Nonlinear Systems

EE 5323 Spring 2012

1. Instructor: Dan Popa
2. Office Location: NH 543
3. Office Hours: Tue/Thu11am-12 pm and 2pm-3pm or by appointment
4. Phone: 817-272-3342
5. Fax: 817-272-5952
TA N/A
6. Email: popa@uta.edu
Course venue NH 112, Tue- Thu 9:30-10:50
Course 1 page flyer

7. Course Prerequisites:

An undergraduate controls course. Please come see me, call me, or email me if you have additional questions prior to signing up for the course.

8. Required Readings/Materials:

Textbooks:

  • J.J.-E. Slotine and W. Li, Applied Nonlinear Control, Prentice-Hall, 1991, ISBN: 0130408905 (required)
  • Ferdinand Verhulst, Nonlinear Differential Equations and Dynamical Systems (Paperback) Springer-Verlag, 2-nd edition, 1999, ISBN: 3540609342 (required)
  • M. Vidyasagar, Nonlinear Systems Analysis (Paperback), Society for Industrial and Applied Mathematic; 2nd edition (October 1, 2002 ISBN: 0898715261, (recommended, on library reserve)
  • Karl Johan Astrom, Bjorn Wittenmark, Adaptive Control (2nd Edition) (Hardcover), Prentice Hall; 2 edition (December 31, 1994), ISBN: 0201558661 (recommended, on library reserve)
  • Hassan K. Khalil, Nonlinear Systems, 2-nd edition, Prentice-Hall 1996 (recommended, on library reserve)
  • J. M. T. Thompson, H. B. Stewart, Nonlinear Dynamics and Chaos (Paperback), John Wiley & Sons; 2 edition (February 19, 2002), ISBN: 0471876844 (recommended, on library reserve)
  • Robot Manipulator Control: Theory and Practice (Control Engineering, 15) by Frank L. Lewis, et al (Hardcover) ISBN: 0824740726 (recommended, on library reserve)
  • Robot Control: Dynamics, Motion Planning, and Analysis/Pc0299-8 (Ieee Press Selected Reprint Series) by Mark W. Spong, F.L. Lewis, C.T. Abdallah (Editor) ISBN: 0780304047 (recommended, on library reserve)
  • Student Edition of MATLAB Version 5 for Windows by Mathworks, Mathworks Staff, MathWorks Inc. ISBN: 0132724774 (recommended)


9. Course Description:
This is an follow-up systems course, containing both introductory as well as some more advanced concepts in nonlinear systems and control. It presents an overview of nonlinear systems, discusses nonlinear stability and control methods, adaptive control and applications ranging from robotic manipulators to fractals.

The course is divided between the following areas:

  • Nonlinear Systems Fundamentals
  • Advanced Concepts in Nonlinear Systems
  • Nonlinear and adaptive Control Methods
10. Course Learning Goals/Objectives:
The goals of the course are as follows: 1) To introduce students to modeling, simulation and control of nonlinear systems. 2) To provide assignments and application examples that will allow students to solidify these concepts. 3) To encourage the use of nonlinear analysis and control concepts in graduate student research from multiple disciplines.
11. Lecture/Topic Schedule
Please note that this schedule is tentative and may change during the semester.
  • Week 1 - January 17, 19 Lectures 1,2
    • Course outline
    • Introduction to nonlinear systems and examples.
  • Week 2 - January 24, 26 Lectures 3,4
    • Review of math concepts used in the course.
    • Some nonlinear systems in engineering.
    • Introduction to analysis in Phase Plane: equilibria, phase-space plots.
    • Homework #1 posted January 26
  • Week 3 - January 31, Feb. 2, Lectures 5,6
    • Introduction to analysis in Phase Plane: equilibria, phase-space plots.
    • Analysis in Phase-Plane: periodic solutions, limit cycles, critical points, method of isoclines, first integrals.
  • Week 4 - Feb. 7, 9, Lectures 7,8
    • Poincare-Bendixon Theorem
    • Stability of nonlinear systems in time domain: definitions of local, global, asymptotic and exponential stability.
    • Homework #1 due Feb. 9, Homework #2 posted on Feb. 9.
  • Week 5 - Feb. 14, 16 Lectures 9, 10
    • Invariant sets, Lyapunov and La Salle's theorems, stability by linearization.
  • Week 6 - Feb. 21, 23 Lectures 11,12
    • Invariant sets, Lyapunov and La Salle's theorems, stability by linearization.
    • Homework #2 due Feb 23
  • Week 7 - Feb 28, March 1, Lecture 13
    • Stability recap and examples
  • Week 8 - March 6, 8 Lectures 14,15
    • Stability of non-autonomous systems, Barbalat's Lemma's.
    • Applications to control of robot manipulators.
    • Homework #3 posted March 6.
  • Week 9 - March 12 Spring break
    • Week 10 - March 20, 22 Lectures 16,17
      • Central Manifold theorem
      • Theory of bifurcations.
      • Homework #3 due March 22, Homework #4 posted March 20
    • Week 11 - March 27, 29 Lectures 18,19
      • Iterative maps, chaos.
    • Week 12 - April 3,5 Lectures 20,21
      • LTV equations and Floquet Theory
      • Applications to fractals.
      • Passivity and positivity concepts.
    • Week 13 - April 10, 12 Lectures 22,23
      • Homework #4 due April 10
      • Midterm (take home) on April 10 (covers nonlinear systems time-domain analysis).
      • Passivity and positivity concepts. Stability analysis in frequency domain: Absolute stability and the Lure Problem, Popov's circle criterion.
    • Week 14 - April 17, 19 Lectures 24,25
      • Describing function method and applications.
      • Midterm due April 17, Homework #5 posted April 17
    • Week 15 - April 24, 26 Lectures 26,27
      • Nonlinear control system design: stabilization and trajectory tracking, nonlinear control methods and examples from robotics.
      • Frobenius' theorem, normal forms, conditions for linearization.
    • Week 16 - May 1, 3 Lectures 28,29
      • I/O feedback linearization
      • Feedback stabilization of nonlinear systems
      • Homework #5 due May 1
      • Course project due May 3
    • Week 17 - May 5
      • Final Exam (In-class, comprehensive)

      • 12. Specific Course Requirements:
      • Homeworks: 5
      • Reading Assignments: After each course. The assigned reading material is given out in order to make you better understand the concepts. Materials from the reading assignments may be part of course exams.
      • Examinations: One midterm (take-home) and one final (in-class).
      • Course Project: Due on May 3, this project requires a 8-10 page requires a paper/report and an in-depth discussion on a research topic of interest for this course. Select a topic of interest early from a list provided in class, and let me know what it is during office hours.
      • Final Examination: Final Exam Comprehensive
      • Missed deadlines for take-home exams and homeworks: Maximum grade drops 15% per late day. Talk to me for full credit on late assignments under extenuating circumstances.
      • Grading Format Weighting: 25% Homeworks 25% Midterm 25% Course Project and 25% Final
      • Academic Dishonesty will not be tolerated. All homeworks and exams are individual assignments. Your take-home exams and homeworks will be carefully scrutinized to ensure a fair grade for everyone.
      • Attendance and Drop Policy: Attendance is not mandatory. However, if you skip classes, you will find the homework and exams more difficult. Assignments are going to be posted here, however, due to the pace of the lectures, copying someone else's notes may be an unreliable way of making up an absence. You are responsible for all material covered in class regardless of absences.
      13. Online Materials