Towards a dominant-polytope complexity reduction in explicit MPC

In this paper a complexity reduction method of explicit MPC based on a dominant polytope is proposed. When a partitioning of explicit MPC consists of many small regions and a single big region it is reasonable to expect more frequent call of the control law associated with the big region than another ones during the control performance. Such an organization of the regions favors the online evaluation of explicit MPC. In the paper a problem to find a dominant polytope over the regions that share the same affine control law is studied. The problem of finding maximum volume polytope inscribed in nonconvex area is known as potato peeling problem in the literature. In this paper we focus to find a suboptimal solution by means of stochastic search.