Freight trains operate in dynamic environments and exhibit time-varying behavior, making static mechanistic models inadequate for capturing these changes. This often results in impractical predictions of train operational states and optimization outcomes. To facilitate planning in such operational conditions, this paper proposes a dynamic modeling method to assess energy consumption and the voltage of traction power supply system (TPSS), and a large-scale adaptive multi-strategy multi-objective competitive swarm optimization algorithm (LA-MOCSO) for solving dynamic optimization challenges. Specific, a mechanistic “train-track-power grid” (TTP) model is first built to calculate power flow and TPSS voltage during multiple train operations. Second, a hybrid modeling approach that combines the mechanistic model and data-driven models is proposed to account for variations in train and environmental characteristics, and a multi-objective optimization model is established aimed at improving energy-efficiency and voltage stability of TPSS. Then, to tackle the complexities of the multi-objective optimization problem, an LA-MOCSO algorithm is proposed, which can be applied to solve the large-scale optimization problem of multi-train long-distance routes. Finally, the high accuracy of the dynamic model was validated with measurement data; the performance and computational efficiency of LA-MOCSO was verified through five algorithms; the comprehensive optimization method can, through the allocation and utilization of regenerative braking energy, further reduce substation energy consumption and maintain grid voltage stability.

Traditional static mechanistic models are hard to accurately capture complex and time-varying dynamics of freight trains, and then the optimized eco-driving strategies might be impractical for real-world operations. To overcome this issue, this paper proposes a hybrid model that combines a “train-track-power grid” mechanistic model with a data-driven model to evaluate both the dynamics and energy consumption of multiple trains. Additionally, a thermal rise model for electrical equipment is developed, and a rapid solution method based on the Laplace transformation is designed to obtain temperature rise. Then, a multi-objective optimization model is formulated to optimize both the energy efficiency of the traction power supply system and the temperature of electrical equipment. To solve the large-scale multi-objective optimization problem encountered in long-distance multi-train operations, a large-scale adaptive multi-strategy multi-objective competitive swarm optimizer (LAMOCSO) is proposed. Experiment results validate the effectiveness of the proposed dynamic modeling approach. Comparisons with four classical algorithms demonstrate that the proposed method can reduce energy consumption by 18.2%, while ensuring that electrical equipment operates within an appropriate temperature range.

In this article, the cooperative control issue is investigated for multitrain system with actuator saturation and state constraints. Considering the uncertainty of the high-speed train dynamics model and the nonstrict repetition of the operating process, a robust adaptive iterative learning control (RAILC) method is proposed for multitrain system cooperative control, where a control-based nonlinear auxiliary system is introduced to realize the finite-time compensation of train actuator saturation. Furthermore, a novel barrier RAILC (BRAILC) method is developed to achieve actively speed and position state constraints, which can ensure the multitrain system maintaining operates within the safe range. As the best of the author’s knowledge, this is the first time that the robust control and adaptive iterative learning control (AILC) are applied in a multitrain system. The Lyapunov function and composite energy function (CEF) are used to analyze the system convergence along the time and iteration axis, respectively. In the time axis of each iteration, the speed and position tracking errors of multiple high-speed train are convergent, and the system state is constrained, thus the proposed controller is reliable in engineering. Furthermore, through iterative learning law, the speed and position tracking error will converge to zero along the iteration axis, which gives the system the ability to intelligently utilize historical data. Finally, the effectiveness of the proposed control method is demonstrated through numerical simulations using data from China railway high-speed 380B (CRH380B) train.

This paper treats the uncertainties in practical train operations as disturbances in train dynamics and proposes a robust optimization method for multi-train operations. First, the indeterministic problem is transformed into a deterministic problem, by linearizing the train dynamics, analyzing the propagation of disturbances, and introducing new state variables. Then, a nonlinear program (NLP) is developed to solve the deterministic problem. The speed profiles of each train are simultaneously optimized to minimize the total traction energy while ensuring safe-separation among adjacent trains. Our results show that operation constraints and absolute safe time headway can always be guaranteed, even in the worst-case scenarios caused by disturbances.

This paper investigates the multi-agent system leader following consensus problem and its application in the intelligent transportation systems (ITS) field. The leader agent provides the desired reference trajectory, and the other follower agents operate cooperatively with the leader under the predefined motion state constraints. The considered agents are second-order nonlinear systems with parameter uncertainties and unknown disturbances. To achieve cooperative operation of the system, a state-constraints multi-agent cooperative adaptive control (SMCAC) method is given for the follower agent. The barrier Lyapunov function (BLF) is constructed to analyze the performance of the method in terms of error convergence and state constraints. The proposed method is then applied to the control of a multi-train system under the train-to-train communication topology. Numerical simulations on a five-train system are given to demonstrate the theoretical analysis.

This paper addresses the distributed adaptive coordinated control for high-speed train (HST) fleet with uncertain parameters. The motion of the train in the fleet is constrained by its adjacent trains, necessitating dynamic adjustment mechanism facilitated through inter-train communication. For the uncertainty, radial basic function neural network (RBFNN) is introduced into the distributed adaptive coordinated control algorithm, which ensures behavioral consistency and short inter-train intervals for each train in the fleet. This paper compares the proposed method with distributed adaptive sliding mode control (DASMC). The simulation demonstrates better performance and benefits of this new algorithm. We show that the algorithm substantially reduces inter-train distance and ensures heightened level of behavioral consistency among all individual trains within the train fleet.

In this paper, the distributed cooperative control of virtual coupling high-speed trains (HSTs) subject to full-state constraints, actuator limitations, dynamical uncertainties and environmental disturbances is investigated. Targeting at the full-state constraints in cooperative operation of HSTs, a distributed nonlinear state-dependent function (DNSDF) is first proposed to convert the state-constrained problem of the leader-following consensus control to the boundedness problem of DNSDF. Then, the distributed control law of each train is designed by combining the command filtering backstepping method and the adaptive neural network approximation technique. Meanwhile, combined with the DNSDF, a novel auxiliary dynamical system (ADS) is designed to compensate for the adverse effects of actuator input saturation, and thus ensure the closed-loop stability of the HSTs system when the state constraints and the input saturation are considered simultaneously. By utilizing the Lyapunov theory, the convergence of the proposed controller is analyzed. Finally, the feasibility and effectiveness of the proposed control scheme are verified by simulations.Note to Practitioners—This work was motivated by the problem of cooperative control for virtual coupling HSTs with different initial states, actuator input saturation, full-state constraints, etc. The proposed approach addresses the train position and speed constraints by applying DNSDF, which can ensure train coordinated operation with relative braking distance and further reduce the tracking interval between trains. Specifically, the upper bound of the train position constraint varies with the real-time position of the preceding train and the relative speed of the adjacent trains, rather than a constant value. More importantly, an ADS is designed based on the DNSDF, which guarantees the stability of the controller when the input saturation and state constraints exist simultaneously, and avoids the chattering phenomenon of the train control input. The simulation results show that the trains can operate cooperatively at any initial speed within the speed limitations. In future, we will focus on the cooperative control of HSTs with communication delay, and the energy saving optimization cooperative control of HSTs.

This paper studies the distributed data-driven event-triggered model free adaptive iterative learning control (ETMFAILC) of multiple high-speed trains (MHSTs) under iteration-varying topologies, which breaks away from the dependence on the train dynamics. Firstly, the nonlinear MHSTs with unknown dynamics are converted into a linear model. Then, combining the proposed event-based triggering condition and the linear model, the ETMFAILC scheme under the fixed topology is designed. Next, theoretical analysis proves the bounded input bounded output (BIBO) stability of MHSTs. Finally, the study is extended to the switching topologies and the validity of the ETMFAILC is verified by a numerical example.

This article considers the speed tracking control problem for high-speed train systems (HSTs) under the condition of passing through neutral sections in the presence of parametric uncertainties. Noticing the prominent feature of HSTs operation, i.e., the spatial repetitiveness, a novel spatial iterative learning control (ILC) scheme is proposed. First, the motion dynamic model of HSTs is constructed with the aid of temporal-spatial conversion. Meanwhile, input saturation constraint is introduced to address the limitation of system power supply capability and the loss of traction/braking force in neutral section. Then, the ILC law and the associated parametric updating law are devised to address the system uncertainties and realize the adaptive tracking control simultaneously. The stability of the closed-loop system and the convergence of the tracking errors are confirmed based on a space-weighted Lyapunov–Krasovskii-like composite energy function (CEF). Finally, numerical simulations are performed to illustrate the effectiveness of the proposed control scheme.

This paper studies the dissipative control problem of the multibody high-speed train (HST) systems with nonuniform sampling mechanisms and logarithmic quantizers, in which the transmitted signals are subject to random fading phenomenon. The tracking error dynamic model of HST is firstly established and the logarithmic quantizers for both the input and output (I/O) signals are designed. The faded I/O signals are described by the Rice fading model, in which the mathematical expectation and variance are given in advance. Then, based on the Lyapunov-Krasovskii functional approach with the consideration of time-varying delay, sufficient conditions are derived to ensure the convergence of tracking error and that HST is strictly dissipative. Further, the design method of the gain matrix is obtained by employing the linear matrix inequalities (LMI) techniques and a compensation algorithm is designed to offset the adverse effect brought by the fading measurements. Finally, the effectiveness of the proposed controller is verified by a numerical example from Japan Shinkansen HST.

With the increasing energy consumption in urban rail transit systems, energy-efficient train operation has been paid significant attention. Considering the application of regenerative braking technology, many studies focus on offline energy-saving train trajectory optimization, in which an accelerating regime is inserted into the train trajectory when there is regenerative braking energy (RBE) that can be utilized. However, in practical operation, train states are dynamic and scheduled trajectory might be useless. This paper proposes a real-time cooperative train control method based on Train-to-Train (T2T) communication technology. According to the train states transmitted through T2T communication, whether there is a train in braking regime is judged. Besides, an accelerating regime is inserted by changing train running modes when there is another train in the braking regime. A cooperative control algorithm is developed to achieve the energy-efficient cooperative control strategy. Besides, simulations based on a real-life metro line demonstrate that the proposed cooperative control method can reduce substation energy consumption and improve the utilization of RBE.

In this paper, a novel delay-dependent robust H∞control criterion for the velocity tracking control of high-speed trains is developed based on a multi-particle model and Lyapunov stability theory. The dynamic model of high-speed trains is proposed with consideration of the nonlinearity of aerodynamic drag, stochastic property of the measuring signals, uncertainties of train mass, resistance and stiffness of the couplers, multiple time-varying state delays, and input delays caused by the transmission process. Numerical simulations are carried out to verify the effectiveness and robustness of the proposed controllers, while the weights of delays are varying, and explore the influences of actuation power distribution on the velocity tracking performance and driving smoothness. Moreover, some useful results are obtained from the comparison between the proposed robust H∞ controller and an existing robust adaptive controller, which can also deal with parameter uncertainties and nonlinearity.

Railway systems may be interrupted by unforeseen events that require quick replanning to a feasible new schedule. This paper deals with the train rescheduling problem on double-track lines. The rescheduling problem is regarded as a conflict detection and resolution procedure. Timed Colored Petri nets are adopted to model the railway system: places represent rail resources, and tokens represent trains. A conflict detection rule is established in accordance with the safety principles of railway operations to predict potential conflicts. A Petri-net-based conflict resolution algorithm adapted from the A* algorithm is designed to search for an optimal or a near-optimal feasible schedule. The algorithm takes into account the railway operational principles when generating new markings, so that the new schedule has less train delays and respects the safety principles. The approach is applied in a case study to a double-track corridor from the Dutch railway network. For small delays, the algorithm can make delayed trains recover to their scheduled timetable within seconds. For large perturbations, the solutions generated by the algorithm can effectively reduce train delays while ensuring traffic safety.