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Nonlinear Control Systems ECSE 6420. Spring 2009 Lecture 1: 12 January 2009. Information. Instructor: Agung Julius ([email protected]) Office hours: JEC 6044 Mon,Wed 3 – 4pm Teaching assistant: He Bai ( [email protected] ) Office hours: CII 8123 Mon 2 – 4pm

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nonlinear control systems ecse 6420

Nonlinear Control SystemsECSE 6420

Spring 2009

Lecture 1: 12 January 2009

information
Information
  • Instructor: Agung Julius ([email protected])
  • 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
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
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).
grading1
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 vs nonlinear systems

Linear systems

Nonlinear systems

linear systems vs nonlinear systems1
Linear systems vs nonlinear systems

Linear systems

Nonlinear systems

linear 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.

ic

System

output

input

what is tricky about nonlinear systems
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
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
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
course outline
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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