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

ENEE 661 - Nonlinear Control Systems

Spring 2017

Last Update: Friday, April 28, 2017

Course Information

Special Announcements (in reverse chronological order)

15. Homework Set 8 posted. NOTE: due date - Thursday, May 4

14. Homework Set 7 posted (distributed previous week by email, due back Friday April 21). Mid-term Examination II is postoponed to TUESDAY April 25, as announced earlier in class. This examination will be based on Lectures 5-11, and 13. The associated problem sets are Homework Set 4 through 7.

13. Homework Set 6 posted (due back in class Tuesday, April 4). Mid-term Examination is moved to April 13.

12. Homework Set 5 posted (due back in class Thursday, March 16)

11. Homework Set 4 posted (due back in class Thursday, March 9)

10. Mid-term Exam I postponed to Thursday, March 2.

9. Fixed more typos in Lecture 4 and Lecture 5 (Tuesday, February 21).

8. Homework Set 2 for Spring 2017 posted - due Tuesday February 14; also added links to books by Edward Nelson.

7. I encourage people to stop by for office hours on Monday.

6. Lecture notes edited to fix typos in Lectures 3 and 4 - February 4, Saturday

5. Homework Set 1 for Spring 2017 posted - due Feb 8, Wednesday

4. Lecture 1 and 2 are updated (typos fixed).

3. Course Outline updated - exam dates, and information on course content and course prerequisites. (January 7)

2. A preliminary set of notes (LaTeX) has been posted. Please do not print this version as it is undergoing some editing. (January 4)

1. A first set of handwritten lecture notes and references has been posted; updated LaTeX version of notes will be posted by first week in January 2017. UPDATED course outline posted.

Lecture Notes by P. S. Krishnaprasad (LaTeX version)

Lecture Notes ENEE661 - Spring 2017 (please do not print, as it is being edited)

Survey Lecture (on some aspects of geometric control theory)

Addendum 1 to Lecture 4 on density evolution


Supporting References (papers, books)

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

Roger Brockett's 1976 Proc. IEEE survey article Nonlinear systems and differential geometry

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)

Wei and Norman's 1964 paper On Global Representations of the Solutions of Linear Differential Equations as a Product of Exponentials

Roger Brockett's 2014 Automatica survey The early days of geometric nonlinear ontrol

Tensor Analysis - book by Edward Nelson see pages 33-36 on kinematic car

Topics in Dynamics I: Flows - book by Edward Nelson


Homework Assignments Spring 2017

Problem Set 1

Problem Set 2

Problem Set 3

Problem Set 4

Problem Set 5

Problem Set 6

Problem Set 7

Problem Set 8


Older Hand-written Weekly Lecture Notes by P. S. Krishnaprasad

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)

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


Older 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

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

Real Analysis Book by Cinlar and Vanderbei - material useful in Systems courses published by Springer in Undergraduate Texts in Mathematics Series as Real and Convex Analysis (recommended)

About Sophus Lie

About Stefan Banach

About A. M. Lyapunov

About G. D. Birkhoff