CDS 240, Spring 2016

Nonlinear Dynamical Systems
Instructors Richard Murray (CDS/BE), murray@cds.caltech.edu John Doyle (CDS), doyle@cds.caltech.edu Lectures: MWF, 2-3 pm, 314 ANB Office hours: by appointment	Teaching Assistant TBD Contact: cds140-tas@cds.caltech.edu Office hours: TBD

Course Description

CDS 240. Nonlinear Dynamical Systems. 9 units (3-0-6); third term. Prerequisites: CDS 140. Analysis of nonlinear dynamical systems modeled using differential equations, including invariant and center manifolds, bifurcations, limit cycles, regular and singular perturbations, the method of averaging, input/output stability. Additional advanced topics may be included based on student and instructor interests. Instructors: Doyle, Murray.

Lecture Schedule

Week	Date	Topic	Suggested Reading/Lecture Notes	Homework
1	28 Mar 30 Mar RMM	Stability of perturbed systems Vanishing perturbations Non-vanishing perturbations Slowiy varying systems	Khalil, 9.1, 9.2, 9.6	HW #1 Due 11 Apr
3	1 Apr 6 Apr RMM	Perturbation theory Periodic perturbations Averaging Singular Perturbations	Khalil, 10.3-10.4, 11.1-11.3, 11.5
3	11 Apr 13 Apr 15 Apr JCD	Interconnected Systems Input/output stability Small gain theorem Passivity Absolute stability, circle criterion, Popov criterion Describing functions	Khalil 4.5, 4.6-4.7 (skim), 5.1-5.4	HW #2 Due 25 Apr
4	18 Apr 20 Apr 22 Apr JCD 25 Apr		Khalil, 6.1-6.5, 7.1-7.2 Rantzer presentation
5	27 Apr 29 Apr RMM	Lagrangian and Hamiltonian systems Lagrangian mechanics Lagrange-d'Alembert equations Conservation laws Hamiltonian systems Stability properties	Marsden, Mechanical systems MLS, Lagrangian dynamics with constraints MLS, Nonholonomic behavior in robotic systems	HW #3 Due 9 May
6	4 May 6 May RMM
7	9 May 11 May JCD	Nonnormal systems	See dropbox folder	HW #4 Due 25 May
8	13 May 16 May JCD
9	23 May 25 May RMM	TBD

References:

Course Textbooks

• H. Khalil, Nonlinear Systems, Prentice Hall; 3rd edition, 2001. ISBN: 978-0130673893
• S. Strogatz, Nonlinear Dynamics And Chaos, Westview Press, 1994. ISBN: 978-0738204536
• F. Verhulst, Nonlinear Differential Equations and Dynamical Systems, Springer; 2ed Edition, 1996. ISBN: 978-3540609346

Additional Sources:

• L. Perko, Differential Equations and Dynamical Systems (3rd), Springer, 2001. ISBN: 978-0387951164
• S. Wiggins, Introduction to Applied Nonlinear Dynamical Systems and Chaos, Springer; 2nd edition, 2003. ISBN: 978-0387001777

Policies

Collaboration Policy

Homeworks are to be done and handed in individually. To improve the learning process, students are encouraged to discuss the problems with, provide guidance to and get help from other students, the TAs and instructors. However, to make sure each student understands the concepts, solutions must be written independently and should reflect your understanding of the subject matter at the time of writing. Copying solutions, using solutions from previous years, having someone else type or dictate any part of the solution manual or using publicly available solutions (from the Internet) are not allowed.

Grading Policy

The final grades will be evaluated based on homework assignments.