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__  
+  { width=100%  
+    
+   colspan=2 align=center   
+  <font color='blue' size='+2'>Introduction to Dynamics</font>__NOTOC__  
+   valign=top  
+   width=50%   
+  '''Instructors'''  
+  * [http://www.cds.caltech.edu/~macmardg Doug MacMynowski] (CDS)  
+  * [http://www.cds.caltech.edu/node/34 Shaunak Sen] (CDS)  
+  * Lectures: Tu/Th, 9:0010:25, 314 ANB  
+  * Office Hours: By appointment  
+   width=50%   
+  '''Teaching Assistant'''  
+  * [http://www.cds.caltech.edu/node/52 Katie Broersma]  
+  * Office hours: Monday 12pm, Steele House Conference Room / Steele House 101  
+  }  
−  +  === 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.  
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−  '''  +  
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−  +  
−  +  
−  == 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: 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! 
−  *  +  
−  *  +  
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−  *  +  
−  *  +  
−  +  
−  * 17  +  
−  +  
−  +  
−  +  
−  +  
+  === 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  
+  * PoincareLindstedt Method  
+  * Periodically Perturbed Systems  
+    
+  * Khalil, 10.110.3  
+  * Strogatz, 7.6  
+  * Verhulst, 9.1, 10.1  
+  * Chapters 1 & 6 in Dynamical Systems, the ThreeBody Problem, and Space Mission Design, Wang Sang Koon, Martin W. Lo, Jerrold E. Marsden, Shane D. Ross, ISBN 9780615240954.  
+  <! * 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, 10.410.6  
+  * Strogatz, 7.6  
+  * Verhulst, 11.111.3, 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 2ad >  
+   valign=top  
+   3  
+   17 Apr <br> 19 Apr  
+   Singular Perturbations  
+  * Finite Interval  
+  * Infinite Interval  
+  * Stability Analysis  
+    
+  * Khalil, 11.111.3, 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 (Midterm 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), 13.113.3 (feedback linearization)  
+  * [http://www.cds.caltech.edu/~macmardg/courses/cds140b/NonlinearControl1.pdf Lecture notes]  
+  <!  
+  * Khalil, 10.110.4, 11.110.3, 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 (Midterm 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 45 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 nonnormal growth  
+   <! Final Project Presentations >  
+  * Tuesday lecture notes: [http://www.cds.caltech.edu/~macmardg/courses/cds140b/nonnormal_growth.pdf lecture notes], [http://www.cds.caltech.edu/~macmardg/courses/cds140b/Optimal_Growth.pdf ENSO and AMOC]  
+  * Thursday class 12:30 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 (tissuelike) 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  
+    
+   '''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  
+  * PoincareBendixon theorem  
+  * Lienard systems  
+    
+  * Strogatz, 7.07.4 <br>  
+  * Perko, 3.13.5, 3.73.8, 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]  
−  +   [http://www.cds.caltech.edu/~motee/HW1.pdf Homework 1]  
−  +  [http://www.cds.caltech.edu/~jerry/hw1_soln.pdf Solutions 1]  
−  =  +   valign=top 
−  +   7 Apr <br> 12 Apr <br> 14 Apr  
+   Stability Theory  
+  * LaSalle's invariance principle  
+  * Stability of nonautonomous systems  
+  * Linearization and converse theorems  
+  * Boundedness and inputtostate stability  
+  * Stability of perturbed systems  
+    
+  * Khalil, 4.14.9, 9.19.2 <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]  
−  +  [http://www.cds.caltech.edu/~jerry/hw2a_solutions.pdf Solutions 2]  
+   valign=top  
+   19 Apr <br> 21 Apr <br> 26 Apr  
+   Bifurcation Theory  
+  * Structural Stability and Peixoto's Theorem  
+  * Various Types of Bifurcations  
+  * HigherDimensional Bifurcation  
+  * Unfoldings of Bifurcations  
+    
+  * Perko, 4.1, 4.2, 4.3  
+  * [http://www.cds.caltech.edu/~motee/lecture79.pdf Lecture Notes 7, 8, and 9]  
+    
+  [http://www.cds.caltech.edu/~motee/HW3.pdf Homework 3]  
−  +  [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, 10.110.4, 11.110.3, 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 >  
+  <!  
+  }  
+  >  
−  +  === References: ===  
−  +  '''Course Textbooks'''  
−  +  * H. Khalil, Nonlinear Systems, Prentice Hall; 3rd edition, 2001. ISBN: 9780130673893  
−  +  * S. Strogatz, Nonlinear Dynamics And Chaos, Westview Press, 1994. ISBN: 9780738204536  
−  +  * F. Verhulst, Nonlinear Differential Equations and Dynamical Systems, Springer; 2ed Edition, 1996. ISBN: 9783540609346  
−  +  
−  +  
−  +  
−  +  
−  +  
−  +  
−  +  '''Additional Sources:'''  
+  * L. Perko, Differential Equations and Dynamical Systems (3rd), Springer, 2001. ISBN: 9780387951164  
+  * S. Wiggins, Introduction to Applied Nonlinear Dynamical Systems and Chaos, Springer; 2nd edition, 2003. ISBN: 9780387001777  
−  ===  +  === 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.  
−  ==  +  == Projects: == 
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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

[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



2  10 Apr 12 Apr 
Averaging Method



3  17 Apr 19 Apr 
Singular Perturbations



4  24 Apr 26 Apr 
No class this week  
5  1 May 3 May (Midterm period) 
Nonlinear control I



6  8 May (Midterm period) 10 May 
Nonlinear control II



7  15 May 17 May 
Lagrangian Coherent Structures 
LCS lecture notes  
8  22 May 24 May 
Turbulence and nonnormal growth 


9  29 May 31 May 

 
[edit] References:
Course Textbooks
 H. Khalil, Nonlinear Systems, Prentice Hall; 3rd edition, 2001. ISBN: 9780130673893
 S. Strogatz, Nonlinear Dynamics And Chaos, Westview Press, 1994. ISBN: 9780738204536
 F. Verhulst, Nonlinear Differential Equations and Dynamical Systems, Springer; 2ed Edition, 1996. ISBN: 9783540609346
Additional Sources:
 L. Perko, Differential Equations and Dynamical Systems (3rd), Springer, 2001. ISBN: 9780387951164
 S. Wiggins, Introduction to Applied Nonlinear Dynamical Systems and Chaos, Springer; 2nd edition, 2003. ISBN: 9780387001777
[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.