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

ENEE 661 - Nonlinear Control Systems

Spring 2015

Last Update December, 2014

Course Information

Special Announcements (in reverse chronological order)








4. 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.



1. A first set of lecture notes and references has been posted - TO BE REVISED

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)

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 Set 5

Problem Sets 6 and 7 (for grade) and Problem Sets 8 and 9 (not for grade)


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