MAT 598

Mathematical Control Theory

Instructor: Matthias Kawski, GWC 354, http://math.asu.edu/~kawski, kawski@asu.edu

NEW TIME: 4.40-5:55 Tuesday – Thursday

Schedule

Line number: 09967

Location: LSE 250

Brief description: Where traditional dynamical systems theory and physics take a primarily descriptive approach, control takes the engineering point of view: analyzing and designing ways to make a system behave in a desired way. A typical simple distinction is “stability” versus “stabilizability”. This course is aimed at a broad audience of mathematically mature students from diverse backgrounds who want to get an overview of some of the main concepts, methodologies and approaches in control. Applications to specific areas such as bio-med, aerospace, and others may be included depending on the interests of the participants. Due to time constraints we will NOT address stochastic systems, linear techniques (complex analysis), infinite dimensional systems (PDEs).

Contents:

Controllability. System approximation
Feedback and stabilization
Observability, observers and dynamic feedback
Introduction to optimal control (dynamic programming, Maximum Principle)

Prerequisites:

MAT 371 and 372 or equivalent (required) (advanced multivariable calculus).

Desirable are some background in the theory of ordinary differential equations, and in real analysis, both at an advanced undergraduate or beginning graduate level. For students with background in differential geometry, abstract algebra, and functional analysis we plan to provide opportunities to explore core topics at more sophisticated levels.

References:

Mathematical Control Theory, E. D. Sontag, Springer Verlag.
to be augmented by course notes by the instructor

If at all interested in the course, please contact the instructor as soon as possible – the earlier we talk, the easier it will be to accommodate special interests of the students.