View source for CDS 140b, Spring 2014

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<font color='blue' size='+2'>Differential Equations and Dynamical Systems</font>__NOTOC__
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'''Instructors'''
* Richard Murray (CDS/BE), murray@cds.caltech.edu
* Doug MacMartin (CDS), macmardg@cds.caltech.edu
* Lectures: MWF, 1-2 pm, 314 ANB
* Office hours: TBD
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'''Teaching Assistant'''
* Katie Broersma (CDS)
* Contact: cds140-tas@cds.caltech.edu
* Office hours: Wed, 3:30-4:30 pm, 101 STH
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=== 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 8 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 ===

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| '''Week'''
| '''Date'''
| '''Topic'''
| '''Suggested Reading/Lecture Notes'''
| '''Homework'''
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| 0
| 31&nbsp;Mar <br> RMM
| Course overview
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| 1
| 2 Apr <br> 4 Apr*  <br> DGM
| Lagrangian and Hamiltonian systems I
* Definition and properties
* Newtonian Systems
| 
*Perko 2.14
* [http://www.cds.caltech.edu/~macmardg/courses/cds140a/MarsdenMechSystems.pdf Marsden, Mechanical systems]
* [http://www.cds.caltech.edu/~macmardg/courses/cds140b/2014_04_04_14_03_32.pdf Lecture notes]
| [[CDS 140b Spring 2014 Homework 1|HW 1]] <br> Due: 10 Apr (Thu)
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| 2
| 9 Apr*<br>11&nbsp;Apr <br> DGM
| Lagrangian and Hamiltonian systems II
* Hamiltonian systems with 2 degrees of freedom
* Mechanical systems
| 
* Perko 3.6
* [http://www.cds.caltech.edu/~macmardg/courses/cds140b/2014_04_04_14_05_21.pdf Lecture notes]
* [http://www.cds.caltech.edu/~macmardg/courses/cds140b/hetero_halos_4-12-00.pdf Notes on Lagrange points]
| [http://www.cds.caltech.edu/~macmardg/courses/cds140b/cds140b-hw2-wi14.pdf HW 2] <br> Due: 17 Apr (Thu)
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| 3
| 18 Apr <br> 21 Apr <br> RMM
| Advanced stability theory
* Non-autonomous (time-varying) systems
* Input-to-state stability, input-output stability, small gain theorem
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* Khalil 4.5, 4.6-4.7 (skim), 5.1-5.4
| [[CDS 140b Spring 2014 Homework 3|HW 3]] <br>
Due 1 May (Thu)
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| 4
| 28&nbsp;Apr '''(12-1 pm)''' <br> 30 Apr <br> RMM
| Stability of perturbed systems
* Vanishing perturbations
* Non-vanishing perturbations
* Slowiy varying systems
| 
* Khalil, 9.1, 9.2, 9.6
| [[CDS 140b Spring 2014 Homework 4|HW 4]]<br>
Due 8 May (Thu)
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| 5
| 5 May <br> 7 May <br> RMM
| Perturbation theory
* Periodic perturbations
* Averaging
* Singular Perturbations
| 
* Khalil, 10.3-10.4, 11.1-11.3, 11.5
| [[CDS 140b Spring 2014 Homework 5|HW 5]]<br>
Due 15 May (Thu)
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| 6
| 12 May <br> 14 May  <br> RMM
| Interconnected systems
* Absolute stability
* Describing functions
|
* Khalil, 7.1-7.2
| [[CDS 140b Spring 2014 Homework 6|HW 6]]<br>
Due 22 May (Thu)
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| 7
| 19 May <br> 21&nbsp;May  <br> DGM
| Nonlinear control I
* Overview of techniques
* Controllability and Lie brackets
* Gain scheduling
* Feedback linearization
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* 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)
* [http://www.cds.caltech.edu/~macmardg/courses/cds140b/NonlinearControl1.pdf Lecture notes]
| [http://www.cds.caltech.edu/~macmardg/courses/cds140b/cds140b-hw7-sp14.pdf HW 7] <br> Due: 29 May (Thu)
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| 8
| 23&nbsp;May* <br> 30 May<br>DGM
| Nonlinear control II
* Backstepping
* Sliding mode control
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* Khalil 14.3, 14.1
* [http://www.cds.caltech.edu/~macmardg/courses/cds140b/Backstepping.pdf Lecture notes]
| [http://www.cds.caltech.edu/~macmardg/courses/cds140b/cds140b-hw8-sp14.pdf HW 8] <br> Due: 6 June (Thu)
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=== 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

=== Policies ===

'''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, with the lowest score dropped in computing the final grade.
<!--The final grades will be evaluated based on homework assignments (75%) and final projects (25%).

== Projects ==

TBD
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[[Category:Courses]]