Towards Safe Inter-train Distance Minimization via Reachability Analysis and Mixed H2/H∞ Control

In high-speed railway, designing a reasonable controller of train control system is an important way to enhance the transportation capacity, while considering more dynamic behaviors of the preceding train, such as position, speed and acceleration etc, through V2V communication. In this paper we propose a novel method towards the safe inter-train distance minimization problem via reachability analysis and mixed H
2
/H
∞
control. Firstly, by considering the disturbance behavior of the preceding train, a linear closed-loop system is modeled, in which the gains of a state feedback and a state feedback/feedforward, refer to Controller A and Controller B respectively, are designed using mixed H
2
/H
∞
control theory. Then, the N-step forward reachable set for the two given controllers is presented to compute the maximum position error, which determines the minimum safe inter-train distance. Furthermore, backward reachability analysis algorithm is used to find the maximal initial state set, which guarantees that the state trajectory stay within the safe set in presence of disturbance. Finally, the proposed method is applied to a typical emergency braking scenario during two-train tracking. The experimental results show that the safety margin can be reduced by 54% and the maximal initial state set can be enlarged conspicuously when a feedforward term is used in the controller.