CDS 140b, Spring 2014

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Differential Equations and Dynamical Systems


  • Richard Murray (CDS/BE),
  • Doug MacMartin (CDS),
  • Lectures: MWF, 1-2 pm
  • Office hours: TBD

Teaching Assistants

  • TBD
  • Contact:
  • 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
0 31 Mar
Course overview
1 2 Apr
4 Apr*
Lagrangian and Hamiltonian systems I
  • Definition and properties
  • Mechanical systems
  • Perko 2.14, 3.6
  • Notes TBD
HW 1
2 9 Apr*
11 Apr
Lagrangian and Hamiltonian systems II TBD HW 2
3 18 Apr
21 Apr
Advanced stability theory
  • Time-varying systems
  • I/O stability, passivity
  • Khalil 4.5, 6.1-6.5
HW 3
4 28 Apr
30 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 4
5 5 May
7 May
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
Singular Perturbations
  • Finite Interval
  • Infinite Interval
  • Stability Analysis
  • Khalil, 11.1-11.3, 11.5
HW 6
7 21 May
23 May*
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
Nonlinear control II
  • Backstepping
  • Sliding mode control
  • Khalil 14.3, 14.1
HW 8
9 26 May
28 May
Project presentations


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


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.