A Cooperative Model Predictive Control Approach for Virtual Coupling Train Arrival in Metro Railways

The synchronous arrival of trains in a virtually coupled train set (VCTS) is crucial to ensure efficient operations. The primary objective of VCTS is to decrease the inter-train spacing while stopping, aiming to minimize the time difference between arrivals. In this paper, we propose a distributed cooperative model predictive control-based (DCMPC) approach for synchronous arrival of VCTS. Firstly, the dynamics model of the unit train in VCTS is constructed, which considers external uncertainties. Then, a novel dynamic penalty matrix updating method is introduced to improve the accuracy and efficiency of unit train stopping. We also present the design of terminal constraints on the DCMPC control problem and the stability proof to ensure the feasibility of the controller. Finally, the effectiveness of the proposed method is verified through simulation experiments with concrete data from the Chengdu Metro Line NO.8 in China. Compared to conventional control approaches, the proposed DCMPC significantly reduces the arrival time difference while increasing the average stopping speed, resulting in a considerable 4% increase in the passing capacity of the line.