MAE
281A - Nonlinear Systems (Winter 2023)
Course
web address: http://flyingv.ucsd.edu/krstic/teaching/281a/281a.html
Instructor: Prof. Miroslav Krstic, 1808 EBUI, krstic@ucsd.edu
Teaching
Assistant: Cenk Demir (cdemir@eng.ucsd.edu) 2101 EBUI
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, PCYNH
(Pepper Canyon Hall) 120
Cancelled
classes: TBD
Make
up classes: TBD
Office
Hours by Instructor: Mondays 11:00-12:00 (1808 EBUI)
Office
Hours by TA:
Mondays
1:00 pm (2101 EBUI)
Wednesdays
11:00 am (2101 EBUI)
Fridays
1:00 pm (2101 EBUI)
Final
Exam: Due Thursday, March 23, 11:00 am - 2101 EBU1
Final
Final (with
solutions)
Grading:
Homework 30% and Final 70%
Homework
Solutions:
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. 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. Center manifold theorem.
Academic
Integrity: Collaboration on homework is encouraged but each student should present
his/her own work in the homework solutions they submit. On the final exam, no
collaboration is allowed. Students who collaborate on the final exam will not
receive a passing grade in the course.