CDS 140b, Spring 2014: Difference between revisions

From Murray Wiki
Jump to navigationJump to search
No edit summary
 
(24 intermediate revisions by 2 users not shown)
Line 14: Line 14:
* Katie Broersma (CDS)
* Katie Broersma (CDS)
* Contact: cds140-tas@cds.caltech.edu
* Contact: cds140-tas@cds.caltech.edu
* Office hours: TBD
* Office hours: Wed, 3:30-4:30 pm, 101 STH
|}
|}


=== 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 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 5 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.
'''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 ===
=== Lecture Schedule ===
Line 40: Line 41:
| Lagrangian and Hamiltonian systems I
| Lagrangian and Hamiltonian systems I
* Definition and properties
* Definition and properties
* Mechanical systems
* Newtonian Systems
|  
|  
*Perko 2.14
*Perko 2.14
* [http://www.cds.caltech.edu/~macmardg/courses/cds140a/MarsdenMechSystems.pdf Marsden, Mechanical systems]
* [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)
| [[CDS 140b Spring 2014 Homework 1|HW 1]] <br> Due: 10 Apr (Thu)
|- valign=top
|- valign=top
Line 50: Line 52:
| Lagrangian and Hamiltonian systems II
| Lagrangian and Hamiltonian systems II
* Hamiltonian systems with 2 degrees of freedom
* Hamiltonian systems with 2 degrees of freedom
* Mechanical systems
|  
|  
* Perko 3.6
* Perko 3.6
| [[CDS 140b Spring 2014 Homework 2|HW 2]] <br> Due: 17 Apr (Thu)
* [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)
|- valign=top
|- valign=top
| 3
| 3
| 18 Apr <br> 21 Apr <br> RMM
| 18 Apr <br> 21 Apr <br> RMM
| Advanced stability theory
| Advanced stability theory
* Time-varying systems
* Non-autonomous (time-varying) systems
* I/O stability, passivity
* Input-to-state stability, input-output stability, small gain theorem
|  
|  
* Khalil 4.5, 6.1-6.5
* Khalil 4.5, 4.6-4.7 (skim), 5.1-5.4
| HW 3
| [[CDS 140b Spring 2014 Homework 3|HW 3]] <br>
Due 1 May (Thu)
|- valign=top
|- valign=top
| 4
| 4
| 28 Apr <br> 30 Apr <br> RMM
| 28&nbsp;Apr '''(12-1 pm)''' <br> 30 Apr <br> RMM
| Perturbation Theory
| Stability of perturbed systems
* Regular Perturbation
* Vanishing perturbations
* Poincare-Lindstedt Method
* Non-vanishing perturbations
* Periodically Perturbed Systems
* Slowiy varying systems
|  
|  
* Khalil, 10.1-10.3
* Khalil, 9.1, 9.2, 9.6
* Strogatz, 7.6
| [[CDS 140b Spring 2014 Homework 4|HW 4]]<br>
* Verhulst, 9.1, 10.1
Due 8 May (Thu)
| HW 4
|- valign=top
|- valign=top
| 5
| 5
| 5 May <br> 7 May <br> RMM
| 5 May <br> 7 May <br> RMM
| Averaging Method
| Perturbation theory
* Periodic Case
* Periodic perturbations
* Periodic Solutions
* Averaging
* General Case
* Singular Perturbations
|  
|  
* Khalil, 10.4-10.6
* Khalil, 10.3-10.4, 11.1-11.3, 11.5
* Strogatz, 7.6
| [[CDS 140b Spring 2014 Homework 5|HW 5]]<br>
* Verhulst,  11.1-11.3, 11.8
Due 15 May (Thu)
| HW 5
|- valign=top
|- valign=top
| 6
| 6
| 12 May <br> 14 May  <br> RMM
| 12 May <br> 14 May  <br> RMM
| Singular Perturbations
| Interconnected systems
* Finite Interval
* Absolute stability
* Infinite Interval
* Describing functions
* Stability Analysis
|
|
* Khalil, 11.1-11.3, 11.5
* Khalil, 7.1-7.2
| HW 6
| [[CDS 140b Spring 2014 Homework 6|HW 6]]<br>
Due 22 May (Thu)
|- valign=top
|- valign=top
| 7
| 7
| 21 May <br> 23&nbsp;May* <br> DGM
| 19 May <br> 21&nbsp;May  <br> DGM
| Nonlinear control I
| Nonlinear control I
* Overview of techniques
* Overview of techniques
Line 107: Line 111:
* Khalil 12.2,12.5 (gain scheduling), 13.1-13.3 (feedback linearization)
* 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)
* Isidori (chapter 2) or Nijmeijer and van der Schaft, 3.1 (for more on controllability)
| HW 7
* [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)
|- valign=top
|- valign=top
| 8
| 8
| 28&nbsp;May <br> 30 May<br>DGM
| 23&nbsp;May* <br> 30 May<br>DGM
| Nonlinear control II
| Nonlinear control II
* Backstepping
* Backstepping
Line 116: Line 121:
|
|
* Khalil 14.3, 14.1
* Khalil 14.3, 14.1
| HW 8
* [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)
|- valign=top
| 9
|  2 Jun <br> 3 Jun
| Project presentations
| <!-- Reading -->
| <!-- Homework -->
|}
|}


Line 146: Line 145:
'''Grading Policy'''  
'''Grading Policy'''  


The final grades will be evaluated based on homework assignments (75%) and final projects (25%).
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 ==
== Projects ==


TBD
TBD
-->


[[Category:Courses]]
[[Category:Courses]]

Latest revision as of 03:46, 1 June 2014

Differential Equations and Dynamical Systems

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

Teaching Assistant

  • Katie Broersma (CDS)
  • Contact: cds140-tas@cds.caltech.edu
  • Office hours: Wed, 3:30-4:30 pm, 101 STH

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.

Lecture Schedule

Week Date Topic Suggested Reading/Lecture Notes Homework
0 31 Mar
RMM 		Course overview
1 2 Apr
4 Apr*
DGM 		Lagrangian and Hamiltonian systems I
  • Definition and properties
  • Newtonian Systems
 HW 1
Due: 10 Apr (Thu)
2 9 Apr*
11 Apr
DGM 		Lagrangian and Hamiltonian systems II
  • Hamiltonian systems with 2 degrees of freedom
  • Mechanical systems
 HW 2
Due: 17 Apr (Thu)
3 18 Apr
21 Apr
RMM 		Advanced stability theory
  • Non-autonomous (time-varying) systems
  • Input-to-state stability, input-output stability, small gain theorem
  • Khalil 4.5, 4.6-4.7 (skim), 5.1-5.4
 HW 3

Due 1 May (Thu)

4 28 Apr (12-1 pm)
30 Apr
RMM 		Stability of perturbed systems
  • Vanishing perturbations
  • Non-vanishing perturbations
  • Slowiy varying systems
  • Khalil, 9.1, 9.2, 9.6
 HW 4

Due 8 May (Thu)

5 5 May
7 May
RMM 		Perturbation theory
  • Periodic perturbations
  • Averaging
  • Singular Perturbations
  • Khalil, 10.3-10.4, 11.1-11.3, 11.5
 HW 5

Due 15 May (Thu)

6 12 May
14 May
RMM 		Interconnected systems
  • Absolute stability
  • Describing functions
  • Khalil, 7.1-7.2
 HW 6

Due 22 May (Thu)

7 19 May
21 May
DGM 		Nonlinear control I
  • Overview of techniques
  • Controllability and Lie brackets
  • Gain scheduling
  • Feedback linearization
  • 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)
  • Lecture notes
 HW 7
Due: 29 May (Thu)
8 23 May*
30 May
DGM 		Nonlinear control II
  • Backstepping
  • Sliding mode control
 HW 8
Due: 6 June (Thu)

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.

Retrieved from "https://murray.cds.caltech.edu/index.php?title=CDS_140b,_Spring_2014&oldid=17398"