Combining zonotopes and support functions for efficient reachability analysis of linear systems

Abstract

Reachability analysis is an important technique for formally verifying continuous systems, as well as for guaranteed state estimation, stability analysis, and controller synthesis. We present a detailed assessment of the computational efficiency for the reachability analysis of linear systems with respect to the two most scalable set representations: zonotopes and support functions. As a result, we propose representing reachable sets as a combination of support functions and zonotopes. This mix of representations can be converted to polyhedra of desired (directional) precision, at a higher precision compared to exclusively using support functions or zonotopes. The benefits are shown by an in-depth analysis of computational complexity and by numerical experiments.