ENEE 661 - Nonlinear Control Systems (P. S. Krishnaprasad)

ENEE 661 - Nonlinear Control Systems

Spring 2015

Last Update April 10, 2015

Course Information

Special Announcements (in reverse chronological order)

8. Mid Term EXAM II moved to Wednesday April 29 (see email about this - also indicates extra office hours)

7. Homework Sets 5, 6 and 7 sent in single file by email to class - staggered due dates respectively April 20, April 22 and April 29

6. Homework Set 4 posted - due date THURSDAY March 12.

5. Mid-term examination 1 is moved to Monday, March 2 (in class, closed-book) due to delay caused by snow closing (course outline updated to reflect this). Homework Assignment 3 - do the online problem set 3 (both parts) - DUE DATE Wednesday, February 25. For material on PLANAR systems refer to my Lecture Notes 4 online (largely a review of undergraduate ODE material). READ Lecture Notes 3 on Contraction etc..

4. Homework 2 is posted - note also reading assignments included in this. Due date Monday February 16, 2015. Note also a correction of a mistake in problem 2 homework 2 - it should have read, from initial (x = 0, y = 0, \theta = \pi/2) to final (x=1, y = 0, \theta = \pi/2). I switched the final coordinates for x and y in the original.

3. Course outline updated - reflects change of time for only the TAKE HOME PART of the final exam - to Wednesday, May 20, 4:00 - 7:00 pm.

2. Homework Problem Set 1 is posted - due date Monday, February 9, 2015, in class at the beginning of class. Associated reading assignment: You are required to read ahead Lecture Notes 1(a), 1(b), 1(c) and be prepared for my presentation of Lecture Notes 2(a) on Monday February 2. Part of the material in Lecture Notes 2(b) is motivation for Lie brackets

1. A first set of lecture notes and references has been posted; UPDATED course outline (with information on finals) posted.

Weekly Lecture Notes by P. S. Krishnaprasad

Lecture 0 (a survey of some aspects of nonlinear control)

Lecture 1(a) (Introducing nonlinear control systems) Lecture 1(b) (Frenet-Serret framing of curves and control on SE(3)) Lecture 1(c) (natural framing of curves and control on SE(3))

Lecture 2(a) (matrix Lie groups and Lie algebras - very basic introduction) Lecture 2(b) (Lie brackets in control - examples)

Roger Brockett's 1973 survey article (Lie Algebras and Lie Groups in Control Theory)

Notes on Lie algebras by Hans Samelson, a classic; Roger Howe's 1983 paper Very basic Lie theory; and corrections to Howe's paper (1984)

Lecture 3(a) (contraction mappings, fixed points, existence and uniqueness of solutions to ODE's) Lecture 3(b) (mean value theorem)

Lecture 4 (planar systems, Hartman-Grobman theorem, Poincare-Bendixson theorem)

Lecture 5 (on Index) Lecture 5 continued (more on Index)

Lecture 6 Lyapunov and Lasalle Theorems; Chetaev Theorem; Region of attraction

Lecture 7 Lyapunov theorems for time-varying systems; Linearization Theorems (stability) and Linearization Theorems (instability)

Lecture 8 Feedback stabilization; feedback linearization

Lecture 9 Stability theory: input-output aspects

Lecture 10 Passivity and Absolute Stability


Homework Assignments

Problem Set 1

Problem Set 2

Problem Set 3 (part 1) part 2

Problem Set 4

Problem Sets 5, 6 and 7


Homework solutions are sent by email

For Matlab problems remember to include your code.



Mid Term I

Mid Term II



Other Resources (OR)

My lecture notes on Optimal Control (ENEE 664)

My lecture notes on (Linear) System Theory (ENEE 660)

Website for Feedback Systems: An Introduction for Scientists and Engineers by K. J. Astrom and R. M. Murray On-line readable book

Notes on Lie Algebras by Hans Samelson A classic

Roger Howe's 1983 paper (Very basic Lie theory); corrections to Howe's paper (1984)

Paper by Wei and Norman on product of exponentials representation (1964)

Motion, Control and Geometry Four expository articles illustrating nonlinear control in action

Two classic papers by Roger Brockett Lie Algebras and Lie Groups in Control Theory (1973) and Nonlinear Systems and Differential Geometry (1976)

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

About Sophus Lie

About Stefan Banach

About A. M. Lyapunov

About G. D. Birkhoff