CDS 140b, Spring 2012

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* [http://www.cds.caltech.edu/~macmardg Doug MacMynowski] (CDS)
 
* [http://www.cds.caltech.edu/~macmardg Doug MacMynowski] (CDS)
 
* [http://www.cds.caltech.edu/node/34 Shaunak Sen] (CDS)
 
* [http://www.cds.caltech.edu/node/34 Shaunak Sen] (CDS)
* Lectures: Tu/Th, 10:30-11:55, 314 ANB
+
* Lectures: Tu/Th, 9:00-10:25, 314 ANB
 
* Office Hours: By appointment
 
* Office Hours: By appointment
 
| width=50% |
 
| width=50% |
 
'''Teaching Assistant'''
 
'''Teaching Assistant'''
 
* [http://www.cds.caltech.edu/node/52 Katie Broersma]
 
* [http://www.cds.caltech.edu/node/52 Katie Broersma]
* Office hours: TBD
+
* Office hours: Monday 1-2pm, Steele House Conference Room / Steele House 101
 
|}
 
|}
  
 
=== Course Description ===
 
=== 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.
+
'''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 five homeworks throughout the semester 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.
  
 
===Announcements ===
 
===Announcements ===
 +
* 22 May 2012: Thursday lecture in 202 Guggenheim at 1pm
 +
* 30 Apr 2012: Next two weeks on nonlinear control; homework 3 will be posted no later than Thursday
 +
* 20 Apr 2012: Homework 2 is posted.
 +
* 4 Apr 2012: Starting 5 Apr 2012, New Class Timing T, Th 9 AM - 10:25 AM, 314 ANB
 
* 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: 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: Doug MacMynowski is traveling the first few weeks of the quarter; direct all questions to Shaunak...
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=== Lecture Schedule ===
 
=== Lecture Schedule ===
  
 +
{| width=100% border=1 cellspacing=0 cellpadding=5
 +
|-
 +
| '''Week'''
 +
| '''Date'''
 +
| '''Topic'''
 +
| '''Suggested Reading/Lecture Notes'''
 +
| '''Homework'''
 +
|- valign=top
 +
|- valign=top
 +
| 1
 +
| 3 Apr <br> 5 Apr
 +
| Perturbation Theory
 +
* Regular Perturbation
 +
* Poincare-Lindstedt Method
 +
* Periodically Perturbed Systems
 +
|
 +
* Khalil, 10.1-10.3
 +
* Strogatz, 7.6
 +
* Verhulst,  9.1, 10.1
 +
* Chapters 1 & 6 in Dynamical Systems, the Three-Body Problem, and Space Mission Design, Wang Sang Koon, Martin W. Lo, Jerrold E. Marsden, Shane D. Ross, ISBN 978-0-615-24095-4.
 +
<!-- * Lecture Notes -->
 +
<!-- Shaunak's link here -->
 +
|
 +
[http://www.cds.caltech.edu/~katheryn/pdffiles/hw1v2.pdf Homework 1]
 +
[http://www.cds.caltech.edu/~katheryn/pdffiles/hw1solution.pdf Solution 1]
 +
<!-- [http://www.cds.caltech.edu/~liu/CDS140b/HW4.pdf Homework 4] -->
 +
<!-- * Problems 1, 3, 4 -->
 +
|- valign=top
 +
| 2
 +
| 10 Apr <br>  12 Apr
 +
| Averaging Method
 +
* Periodic Case
 +
* Periodic Solutions
 +
* General Case
 +
|
 +
* Khalil, 10.4-10.6
 +
* Strogatz, 7.6
 +
* Verhulst,  11.1-11.3, 11.8
 +
* Coupled oscillator models with no scale separation, Philip Du Toit, Igor Mezić, Jerrold Marsden, Physica D 238 (2009) 490–501.
 +
| <!-- [http://www.cds.caltech.edu/~liu/CDS140b/HW4.pdf Homework 4]-->
 +
<!-- * Problems 2a-d -->
 +
|- valign=top
 +
| 3
 +
| 17 Apr <br>  19 Apr
 +
| Singular Perturbations
 +
* Finite Interval
 +
* Infinite Interval
 +
* Stability Analysis
 +
|
 +
* Khalil, 11.1-11.3, 11.5
 +
* Chapter 9, Mathematical Biology: I. An Introduction, J. D. Murray, Springer; 3rd edition.
 +
 +
|
 +
[http://www.cds.caltech.edu/~katheryn/pdffiles/hw2.pdf Homework 2]
 +
[http://www.cds.caltech.edu/~katheryn/pdffiles/hw2solution.pdf Solution 2]
 +
|
 +
<!--* Problems 4, 5, 6, 7 -->
 +
|- valign=top
 +
| 4
 +
| 24 Apr <br>  26 Apr
 +
| No class this week
 +
| <!-- [[Guest Lecture, CDS 140B, Spring 2011 | Guest Lecture]] -->
 +
| <!-- [http://www.cds.caltech.edu/~liu/CDS140b/Guest_Lecture_1.pdf Lecture Slides] -->
 +
|
 +
|- valign=top
 +
| 5
 +
| 1 May <br>  3 May (Mid-term period)
 +
| Nonlinear control I
 +
* Overview of techniques
 +
* Controllability and Lie brackets
 +
* Gain scheduling
 +
* Feedback linearization
 +
|
 +
* Isidori (chapter 2) or Nijmeijer and van der Schaft, 3.1 (for more on controllability)
 +
* Khalil 12.2,12.5 (gain scheduling), 13.1-13.3 (feedback linearization)
 +
* [http://www.cds.caltech.edu/~macmardg/courses/cds140b/NonlinearControl1.pdf Lecture notes]
 +
<!--
 +
* Khalil, 10.1-10.4, 11.1-10.3, 11.5
 +
* [http://www.cds.caltech.edu/~liu/CDS140b/Lecture10.pdf Lecture Note 10]
 +
* [http://www.cds.caltech.edu/~liu/CDS140b/Lecture11.pdf Lecture Note 11]
 +
* [http://www.cds.caltech.edu/~liu/CDS140b/Lecture12.pdf Lecture Note 12]
 +
* [http://www.cds.caltech.edu/~liu/CDS140b/Perturbation.pdf Notes on Perturbation]
 +
-->
 +
|
 +
[http://www.cds.caltech.edu/~macmardg/courses/cds140b/hw3.pdf Homework 3]
 +
[http://www.cds.caltech.edu/~katheryn/pdffiles/hw3solutionsb.pdf Solution 3]
 +
| <!-- [http://www.cds.caltech.edu/~liu/CDS140b/HW4.pdf Homework 4] -->
 +
|- valign=top
 +
| 6
 +
| 8 May (Mid-term period) <br> 10 May
 +
| Nonlinear control II
 +
* Backstepping
 +
* Sliding mode control
 +
|
 +
* Khalil 14.3, 14.1
 +
* [http://www.cds.caltech.edu/~macmardg/courses/cds140b/Backstepping.pdf Lecture notes]
 +
* And here are lecture notes from Ae240 (flow control), MW 4-5 in 306 Thomas: [http://www.cds.caltech.edu/~macmardg/courses/cds140b/Optimization.pdf Optimization], [http://www.cds.caltech.edu/~macmardg/courses/cds140b/Estimation.pdf Estimation]
 +
|
 +
[http://www.cds.caltech.edu/~macmardg/courses/cds140b/hw4.pdf Homework 4]
 +
[http://www.cds.caltech.edu/~katheryn/pdffiles/hw4solutions.pdf Solution 4]
 +
|
 +
|- valign=top
 +
| 7
 +
| 15 May <br> 17 May
 +
|
 +
Lagrangian Coherent Structures
 +
| [http://www.cds.caltech.edu/~macmardg/courses/cds140b/LCS_1.pdf LCS lecture notes]
 +
| <!-- Reading -->
 +
| <!-- Homework -->
 +
|- valign=top
 +
| 8
 +
| 22 May <br> 24 May
 +
| Turbulence and non-normal growth
 +
| <!-- Final Project Presentations -->
 +
* Tuesday lecture notes: [http://www.cds.caltech.edu/~macmardg/courses/cds140b/non-normal_growth.pdf lecture notes], [http://www.cds.caltech.edu/~macmardg/courses/cds140b/Optimal_Growth.pdf ENSO and AMOC]
 +
* Thursday class 1-2:30 in 202 Guggenheim
 +
| <!-- Reading -->
 +
| <!-- Homework -->
 +
|- valign=top
 +
| 9
 +
| 29 May <br> 31 May
 +
|
 +
* Tuesday: Chaos
 +
* Thursday: Final Project Presentations
 +
* "Perturbation and stability analyses of bubble dynamics in a linear viscoelastic (tissue-like) medium", C. Hua
 +
* Overview of "Multiple Lyapunov Functions and other analysis tools for switched and hybrid systems", S. Livingston
 +
* "Bifurcations in two layer model of ice albedo feedback", R. Wills
 +
| <!-- Reading -->
 +
| <!-- Homework -->
 +
|}
 +
 +
<!-- Lecture schedule from previous year -->
 +
<!-- -->
 +
<!-- -->
 +
<!-- -->
 +
<!--
 
{| width=100% border=1 cellspacing=0 cellpadding=5
 
{| width=100% border=1 cellspacing=0 cellpadding=5
 
|-
 
|-
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| <!-- Reading -->
 
| <!-- Reading -->
 
| <!-- Homework -->
 
| <!-- Homework -->
 +
<!--
 
|- valign=top
 
|- valign=top
 
| 19 May <br> 24 May  
 
| 19 May <br> 24 May  
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| <!-- Reading -->
 
| <!-- Reading -->
 
| <!-- Homework -->
 
| <!-- Homework -->
 +
<!--
 
|}
 
|}
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-->
  
 
=== References: ===
 
=== References: ===
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'''Course Textbooks'''
 
'''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
 
* 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
+
* F. Verhulst, Nonlinear Differential Equations and Dynamical Systems, Springer; 2ed Edition, 1996. ISBN: 978-3540609346
  
 
'''Additional Sources:'''
 
'''Additional Sources:'''
 
+
* L. Perko, Differential Equations and Dynamical Systems (3rd), Springer, 2001. ISBN: 978-0387951164
* 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
 
* S. Wiggins, Introduction to Applied Nonlinear Dynamical Systems and Chaos, Springer; 2nd edition, 2003. ISBN: 978-0387001777
  
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'''Lecture notes:'''  
 
'''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.  
+
A brief description of the mathematical concepts presented during the lectures may be posted as lecture notes. These should assist students with the mathematical concepts presented during the lecture. Complete lecture notes will not be posted.  
  
 
'''Collaboration Policy'''  
 
'''Collaboration Policy'''  
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'''Grading Policy'''  
 
'''Grading Policy'''  
  
The final grades will be evaluated based on homework assignments (5*12%=60%), final projects (30%), and participation in class (10%).  
+
The final grades will be evaluated based on homework assignments (5*15%=75%) and final projects (25%).  
  
 
'''Late Homework'''  
 
'''Late Homework'''  
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== Projects: ==
 
== Projects: ==
 
 
 
<table width=100%>
 
<tr valign=top>
 
<td>
 
'''Instructor'''
 
* [http://www.cds.caltech.edu/~macmardg/ Doug MacMynowski], macmardg@cds.caltech.edu
 
* Lectures: MWF 2-3 pm, 107 Annenberg
 
* Office hours (DGM): Mondays, 11-12 am (by appt!)
 
* Prior years: [http://www.cds.caltech.edu/~murray/wiki/CDS_110b%2C_Winter_2007 WI07][http://www.cds.caltech.edu/~murray/wiki/CDS_110b%2C_Winter_2008 WI08] [https://www.cds.caltech.edu/help/cms.php?op=wiki&wiki_op=view&id=223 WI09] [http://www.cds.caltech.edu/~macmardg/wiki/index.php?title=CDS_110b%2C_Winter_2010 WI10]
 
</td><td>
 
'''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).
 
</td></tr>
 
</table>
 
 
== Announcements ==
 
<table align=right border=0>
 
<tr>
 
<td>
 
[[#Old Announcements|Archive]]
 
</td></tr>
 
</table>
 
* 16 Mar 11: Final solution: [http://www.cds.caltech.edu/~macmardg/courses/cds110b/wi11/pdf/solns/fnsoln-wi11.pdf 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 [[media:Homework6_CDS110b_Winter11.pdf | Homework 6]].
 
* 18 Feb 11: A corrected version (Version 2) of the notes handed out in class today: [[media:FixedLagSmootherV2.pdf | 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: [[media:Chapt9Simon.pdf | 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: [[media:Homework5_CDS110b_Winter11.pdf | 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 [http://robotics.caltech.edu/~jwb/KalmanIntro.pdf here (in PDF format)]
 
 
 
 
= Course Syllabus =
 
<table align=right border=1 width=20% cellpadding=6>
 
<tr>
 
<td>
 
<center>'''Contents'''</center>
 
<ul>
 
<li> [[#Grading|Grading]] </li>
 
<li> [[#Lectures and Recitations|Lectures/Recitations]] </li>
 
<li> [[#Collaboration Policy|Collaboration Policy]] </li>
 
<li> [[#Software|Software]] </li>
 
<li> [[#Course Text and References|Course Text]] </li>
 
<li> [[#Course_Schedule|Course Schedule]]</li>
 
</ul>
 
</td></tr>
 
</table>
 
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
 
 
=== Lectures ===
 
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).
 
 
=== Grading ===
 
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.
 
 
=== Software ===
 
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 [http://software.caltech.edu IMSS] (Caltech students only).  An online tutorial is available at
 
<center>
 
http://www.engin.umich.edu/group/ctm/basic/basic.html
 
</center>
 
 
=== Course Text and References ===
 
 
The primary course texts are
 
[http://www.cds.caltech.edu/~murray/amwiki/index.php?title=Supplement:_Optimization-Based_Control ''Optimization-based Control''] by Murray, 2008 (for the first 7 weeks), and [http://www.cds.caltech.edu/~macmardg/courses/cds110b/dft/dft.html ''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:
 
 
* [http://users.cecs.anu.edu.au/~john/papers/BOOK/B02.PDF  Brian D.O. Anderson and John B. Moore, '''Optimal Filtering''', Prentice-Hall, 1979]
 
*[http://www.kxcad.net/cae_MATLAB/Matlab_Ebooks/Grewal,%20Andrews.%20Kalman%20filtering..%20theory%20and%20practice%20using%20MATLAB%20(2ed.,%20Wiley,%202001)(410s).pdf M.S. Grewal & A.P. Andrews, '''Kalman Filtering: Theory and Practice Using MATLAB''', 2nd ed., John Wiley & Sons, 2001];
 
* [http://www2.elo.utfsm.cl/~ipd481/Papers%20varios/kalman1960.pdf A ''transcribed'' copy of Kalman's original 1960 paper on the discrete time filter];
 
 
=== Course Schedule ===
 
A detailed course schedule is available on the [[CDS 110b, Winter 2011 - Course Schedule|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).  [http://www.cds.caltech.edu/~macmardg/courses/cds110b/wi10/costs.mat 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: [http://www.cds.caltech.edu/~macmardg/courses/cds110b/wi11/matlab/ltv.m 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.
 
 
<!--
 
* 8 Feb 10: Data file for HW #5: [http://www.cds.caltech.edu/~macmardg/courses/cds110b/wi10/GEMdat.mat GEMdat.mat].  Please look at this early; you WILL want to ask questions in office hours.
 
* 6 Feb 10: Solution matrices for HW #4, problem 1: (J1 and J2 are the value function (cost-to-go) from the respective node for cases 1 and 2; D1 and D2 give the optimal direction ("1"=south, "0"=east) at each node).  [http://www.cds.caltech.edu/~macmardg/courses/cds110b/wi10/DPsolns.mat DPsolns.mat]
 
* 27 Jan 10: Cost matrices for use in HW #4, problem 1: (JS and JE are the costs for traveling south or east, respectively).  [http://www.cds.caltech.edu/~macmardg/courses/cds110b/wi10/costs.mat costs.mat]
 
* 20 Jan 10: You might also find these notes useful on optimization: [http://www.cds.caltech.edu/~macmardg/courses/cds110b/wi10/pdf/Optimization.pdf Optimization]
 
* 11 Jan 10: HW #2 is posted (note "OBC" means "Optimization-Based Control", the text.  On HW, that is simply FYI, since the problem is fully reproduced in the HW.)
 
--!>
 

Latest revision as of 15:45, 31 May 2012

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

Introduction to Dynamics

Instructors

Teaching Assistant

  • Katie Broersma
  • Office hours: Monday 1-2pm, Steele House Conference Room / Steele House 101

[edit] 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 five homeworks throughout the semester 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.

[edit] Announcements

  • 22 May 2012: Thursday lecture in 202 Guggenheim at 1pm
  • 30 Apr 2012: Next two weeks on nonlinear control; homework 3 will be posted no later than Thursday
  • 20 Apr 2012: Homework 2 is posted.
  • 4 Apr 2012: Starting 5 Apr 2012, New Class Timing T, Th 9 AM - 10:25 AM, 314 ANB
  • 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!

[edit] Lecture Schedule

Week Date Topic Suggested Reading/Lecture Notes Homework
1 3 Apr
5 Apr
Perturbation Theory
  • Regular Perturbation
  • Poincare-Lindstedt Method
  • Periodically Perturbed Systems
  • Khalil, 10.1-10.3
  • Strogatz, 7.6
  • Verhulst, 9.1, 10.1
  • Chapters 1 & 6 in Dynamical Systems, the Three-Body Problem, and Space Mission Design, Wang Sang Koon, Martin W. Lo, Jerrold E. Marsden, Shane D. Ross, ISBN 978-0-615-24095-4.

Homework 1 Solution 1

2 10 Apr
12 Apr
Averaging Method
  • Periodic Case
  • Periodic Solutions
  • General Case
  • Khalil, 10.4-10.6
  • Strogatz, 7.6
  • Verhulst, 11.1-11.3, 11.8
  • Coupled oscillator models with no scale separation, Philip Du Toit, Igor Mezić, Jerrold Marsden, Physica D 238 (2009) 490–501.
3 17 Apr
19 Apr
Singular Perturbations
  • Finite Interval
  • Infinite Interval
  • Stability Analysis
  • Khalil, 11.1-11.3, 11.5
  • Chapter 9, Mathematical Biology: I. An Introduction, J. D. Murray, Springer; 3rd edition.

Homework 2 Solution 2

4 24 Apr
26 Apr
No class this week
5 1 May
3 May (Mid-term period)
Nonlinear control I
  • Overview of techniques
  • Controllability and Lie brackets
  • Gain scheduling
  • Feedback linearization
  • Isidori (chapter 2) or Nijmeijer and van der Schaft, 3.1 (for more on controllability)
  • Khalil 12.2,12.5 (gain scheduling), 13.1-13.3 (feedback linearization)
  • Lecture notes

Homework 3 Solution 3

6 8 May (Mid-term period)
10 May
Nonlinear control II
  • Backstepping
  • Sliding mode control

Homework 4 Solution 4

7 15 May
17 May

Lagrangian Coherent Structures

LCS lecture notes
8 22 May
24 May
Turbulence and non-normal growth
9 29 May
31 May
  • Tuesday: Chaos
  • Thursday: Final Project Presentations
  • "Perturbation and stability analyses of bubble dynamics in a linear viscoelastic (tissue-like) medium", C. Hua
  • Overview of "Multiple Lyapunov Functions and other analysis tools for switched and hybrid systems", S. Livingston
  • "Bifurcations in two layer model of ice albedo feedback", R. Wills

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[edit] 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

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