Cds110b WI14: Difference between revisions

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|  TBD I
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| Behavior of differential equations
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* Stable and unstable manifolds 
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* Stability of equilibrium points
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| Perko, 2.7-2.10
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* [[Media:cds140a-wi11-Week4Notes.pdf|Some notes]]
* [[Media:cds140a-wi11-InvManRemark.pdf|Remark on invariant manifolds]]
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| | [[CDS 140a Winter 2014 Homework 4|HW 4]] <br> Due: 5 Feb (Wed)
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| 4 Feb <br> 6 Feb
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| Non-hyperbolic differential equations
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* Lyapunov functions
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* Center manifold theorem
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| Perko, 2.11-2.13
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* [[Media:cds140a-wi11-Week5Notes.pdf|Notes on Lyapunov]]
* [[Media:cds140a-wi11-Week5NotesCMT.pdf|Notes on Center Manifold]]
* [[Media:cds140a-wi11-CMTLimitCycleExample.pdf|An Example (Center Manifold / Limit Cycle)]]
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| [[CDS 140a Winter 2014 Homework 5|HW 5]] <br> Due: 12 Feb (Wed)
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| 11 Feb <br> 13 Feb
| 11 Feb <br> 13 Feb
| Hamiltonian systems
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* Gradient and Hamiltonian systems
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* Energy based stability methods
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* Applications
| Perko 2.14 + notes
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* [http://www.cds.caltech.edu/~macmardg/courses/cds140a/L6-Hamiltonian.pdf Scanned lecture notes]
* [http://www.cds.caltech.edu/~macmardg/courses/cds140a/MarsdenMechSystems.pdf Marsden, Mechanical systems]
* [[Media:cds140a-wi11-Week6NotesHamGrad.pdf|Gradient and Hamiltonian Systems]]
* [[Media:cds140a-wi11-Week6NotesLagHamSum.pdf|Lagrangian, Summary]]
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| [[CDS 140a Winter 2014 Homework 6|HW 6]] <br> Due: 19 Feb (Wed)
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| 18&nbsp;Feb* <br> 20 Feb* <br> 25 Feb
| 18&nbsp;Feb* <br> 20 Feb* <br> 25 Feb
| Limit cycles
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* Limit sets and attractors
* Periodic orbits and limit cycles
* Poincare' map
* Bendixson criterion for limit cycles in the plane
| Perko, 3.1-3.5, 3.7, 3.9
| Perko, 3.1-3.5, 3.7, 3.9
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* [http://www.cds.caltech.edu/~murray/courses/cds140/wi11/caltech/L7-1_orbits-15Feb11.pdf Lecture notes on orbits and attractors]
* [http://www.cds.caltech.edu/~murray/courses/cds140/wi11/caltech/L7-2_limitcycles-17Feb11.pdf Lecture notes on limit cycles]
* [http://www.cds.caltech.edu/~murray/courses/cds140/wi11/caltech/L7-3_bfs_oscillators.pdf BFS notes on oscillators]
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| [[CDS 140a Winter 2014 Homework 7|HW 7]] <br> Due: 5 Mar (Wed)
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| 27 Feb <br> 4 Mar <br> 6 Mar
| 27 Feb <br> 4 Mar <br> 6 Mar
| Bifurcations
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* Structural stability
* Bifurcation of equilibrium points
* Hopf bifurcation
| Perko 4.1-4.4 + notes
| Perko 4.1-4.4 + notes
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Revision as of 22:29, 8 January 2014

CDS 110b: Introduction to Control Theory

Instructors

  • John Doyle, doyle@cds.caltech.edu
  • Lectures: Tu/Th, 9-10:30, 105 ANB
  • Office hours: TBD (please e-mail to schedule)

Teaching Assistants

  • Vanessa Jonsson, Nikolai Matni
  • Contact: cds110-tas@cds.caltech.edu
  • Office hours: TBD

Course Description

Announcements

  • 8 Jan 2014: web page creation, uploaded lecture 1 material


Lecture Schedule

Date Topic Reading Homework
7 Jan
9 Jan 		Robustness, fragility, complexity and control I
  • Examples in neuroscience, glycolysis, technology
14 Jan
16 Jan 		TBD
21 Jan
23 Jan
28 Jan
30 Jan
4 Feb
6 Feb
11 Feb
13 Feb
18 Feb*
20 Feb*
25 Feb 		Perko, 3.1-3.5, 3.7, 3.9
27 Feb
4 Mar
6 Mar 		Perko 4.1-4.4 + notes HW 8
Due: 12 Mar (Wed)
11 Mar*
Course review Final exam
Due: 19 Mar (Wed)



Course Text and References

The main course text is

You may find the following texts useful as well:

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