Disturbance Rejection MPC Framework for Input-Affine Nonlinear Systems

This article proposes a novel disturbance rejection model predictive control (DRMPC) framework to improve the robustness of model predictive control (MPC) for a broad class of input-affine nonlinear systems with constraints and state-dependent disturbances. The proposed controller includes two parts - a disturbance compensation input and an optimal MPC control input. The former one is designed to compensate for the matched disturbance actively. This is made possible via a disturbance observer that estimates the disturbance and by adopting a space decomposition method. The residual disturbance is then handled in the MPC optimization problem by appropriate tightening of the constraints and designing the terminal constraint. Under reasonable assumptions, recursive feasibility and regional input-to-state practical stability (regional ISpS) of the closed-loop system are shown. Furthermore, we extend the DRMPC framework toward the tracking problem and apply it to a nonholonomic mobile robot. The performance of the proposed approach is demonstrated by a numerical example of the nonholonomic mobile robot.