Robust MPC for tracking changing setpoints in discrete‐time non‐linear systems with non‐additive unknown disturbance

Abstract

This paper develops a novel observer-based robust tracking predictive controller for discrete-time nonlinear affine systems capable of dealing with changing setpoints and non-additive non-slowly varying unknown disturbance with bounded variations. The existence of disturbance and/or sudden changes in a setpoint may lead to feasibility and stability issues in the stabilizing terminal constraint-based MPC. Since robust tracking MPCs usually consider additive disturbance, the recursive feasibility of these methods may be lost in the presence of non-additive non-slowly varying disturbance. The robust tracking MPC presented here extends the artificial reference-based MPC to deal with both changing setpoints and non-additive non-slowly varying disturbance. The key idea is the addition of tightened input and state constraints as new system constraints. The authors also guarantee the boundedness of disturbance observation error and closed-loop tracking error. In this method, the optimal tracking error converges asymptotically to the terminal region, and the perturbed system tracking error remains in a variable size tube around the optimal tracking error. It is shown that the proposed controller can achieve offset-free tracking in the presence of constant disturbance. The simulation results of the satellite attitude control system are provided to demonstrate the efficiency of the proposed predictive controller.