April 22, 2011, 1100 Webb

Many problems arising in control and optimization require the treatment of such systems in which continuous dynamics and discrete events coexist. In this talk, we report some of our recent findings on switching diffusions. The states of the systems have two components. The discrete component is a random jump process and the continuous component is a solution of a differential equation. One of the difficulties is the discrete component depends on the continuous state. Motivational examples from wireless communications, identification, finance, two-time-scale Markovian systems, and manufacturing will be presented. To effectively handle optimal controls of average cost per unit time problems, we present conditions under which there is a unique invariant measure for the limit control problems. Then we study stability and stabilization of the underlying systems, and treat numerical solution for related control and game problems.

George Yin received the B.S. degree in mathematics from the University of Delaware in 1983, M.S. in Electrical Engineering, and Ph.D. in Applied Mathematics from Brown University in 1987. He joined Wayne State University in 1987 and became a professor in 1996. His research interests include stochastic systems, applied stochastic processes and applications, stochastic approximation, identification, signal processing, and control and optimization. He severed on many technical committees and conference program committees; he was the editor of SIAM Activity Group on Control and Systems Theory Newsletters, Co-chair of 1996 AMS-SIAM Summer Seminar in Applied Mathematics and 2003 AMS-IMS-SIAM Summer Research Conference: Mathematics of Finance, Co-organizer of 2005 IMA Workshop on Wireless Communications and 2006 IMA PI conference. He is Co-chair of 2011 SIAM Control Conference, Program Director of SIAM Activity Group on Control and Systems Theory, is an associate editor of Automatica and SIAM Journal on Control and Optimization, and is on the editorial board of a number of other journals; he was an Associate Editor of IEEE Transactions on Automatic Control. He is an IEEE Fellow, and is Vice President elected of Wayne State University Academy of Scholars.