Safety Verification of Neural Feedback Systems Based on Constrained Zonotopes

Abstract

Artificial neural networks (ANNs) have been utilized in many feedback control systems and introduced new challenges regarding the safety of the system. This paper considers the problem of verifying whether the trajectories of a system with a feedforward neural network (FNN) controller can avoid unsafe regions, using a constrained zonotope-based reachability analysis approach. FNNs with the rectified linear unit activation function are considered in this work. A novel set-based method is proposed to compute both exact and overapproximated reachable sets for linear discrete-time systems with FNN controllers, and linear program-based sufficient conditions are presented to certify the safety of the neural feedback systems. Reachability analysis and safety verification for neural feedback systems with nonlinear models are also considered. The computational efficiency and accuracy of the proposed method are demonstrated by two numerical examples where a comparison with state-of-the-art methods is also provided.