AA 599 Spring 04

AA 599
Geometric Methods for Nonlinear Control Systems

Spring 2004

Instructor

Prof. Kristi A. Morgansen
morgansen@aa.washington.edu

Office Hours

M 11:30-12:30, Th 1-2pm
Gug. 310

Course Description

This course provides tools for analysis and design of nonlinear control systems focusing on differential geometric methods. We will begin with a refresher of the tools covered in Manifolds and Geometry for Systems and Control (AA599D/EE546 W04). From these tools we will rigorously investigate controllability, observability, feedback linearization, invariant distributions, local coordinate transformations, and Volterra series. Particular emphasis will be given to systems evolving on Lie groups and linearly uncontrollable systems. Examples will be drawn from robotics, quantum physics, materials processing, and computer vision.

Prerequisite: Manifolds and Geometry for Systems and Control (AA599D/EE546 W04) or permission of instructor

Lectures: T/TH 10:30-11:50am, MEB 102
Homework section: Th 4-5pm, EE1 026

Week	Topic	Reading	Homework
1	Introduction and background material	Isidori 1.1-1.3	HW1 [Soln 1]
2	Frobenius Theorem and reachability	Isidori 1.4-1.8	HW2 [Soln 2]
3	Observability and local transformations	Isidori 1.9, 4.1	HW3 [Soln 3]
4	Feedback linearization	Isidori 4.2	HW4 [Soln 4]
5	Volterra series expansions	Isidori 3.2	Midterm [soln]
6	Stability	Isidori 4.4, handout	HW5 [Soln 5]
7	Systems on Lie groups	handout	HW6 [Soln 6]
8	Approximate tracking	handout	HW7 [Soln 7]
9	Optimal control	handout

Final Exam

Lecture Notes

Lie brackets

Observability

Feedback linearization

Stability (from Khalil, ch. 3)

Optimization

Trajectory tracking

Homework and Exam Policy

Collaboration on homework assignments is allowed. You may consult outside reference materials, other students, or the instructor. All solutions that are handed in should reflect your understanding of the subject matter at the time of writring. No collaboration is allowed on the midterm or the final exam.

Grading

The final grade will be based on homework, a midterm, and a final exam.

Homework: 50%. There will be 8 homework assignments due at 5pm on Tuesdays. Each problem set will have about 6 problems. Late homework will not be accepted without prior permission from the instructor.
Midterm: 15% The midterm will be a take-home exam posted on Thursday, April 22 and due Thursday April 29.
Final exam: 20% The final exam will most likely be a take-home exam. If it is in class, it will take place on Thursday March 18, 10:30-12:30pm.
Project: 15% Each student will be required to complete a project based on techniques from the course. Projects must be approved by the instructor no later than week 6 of the course.

Course Text

The required reading source for the course is

A. Isidori, Nonlinear Control Systems, 3 ed., Springer, 1995.

Additional references are on reserve in the library:

H. Nijmeijer and A van der Schaft, Nonlinear Dynamical Control Systems, Springer-Verlag, 1990.
H. Khalil, Nonlinear Systems, 2ed, Prentice Hall, 1995.

Web page maintained by K. Morgansen (morgansn@u.washington.edu)
Last updated: 18-Sep-2003