Robust Tube MPC with Multi-step Tracking for Uncertain Constrained Linear Systems

In this paper, an optimal robust tracking scheme is proposed for systems with bounded disturbances. This method uses multi-step reference inputs as decision variables to design the controller and realize model predictive control (MPC) rolling optimization, which makes the optimization scheme more flexible and reduces the burden of the controller to a certain extent. To ensure that the disturbed state converges to the bounded positive invariant set centered on the optimal tracking point, the optimized MPC objective function is designed. Furthermore, it is theoretically shown that the proposed robust tube model predictive control (RTMPC) strategy is recursively feasible under some derived conditions, and the closed-loop system is stable. Finally, a numerical example and comparison study are conducted to illustrate the efficacy of the proposed method.