Math 509: Theory of Optimal Control

Terry Rockafellar

Spring 1999, Monday/Wednesday 8:00-9:15 AM
In a wide range of mathematical models, a "system" can be described by a state, such as a vector in an n-dimensional space, that varies in continuous or discrete time. Often there are parameters, called controls, which can be manipulated in time so as to influence what happens. The question then is how to exercise that influence optimally with respect to some goal.

This course deals with the underpinnings of the subject as a branch of optimization that is especially concerned with ordinary differential equations and their discrete-time analogs. It serves also as a vehicle for recently developed ideas of variational analysis that extend the classical "calculus of variations" in many interesting ways.

It will be taught on the basis of distributed lecture notes rather than a textbook. Grades will be based primarily on homework assignments.

As a prerequisite, students should have taken MATH 515 (winter quarter) and they ought to know real analysis on the level of MATH 426 at least. They do not need to have taken advanced courses in differential equations or the calculus of variations.