**Discontinuous Feedback in Nonlinear Control:**

**Observation and Optimization**

**by**

**Professor Yuri Ledyaev**

**Western Michigan
University **

**Mathematics Department
**

**Friday, February 17, 2012**

**3:30 – 4:30p.m**

**Rm. 1500 EECS**

**Abstract: **It is well known that due
to some topological obstacles many control tasks for nonlinear control
dynamical system cannot be performed effectively by using only continuous
feedback controls . In mid 1990s Clarke, Ledyaev, Sontag, and Subbotin
introduced a concept of discontinuous feedback control to demonstrate
that any asymptotically controllable nonlinear system can be stabilized
by (possibly discontinuous) feedback control. This feedback concept provided a
precise and convenient mathematical model for performance analysis of digital
computer-aided control and control over networks.

In
this talk, we illustrate applications of this discontinuous feedback for some
problems of stabilization, dynamic observers characterization and team optimal
pursuit.

**Biosketch:** Yuri Ledyaev's main research
interests lie in control theory (in particular, stabilization, optimal control,
differential games), theory of differential inclusions, nonlinear
functional and nonsmooth analysis (in particular, nonsmooth
analysis' applications in control theory and optimization). He received his
Ph.D. degree from Moscow Institute for Physics and Technology in 1980 and his
Dr.Sc. degree from Steklov Institute of Mathematics in 1990. He was with
Department of Mathematics of Moscow Institute for Physics and Technology during
1980-1984, since 1984 he has been with Steklov Institute of Mathematics of
Russian Academy of Sciences where he was a Principal
Researcher at the Department of Differential Equations founded by
L.S.Pontryagin. He is a full Professor at the Department of
Mathematics , Western Michigan University since 2000. Currently he is a
member of the Editorial Boards of "Journal of Dynamical and Control Systems
" and "Mathematics of Control, Signals, and Systems".