In this paper, the speed and position tracking problem of high-speed trains is investigated in the presence of actuator faults. A multi-agent system model is constructed, where each vehicle of the train is regarded as a controllable agent. A distributed adaptive controller is then proposed for healthy train system based on terminal sliding mode control. Further, a distributed adaptive fault-tolerant controller (DAFC) is designed for high-speed trains considering actuator faults, and an auxiliary system is introduced to cope with the influence of input saturation. To the best of our knowledge, it is the first time that the distributed fault-tolerant control is considered in a multi-agent system model, which can better utilize the residual power of each vehicle when actuator faults occur. The stability of the closed-loop control system is analyzed through Lyapunov theory, and it is proven that the speed and position tracking errors of all vehicles are cooperative convergence. The simulation results are presented to demonstrate the effectiveness of the proposed DAFC. Compared with the existing method, the proposed DAFC reduces the average speed and position control errors by 54.3% and 55%, respectively.

Eco-driving for trains has traditionally focused on minimizing mechanical energy consumption at wheels, while completely ignoring traction chain losses that are rather significant. This paper presents a computationally efficient approach to minimize the total electrical energy consumption from traction substations (TS). After a nonlinear and non-convex program is formulated in time domain, a nonlinear and non-convex program is formulated in space domain to overcome the drawbacks of the model in time domain. By convex modeling steps, the non-convex program in space domain is reformulated as a convex program that can be efficiently solved. To further reduce computational effort, a real-time iteration sequential quadratic programming (SQP) algorithm is proposed to solve the convex program in a model predictive control framework. Numerical results indicate that the proposed SQP method yields a near-optimal solution with high computational efficiency. Compared to a traditional mechanical energy consumption model, a TS-to-traction energy efficiency can be improved.

This study proposes an integrated eco‐driving controller, in which speed profile and power split optimisation are simultaneously treated. A speed profile controller is designed based on a multi‐phase dynamic programming (DP) algorithm, which is utilised to optimise speed trajectories with the detailed model of the traction power system, vehicle dynamics system, and signal constraints at intersections. The optimised speed and demand power profiles are designed as the reference of the power split optimal controller. A DP algorithm is presented to determine voltage trajectories of supercapacitors with power plant voltage limitations and dynamic power losses. The performance of the proposed integrated method is evaluated by numerical simulation based on an actual route of Chengdu Tramway Line 2. The energy reduction can be achieved by the speed profiles controller, compared to the eco‐cruising benchmark strategies. Energy efficiency can be further improved by the integrated eco‐driving controller. Moreover, the influences of green signal time windows and trip time on the shape of the optimised solution are investigated. For a given journey, the trip time with minimum energy consumption can be obtained. The integrated eco‐driving control method can be implemented by driver assistant systems or automatic train operation systems.

The permanent magnet synchronous motor (PMSM) has recently garnered significant interest due to its high efficiency, lightweight, and low life cycle cost, positioning it as a strong candidate for the next-generation traction system in railway applications. By comparing the widely used induction motor (IM) with the PMSM, this paper integrates the dynamic motor efficiency map, which plays a crucial role in energy saving, into the energy-efficient train control (EETC) problem. The paper adopts auxiliary variables and utilizes data transformation to perform double surface-fitting for highly nonlinear and non-convex dynamic efficiency. This transformation naturally distinguishes the train traction and braking operating states, further enhancing the solution accuracy of the EETC model. Results reveal that the proposed model, while maintaining high computational accuracy, can achieve millisecond-scale computation time, and the results are closer to the actual distribution of train operating points. Based on a real case analysis of Qingdao Metro Line, it was found that replacing the IM with PMSM as a traction motor does not require adjustments to the train operation control strategy, and the PMSM can save at least 1.01 kWh/km, achieving an energy-saving rate of 12.96%.

Aiming to minimize the total electricity usage in realistic operation of urban rail transit (URT) trains, this paper establishes the coupled model for the train-line-electric network-timetable (TLET) comprehensive system, and proposes a multi-train cooperative eco-driving method to achieve the system energy optimal. The dynamic power flow within the DC railway system with multiple trains is analyzed by modeling the traction power supply system (TPSS), and an improved power flow calculation (PFC) method is proposed to calculate the dynamic power flow distribution. To achieve the total substation energy minimization, a space-time-speed (STS) three-dimensional network is presented to transform continuous train motion process into discrete states on space-speed plane, and a multiple individuals dynamic programming (MIDP) algorithm is throughly developed to cooperatively optimize the multi-train trajectories along the time horizon, with which the optimal speed profiles and timetables of each train can be obtained simultaneously. Moreover, a computationally efficient heuristic algorithm together with a train-to-train (T2T) communication policy are developed as a comparative study. Numerical experiment with field data from Guangzhou Metro Line 8 is implemented, to illustrate the energy-saving performance of the proposed methods.

With the energy consumption rising in rail transport, the railway sector is showing increasing interest in the energy-efficient operation of freight trains. Freight trains require more complicated driving strategies than ordinary passenger trains do due to their heavy loads, especially in the long-distance steep downhill (LDSD) sections that are very common in freight rail lines in China. This paper studies the energy-efficient operation of a freight train considering LDSD sections. An optimal control model including regenerative and pneumatic braking is developed for the freight train. Then, when a train leaves/enters the LDSD section, we verify the uniqueness of control transitions and discuss the speed profile linkage between LDSD and its adjacent sections, which indicates that the periodic braking should be applied on LDSD sections for optimality. Additionally, given the same running time for the entire journey, our analysis shows that electrical braking-full braking strategy is more energy-efficient than coasting-full braking strategy on LDSD sections. Finally, a numerical algorithm for the optimal driving solution is proposed. The simulation results demonstrate that the driving strategies generated by the proposed algorithm performs better than those from fuzzy predictive control and field operation regarding energy saving.