Backward Reachability Analysis of Neural Feedback Systems Using Hybrid Zonotopes

Abstract

The proliferation of neural networks in safetycritical applications necessitates the development of effective methods to ensure their safety. This letter presents a novel approach for computing the exact backward reachable sets of neural feedback systems based on hybrid zonotopes. It is shown that the input-output relationship imposed by a ReLUactivated neural network can be exactly described by a hybrid zonotope-represented graph set. Based on that, the one-step exact backward reachable set of a neural feedback system is computed as a hybrid zonotope in the closed form. In addition, a necessary and sufficient condition is formulated as a mixedinteger linear program to certify whether the trajectories of a neural feedback system can avoid unsafe regions in finite time. Numerical examples are provided to demonstrate the efficiency of the proposed approach.