Multiobjective Model Predictive Control for Virtually Coupled Train Set Under Heterogeneous Slopes and Uncertain Dynamics

IoT-based virtual coupling systems enable reduced headways for high-speed trains, yet most Virtually Coupled Train Set (VCTS) studies still rely on a leader-follower paradigm where followers simply match the leader’s speed. Under position-dependent slopes/speed limits, asynchronous departures, and uncertain train dynamics, it remains difficult to jointly achieve traffic efficiency, cooperative tracking accuracy, and ride comfort. This paper proposes a hierarchical multi-objective Model Predictive Control (MPC) framework for follower trains in VCTS with amulti-stepdecision structure consisting of an offline tightening design and an online two-step regulation procedure.Offline, we solve an optimization-based tightening design that jointly determines tightened constraint sets and disturbance-affine feedback gains under Automatic Train Protection (ATP) supervision, improving traffic-efficiency potential by reducing conservatism that can otherwise trigger unnecessary braking actions and degrade throughput.Online, a two-step regulation is executed under uncertainty: first, a tracking-prioritized robust MPC enforces ATP-compliant operation; second, using the resultingoptimal and feasibletracking-cost information consistent with the offline-designed feedback gains, we construct a Lyapunov-based constraint that yields an explicit tracking-cost tolerance bound, within which a comfort-oriented MPC improves ride comfort. A comfort-aware adaptive mechanism then tunes the tolerance online for more consistent tracking-comfort behaviour. The proposed distributed framework is proved to be recursively feasible and input-to-state stable. Simulations on the Beijing-Tianjin high-speed railway line with CR400BF parameters demonstrate that, compared with representative weighted-sum and lexicographic baselines, the proposed method achieves a more reliable tracking-comfort trade-off with less conservative traffic-efficiency performance.