Robust Adaptive Nonlinear MPC for Dynamic Tracking of Heavy-Haul Virtually Coupled Trains

Virtual coupling (VC) enhances heavy-haul railway capacity, yet existing point-mass controllers with fixed safety margins inadequately address internal longitudinal dynamics and fault-induced degradation of safety protection. This study proposes a robust adaptive nonlinear model predictive control (RA-NMPC) framework for virtually coupled heavy-haul trains. By integrating an equivalent multi-mass model with pneumatic-brake delay representation, the framework captures large-inertia longitudinal dynamics while enforcing constraints on train separation, speed, and longitudinal jerk. The controller features online braking adaptation based on prediction residuals, constraint tightening under bounded uncertainty, and fault-driven reconfiguration between Relative Braking Distance (RBD) and Absolute Braking Distance (ABD) safety boundaries. To meet strict real-time requirements, a hybrid IPSO-SQP solver is designed. Benchmark evaluations demonstrate 100% rolling-problem feasibility and a maximum solution time of 140.8 ms, with all solutions completed within the 200 ms control deadline; SQP refinement further reduced the IPSO candidate objective by 27.03% on average. Validation using field data at 20, 60, and 80 km/h shows continuous tracking behavior, with longitudinal jerk remaining within ±0.8 m/s3. These results support the computational efficiency and tracking feasibility of the proposed framework under the evaluated heavy-haul operating conditions.