Hybrid Systems: Computation and Control
Volume 1569 of the series Lecture Notes in Computer Science pp 238255
Computing Controllers for Nonlinear Hybrid Systems
 Claire TomlinAffiliated withDepartment of Aeronautics and Astronautics, Stanford University
 , John LygerosAffiliated withDepartment of Electrical Engineering and Computer Sciences, University of California
 , Shankar SastryAffiliated withDepartment of Electrical Engineering and Computer Sciences, University of California
Abstract
We discuss a procedure for synthesizing controllers for safety specifications for hybrid systems. The procedure depends on the construction of the set of states of a continuous dynamical system that can be driven to a subset of the state space, avoiding another subset of the state space (the ReachAvoid set). We present a new characterization of the ReachAvoid set in terms of the solution of a pair of coupled HamiltonJacobi partial differential equations. We also discuss a computational algorithm for solving such partial differential equations and demonstrate its effectiveness on numerical examples.
 Title
 Computing Controllers for Nonlinear Hybrid Systems
 Book Title
 Hybrid Systems: Computation and Control
 Book Subtitle
 Second International Workshop, HSCC’99 Berg en Dal, The Netherlands, March 29–31, 1999 Proceedings
 Pages
 pp 238255
 Copyright
 1999
 DOI
 10.1007/3540489835_22
 Print ISBN
 9783540657347
 Online ISBN
 9783540489832
 Series Title
 Lecture Notes in Computer Science
 Series Volume
 1569
 Series ISSN
 03029743
 Publisher
 Springer Berlin Heidelberg
 Copyright Holder
 SpringerVerlag Berlin Heidelberg
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 Editors

 Frits W. Vaandrager ^{(4)}
 Jan H. van Schuppen ^{(5)}
 Editor Affiliations

 4. Computing Science Institute, University of Nijmegen
 5. CWI
 Authors

 Claire Tomlin ^{(6)}
 John Lygeros ^{(7)}
 Shankar Sastry ^{(7)}
 Author Affiliations

 6. Department of Aeronautics and Astronautics, Stanford University, Stanford, CA, 943054035
 7. Department of Electrical Engineering and Computer Sciences, University of California, Berkeley, CA, 947201770
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