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Reachability analysis is a formal method to guarantee safety of dynamicalsystems under the influence of uncertainties. A major bottleneck of allreachability algorithms is the requirement to adequately tune certain algorithmparameters such as the time step size, which requires expert knowledge. In thiswork, we solve this issue with a fully-automated reachability algorithm thattunes all algorithm parameters internally such that the reachable set enclosuresatisfies a user-defined accuracy in terms of distance to the exact reachableset. Knowing the distance to the exact reachable set, an inner-approximation ofthe reachable set can be efficiently extracted from the outer-approximationusing the Minkowski difference. Finally, we propose a novel verificationalgorithm that automatically refines the accuracy of the outer- andinner-approximation until specifications given by time-varying safe and unsafesets can either be verified or falsified. The numerical evaluation demonstratesthat our verification algorithm successfully verifies or falsifies benchmarksfrom different domains without any requirement for manual tuning.

Fully-Automated Verification of Linear Systems Using Inner- and Outer-Approximations of Reachable Sets