CDS 140b, Spring 2014

Differential Equations and Dynamical Systems
Instructors Richard Murray (CDS/BE), murray@cds.caltech.edu Doug MacMartin (CDS), macmardg@cds.caltech.edu Lectures: MWF, 1-2 pm Office hours: TBD	Teaching Assistants TBD Contact: cds140-tas@cds.caltech.edu Office hours: TBD

Course Description

CDS 140b is a continuation of CDS 140a. A large part of the course will focus on tools from nonlinear dynamics, such as perturbation theory and averaging, advanced stability analysis, the existence of periodic orbits, bifurcation theory, chaos, etc. In addition, guest lecturers will give an introduction to current research topics in dynamical systems theory. There will be 5 homeworks throughout the term but no exams. Instead, the students are required to select a research topic and a journal paper related to CDS140b and present a brief review of the paper. The details of the projects will be discussed in the class.

Lecture Schedule

Week	Date	Topic	Suggested Reading/Lecture Notes	Homework
1	31 Mar 2 Apr 4 Apr*	Perturbation Theory Regular Perturbation Poincare-Lindstedt Method Periodically Perturbed Systems	Khalil, 10.1-10.3 Strogatz, 7.6 Verhulst, 9.1, 10.1	HW 1
2	7 Apr 9 Apr* 11 Apr	Averaging Method Periodic Case Periodic Solutions General Case	Khalil, 10.4-10.6 Strogatz, 7.6 Verhulst, 11.1-11.3, 11.8	HW 2
3	14 Apr*+ 16 Apr*+ 18 Apr+	Singular Perturbations Finite Interval Infinite Interval Stability Analysis	Khalil, 11.1-11.3, 11.5	HW 3
4	21 Apr+ 23 Apr *+ 25 Apr*+	Nonlinear control I Overview of techniques Controllability and Lie brackets Gain scheduling Feedback linearization	Khalil 12.2,12.5 (gain scheduling), 13.1-13.3 (feedback linearization) Isidori (chapter 2) or Nijmeijer and van der Schaft, 3.1 (for more on controllability)	HW 4
5	28 Apr 30 Apr 2 May*	Nonlinear control II Backstepping Sliding mode control	Khalil 14.3, 14.1	HW 5
6	5 May 7 May 9 May*	Advanced topic #1	Topics to be chosen from: Advanced stability theory (Lasalle's invariance principle, time-varying systems, etc) Advanced bifurcation theory (higher co-dimension, unfoldings) Lagrangian/Hamiltonian systems Introduction to chaos
7	12 May 14 May 16 May*	Advanced topic #2
8	19 May 21 May 23 May	Advanced topic #3
9	28 May 30 May	Project presentations

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 (75%) and final projects (25%).

Late Homework

Each student is allowed one late day which means only one homework assignment may be handed in up to one day late. Other than this day, late homework will not be accepted. Exceptional circumstances (such as medical situations) with appropriate documentation will be considered by the instructors.

Projects

TBD