Mth 477/577 Control Theory

Mathematical Control Theory I

Mth 477/577:001 (CRN 44986/44987)

Winter 2011

T, Th 14:00--15:15
Room SH201

Notes: The last homework assigment has been posted. It depends in part on material from this week so you may not be able to work it out in full until the end of this week (or you can study the notes posted below).

Examination Schedule: The final exam will take place on the official date and time during finals week (in the same classroom): Monday, March 14, 10:15am -12:05pm.

SYLLABUS	HOMEWORK	LECTURES
Review Assignment: Due Tuesday, 01/11	Hw 1	Week 1
Book References	Hw 2	Week 2
	Hw 3	Week 3
	Hw 4	Week 4
	Hw 5	Week 5
	Hw 6	No notes on week 6 (exam week)
		Week 7
		Week 8
		Week 9

Catalog Description for Mth 477,8/577,8
Mathematical foundations of linear time invariant control systems. Controllability, observability, stabilizability, feedback. Elements of the calculus of variations and optimal control. Dynamic programming. Pontryagin maximum principle. Applications. Prerequisite: Mth 256. Recommended: Mth 253, 254.

Topics for this term

Basic definitions, examples from engineering, biology and economics
Brief historic development of key ideas
Matrix algebra background: Cayley-Hamilton theorem, Jordan Canonical form, exponential of a matrix
Differential equations background: forced oscillators, variation of constants formula for control systems
Controllability for discrete and continuous time systems, Kalman’s Controllability theorem
Observability, rank characterization for continuous and discrete systems, duality between controllability and observability
Kalman’s controllability decomposition, uncontrollable subsystem
State feedback, Pole placement theorem
Classical PID control
Output feedback and pole placement
Observers
Sampled systems
Lyapunov Stability, Lyapunov’s equation
Stabilizability
Input-output stability

Reference. There is no required textbook, but the book below is recommended for reference. Class notes will be posted for most of the material.

A Linear Systems Primer, by Panos J Antsaklis and Anthony N Michel, Birkhäuser Boston. ISBN: 9780817644604

New development: During the 2011-2012 academic year there will be a 600-level sequence of Topics in Advanced Control Theory. This may be of interest for those wishing to continue the studies in control in more depth.

Useful links

Theorem.net links related to control theory.
Mathematical Control Theory, by Eduardo Sontag
The following link Unsolved Problems points to a book by Blondel and Megretski with a collection of mathematical open problems in the field of control systems. The full book is available on line from Princeton University Press. The website also contains links to solutions or partial solutions already available to some of them A link to another earlier book of open problems is Open Problems in Systems and Control Theory.

OLD NOTES

This is a new course in applied mathematics which provides a mathematical introduction to Control Theory. Control Theory has strong links to various other fields, in particular engineering and biology. This website is under construction but there is some basic information about the course below. More details will be posted closer to the Winter term.
See flyer.

Notice: there was a typo in the notes for week 1 which has now been corrected. The solutions listed in section 6 (second bullet) should one have alpha+beta and the other alpha-beta.

There was a typo in problem 7 of hw1. It should have been that the system is controllable if k is NOT an eigenvalue of A. The corrected version has been posted.
Revised notes for week 2 have been posted to correct a few minor typos. You could also benefit from Appendices A1, through A8 in the recommended text.

MATH477/577:001 Homepage/Gerardo Lafferriere / gerardoL@pdx.edu / revised : 02/28/11