Decision and Control Lecture Series
Coordinated Science Laboratory
“Entropy and Minimal Data Rates for State Estimation and Model Detection”
Daniel Liberzon, Ph.D.
University of Illinois
Wednesday, January 25, 2017
3:00 p.m. to 4:00 p.m.
CSL Auditorium (B02)
We introduce and study novel notions of estimation entropy for continuous-time nonlinear systems, formulated in terms of the number of functions that approximate all system trajectories up to an exponentially decaying error. We 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 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. We then discuss an application of this estimation procedure to determining, from quantized state measurements, which of two competing models of a dynamical system is the true model. We show that under a mild assumption of exponential separation of the candidate models, detection always happens in finite time.
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 now a professor in the Electrical and Computer Engineering Department and 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 2002 IFAC Young Author Prize and the 2007 Donald P. Eckman Award. He delivered a plenary lecture at the 2008 American Control Conference. He has served as Associate Editor for the journals IEEE Transactions on Automatic Control and Mathematics of Control, Signals, and Systems. He is a fellow of IEEE since 2013 and of IFAC since 2016.