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ECE 453 - Optimal Control

Fall 2001, ECE, University of Illinois at Urbana-Champaign

 
"Since the building of the universe is perfect and is created   
by the wisdom creator, nothing arises in the universe in which 
one cannot see the sense of some maximum or minimum."          

                                                 ---- L. Euler

[Administrative | Outline | Homeworks | Handouts | Online Resource]

Final exam scores and grades:

Your final exam scores and course grades are listed below after the last four digits of your social security numbers (The correlation between the grades and the final exam scores is only coincidental): Traditionally, I will not give the final exam back to you. You however may drop by and check the grading if you have serious doubt about your scores (although I have been very lenient in grading). Have a good summer. Hope that you have learned something from this course.

Note about the final exam. There was a typo in the Dynamical Programming problem which makes the given form of cost fuction incorrect. If you did not notice that, I will only deduct 3 points given that you have the rest of the formulae correct.

Announcements

Administrative Information

 Instructor: Professor Yi Ma
Lectures: TuTh 10:00am-11:20am, 245 EL
Office hours: Tu 2:00pm-3:30pm, 145 CSL
Office: 145 CSL, Phone: 244-0871
Email: yima@uiuc.edu
After hour appointments: through email.

Course Discription:
This is a second-year graduate course on control theory and systems. Prerequisites include an introductory graduate level control course which is equivalent to ECE 415, and some background in probability at the level of ECE313 (or better ECE434). In addition, you should be comfortable with basic notions in set theory (unions, intersections, sequences, etc.), signal and systems (matrix manipulations, linear differential or difference equations, calculus).

This course focuses on the theoretical and algorithmic foundations of optimal control theory, and will deal with primarily deterministic dynamical systems described in continuous time. Some aspects of stochastic and nonlinear constrol systems will be covered. If time allows, extensions of the single-criterion dynamic optimiztion theory to game-theory based approaches as well as H-infinity optimal control will be studied.
Main Texts:
*Andrew P. Sage and Chelsea C. White, Optimum systems control second edition , Prentice Hall, 1977. (out of print but reserved in the Engineering library and will hand out some chapters in hardcopies).
*Tamer Basar and Pierre Bernhard, H-infinity Optimal Control and Related Minimax Design Problems: A Dynamical Game Approach, second edition, Birkhauser, 1995. (Available at the bookstore).
Reserved References (in the engineering library):
*D.P. Bertsekas, Dynamic Programming and Optimal Control, Volume I, 2nd edition, Athena Scientific 2000.
*S.P. Sethi and G.L. Thompson, Optimal Control Theory, 2nd edition, Kluwer Academic Publishers, 2000.
*B.D.O. Anderson and J.B. Moore, Optimal Control: Linear Quadratic Methods, Prentice Hall, 1990.
*M. Athans and P.L. Falb, Optimal Control, McGraw Hill, 1966.
*A.E. Bryson and Y.C. Ho, Applied Optimal Control, 2nd ed., Blaisdel, 1975.
*L.B. Lee and L. Markus, Foundations of Optimal Control Theory, Wiley, 1967.
*F.L. Lewis and V.L. Syrmos, Optimal Control, Wiley, 1995.
*P.V. Kokotovic and H.K. Khalil and J. O'Reilly, Singular Perturbation Methods in Control, Academic Press, 1986.
*T. Basar and G.J. Olsder, Dynamic Noncooperative Game Theory, SIAM Classics in Applied Mathematics, 1999.
There are plenty of books on optimal control and calculus of variations in the library which are useful. I recommend you to find one which fits your background and taste. The process of finding the best reference (for yourself) is the most rewarding.
Grading Policy: Homework (25%), Midterm (25%) and Final Exam (50%). Grading will be based on the curve (so do not panic if you get low scores on your tests - others probably did worse than you).
*Homework (25%): You are allowed to discuss on the homework in small groups (of 2-3 persons), but you must write the solution independently to hand in. No late homework will be accepted (unless an extension is granted by the instructor to the whole class).
*Midterm Exam (25%), Time: 7-10pm, March 12th, and Place: 245 EL.
*Final Exam (50%), Time: 8-11am, May 9th; and Place: 245 EL. If you are among the top 10% in the final, you will get an "A" no matter how badly you have flunked your midterm or homeworks. But if you want to get an "A+", you need to do well in all three categories.

Course Outline

I. Introduction
1. Formulation of optimal control problems
2. Parameter optimization versus path optimization
3. Local and global optima; general conditions on existence and uniquenes.
4. Some basic facts from finite-dimensional optimization.
II. The Calculus of Variations
1. The Euler-Lagrange equation
2. Path optimization subject to constraints
3. Weak and strong extrema
III. The Minimum (Maximum) Principle and the Hamilton-Jacobi Theory
1. Pontryagin's minimum principle
2. Optimal control with state and control constraints
3. Time-optimal control
4. Singular solutions
5. Hamilton-Jacobi-Bellman (HJB) equation, and dynamical programming
6. Viscosity solutions to HJB
IV. Linear Quadratic Gaussian (LQG) Problems
1. Finite-time and infinite-time state (or output) regulators
2. Riccati equation and its properties
3. Tracking and disturbance rejection
4. Kalman filter and duality
5. The LQG design
V. Nonholonomic System Optimal Control

VI. Game Theoretic Optimal Control Design

Homeworks & Solutions

Note: If you found errors in problem & solution sets, please contact me.

Handouts

Useful Resource Links
Yi Ma | yima@uiuc.edu
Last updated 02/06/03