Tracking error analysis for multi-train systems under velocity constraints and parameter uncertainties.

This paper investigates the cooperative tracking error for multi-train systems subject to velocity constraints and time-varying resistance parameter uncertainties. A distributed tracking control algorithm, utilizing only relative position measurements between adjacent trains, is proposed to enable all trains to track a desired operational velocity while maintaining a desired formation. To analyze the coupled effects of velocity saturation and parameter uncertainties, we introduce a time-varying scaling factor to handle the saturation nonlinearity, transforming the original system into an equivalent form with a bounded, non-vanishing disturbance term. We rigorously prove ultimate boundedness of the disagreement state, the relative position errors, and the absolute velocity errors. Furthermore, explicit analytical expressions for the corresponding ultimate bounds are derived. Numerical simulations of a multi-train system are presented to validate the effectiveness of the proposed control law and the accuracy of the theoretical error analysis.