Probabilistic regulation in stochastic hybrid systems subject to safety constraints

A dynamic programming-based solution to the problem of maximizing the probability of attaining a target set before hitting a cemetery set for stochastic hybrid systems is presented in this article. Under mild hypotheses we establish that there exists a deterministic stationary policy that achieves the maximum value of the aforesaid probability. We demonstrate how this probability can be recast as the maximization of an expected total reward until the first hitting time to either the target or the cemetery set.