Cds110b WI14: Difference between revisions

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* 8 Jan 2014: web page creation, uploaded lecture 1 material  
* 8 Jan 2014: web page creation, uploaded lecture 1 material  
=== Lecture Schedule ===
{| class="mw-collapsible " width=100% border=1 cellpadding=5
|-
| '''Date'''
| '''Topic'''
| '''Reading'''
| '''Homework'''
|- valign=top
|- valign=top
| 7 Jan <br>  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<br>
| [[CDS 140a Winter 2014 Homework 1|HW 1]] <br> Due: 15 Jan (Wed)
|- valign=top
| 14 Jan <br> 16 Jan
| Linear Differential Equations II
* S + N decomposition, Jordan form
* Stability theory
* Linear systems with inputs (nonhomogeneous systems)
| Perko, 1.7-1.10
| [[CDS 140a Winter 2014 Homework 2|HW 2]] <br> Due: 22 Jan (Wed)
|- valign=top
| 21 Jan <br> 23 Jan
| Nonlinear differential equations
* Existence and uniqueness
* Flow of a differential equation
* Linearization
| Perko, 2.1-2.6
| [[CDS 140a Winter 2014 Homework 3|HW 3]] <br> Due: 29 Jan (Wed)
|- valign=top
| 28 Jan <br> 30 Jan
| Behavior of differential equations
* Stable and unstable manifolds 
* Stability of equilibrium points
| Perko, 2.7-2.10
<!--
* [[Media:cds140a-wi11-Week4Notes.pdf|Some notes]]
* [[Media:cds140a-wi11-InvManRemark.pdf|Remark on invariant manifolds]]
-->
| | [[CDS 140a Winter 2014 Homework 4|HW 4]] <br> Due: 5 Feb (Wed)
|- valign=top
| 4 Feb <br> 6 Feb
| Non-hyperbolic differential equations
* Lyapunov functions
* Center manifold theorem
| Perko, 2.11-2.13
<!--
* [[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)]]
-->
| [[CDS 140a Winter 2014 Homework 5|HW 5]] <br> Due: 12 Feb (Wed)
|- valign=top
| 11 Feb <br> 13 Feb
| Hamiltonian systems
* Gradient and Hamiltonian systems
* Energy based stability methods
* Applications
| Perko 2.14 + notes
<!--
* [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]]
-->
| [[CDS 140a Winter 2014 Homework 6|HW 6]] <br> Due: 19 Feb (Wed)
|- valign=top
| 18&nbsp;Feb* <br> 20 Feb* <br> 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
<!--
* [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]
-->
| [[CDS 140a Winter 2014 Homework 7|HW 7]] <br> Due: 5 Mar (Wed)
|- valign=top
|- valign=top
| 27 Feb <br> 4 Mar <br> 6 Mar
| Bifurcations
* Structural stability
* Bifurcation of equilibrium points
* Hopf bifurcation
| Perko 4.1-4.4 + notes
<!--
* [http://www.cds.caltech.edu/~murray/courses/cds140/wi11/caltech/L8-1_parmsens-24Feb11.pdf Lecture notes on structural stability, parameter sensitivity]
* [http://www.cds.caltech.edu/~murray/courses/cds140/wi11/caltech/L8-1_bfs_sensitivity.pdf BFS notes on parameter sensitivity]
* [http://www.cds.caltech.edu/~murray/courses/cds140/wi11/caltech/L8-2_bifurcations-01Mar11.pdf Lecture notes on bifurcations]
-->
| [[CDS 140a Winter 2014 Homework 8|HW 8]] <br> Due: 12 Mar (Wed)
|- valign=top
| 11 Mar* <br>
| Course review
| <!-- Reading -->
| Final exam  <br> Due: 19 Mar (Wed)
|}


=== 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 CollapseHomework
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:

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