Hybrid dynamical systems and feedback control
The potency of feedback control is enhanced by using algorithms that combine classical dynamic elements with logic states that facilitate decision-making capabilities. The resulting closed-loop system is a hybrid dynamical system, one in which the overall state changes continuously in some regions of the state space and changes instantaneously at other points. Additional examples of hybrid systems include mechanical systems with impacts and electrical circuits with impulsive behavior. Hybrid dynamical systems have been studied extensively for over twenty years, although until recently little attention has been given to issues related to robustness, a crucial property for engineered hybrid control systems where robustness to modeling errors and measurement noise is paramount. Over the last five years, significant progress has been made for hybrid systems on stability analysis tools and robustness results that parallel what is available for differential and difference equations. In this lecture, some of these tools and results will be described and their impact on control design will be illustrated. Most of the material is presented at a introductory level so that no familiarity with hybrid systems is needed to understand the main points.
Andrew R. Teel received the A.B. degree in engineering sciences from Dartmouth College in 1987, and the M.S. and Ph.D. degrees in electrical engineering from the University of California, Berkeley, in 1989 and 1992, respectively. After receiving the Ph.D., he was a postdoctoral fellow at the Ecole des Mines de Paris in Fontainebleau, France. From 1992 to 1997 he was a faculty member in the Electrical Engineering Department at the University of Minnesota. In 1997, he joined the faculty of the Electrical and Computer Engineering Department at the University of California, Santa Barbara, where he is currently a professor. 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 the 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. He is a Fellow of the IEEE and the International Federation of Automatic Control.