|
|
AA 546 |
Spring 2006
|
Instructor Prof. Kristi
A. Morgansen |
Office Hours T |
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
Homework section: W
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 writing. No collaboration is allowed on the midterm or the final exam.
Grading
The final grade will be based on homework, a midterm, a final exam and a project.
· Homework: 50%. There will be 8 homework assignments. 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 Tuesday, April 25 and due Tuesday May 2.
· Final exam: 20% The final exam will most likely be a take-home exam.
· Project: 15% Each student will be required to complete a project based on techniques from the course. For your project, you may choose any nonlinear system, and perform the following analysis steps: model justification, controllability, observability, feedback linearization, design of a trajectory tracking controller. The system may be anything, and use of research topics is encouraged. Project plans are due May 2. Final project presentations will be during finals week.
Homework Section: There will be an optional weekly homework solving section. In these sections, students will present the solutions to homework problems. This activity will help with technical presentation skills as well as problem solving techniques.
Course Text
The required reading source for the course is
- H. Nijmeijer and A van der Schaft, Nonlinear Dynamical Control Systems, Springer-Verlag, 1990.
Additional references are on reserve in the library:
- A. Isidori, Nonlinear Control Systems, 3 ed., Springer, 1995.
- H. Khalil, Nonlinear Systems, 2ed, Prentice Hall, 1995.
Schedule
|
Date |
Topics |
Reading |
Assignments |
|
Mar 28 |
Introduction |
NV 1-2.1, |
Homework #1: Assignment
|
|
Mar 30 |
Frobenius Theorem |
2.2-2.3 |
|
|
Apr 4 |
Reachability and controllability LECTURE TO BE RESCHEDULED |
3.1 |
Homework #2: Assignment |
|
Apr 6 |
|
|
|
|
Apr 11 |
Observability and local transformations |
3.2, |
Homework #3: Assignment |
|
Apr 13 |
|
|
|
|
Apr 18 |
Feedback linearization |
5-6, |
Homework #4: Assignment |
|
Apr 20 |
|
|
|
|
Apr 25 |
Volterra
series expansions |
4 |
Midterm
|
|
Apr 27 |
|
|
|
|
May 2 |
Stability |
10, |
Homework #5: Assignment |
|
May 4 |
|
|
|
|
May 9 |
Systems on Lie Groups |
Bullo/Lewis |
Homework #6: Assignment |
|
May 11 |
|
|
|
|
May 16 |
Approximate tracking |
Bullo/Lewis |
Homework #7:
Assignment |
|
May 18 |
|
|
|
|
May 23 |
Optimal control |
Homework #8: Assignment (Solutions (partial)) |
|
|
May 25 |
|
|
|
|
May 30 |
Advanced topics |
Notes |
|
|
Jun 1 |
|
|
|
|
|
FINAL EXAMINATION |
|
FINAL (Solutions) |
Web page maintained by K. Morgansen (morgansn@u.washington.edu)
Last updated: 7-Jun-06