Dan O. Popa, Nonlinear Systems EE 5323, Spring 2012 EE 5323 Fall 2012 Nonlinear Systems Lectures: Tue/Thu, 9:30-10:50 pm, NH 112 Instructor: Dan Popa, Ph.D., Associate Professor, EE Office hours: Tue/Thu 11:00 am – 12:00 pm, 2:00 pm-3:00 pm, NH 543 Course info: Grading policy: 5 Homeworks – 25% Midterm(take-home) – 25% Course project – 25% Final (in-class) – 25%

Dan O. Popa, Nonlinear Systems EE 5323, Spring 2012 Syllabus Part 1: Nonlinear Systems Analysis in the time domain 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.

Dan O. Popa, Nonlinear Systems EE 5323, Spring 2012 Syllabus Part 1: Nonlinear systems analysis in the time-domain 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 –Stability of non-autonomous systems, Barbalat's Lemma's. –Applications to control of robot manipulators. –Homework #2 due Feb 23, Homework #3 posted on Feb. 23. Week 7 - Feb 28, March 1, Lecture 13 –Stability recap and examples Week 8 - March 6, 8 Lectures 14,15 –Central Manifold Theorem. –Homework #3 due March 8

Dan O. Popa, Nonlinear Systems EE 5323, Spring 2012 Syllabus Part 2: Nonlinear iterative maps and phase-domain analysis of nonlinear systems Week 9 - March 12 –Spring break Week 10 - March 20, 22 Lectures 16,17 –Theory of bifurcations. –Homework #4 posted March 20 Week 11 - March 27, 29 Lectures 18,19 –Iterative maps, chaos. –Applications to fractals. Week 12 - April 3,5 Lectures 20,21 –Homework #4 due April 3 –Midterm (take home) on April 3 (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.

Dan O. Popa, Nonlinear Systems EE 5323, Spring 2012 Syllabus Part 3: Nonlinear control Week 13 - April 10, 12 Lectures 22,23 –Describing function method and applications. –Midterm due April 10, Homework #5 posted April 10 Week 14 - April 17, 19 Lectures 24,25 –Nonlinear control system design: stabilization and trajectory tracking, nonlinear control methods and examples from robotics. Week 15 - April 24, 26 Lectures 26,27 –Frobenius' theorem, normal forms, conditions for linearization. –Homework #5 due April 24. –I/O feedback linearization Week 16 - May 1, 3 Lectures 28,29 –Feedback stabilization of nonlinear systems –Course project due May 3 Week 17 - May 5 –Final Exam (In-class, comprehensive)

Dan O. Popa, Nonlinear Systems EE 5323, Spring 2012 Syllabus Grading policy: –On-curve. It will be difficult to get 90+% on exams in this course. –Homeworks: 7. Homeworks contain both written and/or computer simulations using MATLAB. Submit code if it is part of the assignments. –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: A midterm (take-home) and one final (in-class). –Course Project: Due on May 3, it will require a 8-10 page paper/report with an in-depth discussion on a research topic of interest for this course. Select a topic of interest early from a lisr and let me know what it is during office hours.

Dan O. Popa, Nonlinear Systems EE 5323, Spring 2012 Textbooks J.J.-E. Slotine and W. Li, Applied Nonlinear Control, Prentice-Hall, 1991, ISBN: (required) Ferdinand Verhulst, Nonlinear Differential Equations and Dynamical Systems (Paperback) Springer-Verlag, 2-nd edition, 1999, ISBN: (required) M. Vidyasagar, Nonlinear Systems Analysis (Paperback), Society for Industrial and Applied Mathematic; 2nd edition (October 1, 2002 ISBN: , (recommended, on library reserve) Karl Johan Astrom, Bjorn Wittenmark, Adaptive Control (2nd Edition) (Hardcover), Prentice Hall; 2 edition (December 31, 1994), ISBN: (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: (recommended, on library reserve) Robot Manipulator Control: Theory and Practice (Control Engineering, 15) by Frank L. Lewis, et al (Hardcover) ISBN: (recommended, on library reserve) Robot Control: Dynamics, Motion Planning, and Analysis/Pc (Ieee Press Selected Reprint Series) by Mark W. Spong, F.L. Lewis, C.T. Abdallah (Editor) ISBN: (recommended, on library reserve) Student Edition of MATLAB Version 5 for Windows by Mathworks, Mathworks Staff, MathWorks Inc. ISBN: (recommended)

Dan O. Popa, Nonlinear Systems EE 5323, Spring 2012 Course Refresher Math: linear/matrix algebra, trigonometry, differential equations. Controls: stability, linear systems. Programming: MATLAB

Dan O. Popa, Nonlinear Systems EE 5323, Spring 2012 Honor Code Missed deadlines for take-home exams and homeworks: Maximum grade drops 15% per late day. Speak to me about missed deadlines for full credit in extenuating circumstances. 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.

Dan O. Popa, Nonlinear Systems EE 5323, Spring 2012 Lecture 1: Intro to Nonlinear Systems Outline: –What are nonlinear systems and why is it important to study them. –Examples of nonlinear systems. –Basic concepts: what this course covers. –Review of concepts used in this course.

Dan O. Popa, Nonlinear Systems EE 5323, Spring 2012 Reading for Week 1 Brief history of feedback control: Chapter 1 from Slotine & Li text Chapter 1 from H. Khalil text