Abstract
In this paper, we consider the problem of bounded reachability analysis of probabilistic hybrid systems which model discrete, continuous and probabilistic behaviors. The discrete and probabilistic dynamics are modeled using a finite state Markov decision process (MDP), and the continuous dynamics is incorporated by annotating the states of the MDP with differential equations/inclusions. We focus on polyhedral dynamical systems to model continuous dynamics. Our broad approach for computing probabilistic bounds on reachability consists of the computation of the exact minimum/maximum probability of reachability within k discrete steps in a polyhedral probabilistic hybrid system by reducing it to solving an optimization problem with satisfiability modulo theory (SMT) constraints.
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