Efficient min-max MPC: Achieving a large domain of attraction with short horizon

This article considers the regulation problem of a constrained linear system with bounded disturbance. The objective is to overcome the offline and online problems of the standard dual-mode min-max model predictive control (MPC). The offline problem is related to the construction of a polyhedral terminal set, which is prohibitively complex especially for high order systems. We propose to replace the polyhedral set with the ellipsoidal one, which is much easier to construct. The online problem is related to the computational burden, which grows exponentially with the prediction horizon N$$ N $$. We show how to employ a new terminal cost function, that results in a new min-max MPC with a large domain of attraction even with N=0$$ N=0 $$ or N=1$$ N=1 $$. Hence the computational complexity is drastically reduced. Two numerical examples with comparison to earlier solutions from the literature illustrate the effectiveness of the proposed approach.