With the ever-growing demand for passenger transportation, a variety of emerging train control approaches are under researched to further improve the efficiency of railway transportation such as the virtual coupling train control technology, where the traditional absolute braking distance control mechanism is replaced by the relative braking distance control approach to shorten the headway between adjacent trains. To enhance the efficiency and safety of the railway transportation system, this paper investigates the multiple trains cooperative control problem under the relative braking distance constraint. First, a dynamic multiple trains motion model is constructed with the consideration of the safe headway distance between consecutive trains. Then, an optimal control model is proposed to compute the train control forces so as to enhance the accuracy of speed and position tracking. However, the relative braking headway constraint is associated with the coupling states among adjacent trains which is time-consuming to be solved directly. To satisfy the real-time requirement of train operation, a trust region method based two-layer framework is further designed to decouple the complicated coupling headway constraints, where the augmented Lagrangian method is adopted to transform the original problem into an unconstrained optimal control problem, and the trust region method is employed to solve the equivalent problem efficiently. Numerical experiments based on the real operational data are implemented to verify the effectiveness and efficiency of the proposed method.

The virtual coupling technology is a promising train control system that connects vehicles through wireless communication instead of physical train couplers. For the virtually coupled train dynamic control system, the strategy for dynamic merge control is one of the most crucial problems to achieve the dynamic formation for train sets with different speed. This article proposes a dynamic merge controller based on the prescribed performance control method. The reference speed trajectories are calculated under different scenarios with respect to the variety of conditions between the leading and following trains. The designed controller can make both the tracking distance error and the speed error asymptotically converge to the zero state, and meanwhile satisfies the transient-state and steady-state performances in presence of unknown external disruptions and uncertain train parameters. Experimental results are provided to demonstrate the performance of designed strategy in enhancing the precise control the virtually coupled trains.

A novel approach based on virtual coupling of train control systems in subway lines has the potential to enhance transportation efficiency. Y-shaped lines have proven to be valuable in improving efficiency, and the rational application of the virtual coupling strategy on these lines can help to alleviate passenger flow pressure. However, train operations can be affected by uncertain disturbances that require real-time adjustments. Due to the complexity of train scheduling on Y-shaped lines, delays may be difficult to manage if they are scheduled according to a single timetable. In this paper, we propose a flexible adjustment of the planned schedule on Y-shaped lines, which considers the switching sequence of turnouts while ensuring safety. We present a mixed-integer programming (MIP) model that optimizes the total train delays, number of stranded passengers, and passenger waiting time. The simulation results demonstrate that our model effectively improves train punctuality while reducing stranded passengers and passenger waiting time.

This paper investigates the disturbance observer based robust cruise control problem for the heavy haul train with input saturation and disturbances. Both uncertain parameters and actuator saturation are taken into account in the dynamic model of the heavy haul train. To reject the influence of disturbances from the input channel, a linear disturbance observer is proposed to approximate the unknown disturbance, and an augmented system is constructed by combining the train state and the disturbance estimation error. According to the Lyapunov stability analysis method and the guaranteed cost control theory, a sufficient condition for the existence of the composite state-feedback control law and the disturbance observer parameter matrix are obtained, the coupler deviation and the disturbance estimation error are stable at the equilibrium point, and meanwhile the minimization of a given train performance index is ensured. Numerical experiments are provided to illustrate the effectiveness of the proposed approach.

With the acceleration of urbanization, the dynamic passenger flow has an ever-growing impact on the actual train operation. In this paper, we propose a learning based intelligent train regulation method with dynamic passenger flow prediction. To capture the characteristics of the dynamic metro passenger flow, a convolutional neural network is established to predict the real-time passenger flow from two dimensions including space and time. As the prediction accuracy is restricted by the insufficiency of the practical passenger flow data, a deep convolutional generative adversarial network is constructed to generate data that have the same distribution as the original passenger flow dataset. Then, by considering the effects of the dynamic passenger flow on the train operation and the train capacity constraints, the dynamic train regulation is formulated as a multi-stage optimal control problem with the objective function of minimizing the train traction energy consumption and the total traveling time of passengers. To efficiently obtain the optimal regulation strategy at each decision step, a deep Q-network algorithm is proposed to solve the formulated problem such the dimensionality curse caused by the excessive state space is avoided. The numerical experiments demonstrate the high efficiency and effectiveness of our proposed algorithm and model.

Focusing on improving the operation efficiency and riding comfort of metro rail lines in the peak hours, this article investigates the real-time train regulation and passenger load control problem with respect to frequent disturbances. To better illustrate the relationship between the train timetable and the on-board passengers, the variations of the departure time and the passenger load are elaborated in the form of a state-space model. Based on the Lyapunov stability theory, the problem of minimizing an upper bound on the quadratic performance function is transformed to a dynamic optimization problem with a set of linear matrix inequalities (LMIs), and a predictive control strategy is designed to guarantee the actual train schedule and number of in-vehicle passengers track the nominal timetable and the expected passenger load with a given disturbance attenuation level. With the objective to reduce the computational workloads and cut down the utilization of wireless transmitting resources, an event-triggered strategy is developed to implement the proposed stabilizing feedback controller only when the measurement error exceeds certain threshold, which has better adaptability to the application in large-scale metro networks. Some numerical examples based on the Beijing Yizhuang Metrol Line are provided for illustration of the effectiveness of the proposed scheme.

For enhancing the operation efficiency of the fully automatic operation (FAO) system in the urban rail transit (URT), this paper investigates the robust dynamic train regulation problem with respect to frequent disruptions and imperfect wireless transmissions. To better express the characteristic of the arriving passengers, the fuzzy passenger arrival rate is adopted to address the uncertainty of the passenger flow, and a T-S fuzzy state-space model is established to express the periodical movement of the train traffic in an URT loop line. By considering the possible packet dropout phenomenon during the wireless data transmissions, which may lead to the instability of the train traffic system and degrade the performance of the regulation strategy, a robust real-time train regulation strategy is developed based on the fuzzy predictive control theory, which distinguishes existing studies in that the uncertainty dropout rate is contemplated to address the complexity of the actual operation environment. A sufficient condition for the proposed control law is presented to guarantee that the nominal train schedule is recovered from disturbed situations with a given attenuation level by means of the$H_{\infty }$performance index, and meanwhile the optimization of the upper bound on the objective function balancing the service efficiency and control cost is achieved. Numerical simulations based on the Beijing subway loop line 2 are presented for demonstration of the effectiveness of the introduced strategy.

In this article, we focus on a joint scheduling problem that considers the corrective maintenance (CM) due to unexpected breakdowns and the scheduled preventive maintenance (PM) in a generic M-machine flow shop. The objective is to find the optimal job sequence and PM schedule such that the total of the tardiness cost, PM cost, and CM cost is minimized. Currently, most existing studies on the PM schedules are based on a fixed PM interval, which is rigid and may lead to poor performance, as the fixed strategy fails to effectively balance the trade-offs between the production scheduling and maintenance. To address this critical research issue, our novel idea is to dynamically update the PM interval based on the real-time machine age, such that the maintenance activity coordinates with the job scheduling to the maximum extent, which results in an overall cost saving. Specifically, a correction factor is introduced to dynamically update the PM interval and to help evaluate whether it is worthwhile to process the job first at the risk of the CM before performing the PM action. To demonstrate the effectiveness of the adaptive strategy, simulations and a case study on mining operations are conducted to show that the adaptive strategy outperforms the existing methods with a less total cost.

Virtually coupled train sets (VCTS) have been proposed to increase the transportation capacity and the flexibility of railway organization. Due to the lack of reliable wireless communications and accurate perceptual information, the promotion of VCTS was challenged. With the development of industrial Internet of Things (IIoT), an IIoT-based VCTS is built in the article based on the popular communication-based train control architecture. Considering the dynamic and complex operation environment, it is difficult to achieve the efficient cooperative control of VCTS. The reason is that the traditional method is frequently trapped into a local optimization. To resolve the problem, we apply reinforcement learning (RL) to obtain an optimal policy for the IIoT-based VCTS, where the traditional artificial potential field (APF) is taken to develop the reward function. RL can thus search the global optimal policy, whereas APF can help RL to reduce the computation complexity. This can substantially increase the efficiency of the proposed approach. Simulation results confirmed that the proposed RL-based cooperative control approach would bring excellent performance in the IIoT-based VCTS.

This paper investigates the robust distributed cruise control problem of multiple high-speed trains under external disturbances. First, by modeling each train as a cascade of point masses connected by spring-like couplers, the longitudinal interaction between adjacent cars are represented by the connected topological graph. Then, under the framework of the communication-based train control technology, the interaction of desirable speed information among trains and the wayside control center is described by the directed topological graph. Next, a distributed cruise controller is designed by taking advantages of the graphic theory such that the multiple trains track different target speeds, and both the distance of neighboring cars and the headway of successive trains are kept in appropriate ranges. Finally, to eliminate the influence of external disturbances, we adopt the disturbance observer to approximate the perturbations, and present a sufficient condition for the existence of the distributed control strategy and the observer gain parameter in form of the linear matrix inequality (LMI). Numerical experiments illustrate that the composite control law is effective in inhibiting the external disturbances, and guaranteeing the safety, efficiency and comfort of high-speed trains' movement.

This paper addresses the robust automatic train regulation problem in high-frequency metro lines with fuzzy passenger arrival rate. Due to the uncertainty of passenger demand, the passenger arrival rate is assumed to be represented by fuzzy variables. A nonlinear state-space model is formulated to describe the characteristic of metro train operation. To satisfy the real-time requirement of train regulation, a fuzzy constrained predictive control approach is designed to optimize a cost function at each decision epoch subject to safety constraints on the control input. Based on the Lyapunov stability theory and model predictive control method, sufficient conditions for the existence of corresponding state feedback control law are given in a set of linear matrix inequalities. Moreover, for reducing delays caused by the uncertain disturbance, the robust train regulation strategy is designed to guarantee that the practical train timetable tracks the nominal one with respect to certain disturbance attenuation level. The effectiveness of the proposed approach is validated by a number of experiments under real running circumstances of Beijing Metro Yizhuang Line of China.