ENEE 664 - Optimal Control

ENEE 664 - Optimal Control

Spring 2016

Last Update - Thursday, March 10, 2016

Course Information

Special Announcements

This is an evolving version of the 2016 course website

(12) (March 10) Homework Set 6 as posted is due back in class March 23, 2016.

(11) (March 7) Mid-term examination March 9 is CLOSED BOOK; no electronics allowed for any purpose during exam (including keeping time); every 15 minutes the time will be indicated on the white board

(10) (March 1) updated Problem Set 5 posted - due in class on March 7 (LATE SUBMISSIONS WILL NOT BE ACCEPTED)

(9) (February 23) updated Problem Set 4 posted - due in class February 29 [LATE SUBMISSIONS WILL NOT BE ACCEPTED]

(8) (February 19) Information sent by email, pertinent to material completed in class

(7) (February 15) updated Problem Set 3 posted - due in class February 22

(6) (February 9) Change in FINAL EXAMINATION Structure and Timing - final examination will consist of two parts: in class Monday, May 16, closed book, 4:00 6:00 pm; and same day open book 7:00 9:00 pm, proctored in assigned room; course outline is updated

(5) (February 9) Do Problem Set 2 - to be returned in class on Monday, February 15

(4) (February 4) If you have a conflict due to initial adjustment period, you may return the Problem Set 1 by WEDNESDAY February 10 in class. You should still expect a new homework set assigned on Monday, February 8 and due back on Monday, February 15.

(3) (February 1) Problem Set part b posted; both parts a and b are due back in class February 8; read Lecture Notes 1 and 2

(2) (January 29) Notes for Lecture 0 (introduction on January 27) posted; part (a) of Problem Set 1 posted

(1) Campus is CLOSED on Monday, January 25, 2016 (recovery from snow emergency); we will make up for the missed class in coming weeks

Weekly Lecture Notes by P. S. Krishnaprasad

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


Lecture 0 (Introduction)

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 part a and part b

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)