Abstract:

We discuss modeling and analysis for a class of stochastic hybrid systems with random-in-time jumps.    In particular, we present natural Lyapunov-based sufficient conditions for asymptotic stability in probability and for an alternative property called recurrence.

We consider models that admit not necessarily unique flows or jumps. In this setting, we emphasize that the solutions must depend causally on the random inputs that affect solutions.  Otherwise, Lyapunov functions may fail to be sufficient for establishing stability properties.  After discussing general models, we show how the analysis results can be used in two different settings.  The first application involves certifying the behavior of control systems where the control signal is updated at random times; this situation is in contrast to the situation where control signal updates are triggered by events or are periodic.  The second application involves certifying the behavior of algorithms that set tolls in societal systems to induce optimal behavior, in the setting where actors in the society exhibit random behavior.

Bio:

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 Distinguished Professor and director of the Center for Control, Dynamical systems, and Computation.  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.  In 2016, he received the Certificate of Excellent Achievements from the IFAC Technical Committee on Nonlinear Control Systems.  He is Editor-in-Chief for Automatica, and a Fellow of the IEEE and of IFAC.