## Center for Applied Mathematics Colloquium

Abstract: In the context of nonlinear dynamics on a finite-dimensional state space, we will examine information requirements for control-enabling tasks such as state estimation, model detection, localization and mapping in an unknown environment. We will discuss the role of topological entropy in determining minimal data rates necessary for solving these tasks. Through examples, we will study simultaneous localization and mapping based on a binary signal generated by an unknown landmark. Anyone having basic familiarity with ordinary differential equations should be able to follow the talk.

Bio: Daniel Liberzon was born in the former Soviet Union in 1973. He did his undergraduate studies in mathematics at Moscow State University. In 1993 he moved to the United States to pursue graduate studies in mathematics at Brandeis University, where he received the Ph.D. degree in 1998 (supervised by Prof. Roger W. Brockett of Harvard University). He is currently a Richard T. Cheng Professor of electrical and computer engineering at the University of Illinois Urbana-Champaign. His research interests include nonlinear control theory, switched and hybrid dynamical systems, 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, 2012).