Difference between revisions of "Cds110b WI14"

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Revision as of 22:21, 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

Perko, 1.1-1.6

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:

  • 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.