Safety-Oriented Distance Control for Train Platoon Under Actuator Delays: A Reachability and Hybrid H2/H∞ Framework

Abstract

Train platoon improves railway efficiency by coordinating train speeds and inter-train distances. However, actuator delays pose a major challenge to maintaining safe dynamic spacing. This study develops a safety-oriented framework that integrates hybrid $H_2/H_{\infty }$ control with reachable set estimation to explicitly compute the minimum safe separation under actuator delays. A unified modelling strategy is proposed that incorporates actuator delays together with real-time acceleration disturbances of the leading train. By using forward reachable set analysis, the effect of actuator delays on position errors is estimated and incorporated into the controller to compensate for such delays, thereby improving the safety and robustness of train platoon tracking. The influence of actuator delays on safety during emergency braking scenarios is evaluated through simulation and field experiments. The results show that the forward reachable set of position errors expands as the actuator delays increase. The adoption of $H_2/H_{\infty }$ controller can reduce the influence of actuator delay on the safety margin by approximately 60%. Compared with the method of eliminating delay using the Lyapunov–Krasovskii functional method, the proposed method ensures the safety of the tracking distance of the train platoon.