642:577 "Selected Mathematical Topics in System Theory I" (Introduction to Control Systems Theory)


Spring 2012

Eduardo Sontag

Meeting time

TTh 1:40-3, Hill 525

Text

Hassan K. Khalil, Nonlinear Systems, Third Edition, Prentice Hall, 2002

Description

Since this course is being offered by request from engineering, it is is primarily oriented to engineering students and will be based upon a standard book used in ECE and MAE departments. The level should be appropriate to graduate students in mechanical, electrical, biomedical, and industrial engineering. As agreed in previous emails, I have NOT ordered the book, since people prefer to buy it online.

There are slides available in Khalil's website that cover the material in the syllabus (see sakai website and my separate course website). I may use the slides as a way to structure the discussion, with blackboard for details. I am placing all the slides as one big file in the Sakai, under "Resources".

My textbook "Mathematical Control Theory: Deterministic Finite Dimensional Systems. Second Edition, Springer, New York, 1998." is the one that I have used in the past, when the audience was mostly mathematics students. The book is available freely online, and could be used for additional reading. The style of the course, however, will be very different - far less abstract than my book - and will focus on nonlinear control design, which is only a small part of my own book.


Summary of topics covered, in rough order; files are found in "resources"; see sakai

introduction
   resource: "khalil_book_41lectures.pdf" (lectures 1-2)

existence and uniqueness for ODE's
   resource: chapter 3 of book, blackboard

2D linear phase planes
   resource: "khalil_book_41lectures.pdf" (lecture 3)

linearization
   resource: "khalil_book_41lectures.pdf" (lecture 4)

bifurcations
   resource: "khalil_book_41lectures.pdf" (lecture 6)

stability and Lyapunov functions
   resource: "khalil_book_41lectures.pdf" (lectures 7,8,9,10, and part of 11)

KL characterization of GAS 
   resources: "proof_k_kl_estimates.pdf" (Khalil, extracted from book)
              "alpha(||x||) < V(x) proof"
              "khalil_book_41lectures.pdf" (some pages from lecture 12, start page 183)

input to state stability (using notes from a summer school short course)
   resource: "slides for ISS and stabilization" (pages 46-69, skipping some]
             [see also "survey paper on ISS"]

stabilization implies ISS stabilization (from a paper of mine)
   resource: "sketch of proof of ISS stabilization"

norms for systems, small-gain theorem 
   resources: "slides on systems norms for linear systems" (from Francis et al's book)
              "khalil_book_41lectures.pdf" (lecture 20, page 315)

feedback stabilization problem: continuous feedback (from the summer school notes)
   resources: "khalil_book_41lectures.pdf" (lecture 25, page 407)
              "slides for ISS and stabilization" (pages 3-20, skipping some)

control-Lyapunov functions, universal formula (Khalil slides)
   resources: "khalil_book_41lectures.pdf" (lecture 30, page 472)
              blackboard proof from my textbook, page 248

normal form, zero dynamics
   resource: "khalil_book_41lectures.pdf" (lecture 22, page 360)

controller form, Lie brackets, feedback linearization
   resource: "khalil_book_41lectures.pdf" (lecture 23, page 377)

stabilization by feedback linearization
   resource: "khalil_book_41lectures.pdf" (lecture 26, page 424)

partial linearization, peaking, backstepping
   resources: "khalil_book_41lectures.pdf" (lectures 27-28, page 436)

Lie algebra conditions for accessibility; car parking example
   resource: lie_algebra_accessibility_slides_from_mct_for_577.pdf  (taken from my textbook)

Prerequisites

For engineering and other non-math department students: working knowledge of undergraduate analysis and linear algebra; for math students: 640:501-502. (Assignments will be more theoretical for math students and more computational for others.)