Complete Robust Hybrid Systems Reachability

This paper introduces robust differential dynamic logic (a fragment of differential dynamic logic) to specify and reason about robust hybrid systems. By small, natural, and practically meaningful syntactic restrictions, specifications are ensured (by construction) to be topologically open and, thus, robust with respect to infinitesimal perturbations without explicit quantitative margins of error in the syntax or in proofs. The main result is a proof of absolute completeness of robust differential dynamic logic for reachability properties of general hybrid systems. The proof is constructive, self-contained, and demonstrates how robustly-correct hybrid systems reachability specifications can be automatically verified through proof.