A Toolbox of Hamilton-Jacobi Solvers for Analysis of Nondeterministic Continuous and Hybrid Systems

Submitted to HSCC 2005. Please do not redistribute 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 systems 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.