Arriving phase is an essential part of the virtually coupled train set (VCTS) operation in metros and significantly influences efficiency. This paper proposes a synchronous and precise control problem in VCTS arriving-phase operation and designs a hierarchical control approach to solve this problem. First, the control problem of VCTS arriving-phase operation is mathematically modeled, capturing the uncertain disturbances and measurement errors in train dynamics and considering input and safety constraints. Then, a two-layer control framework is designed, with the upper layer for coordinated trajectory planning and the lower layer for offset-free tracking of each train (unit) in VCTS. Specifically, in the upper layer, all units in VCTS are coordinated in an optimization problem to generate the reference trajectories that increase the synchronicity of arrival; in the lower layer, to track the reference trajectory, we propose an offset-free model predictive control (MPC) approach, which is based on an observer to handle uncertain disturbances and measurement errors. The stability of the offset-free MPC approach is proved, such that all units in VCTS can arrive at the station synchronously and precisely. Finally, experimental results demonstrate the performance of the proposed hierarchical approach.

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.

Virtual coupling is a novel railway transport concept that allows trains to split and join on-the-fly by switching from mechanical to virtual couplers. One of the main challenges in applying virtual coupling in metro railways is to reduce the tracking distance between trains without compromising safety. This paper proposes a relative operation-based train separation model to reduce the safe distance between trains. This model applies a fault tolerance principle. The principle is that the preceding train normally operates for a time interval from its last-known state before initiating an emergency brake to stop the train. A difficulty in applying the proposed model is to predict the boundary of all possible time-position trajectories of the preceding train, which is the reachability problem of a hybrid system. To solve this problem, we formalise the operation of the preceding train by a parameterized hybrid automaton. A polytope-based algorithm is then developed for computing an over-approximated reachable set of the automaton. We compare our approach with a state-of-the-art relative braking distance-based train separation model for virtual coupling on a concrete metro line in Chengdu, China, and evaluate the method with several benchmarks. The results demonstrate that the relative operation-based model substantially reduces the safe distances between trains. Compared to conventional approaches, the proposed model provides a considerable 90.7% decrease in unnecessary waiting time at railway stations for virtually coupled trains and a 4.9% increase in the capacity of the given railway lines.

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.

A virtually coupled train set (VCTS) is regarded as a complete train. To better serve passengers, train units (TUs) in a VCTS require synchronous stopping and departure with small tracking distances during the station operation stage. However, under the existing predecessor–follower framework, the TUs operate independently. The latter TU is limited by vehicle performance and safety constraints, making it unable to operate synchronously with the front TU. Moreover, the characteristics of a few midway evaluation indicators and complex constraints also make it difficult to solve the operation strategy of the VCTS. This article realizes the synchronous operation of a VCTS through coordination and designs coordinated operation guidance. On this basis, an optimization model for the synchronous operation of a VCTS is constructed, and it is solved using a multiagent reinforcement learning algorithm to obtain a coordinated driving curve. First, guidance curves are generated based on the guidance of coordinated operation to guide the initial search of the algorithm. Second, the algorithm takes multimirror scene synchronization training to quickly accumulate data and design a prediction-based action management module to adjust violation decisions. Finally, the data supervision and management module ensures the effective learning of valuable data. The coordinated driving curve generated based on the Hebei Jingche test line has good synchronization indicators, and the realization of the field vehicle tracking curve proves the engineering usability.