An improved robust model predictive control design in the presence of actuator saturation

A new robust model predictive control (RMPC) design algorithm is proposed for a linear uncertain system with a polytopic description and subject to actuator saturation. This algorithm involves the solution of an infinite horizon LQR problem for the uncertain system in the presence of actuator saturation at each time instant and the implementation of the first element of the resulting optimal control profile. By expressing a saturating linear feedback law on a convex hull of a group of auxiliary linear feedback laws and the actual linear feedback law, the LQR problem can be solved for a group of linear polytopic systems in the absence of saturation, with heavier weighting placed on the system corresponding to the actual linear feedback law. The additional design freedom in choosing the relative weighting on the actual and auxiliary feedback laws allows further improvement of the closed-loop system performance over those resulting from the existing algorithms. A numerical example illustrates the effectiveness of the proposed algorithm.