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, 314 ANB Office hours: TBD	Teaching Assistant Katie Broersma (CDS) Contact: cds140-tas@cds.caltech.edu Office hours: Wed, 3:30-4:30 pm, 101 STH

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
0	31 Mar RMM	Course overview
1	2 Apr 4 Apr* DGM	Lagrangian and Hamiltonian systems I Definition and properties Newtonian Systems	Perko 2.14 Marsden, Mechanical systems Lecture notes	HW 1 Due: 10 Apr (Thu)
2	9 Apr* 11 Apr DGM	Lagrangian and Hamiltonian systems II Hamiltonian systems with 2 degrees of freedom Mechanical systems	Perko 3.6 Lecture notes Notes on Lagrange points	HW 2 Due: 17 Apr (Thu)
3	18 Apr 21 Apr RMM	Advanced stability theory Non-autonomous (time-varying) systems Input-to-state stability, input-output stability, small gain theorem	Khalil 4.5, 4.6-4.7 (skim), 5.1-5.4	HW 3 Due 1 May (Thu)
4	28 Apr (12-1 pm) 30 Apr RMM	Stability of perturbed systems Vanishing perturbations Non-vanishing perturbations Slowiy varying systems	Khalil, 9.1, 9.2, 9.6	HW 4
5	5 May 7 May RMM	Averaging Method Periodic Case Periodic Solutions General Case	Khalil, 10.4-10.6 Strogatz, 7.6 Verhulst, 11.1-11.3, 11.8	HW 5
6	12 May 14 May RMM	Singular Perturbations Finite Interval Infinite Interval Stability Analysis	Khalil, 11.1-11.3, 11.5	HW 6
7	21 May 23 May* DGM	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 7
8	28 May 30 May DGM	Nonlinear control II Backstepping Sliding mode control	Khalil 14.3, 14.1	HW 8
9	2 Jun 3 Jun	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%).

Projects

TBD