Robust nonlinear MPC without terminal constraint for tracking changing setpoints in the presence of non‐additive unknown disturbance

Abstract

This paper develops a novel robust tracking model predictive control (MPC) without terminal constraint for discrete‐time nonlinear systems capable to deal with changing setpoints and unknown non‐additive bounded disturbances. The MPC scheme without terminal constraint avoids difficult computations for the terminal region and is thus simpler to design and implement. However, the existence of disturbances and/or sudden changes in a setpoint may lead to feasibility and stability issues in this method. In contrast to previous works that considered changing setpoints and/or additive slowly varying disturbance, the proposed method is able to deal with changing setpoints and non‐additive non‐slowly varying disturbance. The key idea is the addition of tightened input and state (tracking error) constraints as new constraints to the tracking MPC scheme without terminal constraints based on artificial references. In the proposed method, the optimal tracking error converges asymptotically to the invariant set for tracking, and the perturbed system tracking error remains in a variable size tube around the optimal tracking error. Closed‐loop input‐to‐state stability and recursive feasibility of the optimization problem for any piece‐wise constant setpoint and non‐additive disturbance are guaranteed by tightening input and state constraints as well as weighting the terminal cost function by an appropriate stabilizing weighting factor. The simulation results of the satellite attitude control system are provided to demonstrate the efficiency of the proposed predictive controller.