Virtual Coupling (VC) is regarded as a breakthrough to the traditional train operation and control for improving the capability and flexibility in railways. It brings benefits as trains under VC are allowed to operate much closer to one another, forming a virtually coupled train set (VCTS). However, the safe and stable spacing between trains in the VCTS is a problem since there are no rigid couplers to connect them into a fixed formation, especially in high-speed scenarios. Due to the close spacing, the interference between trains becomes non-negligible as various maneuvers of the preceding train can significantly affect driving behaviors of the following train; this results in fluctuating spacing and therefore an unstable VCTS. Aiming at minimizing the interference and maintaining constantly safe spacing between trains in the VCTS, this paper presents a distributed model predictive control (DMPC) approach for solving the high-speed VCTS control problem. Particularly, the proposed control method focuses on the feasibility and stability of this problem, with considerations of the coupled constraint of safety braking distance and the individual constraints of speed limit variations and restricted traction/braking performance. To guarantee feasibility and stability, the terminal controller and invariant set of the DMPC are designed. For rigor, sufficient conditions of feasibility and stability are mathematically proved and derived. Based on the data of the Beijing-Shanghai high-speed railway line, numerical experiments are conducted to verify the correctness of derived sufficient conditions and the effectiveness of the proposed control method under interference and disturbances.

In order to meet the rapid growth of railway transportation demand, the technology that can improve its capacity has been widely concerned. Virtual Coupling (VC) is a new technology to improve capacity by decreasing headways between successive trains. Its basic principle is to control the train formation operation in coordination with the goal of keeping the same speed under the support of data transmission technology such as train-to-train communication. Our paper first reviews the existing theoretical research on train formation operation control, which is divided into four categories: train following, feedback control, optimal control and computational intelligent method. Secondly, by reviewing the related projects in Europe and China, based on the scenario analysis method, five general scenarios and two emergency scenarios in the whole process of VC operation are sorted out. Then, an original, complete list of performance indicators (PIs) is proposed for evaluating the performance of VC in different scenarios. Additionally, the paper gives a brief insight into VC operation by providing an adequate context to understand the proposed PIs.

The single train trajectory optimization, also known as speed profile optimization (SPO), is a traditional problem to minimize the traction energy consumption of trains. As a kind of optimal method, reinforcement learning (RL) has been used to solve the SPO problem. In the learning process of a common RL algorithm, a soft constraint (punishment) is always used to keep the agent away from unsafe states. However, a soft constraint can not guarantee and explain the safety of the result. For the SPO problem, it means that the optimized speed profile obtained by a simple RL may break the speed limit which is unacceptable in reality. This paper proposes a protection mechanism called Shield and constructs a Shield SARSA ( S -SARSA) algorithm to protect the learning process of the high-speed train. Four different reward functions are used to compare the protective efficacy between the proposed algorithm and the soft constraint. The numerical experiments based on the line data from Wuxi East to Suzhou North verify the protective efficacy and effectiveness.

With the rapid development of Metro, it has aroused more attention to its energy efficiency. The regenerative energy is a kind of energy generated by a braking train, which can be used by other trains nearby. Due to the application of regenerative braking and automatic train operation function, more and more studies focus on using regenerative energy by optimal train control. To maximize the utilization of regenerative energy for a couple of trains, we formulate a model and design an algorithm for maximizing the utilization of regenerative energy (MURE) by using the proposed approximate dynamic programming (ADP) approach to adjust the speed curve of the accelerating train. Then, we discuss three approximation methods for the proposed ADP-based approach such as rollout method, interpolation method, and neural network. The rollout algorithm could improve the basic policy for train control with carefully designing. The function approximation method using interpolation could further decrease the energy consumption with assuring punctuality. The neural network approximation usually cannot realize the effect superior to the interpolation strategy due to its complex structure, and it needs more computation time. Finally, the analysis of regenerative energy utilization is given by implementing the numerical experiments with field data from the Yizhuang line, Beijing subway. The numerical results show its effectiveness and stability.