This paper presents a distributed model predictive control (DMPC) approach for a virtually coupled train set (VCTS) with communication delays. Specifically, we stabilize the real-time states of VCTS and guarantee the satisfaction of safety constraints in automatic train protection systems with delayed states, which fills the gap in the existing literature. First, using the predicted trajectories at previous instants, the real-time states of VCTS are estimated from delayed states obtained through communication. Then, compatibility constraints are designed to regulate predicted control inputs, such that the error between the predicted and actual trajectories in the prediction horizon can be confined in a sequence of sets. Next, linear matrix inequalities are derived to tune cost functions, terminal sets and terminal controllers, which guarantee the stability and recursive feasibility of DMPC. Finally, experimental results demonstrate the performance of our approach in both cruising and speed-varying operations. The minimal spacing policies are evaluated with different communication delays and parameters in DMPC based on our mathematical designs.

The emerging virtual coupling technology aims to connect multiple train units as a virtually coupled train set (VCTS) with outstanding operation efficiency and flexibility. This paper studies the nonlinear formation control of VCTS, particularly considering the uncertainties from external disturbances and the practical modeling of formations. To solve this problem, we propose a distributed robust nonlinear model predictive control approach using tube techniques. Based on the analysis of contractiveness, nonlinear tubes are constructed to confine the uncertain trajectory influenced by uncertainties from the formation model, disturbances and distributed prediction. Specifically, to facilitate tube construction, compatibility constraints are deployed to restrict uncertainties from distributed prediction. Furthermore, the robust constraint satisfaction, recursive feasibility and stability of VCTS operations are established. Finally, based on the practical data in field tests, comparative experiments are conducted to demonstrate the advantages of our approach in control performance and computational efficiency.

Virtual coupling deploys the relative-braking distance (RBD) to keep a minimal distance between successive units in a virtually coupled train set (VCTS). However, it is still challenging to design a control approach that addresses RBD in a stable and computation-efficient way. Thus, this paper proposes a tube model predictive control (MPC) approach to solve this problem. The nonlinear model is formulated to capture the movement of VCTS with RBD. In the prediction horizon, we linearize the model at each instant, such that the controller is calculated by solving a computationally efficient quadratic programming problem. Tubes are constructed to confine the tracking errors from linearization. Finally, experiments are carried out and relevant results show that the proposed tube MPC can operate VCTS as well as nonlinear MPC, but save by over 70% computation time.

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.

Virtual Coupling (VC) is an emerging topic in the railway industry. It breaks the long-distance limitation and enables trains to operate at closer distances with new safety distance constraints. The new safety distance has high-order nonlinear time-varying because it is closer to the characteristics of virtually coupled trains (VCTs). This makes it difficult for the Automatic Train Operation (ATO) system to track the front virtually coupled train (VCT) in real-time and cannot guarantee stop synchronization. VCTs are equivalent to a physically connected train. So synchronous operation is very important. In order to solve the above problems, this paper takes the entire VCTs as optimization object and takes synchronized stopping, punctuality, and precise stopping as optimization indicators. The reinforcement learning Deep Q Network (DQN) algorithm is used to solve the optimization problem to seek the reference speed curve of each VCT. ATO performs real-time control on the basis of reference speed curve, which reduces calculation pressure and ensures synchronous operation of VCTs. Moreover, this paper improves DQN algorithm according to operation scenarios of VCTs to make the solution faster. Finally, we conduct a simulation experiment with the scene of Beijing Metro Line 11. The experiment demonstrates the effectiveness of this method for stopping synchronization and the superiority of the improved DQN algorithm for VCTs running scenarios.

Virtual Coupling (VC) is a hot topic in railways. A virtually coupled train set operates as a single train and consists of multiple unit trains (UTs). Each UT keeps a desired gap distance with its predecessor by following a spacing policy. Constant time headway (CTH) spacing policy is widely adopted in the existing studies about VC. Arrival time difference (ATD), i.e., the difference between the time instants of two successive UTs arriving at a platform, is large when using CTH. It is not expected because the passengers loading of all UTs should operate at the same time. This paper firstly analyzes the causes of ATD mathematically and proves ATD is inevitable when adopting CTH. Then, the change tendency of ATD with respect to each parameter is analyzed. The above analysis indicates that CTH is not suitable for the arrival process. Thus, a quadratic spacing policy is designed to reduce ATD. Experimental results show that ATD can hardly be reduced by only optimizing the parameters of CTH, but the quadratic spacing policy greatly reduces it.

We propose a noncoherent decoder-assisted (NDA) frame synchronizer, a two-stage, synchronization scheme based on the list-synchronization principle [P. Robertson, 1992], [M. Howlader and B. Woerner, 2001], for serially concatenated coded differential modulation (SCCD) system [K. R. Narayanan and G. L. Stuber, 1999] in packet transmission. For the first stage, we derive a suitable noncoherent maximum likelihood (SNML) rule, more effective for the noncoherent decoder's operating region of smaller channel phase offsets, to provide a reliable list of potential frame starting positions. For the second stage, we propose a hybrid sync method by exploiting the combined sign difference ratio (SDR) and sync word log-likelihood ratio (SW LLR) information [M. Howlader and B. Woerner, 2001] to obtain more reliable final decisions and reduce computational complexity. Performance and complexity of the proposed scheme are evaluated under constant and time-varying phase offsets in the AWGN channel via Monte Carlo simulation.

In this paper, we propose a detection technique for a serially concatenated coded MSK (SC-MSK) modulated signal, based on the noncoherent BCJR (N-BCJR) algorithm, where an exponentially decaying observation window (EDW) in the N-BCJR algorithm is used to get better use of the channel phase memory and reduce the state as well as metric computational complexity. We also derive the decoding metrics of N-BCJR for the Rayleigh fading channel without channel state information (CSI) and incorporate the EDW in the metrics. The BER performance of the proposed noncoherent SC-MSK, using EDW and a rectangular window (RW), are compared via Monte Carlo simulation in both AWGN and slow, flat Rayleigh fading channels.

We propose a noncoherent, decoder-assisted (NDA) frame synchronizer, a two-stage synchronization scheme based on the list-synchronization principle, for the serially concatenated coded differential modulation (SCCD) system in the packet transmission. For the first stage, we derive a suitable noncoherent, maximum likelihood (SNML) rule, more effective for the noncoherent decoder's operating region of smaller channel phase changes, to provide a reliable list of potential frame starting positions. For the second stage, we propose a hybrid sync method by exploiting the combined sign difference ratio (SDR) and sync word Log-likelihood ratio (SW LLR) information to obtain more reliable final decisions and reduce computational complexity. Performance and complexity of the proposed scheme are evaluated under constant and time-varying phase changes in the AWGN channel via Monte Carlo simulation.