Dr. Teel, Andrew
Department of Electrical and Computer Engineering
University of California, Santa Barbara
Seminar Information
This talk presents results on stochastic approximations of hybrid dynamical systems. It starts with an overview of hybrid systems. These systems involve state variables that sometimes change continuously and sometimes jump. The solutions to a hybrid system are subject to the interplay of the system’s flow set, flow map, jump set, and jump map. In the context of this talk, a stochastic approximation of a hybrid system is one where an iterative algorithm replicates, approximately and in average or expected value, the effect of the continuous-time flow map on the flow set. For simplicity, the talk focuses on the case where the flow set and jump set are bounded. For the case of compact time domains, under appropriate assumptions each solution of the stochastic approximation is close, almost surely, to some solution of the original hybrid system. Similar results can be established for closeness with high probability. For the case of unbounded time domains, under appropriate assumptions almost every sample path of each solution of the stochastic approximation converges to the Omega-limit set of the original hybrid system. These assertions are enabled by robustness results for hybrid systems that have been established over the last two decades. An extremum-seeking example for a system with mode switching is used to illustrate the utility of the stochastic approximation framework for hybrid systems.
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. In 2020, he and his co-authors received the HSCC Test-of-Time Award. He is Editor-in-Chief for Automatica, and a Fellow of the IEEE and of IFAC.