Computational Approaches to Reachability Analysis of Stochastic Hybrid Systems

TitleComputational Approaches to Reachability Analysis of Stochastic Hybrid Systems
Publication TypeConference Papers
Year of Publication2007
AuthorsAbate, A., S. Amin, M. Prandini, J. Lygeros, and S. Sastry
EditorBemporad, A., A. Bicchi, and G. Buttazzo
Conference NameHybrid Systems: Computation and Control
PublisherSpringer Berlin Heidelberg
Conference LocationBerlin, Heidelberg
ISBN Number978-3-540-71493-4

This work investigates some of the computational issues involved in the solution of probabilistic reachability problems for discrete-time, controlled stochastic hybrid systems. It is first argued that, under rather weak continuity assumptions on the stochastic kernels that characterize the dynamics of the system, the numerical solution of a discretized version of the probabilistic reachability problem is guaranteed to converge to the optimal one, as the discretization level decreases. With reference to a benchmark problem, it is then discussed how some of the structural properties of the hybrid system under study can be exploited to solve the probabilistic reachability problem more efficiently. Possible techniques that can increase the scale-up potential of the proposed numerical approximation scheme are suggested.