Coordination and merging for virtual coupling trains at junction: A robust and stable MPC method with virtual pilot injection

Virtual Coupling (VC) technology is expected to increase railway capacity and enable flexible coordinated train formations in complex scenarios. A representative VC operation occurs at track junctions, where trains merge and transition among coupling, coupled, and decoupled states. This paper investigates the problem of integrating the sideline train into mainline virtually coupled train set (VCTS) while maintaining coupling-state continuity, and proposes an MPC-based virtual pilot injection (VPI) strategy. A virtual pilot trajectory is planned, and distributed MPC controllers are designed under a leader–follower information framework to achieve smooth merging and recoupling. Robustness and stability are theoretically established to account for disturbances and unreliable communication. Extensive simulation results demonstrate that, compared with existing methods, the proposed approach significantly reduces the coupling time under both ideal operating conditions and scenarios with disturbances and delays, while maintaining effective safety protection even in extreme cases.