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Simulation Based Computation of Certificates for Safety of Hybrid Dynamical Systems
In this paper, we present an algorithm for synthesizing
certificates---so-called barrier certificates---for safety of hybrid dynamical
systems. 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