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In this paper, we present an algorithm for synthesizingcertificates---so-called barrier certificates---for safety of hybrid dynamicalsystems. Unlike the usual approach of using constraint solvers to compute thecertificate from the system dynamics, we synthesize the certificate from systemsimulations. This makes the algorithm applicable even in cases where thedynamics is either not explicitly available, or too complicated to be analyzedby constraint solvers, for example, due to the presence of transcendentalfunction symbols.  The algorithm itself allows the usage of heuristic techniques in which caseit does not formally guarantee correctness of the result. However, in casesthat do allow rigorous constraint solving, the computed barrier certificate canbe rigorously verified, if desired. Hence, in such cases, our algorithm reducesthe problem of finding a barrier certificate to the problem of formallyverifying a given barrier certificate.

Simulation Based Computation of Certificates for Safety of Hybrid Dynamical Systems