Simulation Based Computation of Certificates for Safety of Hybrid Dynamical Systems
For researchers and engineers verifying safety of hybrid systems with complex or black-box dynamics, this work offers a simulation-based method to obtain barrier certificates, though it is incremental as it builds on existing certificate verification.
The paper presents an algorithm to synthesize barrier certificates for safety verification of hybrid dynamical systems using system simulations instead of constraint solvers, enabling application to systems with complex or unavailable dynamics. The approach can produce certificates that are formally verifiable when rigorous constraint solving is possible.
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.