Multi‐Step Control Set‐Based Nonlinear Model Predictive Control with Persistent Disturbances

A robust model predictive control algorithm is proposed for a constrained nonlinear system with bounded persistent disturbance in this paper. Based on polytopic descriptions that include the initial system, the proposed algorithm computes a series of multi‐step control sets offline and the convex combination of them online respectively by solving convex optimization problems described by a few linear matrix inequalities. At each sampling time, the control moves satisfying the control constraint are obtained and implemented in the system. The controller design is illustrated with two examples. The proposed MPC controller achieves closed‐loop input‐to‐state (practical) stability (ISS/ISpS) and strong robustness in respect of bounded persistent disturbances.