Robust Model Predictive Control Strategy for Virtually Coupled Train Sets Using Time-Varying Tubes

Advanced Virtual Coupling (VC) technology can improve rail transit capacity by reducing train spacing. Due to the inevitable time-varying uncertainties of tunnel resistance and other disturbances, it is a great challenge to design an optimal controller for Virtually Coupled Train Set (VCTS), especially considering safety constraints and less conservative control performance. To overcome these problems, this paper proposes a novel robust Model Predictive Control (MPC) strategy for VCTS based on time-varying tubes, which is different from the existing methods based on fixed size tubes. First, the VCTS system is modeled considering complex constraints and bounded disturbances. Secondly, on the basis of analyzing the influence of disturbances, the optimal control problem is constructed by using time-varying tubes for constraints tightening. Furthermore, a distributed robust MPC algorithm is proposed to realize cooperative operation control, and its recursive feasibility and input-to-state stability are proved. Finally, numerical simulations are provided to show that the time-varying tubes can obtain a larger feasible domain of the optimal control problem than the fixed size tubes, which is conducive to reducing the conservativeness of controller, and the proposed algorithm can deal with disturbances effectively.