Virtual Coupling has been a hot research topic in railways in recent years. The proposed control methods in the existing literature for virtually coupled train sets (VCTS) mainly try to operate train units with the constraint of maintaining a small gap distance, but pay insufficient attention to the needs in the entering station process, which affects the work of VCTS in a station and is thus one of the most important part of VCTS in unban rail transits. To fill this gap, this paper firstly proposes an unsynchronized stopping problem between the train units in a VCTS when entering a station, defines the concept and the calculation method of stopping time difference between the train units. Then, inspired by the multi-agent cooperative control methods in related fields, a cooperative control-based reference curve generating method for VCTS is proposed. Followed by it, a mathematical optimization model to generate the reference curves for the train units in a VCTS is formulated, and a reinforcement learning DQN (deep Q network) based algorithm is designed to solve this problem. Optimized reference curves for each train units are generated automatically, considering the global objects and all constraints of VCTS. Finally, based on the real data of trains and lines from Beijing Metro Line 11, numerical simulation experiments are conducted. Experimental results prove the effectiveness of the proposed method which outperforms a commonly used control method of VCTS in the literature.
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