ECE6553 - Spring 2011
Optimal Control and Optimization

Magnus Egerstedt

Phone
Email
Office
(404) 894-3484   
magnus@ece.gatech.edu  
TSRB 432     

Office hours: Wednesdays 1-3 or by appointment

Teaching Assistant: Greg Droge


This course investigates how dynamical systems should be controlled in the best possible way!

             



COURSE DESCRIPTION
The course will be divided into five parts, corresponding to the following topics:
     (1) Parameter Optimization (optimality conditions, constraints, numerical methods)
     (2) Calculus of Variations (infinite dimensional systems, directional derivatives, costates)
     (3) The Maximum Principle (Hamiltonians, constraints, bang-bang control)
     (4) LQ (dynamic programming, Riccati equations, linear-quadratic regulators)
     (5) Global Methods (Hamilton-Jacobi theory)

COURSE WEBSITE
This page: http://users.ece.gatech.edu/~magnus/ece6553.html

WORKLOAD
Your responsibilities in this class will fall into two main categories:
1. The homework sets (one problem set roughly every third week) = 50%. The credit will be divided between programming assignments and theoretical exercises.
2. The midterm and final exams = 20% + 30% = 50% They will cover all the material presented in the class. They will be closed-book, closed-note, closed-calculator exams.

PROGRAMMING
The objective with the programming assignments is to see how to bridge the gap between what is done in class and how to actually apply it. (The actual programming involved will be very minor.) The assignments will be Matlab-based.

READING
The course textbook is Arturo Locatelli, Optimal Control: An Introduction, Birkhauser, 2001 (AL) and it will be complemented by the recommended reading Donald E. Kirk, Optimal Control Theory: An Introduction, Dover Publications, 2004 (DK). An excellent additional source is Daniel Liberzon's upcoming book Calculus of Variations and Optimal Control Theory, available for free at https://netfiles.uiuc.edu/liberzon/www/publications.html.

TIME AND PLACE
The lectures will be held at 9:30-11:00 Tuesdays and Thursdays in Van Leer W200.

PREREQUISITS Some knowledge of linear algebra, linear control systems, and differential equations will certainly make your life a little easier. ECE6550 is the perfect background for this course.

HONOR CODE
Although you are encouraged to work together to learn the course material, the exams and homework are expected to be completed individually. All conduct in this course will be governed by the Georgia Tech honor code.



SCHEDULE

 
Date Lecture subject Reading/Homework

Jan. 11 SNOW DAY
Jan. 13 SNOW DAY

PARAMETER OPTIMIZATION
Jan. 18 Introduction to optimization
Jan. 20 Equality constraints
Jan. 25 Inequality constraints
Jan. 27 Numerical methods 6(DK)

CALCULUS OF VARIATIONS
Feb. 1 Infinite dimensional optimization 4(DK), HW1 (optimization)
Feb 3 Variations 4(DK)
Feb. 8 Switch-time optimization

THE MAXIMUM PRINCIPLE
Feb. 10 The Hamiltonian 5(DK), 6(AL)
Feb. 15 Terminal constraints 5(DK), 6(AL), HW2 (calculus of variations)
Feb. 17 Splines
Feb. 22 Terminal manifolds 5(DK), 6(AL)
Feb. 24 Review
Mar. 1 MIDTERM
Mar. 3 Free final times 5(DK), 6(AL)
Mar. 8 Min-time and bang-bang control 5(DK), 6(AL)
Mar. 10 Pontryagin's maximum principle 5(DK), 6(AL), HW3 (Bolza problems)
Mar. 15 Control and state constraints 5(DK), 6(AL)
Mar. 17 Numerical methods 6(DK)

LINEAR-QUADRATIC CONTROL
Mar. 22 Spring break - NO CLASS
Mar. 24 Spring break - NO CLASS
Mar. 29 Dynamic programming 3(DK)
Mar. 31 Bellman's equation 3(DK), HW4 (the maximum principle)
Apr. 5 LQ 3(AL)
Apr. 7 The Riccati equation 3(AL)
Apr. 12 Infinite horizon control 4(AL)

GLOBAL METHODS
Apr. 14 Hamilton-Jacobi theory 2(AL)
Apr. 19 Global conditions 2(AL), HW5 (LQ)
Apr. 21 Numerical methods 6(DK)
Apr. 26 At the research frontier
Apr. 28 Review
May 5 FINAL EXAM: 8:00-10:50