This talk focuses on new results in the area of stochastic hybrid systems. We describe a modeling framework that permits the interaction of jumps and flows, as well as stochastic and adversarial effects in dynamical systems. Due to various sources of non-uniqueness, we call these systems "stochastic hybrid inclusions".   This feature is in contrast to the uniqueness of solutions that is a part of most existing results for stochastic hybrid systems. We give examples of systems that fit into the inclusion framework, describe what is meant by a solution to these systems, and illustrate Lyapunov-based sufficient conditions for various notions of stochastic stability. To pave the way, we first briefly review existing frameworks for stochastic hybrid systems and recent results for non-stochastic hybrid inclusionss.

 

Andrew R. Teel received his A.B. degree in Engineering Sciences from Dartmouth College in Hanover, New Hampshire, in 1987, and his M.S. and Ph.D. degrees in Electrical Engineering from the University of California, Berkeley, in 1989 and 1992, respectively. After receiving his Ph.D., he was a postdoctoral fellow at the Ecole des Mines de Paris in Fontainebleau, France.

 

In 1992, he joined the faculty of the Electrical Engineering Department at the University of Minnesota, where he was an assistant professor until 1997. Subsequently, he joined the faculty of the Electrical and Computer Engineering Department at the University of California, Santa Barbara, where he is currently a professor. His research interests are in nonlinear and hybrid dynamical systems, with a focus on stability analysis and control design.

 

He has received NSF Research Initiation and CAREER Awards, the 1998 IEEE Leon K. Kirchmayer Prize Paper Award, the 1998 George S. Axelby Outstanding Paper Award, and was the recipient of the first SIAM Control and Systems Theory Prize in 1998. He was the recipient of the 1999 Donald P. Eckman Award and the 2001 O. Hugo Schuck Best Paper Award, both given by the American Automatic Control Council, and also received the 2010 IEEE Control Systems Magazine Outstanding Paper Award. He is an area editor for Automatica, and a Fellow of the IEEE and of IFAC.