Cooperative Control of Virtual Coupled High-Speed Trains with the Consideration of Ride Comfort: A Distributed Tube-Based Model Predictive Control Approach

In this work, a distributed tube-based model predictive control (TMPC) method is proposed to address the cooperative control of virtual coupled high-speed trains (HSTs), which ensures the ride comfort of passengers. Firstly, a nonlinear MPC scheme is developed based on the train nominal dynamics to address the cooperative operation among multiple HSTs with different initial states. Especially, the constraints related to the passenger comfort, including the acceleration and the acceleration change rate, are transformed into the input and the input increment constraints of the MPC respectively, which ensures the ride comfort of the HSTs. Subsequently, the recursive feasibility and stability of the MPC are proved theoretically. Secondly, an auxiliary feedback controller is devised based on the actual train dynamics of the train to deal with the external disturbances while improving the operational stability. The auxiliary feedback controller, comprising a discrete-time sliding mode control (DSMC) and a discrete-time disturbance observer (DTDO), utilizes the optimal state sequences generated by the nonlinear MPC as a reference for the feedback control. Additionally, the stability of the auxiliary feedback controller is strictly proved. Finally, the effectiveness of the proposed distributed TMPC is verified through simulations.