AME 654: Geometric Nonlinear Control

This course is an introduction to nonlinear control with emphasis on differential geometric methods. Topics covered include linear and nonlinear dynamical systems analysis methods, Lyapunov theory and related controls applications, bifurcation analysis and related control applications and differential geometry and nonlinear control from the differential geometric point of view.

• B. Goodwine
• Office: 367 Fitzpatrick
• Email: goodwine@controls.ame.nd.edu

• Final exam.
• Syllabus August 23, 2003.
• Source code for the logistic map example from class, and a slightly more complicated version which generates more plots.

• Homework 1, due September 4, 2003.
• Homework 2, due September 11, 2003.
• Homework 3, due September 18, 2003.
• Homework 4, due September 25, 2003.
• Homework 5, due October 2, 2003.
• Homework 6, due October 9, 2003.
• Midterm Exam, due November 4, 2003.
• Homework 7, due November 6, 2003.
• Homework 8, due December 4, 2003.

1. Nonlinear systems introduction - subtleties, complexities and examples;
2. Mathematical preliminaries;
3. Dynamical systems overview;
4. Lyapunov theory and control applications;
5. Bifurcations and control applications;
6. Basic differential geometry;
7. Linearization by state feedback;
8. Design examples using linearization;
9. Controllability and observability;
10. Steering drift-free systems;
11. Application to stratified systems, legged robotic locomotion and robotic manipulation.