ECE 528 - Analysis of Nonlinear Systems

Spring 2005, ECE, Univ. of Illinois at Urbana-Champaign

"All stable processes we shall predict. All unstable processes we shall control." ---- John von Neumann

[Announcements | Administrative | Homework | Handouts | Resources]

Announcements

May 8, 10:00am, final exam , due by noon 12:00pm Monday, May 9. (In Problem 2, "D1" and "D2" mean the partial derivatives with respect to the first (x) and second (z) variables, repsectively.
May 5, solution 6 is posted below. For those who take final tommorow, please make sure to drop by my office before 10:00am to pick up the problem set.
May 2, Apparently tommorow is the last day of lecture. That changes our plan a little bit:
- Course Evaluation needs to be done in tommorow's lecture. Please bring with your a B2 pencil for filling out the forms. I also need a volunteer to collect/mail the forms.
- The original plan is that HW#6 is not due till Thursday. Well, if you have finished the homework, you may turn it in tommorow in class. But I will keep the window open till Thursday noon accepting homeworks -- You may drop it at my office CSL 145 (slide under the door if I am not in). I will post the solution to Hw#6 in the afternoon of Thursday...
- As for the Final, we agree to have two batches: one batch on this Friday (from 10am to Saturday 10am); another batch on this Sunday (from 10am to Monday 10am). I am going to collect names of people who prefer to go with the first batch. The problems will be the same, but I do not suppose it is to your advantage to leak the problems to others...
Final Exam (one-day take-home) is temporarily set to be on Sunday, May 8.
April 19, homework 6 is assigned below, due on Thursday, May 5.
April 19, solution 5 is posted below.
April 18, solution 4 is posted below, homework 6 will be out soon.
April 5, homework 5 is assigned below, due on Thursday, April 14.
Due to the breakdown of our computer server two weeks ago, my record of your homework 2 grades was wiped out. I may need you to bring you graded homework 2 back to me sometime.
Homework 4 will not be due till Tuesday, March 29 (after Spring Break).
Typo in the exam: The second inequality of problem 4, the left hand side should be (total) derivative with respect to time t, not x. (Or does that matter?)
March 13, 10:00am, midterm exam , due on 10:00am Monday, March 14.
February 28, homework 4 is assigned below, due on Thursday, March 17 (after the midterm but before the spring break).
February 24, solution 3 is posted below.
February 21, the one-day take-home midterm exam is temporarily chosen to be from 10am March 13 to 10am March 14.
February 11, homework 3 is assigned below, due on Thursday, February 24.
February 10, solution 2 is posted below and homework 3 will be out soon (tomorrow?).
January 28, homework 2 is posted, due on Thursday, February 10.
January 27, solution 1 is posted below and homework 2 will be out tomorrow.
January 18, homework 1 is posted below, due on Thursday, January 27.
January 11, welcome to the world of nonlinear dynamics!

Administrative Information

Instructor: Professor Yi Ma
Classes: TuTh 1:30am-2:50am, 169 Everitt Laboratory
Office Hours: Tuesday 3:00pm-5:00pm
Office Address: 145 CSL, Phone: 244-0871
Email: yima@uiuc.edu
Appointments: requested through email only!

Prerequisites:

*ECE 515 or equivalent; one of MATH 385, MATH 386, MATH 441; or consent of instructor.
*Some experience with MATLAB, numerically solving differential equations.
*Some exposure to differential geometry and real analysis is desirable but not really needed.
*However, sophistication of mathematical thought is more important than formal pre-requisites.

Required Textbook:

* Nonlinear Systems, Hassan Khalil, 3rd edition, Prentice Hall, 2002.

Supplementary Textbook:

* Nonlinear Systems -- Analysis, Stability, and Control, Shankar Sastry, Springer, 1999.

References (Reserved in the Engineering Library):

* Mathematical Control Theory, E. D. Sontag, 2nd edition, Springer, 1998.
* Ordinary Differential Equations, V. I. Arnold, Springer Verlag, 1997.
* Nonlinear Control Systems, A. Isidori, 3rd edition, Springer Verlag, 1995.
* Nonlinear Systems Analysis, M. Vidyasagar, 2nd edition, Prentice Hall, 1993.
* An Introduction to Differential Manifolds and Riemannian Geometry, W. Boothby, Academic Press, 1986.

Grading Policy: Homework (40%), Midterm (20%), and Final (40%).

*Homework: You are allowed to discuss on the homework in small groups, but you must write the solution independently to hand in. No late homework will be accepted (unless an extension is granted by the instructor to the whole class).
*Exams: We will have one-day take-home (open-library) exams for midterm and final. No discussion among students is allowed.
*If you are no. 1 in the final, you will get an "A" no matter how badly you have flunked your midterm or homework.

Course Outline (download the pdf file)

*The course will follow more closely the outline than any textbooks.

Homeworks and Solutions

There will be a homework assignment almost every other week. Homework is usually due one week after it is assigned. Late homework will not be accepted! Homework problem sets and solutions are given below in pdf. If there are any typos/mistakes in the solution, please notify me.

Homework 1 , due on Thursday, January 27.
Solution 1 , out on Thursday, January 27.
Homework 2 , due on Thursday, February 10.
Solution 2 , out on Thursday, February 10.
Homework 3 , due on Thursday, February 24.
Solution 3 , out on Thursday, February 24.
Homework 4 , due on Thursday, March 17.
Solution 4 , out on Monday, April 18.
Homework 5 , due on Thursday, April 14.
Solution 5 , out on Tuesday, April 19.
Homework 6 , due on Thursday, May 5.
Solution 6 , out on Thursday, May 5.

Handouts

Online Resources

Learn history of mathematics at http://www-groups.dcs.st-and.ac.uk/~history/BiogIndex.html about the origins of nonlinear dynamical systems, tracing back to Joseph-Louis Lagrange, Henri Poincaré, Aleksandr M. Lyapunov , Lev Semenovich Pontryagin .

Yi Ma | yima@uiuc.edu

Last updated 01/17/05