Robust linear matrix inequality-based model predictive control with recursive estimation of the uncertainty polytope

The present work is concerned with the recursive estimation of the uncertainty polytope in a robust model predictive control (RMPC) framework. For this purpose, the unknown but bounded error method is employed to update the uncertainty polytope on the basis of sensor measurements at each sampling period. The recursive feasibility and asymptotic stability properties of the proposed approach are demonstrated as an extension of previous results concerning the RMPC formulation. For illustration, a simulated example involving an angular positioning system is presented. The results show that the proposed scheme provides a performance improvement, as indicated by the resulting cost function values.