Nonlinear Control SystemsECSE 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 Textbook: H.K. Khalil, Nonlinear Systems 3rd ed,

Prentice Hall.

Online contents: www.ecse.rpi.edu/~agung (Notes, HW sets) WebCT (grades)

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?

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).

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.

Linear systems vs nonlinear systems

Linear systems

Nonlinear systems

Linear systems vs nonlinear systems

Linear systems

Nonlinear systems

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.

System

ic

outputinput

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

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.

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

Multistability in nature

toggle switch

Robust oscillation

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.