Simulation Based Computation of Certificates for Safety of Hybrid Dynamical Systems

In this paper, we present an algorithm for synthesizing certificates for safety of continuous time dynamical systems, so-called barrier certificates. Unlike the usual approach of using constraint solvers to compute the certificate from the system dynamics, we synthesize the certificate from system simulations. This makes the algorithm applicable even in cases where the dynamics is either not explicitly available, or too complicated to be analyzed by constraint solvers, for example, due to the presence of transcendental function symbols. The algorithm itself allows the usage of heuristic techniques in which case it does not formally guarantee correctness of the result. However, in cases that do allow rigorous constraint solving, the computed barrier certificate can be rigorously verified, if desired. Hence, in such cases, our algorithm reduces the problem of finding a barrier certificate to the problem of formally verifying a given barrier certificate.