Chapter

Hybrid Systems: Computation and Control

Volume 4416 of the series Lecture Notes in Computer Science pp 4-17

Computational Approaches to Reachability Analysis of Stochastic Hybrid Systems

  • Alessandro AbateAffiliated withUniversity of California, at Berkeley - Berkeley, CA
  • , Saurabh AminAffiliated withUniversity of California, at Berkeley - Berkeley, CA
  • , Maria PrandiniAffiliated withPolitecnico di Milano - Milano
  • , John LygerosAffiliated withETH Zurich - Zurich
  • , Shankar SastryAffiliated withUniversity of California, at Berkeley - Berkeley, CA

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Abstract

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.