Nonlinear Control Theory

The course covers analysis and design of nonlinear control systems using Lyapunov theory and geometric methods. Topics Include properties of solutions of nonlinear systems, Lyapunov stability analysis, feedback linearization, and nonlinear control design tools. Prerequisite(s): basic knowledge of ordinary differential equations; basic knowledge of linear algebra and basic knowledge of linear control theory. Enrollment restricted to graduate students or permission of instructor.

Text Book: Nonlinear Systems, H. Khalil, Prentice-Hall, 3^{rd} Ed., 2002 or 2^{nd} Ed., 1996

Reference: Nonlinear Systems Analysis, M. Vidyasagar, Prentice-Hall, 2^{nd} Ed., 1996

Nonlinear Control Systems, A. Isidori, Springer, 3rd Ed., 1995

Lectures: Monday, Wednesday and Friday 9:30AM - 10:40AM, BE 169

Office Hours: Thursday, 1:30pm - 3:00pm, BE 361A.

Tentative Schedule

Week 1: Introduction of nonlinear systems and review of linear control system theory. Read Chapter 1.

Week 2: Mathematical preliminaries, local Existence and Uniqueness Theorem (Theorem 3.1). Discussion on Lipschitz continuity, Gronwell inequality (Appendix A), and Global Existence and Uniqueness Theorem (Theorem 3.2).

Week 3: Continuous dependence on initial conditions and parameters (Section 3.2), sensitivity equations (Section 3.3), and Definition of Lyapunov Stability for autonomous systems (Section 4.1).

Week 4: Lyapunov stability theory for autonomous systems (Section 4.1) and Lasalle’s Invariance Principle (Section 4.2),

Week 5: Linearization and linear state feedback control (Section 4.3), Brockett’s necessary conditions, feedback linearizble normal form.

Week 6: Input-state feedback linearization and input-output linearization (Chapter 14).

Week 7: Lyapunov-based nonlinear control design. Backstepping for lower triangular systems (Section 14.3), adaptive backstepping with linear and nonliner parameterization.

Week 8. Lyapunov stability theory for time-varying nonlinear systems, comparison functions, uniform stability, exponential stability (Section 4.4, 4.5).

Week 9. Time-varying systems and linearization (Section 4.6), and Converse Theorems (Section 4.7).

Week 10. Nonlinear observer design and output-feedback control.

Students with disabilities: If you qualify for classroom accommodations because of a disability, please get an Accommodation Authorization from the Disability Resource Center (DRC) and submit it to me in person outside of class (e.g., office hours) within the first two weeks of the quarter. Contact DRC at 459-2089 (voice), 459-4806 (TTY), or http://drc.ucsc.edu for more information on the requirements and/or process.