The increasing need for capacity has led the railway industry to explore new train control systems based on a concept called virtual coupling. Inspired by the platooning of autonomous vehicles, the safe operation of virtual coupling is guaranteed by a relative brake distance-based train separation method. This paper proposes a novel long short-term memory (LSTM)-based model predictive control (MPC) method for train operations. An MPC-based control design for virtual coupled train operations is presented. The LSTM is introduced to model the dynamics of the preceding train to approximate the actual train operations. With the train dynamics models, the operation trajectories of the preceding train are predicted based on planned control inputs. A study of a metro line in Chengdu was chosen to analyze the proposed control approach. The simulation results of different scenarios show that compared with the conventional MPC methods, the proposed LSTM-based MPC can reduce the speed differences and position differences of tracking trains by up to 35 % and 25 % , respectively.

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Recently, virtual coupling has aroused increasing interest in regard to achieving flexible and on-demand train operations. However, one of the main challenges in increasing the throughput of a train network is to couple trains quickly at junctions. Pre-programmed train operation strategies cause trains to decelerate or stop at junctions. Such strategies can reduce the coupling efficiency or even cause trains to fail to reach coupled status. To fill this critical gap, this paper proposes a cooperative game model to represent train coupling at junctions and adopts the Shapley theorem to solve the formulated game. Due to the discrete and high-dimensional characteristics of the model, the optimal solution method is non-convex and is difficult to solve in a reasonable amount of time. To find optimal operation strategies for large-scale models in a reasonable amount of time, we propose an improved particle swarm optimization algorithm by introducing self-adaptive parameters and a mutation method. This paper compares the strategy for train coupling at junctions generated by the proposed method with two naive strategies and unimproved particle swarm optimization. The results show that the operation time was reduced by using the proposed cooperative game-based optimization approach.