Winter 2016
M, W, F
10:15--11:10
Room NH 385
This is
a course in applied mathematics which provides a mathematical
introduction to Control Theory. Control Theory has strong
links to various areas of mathematics and other fields, in particular
engineering and biology.
More details will be
posted closer to the Winter term. Before then, feel free to
contact the instructor at gerardoL@pdx.edu
Intended audience:
this course usually appeals to a diverse audience. Mahtematics
students interested in applied topics, engineering students interested
in a deeper understanding of the ideas of feedback and control, and
science students interested in more mathematical tools for the analysis
of applied models.
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 Winter 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.
The textbool for the course is listed below. This will be supplemented
with class notes on the main topics, to be posted on the D2L site.
A Linear
Systems Primer, by Panos J Antsaklis and Anthony N Michel, Birkhäuser Boston. ISBN: 9780817644604