Difference between revisions of "Cds110b WI14"

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| 14 Jan <br> 16 Jan
 
| 14 Jan <br> 16 Jan
|  TBD I
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|  TBD  
 
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| 28 Jan <br> 30 Jan
 
| 28 Jan <br> 30 Jan
| 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]]
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* [[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
 
| 4 Feb <br> 6 Feb
| 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]]
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* [[Media:cds140a-wi11-Week5NotesCMT.pdf|Notes on Center Manifold]]
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* [[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
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| Perko 2.14 + notes
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<!--
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* [http://www.cds.caltech.edu/~macmardg/courses/cds140a/L6-Hamiltonian.pdf Scanned lecture notes]
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* [http://www.cds.caltech.edu/~macmardg/courses/cds140a/MarsdenMechSystems.pdf Marsden, Mechanical systems]
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* [[Media:cds140a-wi11-Week6NotesHamGrad.pdf|Gradient and Hamiltonian Systems]]
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* [[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
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* Periodic orbits and limit cycles
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* Poincare' map
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* Bendixson criterion for limit cycles in the plane
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| 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]
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* [http://www.cds.caltech.edu/~murray/courses/cds140/wi11/caltech/L7-2_limitcycles-17Feb11.pdf Lecture notes on limit cycles]
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* [http://www.cds.caltech.edu/~murray/courses/cds140/wi11/caltech/L7-3_bfs_oscillators.pdf BFS notes on oscillators]
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-->
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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
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* Bifurcation of equilibrium points
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* Hopf bifurcation
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| 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:

  • K. J. Åström and R. M. Murray, ', Princeton University Press, 2008.
  • B. Friedland, Control System Design: An Introduction to State-Space Methods, Dover, 2004.
  • F. L. Lewis and V. L. Syrmos, Optimal Control, Second Edition, Wiley-IEEE, 1995. (Google Books)
  • A. D. Lewis, A Mathematical Approach to Classical Control, 2003.