ENEE 664 - Optimal Control

ENEE 664 - Optimal Control

Spring 2019

Last Update - Wednesday, April 10, 2019

Course Information

Special Announcements in reverse chronological order

Keeping track of weekly progress in spring 2019

(12) Homework 8 posted and emailed along with paper by Lax. Due date for HW 8 is Wednesday April 17 in class (before Midterm 2 starts).

(11) Homework Set 7 posted and emailed (on calculus of variations - due back April 8, Monday). Mid-term Examination II is moved to WEDNESDAY, APRIL 17. Material covered up to and during the week of April 10 will be relevant to the exam.

(10) I have provided a link below to the announcement of the award of the 2019 Abel Prize to Professor Karen K. Uhlenbeck. This was in recognition “for her pioneering achievements in geometric partial differential equations, gauge theory and integrable systems, and for the fundamental impact of her work on analysis, geometry and mathematical physics.” All this is an outgrowth of the subject of calculus of variations, as explained in both informal as well as technical terms at the Abel Prize website. Read for inspiration and more.

(9) Homework Set 6 (focusing on Frechet derivatives, Lagrange multiplier theorem etc. based on Lecture Notes 5) - to be completed and returned to the GTA in his office by Friday, March 15, 2019.

(8) Homework set 5 (focusing on Gateaux and Frechet derivatives) posted - to be completed by Monday, March 4.

NOTE - first Midterm on March 4 is in class closed book variety, based on material covered until today - February 25.

(7) Fix to legibility issue in page 12 of Lecture 4 notes included.

(6) Homework set 4 due back in class on Monday, February 25. Lecture Notes 4 posted - same as from 2019. Work through the chapters of Cinlar and Vanderbei on Sets and Metric Spaces (upto and including page 44) as a background resource - as needed when you read my lecture notes. Also work through the first chapter of Liberzon's book (to get the notion of local extrema, necessary conditions etc.). If you complete these readings by the end of this month you would be prepared for advanced material.

(5) Homework set 3 due back in class on Monday, February 18. Lecture Notes 3 posted - same as from 2016.

(4) Homework set 2 due back in class on Monday, February 11. Lecture Notes 2 posted - same as from 2016.

(3) Weekly discussion sessions 5:15-7:15 pm on TUESDAYS in room CSI 2107.

(2) Lecture Notes 0 and 1 are posted (same as from 2016).

Homwework Set 1 (both parts (a) and (b)) - to be returned Monday February 4 in class.

(1) Textbook for the course is Daniel Liberzon's Calculus of Variations and Optimal Control Theory

Weekly Lecture Notes by P. S. Krishnaprasad 2019

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


Lecture 0 (Introduction)

Lecture 1

Lecture 2

Lecture 3 - be sure to check yellow post-it comments on several pages (minor corrections)

Lecture 4 and an addendum and Lecture 4 Page 12 fix

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

A classic lecture by Feynman

Lecture 6

Lecture 7 and solution to Queen Dido's problem

Lecture 7 addendum (on transversality condition)

announcement of Abel Prize 2019 award to Professor Karen K. Uhlenbeck

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

Published version of Cinlar Vanderbei book in Springer Undergraduate Texts series

About C. Caratheodory

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