Math 642:577 Introduction to Control Systems Theory
("Topics in System Theory")
Fall 2006
Class meeting time and place:
Wednesdays 10:00am - 01:00pm, BioMaPS seminar room, Hill 260.
What is control theory?
Control Systems Theory deals with the basic principles underlying the analysis
and design of control systems. To "control" an object means to influence its
behavior so as to achieve a desired goal. In order to implement this
influence, engineers build devices that incorporate various mathematical
techniques. These devices range from Watt's steam engine governor to the
sophisticated microprocessor controllers found in consumer items ---such as CD
players and automobiles--- or in industrial robots and airplane autopilots.
Similarly, in a biological context, feedback loops underlie homeostasis at the
organism level as well as the regulation of concentrations of enzymes and
other species at the cell level.
What will the course cover?
The course will cover the core concepts and results, with an emphasis on
foundational aspects: The algebraic theory of linear systems (including
controllability, observability, feedback equivalence, realization, and
minimality), stability via Lyapunov as well as input/output methods, ideas of
optimal control, observers and dynamic feedback, tracking, Kalman filtering,
and basic facts about frequency domain such as the Nyquist criterion.
Applications from engineering and biology will be used to illustrate the
concepts.
Basic knowledge of
differential equations and linear algebra.
Any other needed material will be developed as needed.
Interesting links:
Please feel free to contact me if you have any questions, prefereabily by
electronic mail (sontag@math).
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