April 06, 2012, Webb 1100

Switched systems and limited-information control are two research areas that have evolved rapidly but separately over the last two decades. In this talk we present a preliminary attempt at their unified study, by considering a stabilization problem for a switched linear system with sampled and quantized state measurements. In our setting, at the sampling times the active mode of the switched system is known, but between the sampling times the switching signal is unknown and is only subject to mild slow-switching assumptions. An important ingredient in our stabilizing quantized feedback control strategy is the propagation of reachable set over-approximations for switched systems, a problem that has received a lot of attention in the hybrid systems literature and for which we propose a novel algorithm.

Daniel Liberzon did his undergraduate studies in the Department of Mechanics and Mathematics at Moscow State University from 1989 to 1993 and received the Ph.D. degree in mathematics from Brandeis University in 1998 (under the supervision of Prof. Roger W. Brockett of Harvard University). Following a postdoctoral position in the Department of Electrical Engineering at Yale University from 1998 to 2000 (under Prof. A. Stephen Morse), he joined the University of Illinois at Urbana-Champaign, where he is now an associate professor in the Electrical and Computer Engineering Department and the Coordinated Science Laboratory. His research interests include switched and hybrid systems, nonlinear control theory, control with limited information, and uncertain and stochastic systems. He is the author of the books "Switching in Systems and Control" (Birkhauser, 2003) and "Calculus of Variations and Optimal Control Theory: A Concise Introduction" (Princeton Univ. Press, 2011). He received the 2002 IFAC Young Author Prize and the 2007 Donald P. Eckman Award and delivered a plenary lecture at the 2008 American Control Conference.