Abstract:

This paper considers the formulation and implementation of model predictive control (MPC) laws with cost functions defined as Minkowski functions of convex, compact sets. We propose constructive procedures for selecting stabilizing terminal elements based on a λ-contractive set. In addition, we describe a set-based implementation of the exact MPC policy based on constrained zonotopes and a suboptimal MPC policy based on a polytopic set approximation. Our numerical simulations demonstrate that the proposed suboptimal set- based policy achieves performance comparable to the standard trajectory-based optimal control formulation, while requiring less computational effort for low-dimensional systems.