MAE 281A - Nonlinear Systems (Winter 2017)

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

Teaching Assistant: Stephen Chen and Shumon Koga, 2101 EBUI, stc007@eng.ucsd.edu and skoga@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, WLH 2207

Cancelled classes: TBD

Make up classes: TBD

Office Hours by Instructor : Mondays, 9-10 am, 1808 EBU1

Office Hours by TA: Mondays and Fridays, 1-2 pm, 2101 EBU1

Final Exam: Thursday, March 23, 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.