CDS 212 Fall 2011

Feedback Control Theory
Instructor John Doyle, doyle@cds.caltech.edu Lectures: Tu/Th, 2:30-4 pm, 314 Annenberg	Teaching Assistants Na (Lina) Li, nali@cds.caltech.edu

Course Description

Introduction to modern feedback control theory with emphasis on the role of feedback in overall system analysis and design. Examples drawn from throughout engineering and science. Open versus closed loop control. State-space methods, time and frequency domain, stability and stabilization, realization theory. Time-varying and nonlinear models. Uncertainty and robustness.

Announcements

• 22 Sep 2011: created homepage; 2010 home page

Textbook

The two primary texts for the course (available via the online bookstore) are

[DFT]	J. Doyle, B. Francis and A. Tannenbaum, Feedback Control Theory, Dover, 2009 (originally published by Macmillan, 1992). Available online at http://www.control.utoronto.ca/people/profs/francis/dft.html.
[DP]	G. Dullerud and F. Paganini, A Course in Robust Control Theory, Springer, 2000.

The following additional texts may be useful for some students:

[FBS]

K. J. Astrom and R. M. Murray, Feedback Systems: An Introduction for Scientists and Engineers, Princeton University Press, 2008. Available online at http://www.cds.caltech.edu/~murray/amwiki.

Lecture Schedule

Week	Date	Trunk	Reading	Homework
1	27 Sep  29 Sep	Norms for signals and systems	DFT Ch 1, 2  DP Ch 3	HW 1
2	4 Oct 6 Oct	Feedback, stability and performance	DFT Ch 3 (FBS 9.1-9.3) (FBS 11.1-11.2)	HW 2
3	11 Oct 13 Oct	Uncertainty and robustness	DFT Ch 4 (FBS 12.1‑12.3)	HW 3
4	18 Oct 20 Oct	Fundamental limits Realization theory, controllability, observability	DFT Ch 6 (FBS 11.4, 12.4), DP Ch 2, 4	HW 4
5	25 Oct 27 Oct	Lyapunov equation and stability conditions LMIs	DP Ch 4 LMIs Ch 2	HW 5
6	1 Nov 3 Nov	KYP lemma Model reduction	DP Ch 4,7 KYP	HW 6
7	8 Nov 10 Nov	Uncertain systems MIMO robust control, Convex optimization	DP Ch 8 MIMO CvxOpt1 CvxOpt2	HW 7
8	15 Nov 17 Nov	Stability of nonlinear systems Sum-of-squares	FBS Ch 4 SOS	HW 8
9	22 Nov
10	29 Nov 1 Dec	Links with information theory and statistical mechanics		HW 9

Grading

The final grade will be based on homework and a final exam:

• Homework (75%) - There will be 9 one-week problem sets, due each Thursday by 5pm in the TA's mailbox on the third floor of Annenberg. Each student may hand in at most one homework late (no more than 5 days).
• Final exam (25%) - The final will be handed out the last day of class and is due back at the end of finals week. Open book, time limit to be decided (likely N hours over a 4-8N hour period).

The lowest homework score you receive will be dropped in computing your homework average. In addition, if your score on the final is higher than the weighted average of your homework and final, your final will be used to determine your course grade.

Collaboration Policy

Collaboration on homework assignments is encouraged. You may consult outside reference materials, other students, the TA, or the instructor. Use of solutions from previous years in the course is not allowed. All solutions that are handed should reflect your understanding of the subject matter at the time of writing.

No collaboration is allowed on the final exam.