A Multi-step Multi-ellipsoid Approach of the Dynamic Output Feedback MPC

This article considers the dynamic output feedback model predictive control (DOFMPC) for the constrained Takagi-Sugeno (T-S) model with bounded disturbance. Unlike the existing approach where the robust positively invariant set is characterized by a single ellipsoid, we characterize it by the intersection of multiple ellipsoids, each corresponds to a vertex sub-model of the T-S model realization. The previous single ellipsoid is then an inner approximation of the intersection of multiple ellipsoids in this article. Therefore, the performance can be improved. We also generalize the multi-ellipsoid approach to the previous multi-step approach and formulate the so-called multi-step multi-ellipsoid approach in this article, which can further enlarge the feasibility region and enhance the performance. The recursive feasibility and the convergence of the approach are guaranteed. The proposed approaches are compared through a numerical problem to show their effectiveness.