Stabilizing Model Predictive Control Based on Flexible Set-Membership Constraints

This paper presents a stabilizing Model Predictive Control (MPC) algorithm based on the off-line computation of a sequence of 1-step controllable sets and a condition that enables flexible, non-monotone convergence towards a suitably chosen terminal set. Such an off-line computed sequence of sets leads to a large region where the MPC algorithm is feasible, regardless of the length of the prediction horizon, while the non-monotone convergence condition is used to improve performance. Both stability and recursive feasibility are guaranteed by construction. The benefits of such an approach are shown in illustrative examples.