Virtual coupling train following control using high order control barrier functions

Virtual Coupling (VC) has gained increasing attention as a next-generation railway signaling solution. Its implementation, however, poses critical control challenges, as following trains must maintain small inter-train spacing under dynamic operating conditions. This paper proposes a decentralized control framework for VC followers, where safety is defined by the relative braking distance (RBD) principle and enforced through High Order Control Barrier Functions (HOCBFs). An adaptive switching heuristic is introduced to compute the reference control force while accounting for potential Train-to-Train (T2T) communication delays. The HOCBF constraints and reference control are embedded into a sequence of Quadratic Programs (QPs) solvable in real time. The proposed method guarantees safety for VC followers without requiring centralized coordination or full trajectory prediction of the preceding trains.