**October 25, 2000 from
3:30 - 4:30 in K9509, SFU
**

**
**

** Francis CLARKE, Université de Lyon and Institut universitaire de
France
Talks on
**

**"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.