles, teleoperation via Internet-like channels, optical storage drives, reconfigurable flight control, disk drives, chemical reactors, VTOL aircraft, compact disc players, anti-ship missiles, and noise control for headphones.

Some papers:

Two papers on model reduction using balancing (covered in class), but in one case generalized to stochastic systems. One regarding HMM's, the other one biology.

• A model reduction algorithm for Hidden Markov Models, by Georgios Kotsalis, Alexandre Megretski, Munther A. Dahleh
• Biochemical network models simplified by balanced truncation, by Wolfram Liebermeister, Ulrike Baur, and Edda Klipp

• Shrikant V. Savant and Haruhiko H. Asada, Shaping structure dynamics with truncation-error bounded reduced-order models for integrated mechanism/control design, Proceedings of the American Control Conference 1998, pp. 3540-3545

• Linear quadratic optimization for models with rational expectations, Hans M. Amman and David A. Kendrick

• K.R. Fister, S. Lenhart, and J. S. McNally, Optimizing chemotherapy in an HIV model, Electronic J. Differential Equations 1998 (1998): 1-12.
• H.R. Joshi, Optimal control of an HIV immunology model, Optimal Control Appl. Methods, 23 (2002): 199-213.
• E. Jung, S. Lenhart, and Z. Feng, Optimal control of treatments in a two strain tuberculosis model, Discrete and Continuous Dynamical Systems 2(2002): 473-482.
• D. E. Kirschner, S. Lenhart, and S. Serbin, Optimal control of the chemotherapy of HIV, Journal of Math Biology 35(1997), 77-96.
• John Carl Panetta and K. Renee Fister, Optimal control applied to cell-cycle-specific cancer chemotherapy, SIAM J. Appl. Math. 60 (2000): 1059-1072
• John Carl Panetta and K. Renee Fister, Optimal control applied to competing chemotherapeutic cell-kill strategies, SIAM J. Appl. Math. 63 (2003):, 1954-1971
• Rebecca V. Culshaw, Shigui Ruan and Raymond J. Spiteri, Optimal HIV treatment by maximising immune response Journal of Math Biology 48(2004): 545-562

• Claudio De Persis, Nonlinear stabilizability via encoded feedback: The case of integral ISS systems, Automatica 42(2006): 1813-1816

• (This is mostly numerical.) For the airplane and inverted-cart examples, do problems 3.2.12-13 (p.90; controllability), 5.1.14-15 (p.188, pole-shifting), 6.2.5-6 (p.272, observability), 7.2.7-8 (p. 325, dynamic feedback). (Last item still to be covered in class.) Ideally, you could do some of these problems for arbitrary parameters (using if needed a symbolic manipulation package such as Maple or Mathematica), but at least do them for appropriate numerical values of parameters.
• (This is a little more theoretical.) For time-varying linear systems (we didn't get to do much of t-v theory), read section 3.5 and work out problems 3.5.7, 3.5.13, 3.5.14, 3.5.20, 3.5.23 (harder but interesting), and 3.5.25.
• (Examples, mostly.) Problems on nonlinear controllability and stabilization (you will need to read some material not covered in class, especially for the stabilization problems): 4.3.14/5 (p. 163), 5.9.4 (p. 241), 5.9.7-8 (p.245), and 5.9.19-20 (p.256).
• (Mix of numerical and easy theoretical.) Problems on quadratic-cost optimal control of linear systems (material to be covered in class, some you'll need to read): 8.2.3-6 (p.368), 8.4.8 (p.388), and 8.3.7-8 (p. 379).
• (Very theoretical.) Lie algebraic controllability: read and work out problems 4.6.1-3 (p.180).
• (Very theoretical.) Feedback linearization: read and work out problems 5.3.11-12 and 5.3.18-19.

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