New Methods for Computing the Terminal Cost for Min-max Model Predictive Control

The aim of this paper is to provide new techniques for computing a terminal cost and a local state-feedback control law that satisfy recently developed min-max MPC input-to-state stabilization conditions. Min-max MPC algorithms based on both quadratic and 1-norms or infin-norms costs are considered. Compared to existing approaches, the proposed techniques can be applied to linear systems affected simultaneously by time-varying parametric uncertainties and additive disturbances. The resulting MPC cost function is continuous, convex and bounded, which is desirable from an optimization point of view. Regarding computational complexity aspects, the developed techniques employ linear matrix inequalities in the case of quadratic MPC cost functions and, norm inequalities in the case of MPC cost functions defined using 1-norms or infin-norms. The effectiveness of the developed methods is illustrated for an active suspension application example.