nonlinear control theory ese617
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Nonlinear Control SystemsECSE 6420
Spring 2009Lecture 1: 12 January 2009
Information
Instructor: Agung Julius (agung@ecse) Office hours: JEC 6044 Mon,Wed 3 – 4pm Teaching assistant: He Bai ([email protected]) 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.