Adaptive Cooperative Control for Virtually-coupled Trains with Time-varying Parameters

This paper presents an adaptive cooperative control framework for virtually-coupled trains operating under time-varying resistance parameters. The proposed methodology integrates real-time parameter identification through a dynamically adjusted adaptive estimation law, establishing a novel control architecture for multiple-train virtual coupling systems. The study initiates by developing a comprehensive multiple-train dynamic model that explicitly incorporates time-varying running resistances. Leveraging Lyapunov stability theory, adaptive parameter update laws are given, enabling precise dynamic tracking against time-varying resistance parameters. These identified parameters are subsequently incorporated into multiple-train tracking spacing error dynamics, yielding an anti-disturbance cooperative control algorithm. In order to enhance system robustness, bounded constraints for unknown time-varying parameters are introduced and a composite Lyapunov function is constructed incorporating these parameter boundaries. Theoretical analysis based on Lyapunov’s stability theorem rigorously proves the asymptotic stability of the multiple-train virtually-coupled formation. Simulation studies demonstrate the designed controller’s effectiveness in maintaining steady formation against time-varying parameters and disturbances.