This paper presents an analytic optimal control method for the virtually coupled train set (VCTS) in high-speed railway, aiming at maintaining consistent speed and safe spacing among trains in the VCTS. The proposed control strategy focuses on both local and string stability under variant maneuvers in the high-speed scenarios. Specifically, a state-space model is firstly formulated to describe the virtually coupled train dynamics, based on which an optimal control formulation is then constructed considering constraints of safe spacing, operation limits and train dynamic performance. To solve the proposed constrained optimal control problem, an analytical algorithm is given based on Pontryagin’s maximum principle. Further, local and string stability are analyzed, and sufficient conditions of stability are mathematically derived to guarantee stable control for both homogeneous and heterogenous VCTS. Numerical simulations were conducted to verify the correctness of derived sufficient stability conditions and the effectiveness of the proposed control strategy under variant maneuvers and disturbances.

本文提出了一种针对高速铁路虚拟耦合列车组（VCTS）的解析最优控制方法，旨在保持VCTS中列车之间的一致速度和安全间距。所提出的控制策略集中于高速场景下变型机动下的局部和弦稳定性。具体而言，首先建立状态空间模型来描述虚拟耦合的列车动力学，然后在此模型的基础上考虑安全间距，运行极限和列车动力学性能的约束，构建最优控制公式。为了解决提出的约束最优控制问题，基于庞特里亚金的最大原理给出了一种解析算法。此外，分析了局部和弦的稳定性，从数学上推导了足够的稳定性条件，以确保对同质和异质VCTS都进行稳定的控制。进行了数值模拟，以验证导出的足够稳定条件的正确性以及在变型机动和干扰下所提出的控制策略的有效性。