Reachability analysis for hybrid systems with nonlinear guard sets

Reachability analysis is one of the most important methods for formal verification of hybrid systems. The main difficulty for hybrid system reachability analysis is to calculate the intersection between reachable set and guard sets. While there exist several approaches for guard sets defined by hyperplanes or polytopes, only few methods are able to handle nonlinear guard sets. In this work we present a novel approach to tightly enclose the intersections of reachable sets with nonlinear guard sets. One major advantage of our method is its polynomial complexity with respect to the system dimension, which makes it applicable for high-dimensional systems. Furthermore, our approach can be combined with different reachability algorithms for continuous systems due to its modular design. We demonstrate the advantages of our novel approach compared to existing methods with numerical examples.