Formal Verification of Stochastic Systems with ReLU Neural Network Controllers
This addresses safety-critical verification for stochastic systems with neural network controllers, which is important for applications like autonomous vehicles and robotics, representing an incremental improvement over existing methods.
The paper tackles formal safety verification for stochastic cyber-physical systems with ReLU neural network controllers by developing a method to compute tight bounds on safety probabilities using a graph abstraction and Satisfiability Modulo Convex formulation, achieving improved verification results compared to a state-of-the-art scheme in a robot navigation example.
In this work, we address the problem of formal safety verification for stochastic cyber-physical systems (CPS) equipped with ReLU neural network (NN) controllers. Our goal is to find the set of initial states from where, with a predetermined confidence, the system will not reach an unsafe configuration within a specified time horizon. Specifically, we consider discrete-time LTI systems with Gaussian noise, which we abstract by a suitable graph. Then, we formulate a Satisfiability Modulo Convex (SMC) problem to estimate upper bounds on the transition probabilities between nodes in the graph. Using this abstraction, we propose a method to compute tight bounds on the safety probabilities of nodes in this graph, despite possible over-approximations of the transition probabilities between these nodes. Additionally, using the proposed SMC formula, we devise a heuristic method to refine the abstraction of the system in order to further improve the estimated safety bounds. Finally, we corroborate the efficacy of the proposed method with simulation results considering a robot navigation example and comparison against a state-of-the-art verification scheme.