CDS 212 Fall 2010

Feedback Control Theory
Instructors John Doyle, doyle@cds.caltech.edu Lectures: Tu/Th, 2:30-4 pm, 314 Annenberg	Teaching Assistants Somayeh Sojoudi, sojoudi@cds.caltech.edu Richard Murray, murray@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

• 9 Nov 2010: Slides for lecture 13 (PD-Ch 8) are now posted.
• 4 Nov 2010: Slides form Prof. Keith Glover's Lecture and the tutorial paper on Hankel norm approximations are now posted.
• 2 Nov 2010: A reference for lectures 9 and 10: Linear Matrix Inequalities in System and Control Theory, Stephen Boyd.
• 7 Oct 2010: Slides for lecture 4 (DFT-Ch 4) are now posted.
• 4 Oct 2010: Office Hours: Wed 4-5pm, 314 Annenberg
• 29 Sep 2010: Slides for lecture 1 are now posted.

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.
[PD]	F. Paganini and G. Dullerud, 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	Branch
1	28 Sep  30 Sep	Norms for signals and systems	DFT Ch 1, 2  DP Ch 3	HW 1
2	5 Oct+ 7 Oct	Feedback, stability and performance	DFT Ch 3 (FBS 9.1-9.3) (FBS 11.1-11.2)	HW 2	6 Oct: Mung Chiang (Princeton), An Axiomatic Theory of Fairness 6 Oct: Mung Chiang (Princeton), Can Random Access Be Optimal?
3	12 Oct+ 14 Oct+	Uncertainty and robustness	DFT Ch 4 (FBS 12.1‑12.3)	HW 3	12 Oct: Raff D'Andrea (ETHZ), Some applications of distributed estimation and control
4	19 Oct 21 Oct+	Fundamental limits	DFT Ch 6 (FBS 11.4, 12.4)	HW 4
5	26 Oct+ 28 Oct*	Stability in state space Realization theory, controllability, observability Lyapunov equation and stability conditions	PD, Ch 2, 4, 5	HW 5
6	2 Nov* 4 Nov*	Model reduction, LMIs Balanced realizations KYP lemma		HW 6	Keith Glover Model reduction Loop shaping
7	9 Nov 11 Nov	Nonlinear systems Stability of nonlinear systems L2-gain for nonlinear systems	FBS, Ch 4	HW 7
8	16 Nov+ 18 Nov	Sum-of-squares Semi-algebraic sets Semidefinite programming Sum-of-squares		HW 8	IPAM: robust optimization
9	23 Nov+				Pablo Parrilo?
10	30 Nov 2 Dec	Links with nformation theory and statistical mechanics			IPAM: applications of optimization

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.

Additional References (Optional)

Date	Reading
28 Sep	AldersonDoyle-tsmca (Paper),Glycolysis (Paper), SuppInfo, 1NetCmplxIntro (Slides)
5 Oct	layering (Slides)
19 Oct	BioMetabModeling (Slides),Glycolysis (Paper),Figures,Chap6 (Slides)