Speaker Daniel Liberzon (University of Illinois, Urbana Champaign)
Place Building 133 Room 204
May 26 (Fri) 16:00~17:00
Nonlinear Control with Limited Information
We discuss nonlinear control problems in which the flow of information between the plant and the controller is limited. Specific focus is on such effects as quantization, time delays, and external disturbances. Our main technical tools are input-to-state stability, Lyapunov functions, and hybrid systems. The overall goal is to build a general theoretical framework for capturing the interplay between control and communication in the context of nonlinear control systems.
May 30 (Tues) 16:00~17:00
Entropy and minimal data rates for state estimation and model detection
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. Ongoing work on entropy of switched systems will also be briefly discussed.
June 2 (Fri) 16:00~17:00
Nonlinear observers robust to measurement errors and their applications in control and synchronization
In this talk we address the problem of designing nonlinear observers that provide robustness to output measurement errors. Our approach is based on the recently introduced concept of quasi-Disturbance-to-Error Stable (qDES) observer. In essence, an observer is qDES if its error dynamics are input-to-state stable (ISS) with respect to the disturbance as long as the plant’s control input and state remain bounded. Lyapunov-based sufficient conditions for checking the qDES property are related to an “asymptotic ratio” characterization of ISS which is of interest in its own right. When combined with a state feedback law robust to state estimation errors in the ISS sense, a qDES observer can be used to achieve output feedback control design with robustness to measurement disturbances. As an illustration of this idea, we treat a problem of stabilization by quantized output feedback. Applications to synchronization of electric power generators and of chaotic systems in the presence of measurement errors will also be presented.
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).
