While reachability analysis is one of the major techniques for formal verification of dynamical systems, the requirement to adequately tune algorithm parameters often prevents its widespread use in practical applications. In this work, we fully automate the verification process for linear time-invariant systems: Based on the computation of tight upper and lower bounds for the support function of the reachable set along a given direction, we present a fully-automated verification algorithm, which is based on iterative refinement of the upper and lower bounds and thus always returns the correct result in decidable cases. While this verification algorithm is particularly well suited for cases where the specifications are represented by halfspace constraints, we extend it to arbitrary convex unsafe sets using the Gilbert-Johnson-Keerthi algorithm. In summary, our automated verifier is applicable to arbitrary convex initial sets, input sets, as well as unsafe sets, can handle time-varying inputs, automatically returns a counterexample in case of a safety violation, and scales to previously unanalyzable high-dimensional state spaces. Our evaluation on several challenging benchmarks shows significant improvements in computational efficiency compared to verification using other state-of-the-art reachability tools.

Reachability analysis fails to produce tight reachable sets if certain algorithm parameters are poorly tuned, such as the time step size or the accuracy of the set representation. The tuning is especially difficult in the context of nonlinear systems where over-approximation errors accumulate over time due to the so-called wrapping effect, often requiring expert knowledge. In order to widen the applicability of reachability analysis for practitioners, we propose the first adaptive parameter tuning approach for reachability analysis of nonlinear continuous systems tuning all algorithm parameters. Our modular approach can be applied to different reachability algorithms as well as various set representations. Finally, an evaluation on numerous benchmark systems shows that the adaptive parameter tuning approach efficiently computes very tight enclosures of reachable sets.