Robust Model Predictive Tracking Control for Constrained Systems With Input Delays and Polytopic Uncertainties

Abstract

This paper considers constrained systems subject to input delays, polytopic uncertainties, and external disturbances, focusing on the core challenge of accurate set‐point tracking and robustness. A robust model predictive tracking control scheme is proposed to address these issues. First, to meet the set‐point tracking requirements of multiple outputs, an augmented state‐space model incorporating state increments and tracking errors is introduced, transforming the original system's tracking control problem into a robust stabilization problem for the augmented system. Next, a state feedback predictive controller is designed. In this case, a worst‐case performance objective function is defined, and a corresponding minimax optimization problem is constructed. The resulting auxiliary problem is then solved via the cone complementarity linearization (CCL) algorithm to handle non‐convex constraints and obtain the controller gain. Finally, a case study of an islanded DC microgrid with two distributed generation units is conducted via simulation. The method achieves set‐point tracking and disturbance rejection of voltage, which verifies its effectiveness.