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We study the verification problem for closed-loop dynamical systems withneural-network controllers (NNCS). This problem is commonly reduced tocomputing the set of reachable states. When considering dynamical systems andneural networks in isolation, there exist precise approaches for that taskbased on set representations respectively called Taylor models and zonotopes.However, the combination of these approaches to NNCS is non-trivial because,when converting between the set representations, dependency information getslost in each control cycle and the accumulated approximation error quicklyrenders the result useless. We present an algorithm to chain approaches basedon Taylor models and zonotopes, yielding a precise reachability algorithm forNNCS. Because the algorithm only acts at the interface of the isolatedapproaches, it is applicable to general dynamical systems and neural networksand can benefit from future advances in these areas. Our implementationdelivers state-of-the-art performance and is the first to successfully analyzeall benchmark problems of an annual reachability competition for NNCS.

Verification of Neural-Network Control Systems by Integrating Taylor Models and Zonotopes