Verifying Stochastic Hybrid Systems with Temporal Logic Specifications via Model Reduction

We present a scalable methodology to verify stochastic hybrid systems for inequality linear temporal logic (iLTL) or inequality metric interval temporal logic (iMITL). Using the Mori–Zwanzig reduction method, we construct a finite-state Markov chain reduction of a given stochastic hybrid system and prove that this reduced Markov chain is approximately equivalent to the original system in a distributional sense. Approximate equivalence of the stochastic hybrid system and its Markov chain reduction means that analyzing the Markov chain with respect to a suitably strengthened property allows us to conclude whether the original stochastic hybrid system meets its temporal logic specifications. Based on this, we propose the first statistical model checking algorithms to verify stochastic hybrid systems against correctness properties, expressed in iLTL or iMITL. The scalability of the proposed algorithms is demonstrated by a case study.