A toolbox of hamilton-jacobi solvers for analysis of nondeterministic continuous and hybrid systems

Authors:
Ian M. Mitchell;Jeremy A. Templeton
Affiliations:
Department of Computer Science, University of British Columbia, Vancouver, BC, Canada;Department of Mechanical Engineering, Stanford University, Stanford, CA
Venue:
HSCC'05 Proceedings of the 8th international conference on Hybrid Systems: computation and control
Year:
2005

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Abstract

Hamilton-Jacobi partial differential equations have many applications in the analysis of nondeterministic continuous and hybrid systems. Unfortunately, analytic solutions are seldom available and numerical approximation requires a great deal of programming infrastructure. In this paper we describe the first publicly available toolbox for approximating the solution of such equations, and discuss three examples of how these equations can be used in system analysis: cost to go, stochastic differential games, and stochastic hybrid systems. For each example we briefly summarize the relevant theory, describe the toolbox implementation, and provide results.