October 25, 2000 from 3:30 - 4:30 in K9509, SFU
Francis CLARKE, Université de Lyon and Institut universitaire de
"The Feedback Problem in Control Theory"
Abstract: In this nontechnical survey, we begin by defining the principal issue in control theory: to design a feedback law having a certain desired effect on the underlying dynamical system. The possible contexts in which this problem can be given a precise formulation are multiple, depending notably on the type of dynamical system considered, the degree of knowledge of the model that is assumed, and the goal that is desired. The actual and potential applications are also widespread, and very important, encompassing as they do such special cases as linear systems theory and optimal control. Here we shall focus primarily upon the stabilization issue for nonlinear systems of ordinary differential equations, a very active area in the last decade. Besides discussing some earlier important results, we shall present more recent work bearing upon the interest (in fact, the absolute necessity) of using discontinuous feedback laws. In particular, this work settles an old problem in the field by proving that every (open-loop) controllable system admits a stabilizing feedback.