ENEE 664 - Optimal Control

ENEE 664 - Optimal Control

Spring 2009

Last Update Friday April 3, 2009, 6:20 pm

Course Information

Special Announcements

(5) Homework set 7 is due at the latest by Monday April 13.

(4) Mid-term examination II will be held in class (closed book) on Thursday, April 16. All material covered until and on April 9 is fair game for questions.

(3) Homework Set 6 should be attempted as is. You have one week - till Thursday, April 2. The Sussmann-Willems paper can be obtained by clicking on one of the links at the bottom of this page.

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

(1) All lecture notes are posted.

Weekly Lecture Notes by P. S. Krishnaprasad

Survey Lecture on Linear Systems


Lecture 1

Lecture 2

Lecture 3

Lecture 4 and an addendum

Lecture 5(a); Lecture 5(b); Lecture 5(c)

Lecture 6

Lecture 7 and solution to Queen Dido's problem

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


Homework solutions:

Problem set 1

Problem set 2

Problem set 3

Problem set 4

Problem set 5

Problem set 6


Some interesting resources on the web

Riccati had an interesting life. Some historical remarks on his life and work due to Sergio Bittanti are available here . See also the page on 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