ME 6402: Nonlinear Control Systems
Offered Every Spring

Hours: 3-0-3
Prerequisite: ME 6401 or equivalent, or with the consent of the instructor
Catalog Description: Analysis of nonlinear systems, geometric control, variable structure control, adaptive control, optimal control, applications.
Textbook: Jean-Jacques Slotine and Weiping Li, Applied Nonlinear Control, Prentice-Hall, 1990.
Instructors: Wayne Book, Ye-Hwa Chen (Spring 2004), Kok-Meng Lee, Nader Sadegh.

Goals:

Evaluation Procedures:

Homework: 15%
  Project: 15%
  Two tests: 20% (each)
  Final: 30%

Mode of instruction:

Lectures 100%

Topics:

  • Why nonlinear control?
  • Nonlinear system behavior.
  • Concept of phase plane analysis.
     
  • Determining time from phase portraits.
  • Phase plane analysis for linear systems.
  • Phase plane analysis for nonlinear systems.
  • Limit cycles.
     
  • Equilibrium points.
  • Linearization and local stability.
  • Lyapunov's direct method.
     
  • System analysis based on Lyapunov's direct method.
  • Control design based on Lyapunov's direct method.
     
  • Lyapunov analysis of non-autonomous systems.
  • Instability theorems.
  • Existence of Lyapunov functions.
  • Lyapunov-like analysis using Barbalat's lemma.
     
  • Positive linear systems.
  • The passivity formalism.
  • Absolute stability.
  • Boundedness of signals.
     
  • Describing functions.
  • Common nonlinearities.
  • Describing function analysis of nonlinear systems.
     
  • Input-state linearization of SISO systems.
  • Input-output linearization of SISO systems.
     
  • Multi-input systems.
  • Sliding surfaces.
  • Continuous approximation of switching control laws.
  • The modelling/performance trade-offs.
     
  • Basic concepts of adaptive control.
  • Adaptive control with output feedback.
     
  • Composite adaptation.
  • Adaptive robot trajectory control.
  • Spacecraft control.
     
  • Optimal process for dynamic systems.
  • Pontryagin's maximum principle.
     
  • Sufficient condition.
  • Optimization problems for dynamic systems with path constraints.
     
  • Time optimal control.
  • Minimum fuel control.
  • Terminal constraint.
  • A minimax-time intercept problem with bounded controls.
     
  • Optimal feedback control in the presence of uncertainty.
  • Control parameter optimization.

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    Revised June 2004