  We study the verification problem for closed-loop dynamical systems with
neural-network controllers (NNCS). This problem is commonly reduced to
computing the set of reachable states. When considering dynamical systems and
neural networks in isolation, there exist precise approaches for that task
based 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 gets
lost in each control cycle and the accumulated approximation error quickly
renders the result useless. We present an algorithm to chain approaches based
on Taylor models and zonotopes, yielding a precise reachability algorithm for
NNCS. Because the algorithm only acts at the interface of the isolated
approaches, it is applicable to general dynamical systems and neural networks
and can benefit from future advances in these areas. Our implementation
delivers state-of-the-art performance and is the first to successfully analyze
all benchmark problems of an annual reachability competition for NNCS.
