CDS 140b, Spring 2012

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This will be the homepage for CDS 140b for Winter 2012.  __NOTOC__
 
This will be the homepage for CDS 140b for Winter 2012.  __NOTOC__
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{| width=100%
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|-
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| colspan=2 align=center |
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<font color='blue' size='+2'>Introduction to Dynamics</font>__NOTOC__
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|- valign=top
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| width=50% |
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'''Instructors'''
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* [http://www.cds.caltech.edu/~macmardg Doug MacMynowski] (CDS)
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* [http://www.cds.caltech.edu/node/34 Shaunak Sen] (CDS)
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* Lectures: Tu/Th, 9:00-10:25, 314 ANB
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* Office Hours: By appointment
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| width=50% |
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'''Teaching Assistant'''
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* [http://www.cds.caltech.edu/node/52 Katie Broersma]
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* Office hours: Monday 1-2pm, Steele House Conference Room / Steele House 101
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|}
  
<table width=100%>
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=== Course Description ===
<tr valign=top>
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'''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.
<td>
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'''Instructor'''
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* [http://www.cds.caltech.edu/~macmardg/ Doug MacMynowski], macmardg@cds.caltech.edu
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* Lectures: MWF 2-3 pm, 107 Annenberg
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* Office hours (DGM): Mondays, 11-12 am (by appt!)
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* 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>
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'''Teaching Assistants''' (cds110-tas@cds)
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* Jerry Cruz, Andy Lamperski
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** please send email requests to cds110-tas@cds, which is read also by Doug.
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* Office hours: Sundays, 4--6 pm in 114 Steele (CDS library).  
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</td></tr>
+
</table>
+
  
== Announcements ==
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===Announcements ===
<table align=right border=0>
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* 22 May 2012: Thursday lecture in 202 Guggenheim at 1pm
<tr>
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* 30 Apr 2012: Next two weeks on nonlinear control; homework 3 will be posted no later than Thursday
<td>
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* 20 Apr 2012: Homework 2 is posted.
[[#Old Announcements|Archive]]
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* 4 Apr 2012: Starting 5 Apr 2012, New Class Timing T, Th 9 AM - 10:25 AM, 314 ANB
</td></tr>
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* 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.
</table>
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* 17 Mar 2012: Doug MacMynowski is traveling the first few weeks of the quarter; direct all questions to Shaunak...
* 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).
+
* 17 Mar 2012: web page creation: the list of topics below has not yet been edited from last year; please ignore!
* 16 Mar 11: Average on final: 43, std 11, but distribution is not at all Gaussian.  (Median 40.5)
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* 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.)
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* 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!)
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* 06 Mar 11: Note that the final exam will be handed out on Wednesday and due the following Wed (March 16) at 5pm.
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* 03 Mar. 11: This is the revised and updated version of [[media:Homework6_CDS110b_Winter11.pdf | Homework 6]].
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* 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)]]
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* 17 Feb 11: The derivations in Chapt. 9 of Simon's book have several bugs/typos, and should not be relied upon
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* 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.
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* 15 Feb 11: [[media:Homework5_CDS110b_Winter11.pdf | Homework #5]] is due Tuesday Feb. 22.
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* 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]
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* 2 Feb 11: Lecture Slides on Estimation Motivation can be found [http://robotics.caltech.edu/~jwb/KalmanIntro.pdf here (in PDF format)]
+
  
 +
=== Lecture Schedule ===
  
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{| width=100% border=1 cellspacing=0 cellpadding=5
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|-
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| '''Week'''
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| '''Date'''
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| '''Topic'''
 +
| '''Suggested Reading/Lecture Notes'''
 +
| '''Homework'''
 +
|- valign=top
 +
|- valign=top
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| 1
 +
| 3 Apr <br> 5 Apr
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| Perturbation Theory
 +
* Regular Perturbation
 +
* Poincare-Lindstedt Method
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* Periodically Perturbed Systems
 +
|
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* Khalil, 10.1-10.3
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* Strogatz, 7.6
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* Verhulst,  9.1, 10.1
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* 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 -->
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|
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[http://www.cds.caltech.edu/~katheryn/pdffiles/hw1v2.pdf Homework 1]
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[http://www.cds.caltech.edu/~katheryn/pdffiles/hw1solution.pdf Solution 1]
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<!-- [http://www.cds.caltech.edu/~liu/CDS140b/HW4.pdf Homework 4] -->
 +
<!-- * Problems 1, 3, 4 -->
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|- valign=top
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| 2
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| 10 Apr <br>  12 Apr
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| Averaging Method
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* Periodic Case
 +
* Periodic Solutions
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* General Case
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|
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* Khalil, 10.4-10.6
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* Strogatz, 7.6
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* Verhulst,  11.1-11.3, 11.8
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* Coupled oscillator models with no scale separation, Philip Du Toit, Igor Mezić, Jerrold Marsden, Physica D 238 (2009) 490–501.
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| <!-- [http://www.cds.caltech.edu/~liu/CDS140b/HW4.pdf Homework 4]-->
 +
<!-- * Problems 2a-d -->
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|- valign=top
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| 3
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| 17 Apr <br>  19 Apr
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| Singular Perturbations
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* Finite Interval
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* Infinite Interval
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* Stability Analysis
 +
|
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* Khalil, 11.1-11.3, 11.5
 +
* Chapter 9, Mathematical Biology: I. An Introduction, J. D. Murray, Springer; 3rd edition.
  
= Course Syllabus =
+
|
<table align=right border=1 width=20% cellpadding=6>
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[http://www.cds.caltech.edu/~katheryn/pdffiles/hw2.pdf Homework 2]
<tr>
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[http://www.cds.caltech.edu/~katheryn/pdffiles/hw2solution.pdf Solution 2]
<td>
+
|
<center>'''Contents'''</center>
+
<!--* Problems 4, 5, 6, 7 -->
<ul>
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|- valign=top
<li> [[#Grading|Grading]] </li>
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| 4
<li> [[#Lectures and Recitations|Lectures/Recitations]] </li>
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| 24 Apr <br> 26 Apr
<li> [[#Collaboration Policy|Collaboration Policy]] </li>
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| No class this week
<li> [[#Software|Software]] </li>
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| <!-- [[Guest Lecture, CDS 140B, Spring 2011 | Guest Lecture]] -->
<li> [[#Course Text and References|Course Text]] </li>
+
| <!-- [http://www.cds.caltech.edu/~liu/CDS140b/Guest_Lecture_1.pdf Lecture Slides] -->
<li> [[#Course_Schedule|Course Schedule]]</li>
+
|
</ul>
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|- valign=top
</td></tr>
+
| 5
</table>
+
| 1 May <br> 3 May (Mid-term period)
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
+
| Nonlinear control I
 +
* Overview of techniques
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* Controllability and Lie brackets
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* Gain scheduling
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* Feedback linearization
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|
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* 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
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| 6
 +
| 8 May (Mid-term period) <br> 10 May
 +
| Nonlinear control II
 +
* Backstepping
 +
* Sliding mode control
 +
|
 +
* Khalil 14.3, 14.1
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* [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]
 +
|
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|- valign=top
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| 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 -->
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|- valign=top
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| 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
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| 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 -->
 +
|}
  
=== Lectures ===
+
<!-- Lecture schedule from previous year -->
The main course lectures are on MWF from 2--3 pm  in 107 Annenberg.  
+
<!-- -->
 +
<!-- -->
 +
<!-- -->
 +
<!--
 +
{| width=100% border=1 cellspacing=0 cellpadding=5
 +
|-
 +
| '''Date'''
 +
| '''Topic'''
 +
| '''Reading/Lecture Notes'''
 +
| '''Homework'''
 +
|- valign=top
 +
|- valign=top
 +
| 29 Mar <br> 31 Mar <br> 5 Apr
 +
| Limit cycles
 +
* Recap
 +
* Ruling out closed orbits
 +
* Index theory
 +
* Poincare-Bendixon theorem
 +
* Lienard systems
 +
|
 +
* Strogatz, 7.0-7.4 <br>
 +
* Perko, 3.1-3.5, 3.7-3.8, 3.12 <br>
 +
* [http://www.cds.caltech.edu/~motee/Lecture1.pdf Lecture Note 1]
 +
* [http://www.cds.caltech.edu/~motee/Lecture2.pdf Lecture Note 2]
 +
* [http://www.cds.caltech.edu/~motee/Lecture3.pdf Lecture Note 3]
 +
* [http://www.cds.caltech.edu/~motee/Lecture4.pdf Supplementary Lecture Notes]
  
The TA will hold office hours on Sundays, 4--6 pm in 114 Steele
+
| [http://www.cds.caltech.edu/~motee/HW1.pdf Homework 1]
(CDS library).  
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[http://www.cds.caltech.edu/~jerry/hw1_soln.pdf Solutions 1]
  
=== Grading ===
+
|- valign=top
The final grade will be based on homework sets, a midterm exam, and a final exam:  
+
| 7 Apr <br>  12 Apr <br> 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
 +
|
 +
* Khalil, 4.1-4.9, 9.1-9.2 <br>
 +
* [http://www.cds.caltech.edu/~liu/CDS140b/Lecture4.pdf Lecture Note 4]
 +
* [http://www.cds.caltech.edu/~liu/CDS140b/Lecture5.pdf Lecture Note 5]
 +
* [http://www.cds.caltech.edu/~liu/CDS140b/Lecture6.pdf Lecture Note 6]
 +
* [http://www.cds.caltech.edu/~liu/CDS140b/Stability.pdf Notes on Stability]
 +
|
 +
[http://www.cds.caltech.edu/~liu/CDS140b/HW2.pdf Homework 2]
  
*''Homework (50%):'' Homework sets will be handed out weekly and due on Mondays by 5 pm to the box outside of 102 SteeleStudents 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).
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[http://www.cds.caltech.edu/~jerry/hw2a_solutions.pdf Solutions 2]
 +
|- valign=top
 +
| 19 Apr <br> 21 Apr <br> 26 Apr
 +
| Bifurcation Theory
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* Structural Stability and Peixoto's Theorem
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* Various Types of Bifurcations
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* Higher-Dimensional Bifurcation
 +
* Unfoldings of Bifurcations
 +
|
 +
* Perko, 4.1, 4.2, 4.3
 +
* [http://www.cds.caltech.edu/~motee/lecture7-9.pdf Lecture Notes 7, 8, and 9]
 +
|
 +
[http://www.cds.caltech.edu/~motee/HW3.pdf Homework 3]
  
* ''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).  
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[http://www.cds.caltech.edu/~jerry/scan0001.pdf Solutions 3]
 +
|- valign=top
 +
| 28 Apr
 +
| [[Guest Lecture, CDS 140B, Spring 2011 | Guest Lecture]]
 +
| [http://www.cds.caltech.edu/~liu/CDS140b/Guest_Lecture_1.pdf Lecture Slides]
 +
|
 +
|- valign=top
 +
| 3 May <br>  5 May <br> 10 May
 +
| Averaging and Perturbation
 +
* Regular Perturbation
 +
* Periodically Perturbed Systems
 +
* Averaging
 +
* Singular Perturbation
 +
* Stability Analysis
 +
|
 +
* 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/~liu/CDS140b/HW4.pdf Homework 4]
 +
|- valign=top
 +
| 12 May <br> 17 May
 +
| Guest Lectures
 +
| <!-- Reading -->
 +
| <!-- Homework -->
 +
<!--
 +
|- valign=top
 +
| 19 May <br> 24 May
 +
| Final Project Presentations
 +
| <!-- Reading -->
 +
| <!-- Homework -->
 +
<!--
 +
|}
 +
-->
  
* ''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).
+
=== References: ===
  
=== Collaboration Policy ===
+
'''Course Textbooks'''
  
Collaboration on homework assignments is encouraged. You may consult
+
* H. Khalil, Nonlinear Systems, Prentice Hall; 3rd edition, 2001. ISBN: 978-0130673893
outside reference materials, other students, the TA, or the
+
* S. Strogatz, Nonlinear Dynamics And Chaos, Westview Press, 1994. ISBN: 978-0738204536
instructor, but you cannot consult homework solutions from
+
* F. Verhulst, Nonlinear Differential Equations and Dynamical Systems, Springer; 2ed Edition, 1996. ISBN: 978-3540609346
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.
+
'''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
  
=== Software ===
+
=== Policies:===
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 ===
+
'''Lecture notes:'''
  
The primary course texts are
+
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.  
[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.
+
'''Collaboration Policy'''
  
* B. Friedland, ''Control System Design: An Introduction to State-Space Methods'', McGraw-Hill, 1986.
+
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.  
* 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:
+
'''Grading Policy'''
  
* [http://users.cecs.anu.edu.au/~john/papers/BOOK/B02.PDF  Brian D.O. Anderson and John B. Moore, '''Optimal Filtering''', Prentice-Hall, 1979]
+
The final grades will be evaluated based on homework assignments (5*15%=75%) and final projects (25%).  
*[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 ===
+
'''Late Homework'''
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).
+
 +
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.
  
== Old Announcements ==
+
== Projects: ==
* 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.
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* 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]
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* 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]
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* 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]
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* 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.)
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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

[edit] Policies:

Lecture notes:

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

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*15%=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.

[edit] Projects:

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