Discontinuous Feedback in Nonlinear Control

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.

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" .