Stanford University

Winter Quarter 2006-2007

Lecture Information: TTh 11am-12:30pm in the Mitchell Earth Sciences Building, Room B67

Instructor

- Professor Claire J. Tomlin, Durand 028A
- tomlin at stanford.edu
- http://sun-valley.stanford.edu/~tomlin
- Office hours: Tues. 1-2pm and Wed. 3-4pm in Durand 028A

- Michael Vitus
- vitus@stanford.edu
- Office hours: Tues. 2-3pm and Wed. 1-2pm in Room 123 in Durand

- Sherann Ellsworth, Durand 028
- sheranne@stanford.edu
- Phone: 650.723.3389

Course Description

First graduate level course in nonlinear systems. Introduction to nonlinear phenomena: multiple equilibria, limit cycles, bifurcations, complex dynamical behavior. Planar dynamical systems, analysis using phase plane techniques. Describing functions. Input-output analysis and stability. Lyapunov stability theory. The Lure problem, Circle and Popov criterion. Feedback linearization, sliding mode control. The course will be punctuated by a rich set of examples, ranging from violin strings to jet engines, from heart beats to artificial neurons, and from population growth to nonlinear flight control.

- Introduction to Nonlinear Phenomena: Multiple Equilibria, Limit Cycles, Complex Dynamics, Bifurcations
- Second Order Nonlinear Systems: Phase Plane Techniques, Limit Cycles - Poincare-Bendixson Theory, Index Theory
- Input-output analysis and stability: Small Gain Theorem, Passivity, Describing Functions
- Lyapunov Stability Theory: Basic stability and instability theorems, LaSalle's theorem, Indirect method of Lyapunov
- Linearization by State Feedback: Input-Output and Full State Linearization, Zero Dynamics, Inversion, Tracking, Stabilization

Handouts

- 1/9 Course Outline
- 1/9 Lecture Notes 1
- 1/11 Lecture Notes 2
- An example using ODE23 to integrate a system with a switch
- MATLAB Tutorial and ODE example
- 1/16 Lecture Notes 3
- 1/18 Lecture Notes 4
- 1/23 Lecture Notes 5
- 1/25 Lecture Notes 6
- 1/30 Lecture Notes 7
- 2/8 Lecture Notes 8
- 2/8 Lecture Notes 9
- 2/13 Lecture Notes 10
- 2/22 Lecture Notes 11
- 3/1 Lecture Notes 12
- 3/6 Lecture Notes 13
- 3/6 Lecture Notes 14
- 3/13 Lecture Notes 15

Homework

- 1/9 Problem Set 1
- 1/18 Problem Set 2
- 1/25 Problem Set 1 Solution
- 1/26 Problem Set 3
- 2/1 Problem Set 4
- 2/1 Problem Set 2 Solution
- 2/8 Problem Set 5
- 2/9 Problem Set 3 Solution
- 2/13 Midterm Practice Problems
- 2/15 Problem Set 4 Solution
- 2/15 Midterm Practice Problems Solutions
- 2/22 Problem Set 6
- 2/28 Midterm Solutions
- 3/2 Problem Set 7
- 3/7 Problem Set 5 Solution
- 3/7 Problem Set 6 Solution
- 3/9 Problem Set 8
- 3/15 Problem Set 7 Solution
- 3/16 Final Practice Problems
- 3/18 Final Practice Solutions

Announcements

- Students enrolled in the course receive an extra 200MB disk quota.
- Section time: Wednesdays, 5:30pm-6:45pm, Thorton 110. First section Wednesday January 24.
- The classroom has been moved to the Mitchell Earth Sciences Building, Room B67
- Mike's office hours have moved to Room 123 in Durand.
- The Midterm will be on February 20th, in class.

Links

- Online Controls Tutorial in MATLAB
- MATLAB Documentation Help Desk
- ODE Software for MATLAB (by Professor Polking at Rice University)

Mailing List

If you have registered for the class successfully, then your email address is already in the class mailing list.

If you have not registered for the class, please send Professor Tomlin an email and she will add your email address to the class mailing list.

Prerequisites

Control Systems (E205); Linear Algebra (Math. 103, 113); Exposure to
differential equations.

Exposure to MATLAB is strongly recommended.

Grading

Homework 30%

Midterm 30%

Final 40%

Textbook and References

The course is based on a set of lecture notes which will be made available
throughout the term.

The following are reference texts which are available in the bookstore.

S. S. Sastry. Nonlinear Systems: Analysis, Stability, and Control. Springer-Verlag, 1999. We will be covering topics from Chapters 1, 2, 5, 9, 10, and selected topics from Chapters 3, 4, and 6.

H. K. Khalil. Nonlinear Systems, 3rd Edition. Prentice-Hall, 2002. The relevant Chapters are 1, 2, 4, 12, 13, 14, and selected topics from 3, 5, 7, 8.