Discontinuous Feedback in Nonlinear Control:

Observation and Optimization




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".