• Professor Claire Tomlin, Durand 028A
• tomlin at stanford.edu
• http://sun-valley.stanford.edu/~tomlin
• Office hours: TTh 1-2pm

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

This course is a second graduate course in nonlinear systems, organized into three parts as described below. The course is structured to emphasize some of the recent research activity in nonlinear analysis and control. We will use concepts from differential geometry, however the course is self contained in that this mathematics will be taught as part of the course.

Part 1: Advanced Topics in Feedback Linearization

• Review of SISO and MIMO Feedback Linearization
• Involutivity, Lie Brackets, Frobenius' Theorem
• Design examples (ie. when Jacobian Linearization is not controllable)
• Robust Linearization, Sliding Mode, Backstepping, Switched Nonlinear Control

• Introduction to Differential Geometry
• Matrix Lie groups, properties, associated Lie algebras, examples
• Control of Systems on Lie Groups
• Design examples: satellite control; quantum control (control of particles on su(n))

• Small gain theorems, passivity, Lure problem, Popov and Circle criteria
• Constructive Lyapunov Theorems
• Application to adaptive control of nonlinear systems

• 4/1 Course Outline (PDF)
• 4/1 Lecture #1 (PDF)
• 4/1 Project Suggestions (PDF)
• 4/6 Lecture #2 (part 1) (PDF)
• 4/6 Lecture #2 (part 2) (PDF)
• 4/8 Lecture #3 (PDF)
• 4/13 Lecture #4 (PDF)
• 4/20 Homework #1(PDF)
• 4/22 Lecture #5 (PDF)
• 4/27 Lecture #6 (part 1) (PDF)
• 4/27 Lecture #6 (part 2) (PDF)
• 4/29 Lecture #7 (part 1) (PDF)
• 4/29 Lecture #7 (part 2) (PDF)
• 5/11 Lecture #8 (Notes for Geometric Nonlinear Control) (PDF)
• 5/11 Homework #2(PDF)
• 5/25 Homework #3(PDF)
• 5/27 Lecture #9 (PDF)
• 5/27 Lecture #10 (PDF)
• 6/3 Special Lecture on Adaptive Linearization (PDF)
• 6/3 Link to Sastry and Bodson, Adaptive Control: Stability, Convergence, and Robustness

• The course will start on Thursday April 1.

• Online Controls Tutorial in MATLAB

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Control Systems (E205); Nonlinear Control (E209 or E209A); Linear Algebra (Math. 103, 113); Exposure to differential equations.
Exposure to MATLAB is strongly recommended.

Homework 50%
Project 50%

The course is based on a set of lecture notes which will be made available throughout the term. References to relevant research papers will also be given.
The following are the recommended reference texts:

S. S. Sastry. Nonlinear Systems: Analysis, Stability, and Control. Springer-Verlag, 1999.

A. Isidori. Nonlinear Control Systems, 3rd Edition. Springer, 1995.

M. Vidyasagar. Nonlinear Systems Analysis, 2nd Edition. Prentice-Hall, 1993.

H. K. Khalil. Nonlinear Systems, 3rd Edition. Prentice-Hall, 2002.