A virtual marshalling train cruise control method and system

Abstract

The present application belongs to the field of rail transit train operation control technology, and specifically discloses a virtual marshalling train cruise control method and system, sets each train in marshalling as a controlled train, defines a virtual leading train not controlled by the outside world to send state information to each controlled train; establishes a longitudinal dynamics model of each train based on train position and speed, and obtains a longitudinal dynamics error model through state transformation; in view of the communication time delay existing in information interaction between trains, designs a collaborative control strategy based on a predictor according to the longitudinal dynamics error model; constructs a cost function, and determines the optimal collaborative control gain of the collaborative control strategy according to the weight matrix of the cost function, and completes the virtual marshalling train cruise control. The present application solves the problems of insufficient consideration of the influence of communication time delay, complex solution of collaborative control gain and unclear upper bound of operation cost in the existing virtual marshalling train collaborative cruise control.

Description

Technical Field

[0001] This invention belongs to the field of rail transit train operation control technology, specifically relating to a virtual train formation cruise control method and system. Background Technology

[0002] Cruise control is a crucial aspect of high-speed train operation, accounting for a significant portion of the entire journey. Therefore, designing effective cruise control strategies to ensure smooth train operation, optimize energy consumption, and accurately track the speed curve generated by the ground system in real time has become a critical issue in high-speed train control.

[0003] Currently, there are few technical solutions that simultaneously consider speed tracking, operational safety, and operating costs during the train's cruise phase. Existing research on optimal cost-preserving cruise control mainly focuses on single-train operations. Method 1 proposes a cost-preserving control method that enables each car to maintain the target speed and stabilize the relative spring displacement near the equilibrium point, while guaranteeing the upper bound of operating costs. Method 2 transforms sufficient conditions into a series of linear matrix inequalities, deriving a cost-preserving intermittent control law that enables freight trains to maintain the required speed and stabilizes the relative spring displacement between coupled cars at the equilibrium point. Method 3 provides sufficient conditions for the optimal cost-preserving sampled data controller for the train system and uses convex optimization methods to determine the minimum cost upper bound. Method 4, for the first time, simultaneously addresses the three issues of speed tracking, operational safety, and operating costs while considering input delay and parameter uncertainty. However, all the above studies employ a strategy of independent control for each car, failing to adopt a distributed control scheme based on information interaction between adjacent cars. Under independent control, each subsystem cannot coordinate adjustments based on the state of adjacent subsystems, making it difficult to achieve optimal performance for the entire system. To address this problem, a cooperative cruise control method with inter-subsystem interaction mechanism and cost-preservation characteristics is proposed, extending the single-train cost-preservation cruise control problem to a multi-train scenario. However, in this method, the optimal control gain is designed by solving linear matrix inequalities to obtain a numerical solution, and the designed optimal cost-preservation control strategy does not consider the impact of communication delay, thus exhibiting a certain degree of conservatism. Summary of the Invention

[0004] The purpose of this invention is to address the problems in existing virtual train formation cooperative cruise control, such as insufficient consideration of communication delay, complex calculation of cooperative control gain, and unclear upper bound of operating cost. This invention proposes a virtual train formation cruise control method and system.

[0005] The technical solution of this invention is: a virtual train formation cruise control method, comprising the following steps: Each train in the trainset is set as a controlled train, and a virtual leader train that is not subject to external control is defined to send status information to each controlled train. Based on the train's position and speed, a longitudinal dynamics model for each train is established, and based on the tracking requirements, a longitudinal dynamics error model is obtained through state transformation. To address the communication delay in information exchange between trains, a predictor-based cooperative control strategy is designed based on the longitudinal dynamic error model. A cost function is constructed based on the tracking state error of the controlled train, the relative state error between trains, and the control energy consumption of the virtual train formation system. The optimal cooperative control gain of the cooperative control strategy is determined based on the weight matrix of the cost function, and the cruise control of the virtual train formation is completed.

[0006] As a preferred option, the longitudinal dynamic model is:

[0007] in, Indicates the number of controlled trains; Indicates train Location, for The derivative; Indicates train speed, For The derivative; The controlled traction or braking force per unit mass; , and The basic drag coefficient is positive.

[0008] As a preferred method, based on the tracking requirements, the specific method for obtaining the longitudinal dynamic error model through state transformation is as follows: Establish the first The longitudinal dynamic error model of the controlled train is as follows:

[0009] in, For positional error, Position error The derivative, Indicates speed error, For speed error The derivative, For error control input, Indicates the desired speed; By stacking the error states of all controlled trains, a global matrix form of longitudinal dynamic error model is obtained as follows:

[0010] in, The global error state vector is formed by stacking the error states of all controlled trains. Global error state vector The derivative, , State matrix , It is the identity matrix. It is a zero matrix. Control matrix , It is a control input vector composed of the control increments of each controlled train.

[0011] As a preferred option, the predictor-based cooperative control strategy includes a self-tracking error feedback term, a relative state error feedback term of adjacent trains, and a time delay prediction compensation term. The predictor-based cooperative control strategy is as follows:

[0012] in, , , and The optimal cooperative control gain is to be determined. , For time-varying communication delay, Indicates time, For Laplace matrix, , , These are the adjacency matrix coefficients.

[0013] As a preferred option, the cost function is expressed as follows:

[0014]

[0015]

[0016]

[0017] in, , and For weight parameters, Indicates the number of controlled trains. The function representing the total cost of multi-train coordinated operation. This represents the performance index of position tracking and relative position coordination. This indicates the performance index of speed tracking and relative speed coordination. This refers to energy consumption performance indicators.

[0018] As a preferred method, the specific approach for determining the optimal cooperative control gain based on the weight matrix of the cost function is as follows: Define an orthogonal matrix Make , for The eigenvalues ​​are obtained. ; Based on the predictor-based cooperative control strategy, the longitudinal dynamic error model is transformed into a subsystem for each controlled train:

[0019] in, , , , , This represents the displacement error after orthogonal transformation. This represents the velocity error after orthogonal transformation. ; Write the cost function in matrix form: ; Suppose there exists a positive definite symmetric matrix. It can satisfy the following Riccati equation:

[0020] in, , ; According to LQR optimal control theory, we can obtain the error system Optimal control strategy that achieves asymptotic stability and minimizes the performance index function for: ; matrix , , and Substitute into the Riccati equation and multiply both sides by . Later based on By comparing the coefficients with the optimal control strategy, we obtain: ; The optimal control gain is then calculated. and The parsing expression is:

[0021] .

[0022] Preferably, the method further includes: For the delay prediction compensation term in the cooperative control strategy, the Pade method is used for approximation, and the error system containing time-varying communication delay is rewritten into a train error dynamics model that includes the current state, delay state and historical integral term by combining the Newton-Leibniz formula. For a train error dynamics model that includes the current state, delay state, and historical integral terms, a Lyapunov-Krasovskii functional is constructed. Sufficient conditions for the existence of a cost-preserving controller are derived by combining linear matrix inequalities. A quantitative relationship between sufficient conditions and maximum communication delay and control gain is established. When the sufficient conditions are met, the upper bound of the actual operating cost of the virtual train formation system is calculated.

[0023] The beneficial effects of this invention are: 1. This invention is aimed at the scenario of cooperative cruise of virtual train formations with communication latency, and simultaneously considers target speed tracking, maintaining safe distance between adjacent trains and optimizing control energy consumption, which can improve the overall control performance of multi-train cooperative operation.

[0024] 2. This invention addresses the time-varying delay in train-to-train communication by designing a predictor-based cooperative control strategy to predict and compensate for delay state information, thereby reducing the adverse effects of communication delay on system stability and tracking performance.

[0025] 3. Based on LQR optimal control technology, this invention derives an analytical expression for the cooperative control gain and establishes a relationship between the control gain and the second smallest eigenvalue of the communication topology matrix, which facilitates engineering calculations and control parameter tuning.

[0026] 4. This invention, by constructing a Lyapunov-Krasovskii functional and combining it with linear matrix inequalities, provides sufficient conditions for the existence of a cost-preserving controller under time-varying communication delay conditions. It can quantitatively describe the relationship between maximum communication delay, delay rate of change, control gain, communication topology eigenvalues, and system stability.

[0027] 5. This invention can calculate the upper bound of the cost of virtual train formation cooperative cruise operation, making the system operating cost predictable and verifiable, which is beneficial for optimizing control parameters based on energy consumption, efficiency and safety requirements in actual operation.

[0028] 6. This invention is applicable to virtual train formation cooperative cruise operation scenarios that include heavy-haul trains, urban rail transit, high-speed trains, and other types of trains, and has strong versatility and engineering application value.

[0029] Secondly, a virtual train formation cruise control system includes: The first module is used to set each train in the formation as a controlled train and define a virtual leader train that is not controlled by the outside world to send status information to each controlled train. The second module is used to establish the longitudinal dynamics model of each train based on the train's position and speed, and to obtain the longitudinal dynamics error model through state transformation based on the tracking requirements. The third module is used to design a predictor-based cooperative control strategy based on the longitudinal dynamic error model to address the communication delay in information exchange between trains. The fourth module is used to construct a cost function based on the tracking state error of the controlled train, the relative state error between trains, and the control energy consumption of the virtual train formation system. It then determines the optimal cooperative control gain of the cooperative control strategy based on the weight matrix of the cost function, thereby completing the cruise control of the virtual train formation.

[0030] Thirdly, an electronic device is provided, comprising: at least one processor; and a memory communicatively connected to the at least one processor; wherein the memory stores instructions executable by the at least one processor, the instructions being executed by the at least one processor to enable the at least one processor to perform the method as described in the first aspect.

[0031] Fourthly, a non-transitory computer-readable storage medium is provided that stores computer instructions for causing a computer to perform the method as described in the first aspect. Attached Figure Description

[0032] Figure 1 The diagram shows a flowchart of a virtual train formation cruise control method.

[0033] Figure 2 The diagram shown illustrates the cooperative cruise operation of virtual train formations.

[0034] Figure 3 The diagram shows the structure of a virtual train formation cooperative cruise control system. Detailed Implementation

[0035] Exemplary embodiments of the present invention will now be described in detail with reference to the accompanying drawings. It should be understood that the embodiments shown and described in the drawings are merely exemplary and are intended to illustrate the principles and spirit of the invention, and are not intended to limit the scope of the invention.

[0036] Example 1: like Figure 1 As shown, a virtual train formation cruise control method includes the following steps: S1. Set each train in the trainset as a controlled train, and define a virtual leader train that is not subject to external control to send status information to each controlled train.

[0037] The virtual leadership train is abstracted from the ground system, and its state is as follows:

[0038] in, This indicates the location of the virtual leadership train. for The derivative; Indicates the speed of the virtual leader train. for The derivative; This indicates the acceleration of the virtual leadership train.

[0039] S2. Based on the train position and speed, establish a longitudinal dynamics model including the virtual lead train and each controlled train, and based on the tracking requirements, obtain the longitudinal dynamics error model through state transformation.

[0040] The longitudinal dynamic model is as follows:

[0041] in, Indicates the number of controlled trains; Indicates train Location, The derivative representing position; Indicates train speed, Indicates speed The derivative; This indicates the controlled traction or braking force per unit mass. , and The basic drag coefficient is positive.

[0042] In virtual formation cruising mode, each controlled train should track the target speed of the virtual lead train and maintain the desired safe distance from adjacent trains. Let... To achieve the desired safe distance, the first [unclear] in equilibrium state The unit mass control force of the train is Define the speed error as... The displacement error is At the same time, there are Therefore, the longitudinal dynamic error model is:

[0043] in, The derivative representing the displacement error, The derivative representing the velocity error.

[0044] Furthermore, by stacking the error states of all controlled trains, a global matrix form of longitudinal dynamic error model is obtained as follows:

[0045] in, The global error state vector is formed by stacking the error states of all controlled trains. Global error state vector The derivative, , State matrix , It is the identity matrix. It is a zero matrix. Control matrix , It is a control input vector composed of the control increments of each controlled train.

[0046] S3. To address the communication delay in information exchange between trains, a predictor-based cooperative control strategy is designed based on the longitudinal dynamic error model.

[0047] The predictor-based cooperative control strategy includes a self-tracking error feedback term, a relative state error feedback term with adjacent trains, and a delay prediction compensation term. By predicting and compensating for the delay state, each controlled train can still generate the current control input using effective cooperative error information even when communication delay exists. The predictor-based cooperative control strategy is as follows:

[0048] in, , , and The optimal cooperative control gain is to be determined. , For time-varying communication delay, For Laplace matrix, , , The coefficients are the adjacency matrix coefficients. The control strategy describes the relative state deviation between trains using a Laplace matrix and mitigates the impact of delay state information on the current control input through predictive compensation terms.

[0049] S4. Construct a cost function based on the controlled train tracking state error, the relative state error between trains, and the control energy consumption of the virtual train formation system, and determine the optimal cooperative control gain based on the weight matrix of the cost function.

[0050] In this embodiment, step S4 specifically includes the following sub-steps: S41. Construct a cost function that characterizes the distributed cooperative features of a multi-train system, using its own tracking error, relative state error between trains, and energy consumption as performance indicators:

[0051]

[0052]

[0053]

[0054] in, , and These are the weight parameters. The function representing the total cost of multi-train coordinated operation. This represents the performance index of position tracking and relative position coordination. This indicates the performance index of speed tracking and relative speed coordination. This refers to energy consumption performance indicators.

[0055] S42. Use LQR optimal design technique to minimize the performance index function to obtain the optimal control gain. and The analytical solution for solving the multi-train cooperative operation optimization problem is as follows: To obtain the optimal cooperative control gain, an orthogonal transformation is first performed on the communication topology matrix. The orthogonal matrix is ​​defined as follows: Make , for The eigenvalues ​​are obtained from , thus we can obtain Then, based on the predictor-based cooperative control strategy, the global matrix form of the longitudinal dynamic error model can be transformed into several subsystems:

[0056] in, , , , , This represents the displacement error after orthogonal transformation. This represents the velocity error after orthogonal transformation. .

[0057] Write the cost function in matrix form: .

[0058] Suppose there exists a positive definite symmetric matrix. It can satisfy the following Riccati equation:

[0059] in, , and These are the positive definite symmetric matrices obtained by solving the Riccati equation. The three unknown parameters in , .

[0060] According to LQR optimal control theory, a system that minimizes error can be obtained. Optimal control strategy that achieves asymptotic stability and minimizes the performance index function The optimal control strategy is as follows:

[0061] .

[0062] matrix , , and After substituting into the Riccati equation, multiply both sides by . Later based on By comparing the coefficients with the optimal control strategy, the following equation relationship can be obtained: .

[0063] The optimal control gain can then be calculated. and The parsing expression is:

[0064] .

[0065] As shown in the above equation, the optimal cooperative control gain is directly related to the second smallest eigenvalue of the communication topology matrix. Therefore, this invention can establish a clear analytical relationship between communication topology connectivity and cooperative controller parameters, avoiding complete reliance on numerical optimization to solve for the control gain, and improving the computability and engineering feasibility of controller design.

[0066] In this embodiment, the method further includes step S5: constructing a Lyapunov-Krasovskii functional, deriving sufficient conditions for the existence of a cost-preserving controller by combining linear matrix inequalities, and establishing a quantitative relationship between sufficient conditions and maximum communication delay and control gain. When the sufficient conditions are met, calculating the upper bound of the actual operating cost of the virtual train system, and completing the cruise control of the virtual train.

[0067] S51. For predictive compensation terms in control strategies The Pade method is used for approximation, and combined with the Newton-Leibniz formula, the error system containing time-varying communication delay is rewritten into a form that includes the current state, the delay state, and the historical integral term:

[0068] in, , , , , , , .

[0069] The above equation transforms the time-delay system after prediction compensation into an integral form that facilitates stability analysis, providing a foundation for the subsequent construction of the Lyapunov-Krasovskii functional, the derivation of the linear matrix inequality conditions, and the calculation of the cost-preserving upper bound.

[0070] S52. Construct the Lyapunov-Krasovskii functional and derive the sufficient conditions for the existence of a cost-preserving controller by combining linear matrix inequalities.

[0071] For a train error dynamics model that includes the current state, time delay state, and historical integral terms, a Lyapunov-Krasovskii functional is constructed. As shown below:

[0072] in, Used to characterize the error energy of the current state. Used to characterize the impact of historical states on the stability of the train system within the actual time-varying delay interval. Used to characterize the distributed impact of historical states within the maximum allowable latency interval. This is used to further describe the higher-order weighted cumulative effect of historical states. , and All of these are time-delay-related integral variables, used to describe the cumulative impact of system historical errors and error derivatives under the influence of communication delay. The upper bound of the communication delay is given, and it satisfies the following conditions: .

[0073] Differentiating the Lyapunov-Krasovskii functional and using the integral inequality for scaling, we obtain:

[0074]

[0075]

[0076] in, Represents the Lyapunov-Krasovskii functional The derivative, Let be a symmetric matrix consisting of system parameters, control gain, upper bound of time delay, and positive definite matrix variables. If four symmetric positive definite matrices can be obtained... , , and Make the inequality If it is true, then we can obtain This ensures the asymptotic stability of the error system of the virtual train formation. , , , , , , , , , , and They represent solving inequalities respectively. The parameters of the positive definite symmetric matrix are obtained.

[0077]

[0078] in:

[0079]

[0080]

[0081]

[0082]

[0083]

[0084]

[0085]

[0086]

[0087]

[0088]

[0089]

[0090]

[0091]

[0092] .

[0093] Furthermore, by incorporating the weighted terms corresponding to tracking error, relative state error, and control energy consumption into the stability analysis process, the following cost-preserving performance term can be defined:

[0094] in, This is the overall performance indicator for collaboration.

[0095] Then define get:

[0096] in, In order to be in The cost-preservation determination matrix after introducing cost function weight terms is shown below:

[0097] The elements in the matrix except , , ， There have been some changes, and all other elements are the same as... The parameters are kept consistent, and each element is determined by train resistance parameters and control gain. and The second smallest eigenvalue of the Laplace matrix Upper bound of communication delay τ max The upper bound of the rate of change of time delay γ and the positive definite matrix variables are jointly determined. Under the condition that... Recalculate the linear matrix inequality under the premise of If the above four positive definite matrices still make If the system is asymptotically stable, it will also have cost-preserving performance.

[0098] S53. Calculate the upper limit of the operating cost of multi-train cooperative cruise.

[0099] Cost of protection judgment matrix At the time of its establishment, there were Regarding its position Interval integration, according to , and We can obtain:

[0100] The upper bound of the cost guarantee for the cooperative operation of virtual train formations is thus obtained as:

[0101] As shown in the above equation, the upper bound of the cooperative cruise operation cost of virtual train formations is jointly determined by the initial position error, the initial speed error, the upper bound of the communication delay, and the positive definite matrix variables in the Lyapunov-Krasovskii functional. This cost upper bound can be used for controller parameter tuning, operating energy consumption estimation, and safety margin design, enabling the cooperative control method to have both stability determination and predictable operating costs.

[0102] In one alternative embodiment, the adjacency matrix coefficients It can be designed to be 1 to reduce the computational burden. In another alternative embodiment, Alternatively, state-dependent time-varying parameters can be set based on the train communication distance to ensure connectivity is maintained.

[0103] In one alternative embodiment, cost function weights , and It can be adjusted according to operational requirements. When train operation prioritizes spacing safety, it can be appropriately increased. and When energy saving is a primary concern for operational tasks, the power consumption can be appropriately increased. .

[0104] In one alternative embodiment, the upper bound of communication latency It can be determined based on measured data of the train communication system or the design requirements of the communication protocol. If the actual communication delay meets... and Then, the stability and upper bound of the system cost can be determined based on the linear matrix inequality given in this invention.

[0105] This invention enables accurate tracking of target speeds by each train and maintenance of safe distances between adjacent trains under time-varying communication delay conditions. Furthermore, the control gain can be analytically solved, making calculations simple. The system operating cost has a clear upper bound, and optimization can be made between control efficiency and energy consumption based on operational requirements, improving its applicability in practical engineering. This invention is applicable to multi-train cooperative cruise operation scenarios involving heavy-haul trains, urban rail transit, and high-speed trains, and is used to achieve target speed tracking, safe distance maintenance, and operating cost optimization under time-varying communication delays between trains. A schematic diagram of virtual train cooperative cruise operation is shown below. Figure 2 As shown in the diagram. A schematic diagram of the virtual train formation cooperative cruise control system is shown below. Figure 3 As shown.

[0106] Example 2: Based on Embodiment 1, this embodiment of the invention provides a virtual train formation cruise control system, which can be used to implement the virtual train formation cruise control method as described in the foregoing embodiments. The system includes: The first module is used to set each train in the formation as a controlled train and define a virtual leader train that is not controlled by the outside world to send status information to each controlled train. The second module is used to establish the longitudinal dynamics model of each train based on the train's position and speed, and to obtain the longitudinal dynamics error model through state transformation based on the tracking requirements.

[0107] The third module is used to design a predictor-based cooperative control strategy based on the longitudinal dynamic error model to address the communication delay in information exchange between trains. The fourth module is used to construct a cost function based on the tracking state error of the controlled train, the relative state error between trains, and the control energy consumption of the virtual train formation system. It then determines the optimal cooperative control gain of the cooperative control strategy based on the weight matrix of the cost function, thereby completing the cruise control of the virtual train formation.

[0108] According to embodiments of the present invention, the present invention also provides an electronic device, a readable storage medium, and a computer program product.

[0109] In an exemplary embodiment, an electronic device includes: at least one processor; and a memory communicatively connected to the at least one processor; wherein the memory stores instructions executable by the at least one processor, the instructions being executed by the at least one processor to enable the at least one processor to perform the method as described in Embodiment 1 above.

[0110] In an exemplary embodiment, the readable storage medium may be a non-transitory computer-readable storage medium storing computer instructions for causing the computer to perform the method described in Embodiment 1 above.

[0111] In an exemplary embodiment, the computer program product includes a computer program that, when executed by a processor, implements the method described in Embodiment 1 above.

[0112] The program code used to implement the methods of the present invention can be written in any combination of one or more programming languages. This program code can be provided to a processor or controller of a general-purpose computer, special-purpose computer, or other programmable data processing device, such that when executed by the processor or controller, the program code causes the functions / operations specified in the flowcharts and / or block diagrams to be implemented. The program code can be executed entirely on the machine, partially on the machine, as a standalone software package partially on the machine and partially on a remote machine, or entirely on a remote machine or server.

[0113] In the context of this invention, a machine-readable medium can be a tangible medium that may contain or store a program for use by or in conjunction with an instruction execution system, apparatus, or device. A machine-readable medium can be a machine-readable signal medium or a machine-readable storage medium. Machine-readable media can include, but are not limited to, electronic, magnetic, optical, electromagnetic, infrared, or semiconductor systems, apparatus, or devices, or any suitable combination of the foregoing. More specific examples of machine-readable storage media include electrical connections based on one or more wires, portable computer disks, hard disks, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fibers, portable compact disk read-only memory (CD-ROM), optical storage devices, magnetic storage devices, or any suitable combination of the foregoing.

[0114] To provide interaction with a user, the systems and techniques described herein can be implemented on a computer having: a display device for displaying information to the user (e.g., a CRT (cathode ray tube) or LCD (liquid crystal display) monitor); and a keyboard and pointing device (e.g., a mouse or trackball) through which the user provides input to the computer. Other types of devices can also be used to provide interaction with the user; for example, feedback provided to the user can be any form of sensory feedback (e.g., visual feedback, auditory feedback, or tactile feedback); and input from the user can be received in any form (including sound input, voice input, or tactile input).

[0115] The systems and technologies described herein can be implemented in computing systems that include backend components (e.g., as a data server), or computing systems that include middleware components (e.g., an application server), or computing systems that include frontend components (e.g., a user computer with a graphical user interface or web browser through which a user can interact with embodiments of the systems and technologies described herein), or any combination of such backend, middleware, or frontend components. The components of the system can be interconnected via digital data communication of any form or medium (e.g., a communication network). Examples of communication networks include local area networks (LANs), wide area networks (WANs), and the Internet.

[0116] Computer systems can include clients and servers. Clients and servers are generally located far apart and typically interact via communication networks. Client-server relationships are created by computer programs running on the respective computers and having a client-server relationship with each other. Servers can be cloud servers, servers in distributed systems, or servers incorporating blockchain technology.

[0117] Those skilled in the art will recognize that the embodiments described herein are intended to help the reader understand the principles of the invention, and should be understood that the scope of protection of the invention is not limited to such specific statements and embodiments. Those skilled in the art can make various other specific modifications and combinations based on the technical teachings disclosed in this invention without departing from the spirit of the invention, and these modifications and combinations are still within the scope of protection of this invention.

Claims

1. A virtual train formation cruise control method, characterized in that, Includes the following steps: Each train in the trainset is set as a controlled train, and a virtual leader train that is not subject to external control is defined to send status information to each controlled train. Based on the train's position and speed, a longitudinal dynamics model for each train is established, and based on the tracking requirements, a longitudinal dynamics error model is obtained through state transformation. To address the communication delay in information exchange between trains, a predictor-based cooperative control strategy is designed based on the longitudinal dynamic error model. A cost function is constructed based on the tracking state error of the controlled train, the relative state error between trains, and the control energy consumption of the virtual train formation system. The optimal cooperative control gain of the cooperative control strategy is determined based on the weight matrix of the cost function, and the cruise control of the virtual train formation is completed.

2. The virtual train formation cruise control method according to claim 1, characterized in that, The longitudinal dynamic model is as follows: in, Indicates the number of controlled trains; Indicates train Location, for The derivative; Indicates train speed, for The derivative; The controlled traction or braking force per unit mass; , and The basic drag coefficient is positive.

3. The virtual train formation cruise control method according to claim 2, characterized in that, Based on the tracking requirements, the specific method for obtaining the longitudinal dynamic error model through state transformation is as follows: Establish the first The longitudinal dynamic error model of the controlled train is as follows: in, For positional error, Position error The derivative, Indicates speed error, For speed error The derivative, For error control input, Indicates the desired speed; By stacking the error states of all controlled trains, a global matrix form of longitudinal dynamic error model is obtained as follows: in, The global error state vector is formed by stacking the error states of all controlled trains. Global error state vector The derivative, , State matrix , It is the identity matrix. It is a zero matrix. Control Matrix , It is a control input vector composed of the control increments of each controlled train.

4. The virtual train formation cruise control method according to claim 3, characterized in that, The predictor-based cooperative control strategy includes a self-tracking error feedback term, a relative state error feedback term between adjacent trains, and a time delay prediction compensation term. The predictor-based cooperative control strategy is as follows: in, , , and The optimal cooperative control gain is to be determined. , For time-varying communication delay, Indicates time, For Laplace matrix, , , These are the adjacency matrix coefficients.

5. The virtual train formation cruise control method according to claim 4, characterized in that, The cost function is expressed as follows: in, , and For weight parameters, Indicates the number of controlled trains. The function representing the total cost of multi-train coordinated operation. This represents the performance index of position tracking and relative position coordination. This indicates the performance index of speed tracking and relative speed coordination. This refers to energy consumption performance indicators.

6. The virtual train formation cruise control method according to claim 5, characterized in that, The method for determining the optimal cooperative control gain based on the weight matrix of the cost function is as follows: Define an orthogonal matrix Make , for The eigenvalues ​​are obtained. ; Based on the predictor-based cooperative control strategy, the longitudinal dynamic error model is transformed into a subsystem for each controlled train: in, , , , , This represents the displacement error after orthogonal transformation. This represents the velocity error after orthogonal transformation. ; Write the cost function in matrix form: ； Suppose there exists a positive definite symmetric matrix. It can satisfy the following Riccati equation: in, , ; According to LQR optimal control theory, we can obtain the error system Optimal control strategy that achieves asymptotic stability and minimizes the performance index function for: ； matrix , , and Substitute into the Riccati equation and multiply both sides by . Later based on By comparing the coefficients with the optimal control strategy, we obtain: ； The optimal control gain is then calculated. and The parsing expression is: 。 7. The virtual train formation cruise control method according to claim 1, characterized in that, The method further includes: For the delay prediction compensation term in the cooperative control strategy, the Pade method is used for approximation, and the error system containing time-varying communication delay is rewritten into a train error dynamics model that includes the current state, delay state and historical integral term by combining the Newton-Leibniz formula. For a train error dynamics model that includes the current state, delay state, and historical integral terms, a Lyapunov-Krasovskii functional is constructed. Sufficient conditions for the existence of a cost-preserving controller are derived by combining linear matrix inequalities. A quantitative relationship between sufficient conditions and maximum communication delay and control gain is established. When the sufficient conditions are met, the upper bound of the actual operating cost of the virtual train formation system is calculated.

8. A virtual train formation cruise control system, characterized in that, include: The first module is used to set each train in the formation as a controlled train and define a virtual leader train that is not controlled by the outside world to send status information to each controlled train. The second module is used to establish the longitudinal dynamics model of each train based on the train's position and speed, and to obtain the longitudinal dynamics error model through state transformation based on the tracking requirements. The third module is used to design a predictor-based cooperative control strategy based on the longitudinal dynamic error model to address the communication delay in information exchange between trains. The fourth module is used to construct a cost function based on the tracking state error of the controlled train, the relative state error between trains, and the control energy consumption of the virtual train formation system. It then determines the optimal analytical solution of the cooperative control gain of the cooperative control strategy based on the weight matrix of the cost function, thereby completing the cruise control of the virtual train formation.

9. An electronic device, characterized in that, include: At least one processor; And a memory communicatively connected to the at least one processor; wherein the memory stores instructions executable by the at least one processor, the instructions being executed by the at least one processor to cause the at least one processor to perform the method according to any one of claims 1-7.

10. A non-transitory computer-readable storage medium storing computer instructions, characterized in that, The computer instructions are used to cause the computer to perform the method according to any one of claims 1-7.

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