Probabilistic reachability and safe sets computation for discrete time stochastic hybrid systems

In this work probabilistic reachability for controlled discrete time stochastic hybrid systems is investigated. By a suitable formulation of the reachability problem within a stochastic optimal control framework, two complementary interpretations and their corresponding computational techniques are suggested. The results can be of interest for solving safety analysis and control design problems for stochastic hybrid systems, by the computation of maximal probabilistic safe sets and maximally safe policies. They can also be employed to solve regulation problems through the interpretation of the desired operating region for the system as a "safe set". The described methodology is applied to a simple temperature regulation problem