Step Simulation/Overapproximation-Based Verification of Nonlinear Deterministic Hybrid System with Inputs

Abstract

We present a simulation-based verification framework for hybrid systems modeled by a subclass of non-linear hybrid automata with inputs. The motivation for using simulation in verification is to obtain information of the system behavior without finding the (usually non-existing or costly-to-get) analytical solution of the system dynamics. The initial state set and input set are partitioned into classes, members of which possess similar behaviors, generating similar simulation traces. In this paper, we give the formula to compute the propagation of error as the simulation proceeds as a function of simulation step error, perturbation of initial state and input. Bounded tube segments are then constructed for each consecutive step based on the error bounds to overapproximate the reachable state set during a specified time interval. A feature of our work, that makes it distinct from prior simulation-based verification works, is that it does not rely on a pre-identified initial partition of initial states/inputs as that would only work under the assumption that the simulations could be done without introducing any perturbations in discrete dynamics. Since there is no way to guarantee this, in our approach, the partitioning is refined in time-steps as needed, yielding a correct approach for simulation-based verification. We developed a prototype tool implementing our algorithms and provided verification results from two benchmarks in this area to show its effectiveness.