Reachability Analysis and Simulation of Stochastic Hybrid Systems using an Adaptive Time Step Scheme

Hybrid stochastic methods partition the system into multiple subsets and describe each subset as a different representation, such as a jump Markov, Poisson, continuous Markov, or deterministic process. In these methods, continuous-state models reduce to the analysis of Stochastic Differential Equations (SDEs) for which many mathematical tools and general solution techniques as numerical schemes are available. Therefore there is a need for numerical schemes that are capable of accurately and efficiently integrating systems of SDEs. In this work we introduce a variable size step algorithm and apply it to stochastic hybrid systems.Finally, as an approach for model checking we propose reachability analysis as an optimal stopping problem.

کلیدواژه ها:

Stochastic Hybrid Systems ، Stochastic Hybrid Automata ، Markov processes ، Reachability problem ، Optimal stopping