Adaptive reachability algorithms for nonlinear systems using abstraction error analysis

Robust Successor and Precursor Sets of Hybrid Systems Using Hybrid Zonotopes

“…A fundamental challenge of reachability analysis is that a given set representation and its operations can only achieve efficient computation of exact successor sets for a limited class of systems [29]. To obtain formal guarantees for broader system classes, over-approximations of successor sets are often computed instead [30]. To this end, Corollary 3 extends the previous results by first considering the affect of using overapproximations of sets on the right side of the identities in ( 6), ( 8), (9), and (13).…”

“…The over-approximated reachable sets up to R 3 are plotted in Figure 6(a), overlaid by exact closed-loop trajectories found by randomly sampling points in X 0 and propagating using (30). Examination of the exact trajectories suggests that a successful nonconvex over-approximation of the reachable sets is achieved.…”

ARCH-COMP23 Category Report: Continuous and Hybrid Systems with Nonlinear Dynamics

“…Settings for CORA. For the smaller initial sets W = 0.01 and W = 0.05, we applied an adaptively-tuned linearization algorithm [45], whereas the larger initial set W = 0.1 required a polynomialization algorithm, where we again used the adaptively-tuned version from [45].…”

“…• The algorithms [10] and [5] for nonlinear continuous-time systems used in CORA have recently been extended by adaptive parameter tuning [45]. This year, the novel fullyautomated algorithm was used for the LALO20 and ROBE21 benchmarks.…”

“…Settings for CORA. In all cases, we used the approach from [45], which adaptively tunes all algorithm parameters during runtime.…”