CDS 140b, Spring 2012

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* [ Nader Motee] (CDS)
* [ Doug MacMynowski] (CDS)
* [ Jun Liu] (CDS)
* [ Shaunak Sen] (CDS)
* Lectures: Tu/Th, 10:30-11:55, 314 ANB
* Lectures: Tu/Th, 10:30-11:55, 314 ANB
* Office Hours: By appointment
* Office Hours: By appointment
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'''Teaching Assistant'''
'''Teaching Assistant'''
* [ Jerry Cruz]
* [ Katie Broersma]
* Office hours: M 4:30-6:00, 230 ANB
* Office hours: TBD
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===Announcements ===
===Announcements ===
* 11 May 2011: Homework #4 posted; due 31 May 2011
* 17 Mar 2012: At least one student has a conflict with the class time; we will see if we can find a time compatible with everyone during the first week of the quarter.
* 29 Apr 2011: Homework #3 posted; due 12 May 2011
* 17 Mar 2012: Doug MacMynowski is traveling the first few weeks of the quarter; direct all questions to Shaunak...
* 14 Apr 2011: Homework #2 is now posted; due 26 Apr 2011
* 17 Mar 2012: web page creation: the list of topics below has not yet been edited from last year; please ignore!
* 4 Apr 2011: [ List of Reserves] (in SFL) for the course has been created
* 2 Apr 2011: Homework #1 is now posted; due 12 Apr 2011
* 18 Mar 2011: web page creation
=== Lecture Schedule ===
=== Lecture Schedule ===

Revision as of 17:55, 17 March 2012

This will be the homepage for CDS 140b for Winter 2012.

Introduction to Dynamics


Teaching Assistant

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 the existence of periodic orbits, bifurcation theory, perturbation theory and averaging, advanced stability analysis, chaos, etc. In addition, guest lecturers will give an introduction to current research topics in dynamical systems theory. There will be five homeworks throughout the semester but no exams. Instead, the students are required to select a research topic and a journal paper related to CD140b and present a brief review of the paper. The details of the projects will be discussed in the class.


  • 17 Mar 2012: At least one student has a conflict with the class time; we will see if we can find a time compatible with everyone during the first week of the quarter.
  • 17 Mar 2012: Doug MacMynowski is traveling the first few weeks of the quarter; direct all questions to Shaunak...
  • 17 Mar 2012: web page creation: the list of topics below has not yet been edited from last year; please ignore!

Lecture Schedule

Date Topic Reading/Lecture Notes Homework
29 Mar
31 Mar
5 Apr
Limit cycles
  • Recap
  • Ruling out closed orbits
  • Index theory
  • Poincare-Bendixon theorem
  • Lienard systems
Homework 1

Solutions 1

7 Apr
12 Apr
14 Apr
Stability Theory
  • LaSalle's invariance principle
  • Stability of nonautonomous systems
  • Linearization and converse theorems
  • Boundedness and input-to-state stability
  • Stability of perturbed systems

Homework 2

Solutions 2

19 Apr
21 Apr
26 Apr
Bifurcation Theory
  • Structural Stability and Peixoto's Theorem
  • Various Types of Bifurcations
  • Higher-Dimensional Bifurcation
  • Unfoldings of Bifurcations

Homework 3

Solutions 3

28 Apr Guest Lecture Lecture Slides
3 May
5 May
10 May
Averaging and Perturbation
  • Regular Perturbation
  • Periodically Perturbed Systems
  • Averaging
  • Singular Perturbation
  • Stability Analysis
Homework 4
12 May
17 May
Guest Lectures
19 May
24 May
Final Project Presentations


Course Textbooks

  • S. Strogatz, Nonlinear Dynamics And Chaos, Westview Press, 1994. ISBN: 978-0738204536
  • L. Perko, Differential Equations and Dynamical Systems (3rd), Springer, 2001. ISBN: 978-0387951164

Additional Sources:

  • H. Khalil, Nonlinear Systems, Prentice Hall; 3rd edition, 2001. ISBN: 978-0130673893
  • F. Verhulst, Nonlinear Differential Equations and Dynamical Systems, Springer; 2ed Edition, 1996. ISBN: 978-3540609346
  • S. Wiggins, Introduction to Applied Nonlinear Dynamical Systems and Chaos, Springer; 2nd edition, 2003. ISBN: 978-0387001777


Lecture notes:

A skeleton file for the lecture notes will be posted the night before each lecture and it will mainly include figures and some text. It is recommended that students come to class with the lecture notes skeleton and use it to fill in the material covered in class. Complete lecture notes will NOT be posted.

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 (5*12%=60%), final projects (30%), and participation in class (10%).

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.



  • Doug MacMynowski,
  • Lectures: MWF 2-3 pm, 107 Annenberg
  • Office hours (DGM): Mondays, 11-12 am (by appt!)
  • Prior years: WI07WI08 WI09 WI10

Teaching Assistants (cds110-tas@cds)

  • Jerry Cruz, Andy Lamperski
    • please send email requests to cds110-tas@cds, which is read also by Doug.
  • Office hours: Sundays, 4--6 pm in 114 Steele (CDS library).



  • 16 Mar 11: Final solution: fnsoln. Please do not circulate to anyone. Also, if you want to keep any solutions, save them, since I will delete them from the server in a few weeks (to minimize risk of dispersal).
  • 16 Mar 11: Average on final: 43, std 11, but distribution is not at all Gaussian. (Median 40.5)
  • 12 Mar 11: Solution for the LQG question of HW 6 posted on schedule page under link for HW 6. (Note that there is a factor of 2pi occasionally missing in the solutions.)
  • 10 Mar 11: Solution for HW 5 posted on schedule page (the rest of that week isn't updated, but the solution link should work!)
  • 06 Mar 11: Note that the final exam will be handed out on Wednesday and due the following Wed (March 16) at 5pm.
  • 03 Mar. 11: This is the revised and updated version of Homework 6.
  • 18 Feb 11: A corrected version (Version 2) of the notes handed out in class today: Notes on the Fixed Lag Smoother (version 2)
  • 17 Feb 11: The derivations in Chapt. 9 of Simon's book have several bugs/typos, and should not be relied upon
  • 16 Feb 11: Chapter 9 (Section 9.3) of the book Optimal State Estimation by Dan Simon provides a more careful derivation of the fixed-lag smoothing results of Section 7.3 of Anderson and Moore.
  • 15 Feb 11: Homework #5 is due Tuesday Feb. 22.
  • 2 Feb 11: Midterm handed out in class. you can find extra copies in a small cardboard box located between the mail slots in the south side of the Steele Building]
  • 2 Feb 11: Lecture Slides on Estimation Motivation can be found here (in PDF format)

Course Syllabus


CDS 110b focuses on intermediate topics in control theory, including optimal control methods, stochastic systems, state estimation using Kalman filters, and modern control design techniques. Upon completion of the course, students will be able to design and analyze control systems of moderate complexity


The main course lectures are on MWF from 2--3 pm in 107 Annenberg.

The TA will hold office hours on Sundays, 4--6 pm in 114 Steele (CDS library).


The final grade will be based on homework sets, a midterm exam, and a final exam:

  • Homework (50%): Homework sets will be handed out weekly and due on Mondays by 5 pm to the box outside of 102 Steele. Students are allowed three grace periods of two days each that can be used at any time (but no more than 1 grace period per homework set). Late homework beyond the grace period will not be accepted without a note from the health center or the Dean. MATLAB code and SIMULINK diagrams are considered part of your solution and should be printed and turned in with the problem set (whether the problem asks for it or not).
  • Midterm exam (20%): A midterm exam will be handed out at the beginning of midterms period (2 Feb) and due at the end of the midterm examination period (8 Feb). The midterm exam will be open book and computers will be allowed (though not required).
  • Final exam (30%): The final exam will be handed out on the last day of class (9 Mar) and due at the end of finals (Wed 16 Mar). It will be an open book exam and computers will be allowed (though not required).

Collaboration Policy

Collaboration on homework assignments is encouraged. You may consult outside reference materials, other students, the TA, or the instructor, but you cannot consult homework solutions from prior years and you must cite any use of material from outside references. All solutions that are handed in should be written up individually and should reflect your own understanding of the subject matter at the time of writing. MATLAB scripts and plots are considered part of your writeup and should be done individually (you can share ideas, but not code).

No collaboration is allowed on the midterm or final exams.


Computer exercises will be assigned as part of the regular homeworks. The exercises are designed to be done in MATLAB, using the Control Toolbox and SIMULINK. Caltech has a site license for this software and it may be obtained from IMSS (Caltech students only). An online tutorial is available at

Course Text and References

The primary course texts are Optimization-based Control by Murray, 2008 (for the first 7 weeks), and Feedback Control Theory for the final few weeks of the quarter.

In addition to the books above, the textbooks below may also be useful. They are available in the library (non-reserve), from other students, or you can order them online.

  • B. Friedland, Control System Design: An Introduction to State-Space Methods, McGraw-Hill, 1986.
  • G. F. Franklin, J. D. Powell, and A. Emami-Naeni, Feedback Control of Dynamic Systems, Addison-Wesley, 2002.

For the Estimation and Kalman Filtering portion of the class, these free on-line sources (in PDF format) may be useful:

Course Schedule

A detailed course schedule is available on the course schedule page (also shown on the "menu bar" at the top of each course page).

Old Announcements

  • 24 Jan 11: HW #4 posted; since no lecture covering this topic before Wednesday, I put the due date as next Tuesday (again)
  • 24 Jan 11: NO class today (Monday)
  • 19 Jan 11: HW #3 posted. Cost matrices for use in HW #3, problem 1: (JS and JE are the costs for traveling south or east, respectively). costs.mat
  • 18 Jan 11: HW #1 average 28.7/30
  • 10 Jan 11: HW # 2 posted (if you downloaded it before 5pm you're missing the third problem). Stay tuned for some useful scripts on the third problem, such as: ltv.m, useful with [t1,x1]=ode45(@ltv,[0 T],[1 0],[],A,B,Kt,t); to compute the initial-time response for a system where the gain Kt varies as a function of time t.
  • 10 Jan 11: Note re HW #1, Q2, there is an additional special case not noted in the problem statement in which the velocity may be less than the maximum. You do not need to say anything about this case.
  • 3 Jan 11: HW #1 available under "schedule" section for week 1.

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