Reachability Analysis of Neural Network Control Systems

Neural network controllers (NNCs) have shown great promise in autonomous and cyber-physical systems. Despite the various verification approaches for neural networks, safety analysis of NNCs remains an open problem. Existing control systems (NNCSs) either can only work on a limited type activation functions, or result non-trivial over-approximation errors with time evolving. This paper proposes framework NNCS based Lipschitzian optimisation, called DeepNNC. We first prove Lipschitz continuity closed-loop NNCSs by unrolling eliminating loops. then reveal working principles applying optimisation illustrate it verifying adaptive cruise model. Compared to state-of-the-art approaches, DeepNNC shows superior performance terms efficiency accuracy over wide range NNCs. also provide case study demonstrate capability handle real-world, practical, complex system. Our tool is available at https://github.com/TrustAI/DeepNNC.