Why Should I Care About Stochastic Hybrid Systems?
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Lecture Details
João P. Hespanha received the Licenciatura in electrical and computer engineering from the Instituto Superior Técnico, Lisbon, Portugal in 1991 and the Ph.D. degree in electrical engineering and applied science from Yale University, New Haven, Connecticut in 1998. From 1999 to 2001, he was Assistant Professor at the University of Southern California, Los Angeles. He moved to the University of California, Santa Barbara in 2002, where he currently holds a Professor position with the Department of Electrical and Computer Engineering. Prof. Hespanha is Associate Director for the Center for Control, Dynamical-systems, and Computation (CCDC), Vice-Chair of the Department of Electrical and Computer Engineering, and a member of the Executive Committee for the Institute for Collaborative Biotechnologies (ICB). From 2004—2007 he was an associate editor for the IEEE Transactions on Automatic Control.
His current 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; and stochastic modeling in biology.
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, the 2006 George S. Axelby Outstanding Paper Award, and the 2009 Ruberti Young Researcher Prize. Dr. Hespanha is a Fellow of the IEEE and an IEEE distinguished lecturer since 2007.
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, in SHSs the rate at which transitions occur depends on both the continuous and the discrete states of the hybrid system. The combination of continuous dynamics, discrete events, and stochasticity results in a modeling framework with tremendous expressive power, making SHSs appropriate to describe the dynamics of a wide variety of systems. This observation has been the driving force behind the several recent research efforts aimed at developing tools to analyze these systems.
In this talk, we use several examples to illustrate the use of SHSs as a versatile modeling tool to describe dynamical systems that arise in distributed control and estimation, networked control systems, molecular biology, and ecology. In parallel, we will also discuss several mathematical tools that can be used to analyze such systems, including the use of the extended generator, Lyapunov-based arguments, infinite-dimensional moment dynamics, and finite-dimensional truncations.