Cds110b WI14

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

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

• J. Doyle, B. Francis, A. Tannenbaum, Feedback Control Theory, Macmillan, 1992.
• R. M. Murray, Optimization-Based Control, Preprint, 2008.

You may find the following texts useful as well:

• K. J. Åström and R. M. Murray, Feedback Systems, 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.