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Nonlinear Control Systems ECSE 6420

Nonlinear Control Systems ECSE 6420. Spring 2009 Lecture 1: 12 January 2009. Information. Instructor: Agung Julius (agung@ecse) Office hours: JEC 6044 Mon,Wed 3 – 4pm Teaching assistant: He Bai ( baih@rpi.edu ) Office hours: CII 8123 Mon 2 – 4pm

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Nonlinear Control Systems ECSE 6420

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  1. Nonlinear Control SystemsECSE 6420 Spring 2009 Lecture 1: 12 January 2009

  2. Information • Instructor: Agung Julius (agung@ecse) • Office hours: JEC 6044 Mon,Wed 3 – 4pm • Teaching assistant: He Bai (baih@rpi.edu) • Office hours: CII 8123 Mon 2 – 4pm • Textbook: H.K. Khalil, Nonlinear Systems 3rd ed, Prentice Hall. Online contents: • www.ecse.rpi.edu/~agung(Notes, HW sets) • WebCT (grades)

  3. Prerequisite(s) The course is for graduate or advanced undergraduate students with working knowledge in differential calculus, linear algebra, and linear systems/control theory. Attendance background?

  4. Grading • Homeworks = 30% • Midterm exam = 25% • Project/presentation = 10% + 5% • Final exam = 30% • Homework sets are due one week after handout. Late submissions will get point deduction (no later than 1 week).

  5. Grading • Project: advanced paper review and presentation, or class project. • Midterm exam will be a take home test. You will have 48 hours to solve the problems. No collaboration is allowed. No late submission! • Final exam will follow schedule.

  6. What is this course about?

  7. ? Linear systems vs nonlinear systems Linear systems Nonlinear systems

  8. Linear systems vs nonlinear systems Linear systems Nonlinear systems

  9. Linear systems • Linear systems are systems that have a certain set of properties. • Linear systems are very nice objects to study because of their regularity. Why? We need structure. ic System output input

  10. What is tricky about nonlinear systems? LACK OF STRUCTURE! Cannot take everything for granted. • Existence and uniqueness of solution to diff. eqns. • Finite escape time

  11. Nonlinear from linear • A lot of techniques that are used for nonlinear systems come from linear systems, because: • Nonlinear systems can (sometime) be approximated by linear systems. • Nonlinear systems can (sometime) be “transformed” into linear systems. • The tools are generalized and extended.

  12. Why study nonlinear systems? • Linearity is idealization. E.g. a simple pendulum. • A lot of phenomena are only present in nonlinear systems. • Multiple (countable) equilibria. Why? • Robust oscillations: where? • Bifurcations • Complex dynamics • Why simulation is not always enough • Why simulation is not always necessary

  13. Multistability in nature toggle switch

  14. Robust oscillation

  15. Course outline • Linear vs Nonlinear • Planar dynamical systems • Fundamental properties • Lyapunov stability theory • Input – output analysis and stability • Passivity • Frequency domain analysis • Nonlinear feedback control • Non-traditional topics: hybrid systems, biological systems, etc.

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