Difference between revisions of "Cds110b WI14"

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* 8 Jan 2014: web page creation, uploaded lecture 1 material  
 
* 8 Jan 2014: web page creation, uploaded lecture 1 material  
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=== Lecture Schedule ===
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{| class="mw-collapsible " width=100% border=1 cellpadding=5
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|-
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| '''Date'''
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| '''Topic'''
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| '''Reading'''
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| '''Homework'''
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|- valign=top
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|- valign=top
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| 7 Jan <br>  9 Jan
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| Linear Differential Equations I
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* Course overview and administration
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* Linear differential equations
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* Matrix exponential, diagonalization
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* Stable and unstable spaces
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* Planar systems, behavior of solutions
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|
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Perko, 1.1-1.6<br>
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| [[CDS 140a Winter 2014 Homework 1|HW 1]] <br> Due: 15 Jan (Wed)
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|- valign=top
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| 14 Jan <br> 16 Jan
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| Linear Differential Equations II
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* S + N decomposition, Jordan form
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* Stability theory
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* Linear systems with inputs (nonhomogeneous systems)
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| Perko, 1.7-1.10
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| [[CDS 140a Winter 2014 Homework 2|HW 2]] <br> Due: 22 Jan (Wed)
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|- valign=top
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| 21 Jan <br> 23 Jan
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| Nonlinear differential equations
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* Existence and uniqueness
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* Flow of a differential equation
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* Linearization
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| Perko, 2.1-2.6
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| [[CDS 140a Winter 2014 Homework 3|HW 3]] <br> Due: 29 Jan (Wed)
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|- valign=top
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| 28 Jan <br> 30 Jan
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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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<!--
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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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-->
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| | [[CDS 140a Winter 2014 Homework 4|HW 4]] <br> Due: 5 Feb (Wed)
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|- valign=top
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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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<!--
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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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-->
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| [[CDS 140a Winter 2014 Homework 5|HW 5]] <br> Due: 12 Feb (Wed)
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|- valign=top
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| 11 Feb <br> 13 Feb
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| 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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-->
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| [[CDS 140a Winter 2014 Homework 6|HW 6]] <br> Due: 19 Feb (Wed)
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|- valign=top
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| 18&nbsp;Feb* <br> 20 Feb* <br> 25 Feb
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| 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
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<!--
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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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|- valign=top
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|- valign=top
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| 27 Feb <br> 4 Mar <br> 6 Mar
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| 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
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<!--
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* [http://www.cds.caltech.edu/~murray/courses/cds140/wi11/caltech/L8-1_parmsens-24Feb11.pdf Lecture notes on structural stability, parameter sensitivity]
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* [http://www.cds.caltech.edu/~murray/courses/cds140/wi11/caltech/L8-1_bfs_sensitivity.pdf BFS notes on parameter sensitivity]
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* [http://www.cds.caltech.edu/~murray/courses/cds140/wi11/caltech/L8-2_bifurcations-01Mar11.pdf Lecture notes on bifurcations]
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-->
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| [[CDS 140a Winter 2014 Homework 8|HW 8]] <br> Due: 12 Mar (Wed)
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|- valign=top
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| 11 Mar* <br>
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| Course review
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| <!-- Reading -->
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| Final exam  <br> Due: 19 Mar (Wed)
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|}
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 +
  
 
=== Course Text and References ===
 
=== Course Text and References ===

Revision as of 22:18, 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
Linear Differential Equations I
  • Course overview and administration
  • Linear differential equations
  • Matrix exponential, diagonalization
  • Stable and unstable spaces
  • Planar systems, behavior of solutions

Perko, 1.1-1.6

HW 1
Due: 15 Jan (Wed)
14 Jan
16 Jan
Linear Differential Equations II
  • S + N decomposition, Jordan form
  • Stability theory
  • Linear systems with inputs (nonhomogeneous systems)
Perko, 1.7-1.10 HW 2
Due: 22 Jan (Wed)
21 Jan
23 Jan
Nonlinear differential equations
  • Existence and uniqueness
  • Flow of a differential equation
  • Linearization
Perko, 2.1-2.6 HW 3
Due: 29 Jan (Wed)
28 Jan
30 Jan
Behavior of differential equations
  • Stable and unstable manifolds
  • Stability of equilibrium points
Perko, 2.7-2.10 HW 4
Due: 5 Feb (Wed)
4 Feb
6 Feb
Non-hyperbolic differential equations
  • Lyapunov functions
  • Center manifold theorem
Perko, 2.11-2.13 HW 5
Due: 12 Feb (Wed)
11 Feb
13 Feb
Hamiltonian systems
  • Gradient and Hamiltonian systems
  • Energy based stability methods
  • Applications
Perko 2.14 + notes HW 6
Due: 19 Feb (Wed)
18 Feb*
20 Feb*
25 Feb
Limit cycles
  • 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 HW 7
Due: 5 Mar (Wed)
27 Feb
4 Mar
6 Mar
Bifurcations
  • Structural stability
  • Bifurcation of equilibrium points
  • Hopf bifurcation
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: