EE222
Nonlinear Systems: Analysis, Stability, and Control

Course information: UCB On-Line Course Catalog and Schedule of Classes

• Professor Claire J. Tomlin, 721 SD Hall
• tomlin at eecs.berkeley.edu
• http://www.eecs.berkeley.edu/~tomlin
• Office hours: Tu 1-2pm, Wed 11-12noon

First graduate level course in nonlinear systems and control. 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
• Nonlinear Control: Linearization by State Feedback for SISO and MIMO systems, Involutivity, Lie Brackets, Frobenius' Theorem, Zero Dynamics, Inversion, Tracking, Stabilization

• 1/22 Course Outline (PDF)
• 1/22 Lecture Notes 1 (PDF)
• 1/22 Short example using ODE23 in MATLAB
• 1/24 Lecture Notes 2 (PDF)
• 1/28 Lecture Notes 3 (PDF)
• 2/4 Lecture Notes 4 (PDF)
• 2/4 Lecture Notes 5 (PDF)
• 2/11 Lecture Notes 6 (PDF)
• 2/11 Lecture Notes 7 (PDF)
• 2/20 Lecture Notes 8 (PDF)
• 2/20 Lecture Notes 9 (PDF)
• 3/7 Extra Lecture on Nyquist Techniques (PDF)
• 2/25 Lecture Notes 10 (PDF)
• 2/25 Lecture Notes 11 (PDF)
• 3/5 Lecture Notes 12 (PDF)
• 3/5 Lecture Notes 13 (PDF)
• 3/13 Lecture Notes 14 (PDF)
• 4/3 Lecture Notes 15 (PDF)
• 4/3 Lecture Notes 16 (PDF)
• 4/3 Lecture Notes 17 (PDF)
• 4/12 Lecture Notes 18 (PDF)
• 4/12 Lecture Notes 19 (PDF)
• 4/12 Lecture Notes 20 (PDF)
• 4/18 Lecture Notes 21 (PDF)
• 4/18 Lecture Notes 22 (PDF)
• 4/25 Lecture Notes 23 (PDF)

• 1/24 Homework 1 (PDF), Solution (PDF)
• 2/5 Homework 2 (PDF), Solution (PDF)
• 2/18 Homework 3 (PDF), Solution (PDF)
• 3/4 Homework 4 (PDF), Solution (PDF)
• 3/18 Midterm Spring 2011 (PDF)
• 4/3 Homework 5 (PDF), Solution (PDF)
• 4/12 Homework 6 (PDF), Solution (PDF)
• 4/23 Homework 7 (PDF), Solution (PDF)
• 5/2 Homework 8 (PDF), Solution (PDF)

• Online Controls Tutorial in MATLAB
• MATLAB help for UC Berkeley EECS
• MATLAB Documentation Help Desk
• ODE Software for MATLAB (by Professor Polking at Rice University)
• Notes on Nyquist (PDF)

Please sign the handout sheet on the first day of lectures (Tues Jan 22), OR email Professor Tomlin, so that your email will be added to the class mailing list.

Homework 30%
Midterm 30%
Final 40%

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

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.