COURSE DESCRIPTION: This course is an introduction to the foundations of nonlinear control theory, with an emphasis on feedback stabilization. As needed, topics from differential geometry and other mathematical disciplines are introduced to support the development of basic concepts. The focus of the course is on mathematical tools for the analysis and design of nonlinear feedback systems, not the hardware and software technology required for their implementation.

INSTRUCTOR: Prof. Randy Freeman

OBJECTIVES: Students will learn a variety of methods for analyzing the structure and behavior of nonlinear feedback systems. They will also learn basic design techniques including feedback linearization, feedback passivation, Lyapunov design, backstepping, and forwarding.

PREREQUISITES: Prior or concurrent registration in EECS 410 or equivalent; a previous course in linear feedback systems (such as EECS 360) is desirable

REQUIRED TEXTS: None

Reference texts:

  1. Hassan K. Khalil, Nonlinear systems, third edition, Prentice Hall, 2002
  2. Jean-Michel Coron, Control and nonlinearity, American Mathematical Society, 2007
  3. Eduardo D. Sontag, Mathematical control theory: deterministic finite dimensional systems, second edition, Springer, 1998.


GRADING: Homework 40% ; Midterm 30%;  Final 30%
 

TOPICS:

  • nonlinear models and stability: nonlinear differential equations, stability of equilibria, stability of invariant sets, stability for systems with inputs
  • feedback linearization: controllability, feedback equivalence, relative degree, differential flatness
  • stabilization: control Lyapunov functions, backstepping, forwarding, dissipativity
  • other topics may include adaptive control, robust control, and receding horizon control