Stochastic Hybrid Systems and their Applications to Networks and Biology

Professor Joåo Hespanha

Department of Electrical and Computer Engineering

University of California, Santa Barbara

Abstract

Hybrid systems combine continuous-time dynamics with discrete modes of operation. The states of such system usually have two distinct components: one that evolves continuously, typically according to a differential equation; and another one that only changes through instantaneous jumps. We present a model for Stochastic Hybrid Systems (SHSs) where transitions between discrete modes are triggered by stochastic events, much like transitions between states of a continuous-time Markov chains. However, the rate at which transitions occur is allowed to depend on both the continuous and the discrete states of the SHS.

Several tools are available to analyze SHSs. Among these, we discuss the use of the extended generator, Lyapunov-based arguments, infinite-dimensional moment dynamics, and finite-dimensional truncations by moment closure. The application of these tools is illustrated in the context of multiple examples. We draw examples from diverse areas such as the modeling of network data traffic under TCP congestion control; the error dynamics in remote state-estimation over networks; and the evolution of the population of molecules undergoing a system of bio-chemical reactions.

Biographical sketch

Joåo P. Hespanha was born in Coimbra, Portugal, in 1968. He received the Licenciatura in electrical and computer engineering from the Instituto Superior TÈcnico, Lisbon, Portugal in 1991 and the Ph.D. degree in electrical engineering and applied science from Yale University, New Haven, Connecticut in 1998, respectively. He currently holds a Professor position with the Department of Electrical and Computer Engineering, the University of California, Santa Barbara. From 1999 to 2001, he was an Assistant Professor at the University of Southern California, Los Angeles. His research interests include hybrid and switched systems; the modeling and control of communication networks; distributed control over communication networks (also known as networked control systems); the use of vision in feedback control; stochastic modeling in biology; and the control of haptic devices.

Dr. Hespanha is the recipient of the Yale University’s Henry Prentiss Becton Graduate Prize for exceptional achievement in research in Engineering and Applied Science, a National Science Foundation CAREER Award, the 2005 best paper award at the 2nd Int. Conf. on Intelligent Sensing and Information Processing, the 2005 Automatica Theory/Methodology best paper prize, and the 2006 George S. Axelby Outstanding Paper Award. Since 2003, he has been an Associate Editor of the IEEE Transactions on Automatic Control.

Friday, April 6. 2007

3:30 – 4:30 p.m.

Rm. 1500 EECS