Sparse Polynomial Zonotopes: A Novel Set Representation for Reachability Analysis

We introduce sparse polynomial zonotopes, a new set representation for formal verification of hybrid systems. Sparse zonotopes can represent nonconvex sets and are generalizations polytopes, Taylor models. Operations like Minkowski sum, quadratic mapping, reduction the size be computed with complexity w.r.t. dimension system. In particular, reachability analysis nonlinear systems, wrapping effect is substantially reduced using as demonstrated by numerical examples. addition, we significantly reduce computation time compared to when dealing dynamics.