Guaranteed Overapproximations of Unsafe Sets for Continuous and Hybrid Systems: Solving the Hamilton-Jacobi Equation Using Viability Techniques

Authors:
Alexandre M. Bayen;Eva Crück;Claire Tomlin
Affiliations:
-;-;-
Venue:
HSCC '02 Proceedings of the 5th International Workshop on Hybrid Systems: Computation and Control
Year:
2002

Citing 4
Cited 5

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Abstract

We show how reachable sets of constrained continuous and simple hybrid systems may be computed using the minimum time-to_ reach function. We present an algorithm for computing a discrete approximation to the minimum time-to-reach function, which we prove to be a converging underapproximation to the actual function. We use the discrete minimum time-to-reach function for simple hybrid systems to compute overapproximations of unsafe zones for aircraft in a sector of the Oakland Air Traffic Control Center, leading to the automatic generation of conflict-free aircraft maneuvers.