Simplification of explicit MPC solutions via inner and outer approximations

The paper proposes to reduce complexity of explicit MPC feedback laws by representing regions over which the law is defined as (possibly non-convex) polygons. Each polygon is then represented only by its boundaries, which reduces the memory footprint of the feedback law. Even though significant amount of memory can be saved this way, the price to be paid is increased computational load associated by performing point location tasks on non-convex objects. To reduce the computational requirements, we therefore propose to devise inner and outer convex approximations of non-convex polygons. Such approximations then allow to perform point location more effectively, leading to reduction of the required on-line computational effort. Several ways to design suitable approximations are presented and efficacy of the proposed procedure is evaluated.