Safety prescribed performance control of virtually-coupled trains with multifold kinematic targets and switching constraints.

Virtual coupling (VC), aimed at achieving closer tracking distances and facilitating flexible train formations, has become an efficacious trend for alleviating the increasing demand for transportation capacity as the continuous advancement of urbanization. This paper investigates safety prescribed performance control (SPPC) for VC trains with multifold kinematic targets and switching constraints (SCs). In comparison to traditional continuous PPC methods, SPPC strategy incorporating discontinuous characteristics is designed to ensure that position and speed errors of VC train formation remain within the maximum overshoot limit within a finite time after the mutation of tracking target. It is achieved by separating the analysis of continuous intervals and discontinuous impulsive points, which ensures the stable properties of the closed-loop system through utilizing the Lyapunov method and strict mathematical justification. To ensure the safe train operation, multiple kinematic targets are considered throughout the entire process, from un-formation to final cooperative VC formation. To avoid the occurrence of unstable switching before the completion of the formation, the monitor output for the mode partition is made subject to the joint effect of position and speed targets. By imposing a minimum dwell time constraint, the train's real-time running state does not switch frequently within a single mode, which eliminates the Zeno phenomenon. Finally, based on implementing several scenarios for multi-train VC formation adhering to SCs, and incorporating the sample data sourced from the high-speed G1 train traversing from Beijing South Railway Station (BSRS) to Jinan West Railway Station (JWRS), the effectiveness of mode partition and the theoretical results in train operations are verified in numerical simulations.