Abstract

This paper investigates cooperative tracking control for virtually coupled multi-train systems subject to nonlinear running resistance, bounded time-varying resistance parameters, state constraints, and actuator saturation. The theoretical contribution is not the separate use of barrier Lyapunov functions, adaptive control, anti-windup compensation, or distributed cooperative control. Instead, the revised analysis establishes a coupled safety-and-boundedness certificate for the actual saturated closed-loop vector field. The closing-speed-aware spacing variable and actuator-authority condition support a first-exit proof of forward invariance, after which a composite Lyapunov analysis couples the saturation residual, anti-windup state, cooperative tracking error, and time-varying parameter-estimation error to establish uniform ultimate boundedness without persistent excitation. This proof architecture distinguishes the proposed controller from recent constrained train-control methods focused separately on velocity/input bounds, distance-oriented full-state barriers, or iteration-indexed learning. Numerical studies with heterogeneous trains, stronger time-varying aerodynamic perturbations, normalized actuator limits, tracking-bound verification, constrained baselines, a near-boundary safety-allocation case, and a quantitative one-factor-at-a-time parameter-sensitivity study are provided.

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