ME 6402: Nonlinear Control Systems

Offered Every Spring


Credit Hours: 3-0-3
Prerequisites: 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.
Textbooks: Jean-Jacques Slotine and Weiping Li, Applied Nonlinear Control, Prentice-Hall, 1990.
Instructors: Wayne Book, Ye-Hwa Chen, Kok-Meng Lee, Nader Sadegh.
Goals: To be familiar with the theory and applications of nonlinear systems (phase plane, describing functions, Lyapunov methods), geometric control, variable structure control, adaptive control, applications to robots and spacecraft, and nonlinear optimal control.
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.
Delivery Mode (%):
Lecture 100
Grading Scheme (%):

Homework

15

Projects

15 

Exams x2

20 (each)

Final

30