22 Junho 2007, 11:08 - Pedro Flores Correia
"Stochastic hybrid systems and their applications to networks and biology"
João Hespanha, University of California Santa Barbara
Date: Friday 22/06/2007,
Place: North Tower, Amphitheater EA5
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.
Short biography: João Hespanha received the Licenciatura in electrical and computer
engineering from the Instituto Superior Tecnico, 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. 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 s
ystems); 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, and the 2005 Automatica Theory/Methodology
best paper prize.