Computational Approaches to Reachability Analysis of Stochastic Hybrid Systems
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.
Unable to display preview. Download preview PDF.
- 2.Abate, A., et al.: Probabilistic Reachability for Safety and Regulation of Controlled Discrete-Time Stochastic Hybrid Systems. In: Proceedings of the 45th IEEE Conference on Decision and Control, San Diego, CA, December 2006, pp. 258–263. IEEE Computer Society Press, Los Alamitos (2006)Google Scholar
- 6.Prandini, M., Hu, J.: Stochastic reachability: Theoretical foundations and numerical approximation. In: Cassandras, C., Lygeros, J. (eds.) Stochastic Hybrid Systems, CRC Press, Boca Raton (2006)Google Scholar
- 7.Fehnker, A., Ivancic, F.: Benchmarks for Hybrid Systems Verifications. In: Alur, R., Pappas, G.J. (eds.) HSCC 2004. LNCS, vol. 2993, pp. 326–341. Springer, Heidelberg (2004)Google Scholar
- 8.Mitchell, I., Templeton, J.: A Toolbox of Hamilton-Jacobi Solvers for Analysis of Nondeterministic Continuous and Hybrid Systems. In: Morari, M., Thiele, L. (eds.) HSCC 2005. LNCS, vol. 3414, pp. 480–494. Springer, Heidelberg (2005)Google Scholar