Nonlinear hybrid reachability using set integration and zonotopic enclosures

The computation of reachable sets for hybrid systems with nonlinear continuous dynamics is addressed. In this context, the computation of the intersection of the reachable set with the guard set is a challenging problem. In a previous work, we have proposed a guaranteed relaxation method expressed as a constraint satisfaction problem to solve the event detection and localization problems underlying flow/guard intersection. The algorithm also relies on bisection operations which may generate a large number of boxes. The main contribution of this paper is to merge the solution domains related to these boxes and corresponding to the reachable set at a given time. An algorithm minimizing the conservatism of a convex enclosure obtained by aggregating several solution domains into one domain is proposed: it relies on a zonotopic representation which is consistent with our continuous reachability approach. The combination of constraint propagation, bisection and merging makes it possible to achieve good algorithm performance, which will be illustrated through a numerical example involving a typical hybrid dynamical system: a bouncing ball with continuous state dimensions up to 4. Our evaluation shows very promising results.