Probabilistic safety verification of stochastic hybrid systems using barrier certificates

The problem of probabilistic safety verification of stochastic hybrid systems is to check whether the probability that a given system will reach an unsafe region from certain initial states can be bounded by some given probability threshold. The paper considers stochastic hybrid systems where the behavior is governed by polynomial equalities and inequalities, as for usual hybrid systems, but the initial states follow some stochastic distributions. It proposes a new barrier certificate based method for probabilistic safety verification which guarantees the absolute safety in a infinite time horizon that is beyond the reach of existing techniques using either statistical model checking or probabilistic reachable set computation. It also gives a novel computational approach, by building and solving a constrained optimization problem coming from verification conditions of barrier certificates, to compute the lower bound on safety probabilities which can be compared with the given threshold. Experimental evidence is provided demonstrating the applicability of our approach on several benchmarks.