Monday, March 11, 2024 - 4:00pm
Event Calendar Category
LIDS Seminar Series
Speaker Name
Daniel Liberzon
Affiliation
UIUC
Building and Room Number
32-155
Abstract
In this talk we will discuss estimation entropy for continuous-time nonlinear systems, which is a variant of topological entropy formulated in terms of the number of functions that approximate all system trajectories up to an exponentially decaying error. We will establish an upper bound on the estimation entropy in terms of the sum of the desired convergence rate and the system's expansion rate multiplied by the system dimension, as well as a lower bound. We will describe an iterative procedure that uses quantized and sampled state measurements to generate state estimates that converge to the true state at the desired exponential rate. The average bit rate utilized by this procedure matches the derived upper bound on the estimation entropy, and no other algorithm of this type can perform the same estimation task with bit rates lower than the estimation entropy. As an application of this estimation procedure, we will study the problem of determining, from quantized state measurements, which of two competing models of a dynamical system is the true model. We will show that under a mild assumption of exponential separation of the candidate models, detection always happens in finite time. Recent work on entropy of switched and interconnected systems will also be briefly discussed.
Biography
Daniel Liberzon was born in the former Soviet Union in 1973. He did his undergraduate studies in the Department of Mechanics and Mathematics at Moscow State University from 1989 to 1993. 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). Following a postdoctoral position in the Department of Electrical Engineering at Yale University from 1998 to 2000 (with Prof. A. Stephen Morse), he joined the University of Illinois at Urbana-Champaign, where he is currently a Richard T. Cheng Professor in the Electrical and Computer Engineering Department and a professor in the Coordinated Science Laboratory. 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). His work has received several recognitions, including the IFAC Young Author Prize in 2002 and the Donald P. Eckman Award in 2007. He delivered plenary lectures at the American Control Conference in 2008 and the IEEE Conference on Decision and Control in 2022, as well as (semi-)plenary lectures at several other conferences. He served as a Senior Editor for the IFAC journal Automatica from 2017 to 2022. He is a fellow of IEEE (since 2013) and IFAC (since 2016).