ENEE 664 - Optimal Control

ENEE 664 - Optimal Control

Spring 2014

Last Update - Sunday, April 27, 2014

Course Information

Special Announcements

(11) Homework Set 8 (with 5 problems) posted - due 05/07/2014. Reading assignment - Prof. Tits' lecture notes chapter 4 on Armijo rule (sections 4.2 and 4.3)

(10) Homework Set 7 (with 5 problems) posted - due 04/09/2014. Reading ASSIGNMENT - Lecture 7 Addendum.

(9) Homework Set 6 (with 4 problems) posted - due 03/31/2014. Explanatory guide to lecture notes 5 posted (path to proof of Lagrange multiplier theorem).

(8) Homework Set 5 (with 5 problems) posted - due 03/05/2014. Additional reading assignment - Professor Andre Tits' Lecture Notes appendix B, pages 173-177. Note that there is a difference between his definition of Gateaux derivative and what I did in class (and in my notes). We will follow our defintion. REMINDER - Exam on March 10.

(7) Homework Set 4 (with 3 problems) posted - due 02/26/2014

(6) Lecture 3 notes corrected - look for comment bubble in formula (a) for solution to Riccati equation based on solving for transition matrix of a system of canonical equations

(5) Homework Set 3 (with 3 problems including MATLAB computation) posted - due 02/19/2014

(4) Homework Set 2 (with 4 problems) posted - due date 02/12/2014

(3) Homework Set 1 (with 4 problems) posted - due date 02/05/2014

(2) There is no required textbook for this course.

(1) All lecture notes (initial version) are posted. Updates will be posted on a regular basis.

Weekly Lecture Notes by P. S. Krishnaprasad

Survey Lecture on Linear Systems and link to ENEE 660 System Theory Notes


Lecture 1

Lecture 2

Lecture 3

Lecture 4 and an addendum

Lecture 4 Page 12 fix

Lecture 5(a), updated; Lecture 5(b); Lecture 5(c) Lecture 5(c) Update; Explanatory guide

Lecture 6

Lecture 7 and solution to Queen Dido's problem

Lecture 7 addendum (on transversality condition)

Lecture 8 on fixed point problems

Lecture 9(a) on Newton's method and additional material (lecture 9(b)) on

mean value theorem

Lecture 10(a) on Newton's method and rate of convergence and

Lecture 10(b) on iterative minimization

Lecture 11(a) on second order necessary conditions

Lecture 11(b) on Taylor's theorem

Lecture 11(c) on second order necessary conditions in the calculus of variations (Legendre)

Lecture 12 on maximum principle

Lecture 13 on Hamilton Jacobi Bellman Equation


Lecture Notes by Professor Andre L. Tits


Homework Assignments

Problem Set 1

Problem Set 2

Problem Set 3

Problem Set 4

Problem Set 5

Problem Set 6

Problem Set 7

Problem Set 8


Homework solutions are sent by email


Some interesting resources on the web

Riccati had an interesting life. For some historical remarks on his life and work, see Riccati at the St. Andrews University archive (also a source of biographical information on other mathematicians).

The Brachystochrone problem was originally set by Johann Bernoulli in June 1696. The paper of Hector J. Sussmann and Jan C. Willems in the IEEE Control Systems Magazine, June 1997, pp 32-44, celebrates this event as a beginning of optimal control theory.

Solution (based on calculus) of Queen Dido's problem by P. D. Lax from American Mathematical Monthly, vol. 102, No. 2, February 1995, pp. 158-159

Book by John T. Betts Practical Methods for Optimal Control and Estimation using Nonlinear Programming

Link to book by Daniel Liberzon on Calculus of Variations and Optimal Control

Real Analysis Book by Cinlar and Vanderbei - material useful in Systems courses

About C. Caratheodory

Impact of Control Technology vignettes, and, full report (warning 35 MB)