Robust Cooperative Control for Heavy-Haul Group Trains via Tube-MPC Considering Wheel–Rail Adhesion

Heavy-haul railways are mainly located in mountainous regions, where wheel–rail adhesion is susceptible to variations in rail-surface conditions, posing challenges to the cooperative operation control of heavy-haul group trains (HHGTs). This paper develops an adhesion-dependent Tube-based model predictive control (Tube-MPC) method for HHGTs by incorporating adhesion conditions into disturbance set construction, robust error Tube design, and nominal constraint tightening. A control-oriented longitudinal dynamics model retaining position-dependent gradient resistance is established to describe the motion of heavy-haul trains. Adhesion-dependent limits on traction and braking forces are imposed as input constraints, while adhesion uncertainty is modeled as a bounded equivalent acceleration disturbance arising from adhesion-induced force mismatch. An ancillary feedback controller is employed to regulate actual-nominal state deviations and ensure robust constraint satisfaction. Simulations are conducted using parameters of approximately 5000 t heavy-haul trains and a real railway gradient profile under dry, wet, and rainy or snowy rail-surface conditions. The results demonstrate that, when the actual disturbance remains within the design bound, the trajectories of all following trains remain within the error Tube. Compared with PID and standard MPC, the proposed approach improves speed coordination and spacing regulation, indicating its effectiveness for the cooperative operation of HHGTs under complex wheel–rail adhesion conditions.