MAE 281A - Nonlinear Systems (Winter 2014)

Department of MAE, UCSD

Course web address: http://flyingv.ucsd.edu/krstic/teaching/281a/281a.html

Instructor: Prof. Miroslav Krstic, 1808 EBUI, 822-1374, krstic@ucsd.edu

Texts:

· Khalil, Nonlinear Systems, Prentice Hall, 2001.

· (supplemental) Krstic, Kanellakopoulos, and Kokotovic, Nonlinear and Adaptive Control Design, Wiley, 1995.

Prerequisites: Linear Systems (MAE 280A) or consent of instructor

Time and Place: TuTh, 8:00-9:20 am, HSS 2152

Office Hours: F, 2-3 pm

Final Exam: Thursday, March 20, 8:00-11:00

Grading:

Homework (pdf) 30%
      

Final 70%

Course Objective: The course will give the students an in-depth introduction to stability and other analysis techniques for nonlinear systems and prepare them for courses on nonlinear control design (MAE 281B) and adaptive control (MAE 282, alternate years). Students from all departments are welcome.

Topics: Existence and uniqueness of solutions of ODEs, sensitivity equations. Stability, direct and converse Lyapunov theorems, LaSalle's theorem, linearization, invariance theorems. Center manifold theorem. Stability of perturbed systems with vanishing and non-vanishing perturbations, input-to-state ability, comparison method. Input-output stability. Perturbation theory and averaging. Singular perturbations. Circle and Popov criteria.

Cancelled classes: January 9, March 11, and March 13

Make up classes: Jan 16, Jan 23, Feb 20, at 11:00-12:20 in Rm 2101 EBU1