Cooperative Event-Triggered Self-Stretched Feedback Control for Multiple Trains Subject to Safety Constraints

This paper addresses the cooperative control of multiple high-speed trains, accounting for parametric uncertainties, with a particular focus on ensuring a safe train tracking distance. The cooperative control problem is first reformulated as an unconstrained stabilization problem for a nonlinear control system using the prescribed performance control technique, which is constrained by safety constraints on the train position and speed. To address the parametric uncertainties arising from the complex operational environment of trains, a neural network-based estimation method is constructed, and a novel adaptive update strategy for the neural network is subsequently devised. An event-triggered distributed control approach is formulated for each train, which allows cooperative operation, enabling the multi-train system to follow a predefined speed profile without encountering input saturation, and the system to reach a state consensus without triggering emergency braking. Specifically, the distributed control laws integrate the integral terminal sliding mode control technique and a novel self-stretched gain feedback control technique to ensure a rapid adjustment process of the train status. To demonstrate the feasibility, effectiveness and merits of the proposed methodology, the results are rigorously analyzed theoretically and numerical experiments are performed.