Zonotope bundles for the efficient computation of reachable sets
Matthias Althoff, Bruce H. Krogh · 2011
We introduce zonotope bundles for computing the set of states reachable by a dynamical system, also known as the reachable set. Reachable set computations suffer from the curse of dimensionality, which has been successfully addressed by using zonotopes for linear systems. However, zonotopes are not closed under intersection leading to challenges when applying them to nonlinear and hybrid problems. We introduce zonotope bundles as the intersection of zonotopes (without explicitly computing the intersection). Zonotope bundles are closed under intersection, while inheriting many positive properties of zonotopes. This is demonstrated for linear, nonlinear, and hybrid systems. A further property of zonotope bundles is that their computation can be easily parallelized.