Min–max tracking model predictive control for linear parameter‐varying systems using polyhedral invariant sets

Abstract In this paper, a min–max tracking model predictive control (MPC) method for linear parameter‐varying (LPV) systems using polyhedral invariant sets is proposed. The method aims to expand the error state stabilizable domain and improve dynamic performance while handling asymmetric system constraints and guaranteeing robust stability under parameter uncertainty, with low computational burden. Firstly, the augmented dynamic formulation is constructed based on the original state‐space model and reference trajectory dynamic model to obtain the tracking error state. Secondly, a min–max optimization problem considering parameter variation and system constraints is formulated based on the tracking error state. Thirdly, a sequence of optimal control laws is offline obtained by solving the optimization problem to design the nested corresponding polyhedral invariant sets. These sets have a larger error state stabilizable domain than ellipsoidal invariant sets. An interpolation method is applied to improve dynamic tracking performance during online control. Finally, the simulation results and comparative analysis substantiate the effectiveness of the proposed min–max tracking MPC method.