ECE6553 - Spring 2017
Optimal Control and Optimization

Magnus Egerstedt

Email
Office
magnus@gatech.edu  
TSRB 436B     

Office hours: Wednesdays 1-3 or by appointment

Teaching Assistant: TBD


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 theoretical exercises and (to a lesser degree) programming assignments.
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 Daniel Liberzon, Calculus of Variations and Optimal Control Theory, Princeton University Press, 2011 (DL). A preliminary version of the book (very close to the actual book) is available for free at http://liberzon.csl.illinois.edu/teaching/cvoc.pdf. Additional, useful sources are Arturo Locatelli, Optimal Control: An Introduction, Birkhauser, 2001 (AL) and Donald E. Kirk, Optimal Control Theory: An Introduction, Dover Publications, 2004 (DK).

TIME AND PLACE
The lectures will be held at 9:30-11:00 Tuesdays and Thursdays in Klaus Advanced Computing building 2456.

PREREQUISITS Some knowledge of linear algebra, linear control systems, and differential equations will certainly make your life a little easier. ECE6550 (or an equivalent linear systems course) 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

PARAMETER OPTIMIZATION
Jan. 10 Introduction to optimization 1(DL)
Jan. 12 Equality constraints 1(DL)
Jan. 17 Inequality constraints 1(DL)
Jan. 19 Numerics: Descent algorithms 6(DK)

CALCULUS OF VARIATIONS
Jan. 24 Infinite dimensional optimization 1(DL), 4(DK)
Jan. 26 Variations 2(DL), 4(DK), HW1 (optimization)
Jan. 31 Costates 3(DL)
Feb. 2 Switch-time optimization

THE MAXIMUM PRINCIPLE
Feb. 7 The Hamiltonian 4(DL), 5(DK), 6(AL)
Feb. 9 Terminal constraints 4(DL), 5(DK), 6(AL)
Feb. 14 Second order systems and cubic splines
Feb. 16 Numerics: Boundary value problems 6(DK), HW2 (calculus of variations)
Feb. 21 Review
Feb. 23 MIDTERM
Feb. 28 Terminal manifolds 4(DL), 5(DK), 6(AL)
Mar. 2 Free final times 4(DL), 5(DK), 6(AL)
Mar. 7 Min-time and bang-bang control 4(DL), 5(DK), 6(AL)
Mar. 9 Pontryagin's maximum principle 4(DL), 5(DK), 6(AL), HW3 (Bolza problems)
Mar. 14 Control and state constraints 5(DK), 6(AL)
Mar. 16 From open-loop to closed-loop: MPC

LINEAR-QUADRATIC CONTROL
Mar. 21 Spring break - NO CLASS
Mar. 23 Spring break - NO CLASS
Mar. 28 Dynamic programming and Bellman’s equation 5(DL), 3(DK)
Mar. 30 LQ 6(DL), 3(AL), HW4 (the maximum principle)
Apr. 4 The Riccati equation 6(DL), 3(AL)
Apr. 6 Rocket science
Apr. 11 Infinite horizon control 6(DL), 4(AL)

GLOBAL METHODS
Apr. 13 Hamilton-Jacobi theory 5(DL), 2(AL), HW5 (LQ)
Apr. 18 Global conditions 5(DL), 2(AL)
Apr. 20 At the research frontier
Apr. 25 Review
May 2 FINAL EXAM: 2:50-5:40