Virtual coupling (VC) is an emerging concept and hot research topic in railways, especially for metro systems. Several unit trains in VC drive with a desired minimum distance, and they, as a whole, are regarded as a single train. In this work, a distributed adaptive model predictive control (AMPC) system is proposed to coordinate the driving of each unit train in VC. To obtain the accurate parameters of train dynamics model in a time varying environment, an estimator of the train dynamics model is designed for each AMPC controller. A variable step descent algorithm along the negative gradient direction is adopted for each estimator, which steers the estimated values of the parameters to real ones. Simulations are conducted and the results are compared with both nominal model predictive control system and AMPC system with fixed steps in the literature. Our proposed AMPC system with variable step (AMPCVS) has better performances than other two systems. Results indicate that there is an improvement of the proposed AMPC system with variable steps system when compared with other two existed systems. A running process of VC in a whole inter-station is also simulated here. Experimental results show that the trains track the desired objective well.

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.