High-speed train cooperative control method and system based on adaptive polynomial approximation

Abstract

The invention provides a high-speed train cooperative control method and system based on adaptive polynomial approximation, and belongs to the technical field of high-speed train formation control. According to the scheme, cooperative control is performed on high-speed train formation through an adaptive control method, so that the whole formation operates stably on the premise of ensuring a safe distance; meanwhile, according to the scheme, a polynomial algorithm is used for approaching additional resistance, a feedback controller is directly designed, the uncertainty of the additional resistance in the multi-train cooperative formation operation process can be effectively dealt with, and it is ensured that the actual speed and displacement of the trains can accurately track a preset target.

Description

Technical Field

[0001] The present invention belongs to the technical field of high-speed train formation control, and in particular relates to a high-speed train cooperative control method and system based on adaptive polynomial approximation. Background Art

[0002] The statements in this section merely provide background information related to the present invention and do not necessarily constitute prior art.

[0003] Train formation refers to a group of trains composed of multiple trains in a certain order, spacing and coordination rules. These trains cooperate with each other during operation, just like a whole, to achieve functions such as synchronous driving, coordinated braking, joint dispatching, etc.

[0004] Existing automated train formation cooperative control schemes include control schemes based on fixed rules and control schemes guided by signal systems. Among them, the control scheme based on fixed rules usually adopts fixed spacing to maintain the order of the train formation, sets different spacing levels according to different types of trains (such as passenger trains, freight trains) or operating speed ranges, and the rear car in the train formation usually follows the front car at a certain speed difference or sets the maximum speed limit of the entire train formation according to line conditions (such as curves, ramps, bridges, etc.) and train types. This method has poor flexibility and cannot cope with various emergencies due to the use of fixed rules; while the control scheme based on signal system guidance divides different circuit sections on the track and uses the short-circuit effect of train wheels on the track circuit to detect the position of the train and transmit the position information to the subsequent train. However, this method has limited information transmission capacity and can only provide simple position and speed command information. Moreover, the track circuit is easily interfered by external factors (such as humid environment, metal foreign matter, etc.), resulting in signal errors or loss. In addition, the update and maintenance cost of this method is high. With the development of railway transportation, its support capacity for complex train formation cooperative control is gradually insufficient. Summary of the invention

[0005] The present invention provides a high-speed train cooperative control method and system based on adaptive polynomial approximation to cope with the uncertainty in the cooperative operation of high-speed train formations, so that the subsequent trains of the high-speed train formation can track the leading train in an orderly manner while maintaining a safe distance, and the actual speed and displacement of the entire formation can accurately track the preset target, while ensuring that the system remains stable during dynamic operation.

[0006] According to a first aspect of an embodiment of the present invention, a high-speed train cooperative control method based on adaptive polynomial approximation is provided, comprising: Based on the force analysis results of each train in the train formation, the longitudinal motion dynamics equation of multi-train cooperative formation is constructed; Based on the longitudinal motion dynamics equation of multi-train cooperative formation, the polynomial function is used to approximate the unknown additional resistance of multiple trains during operation, and the longitudinal motion dynamics equation of multi-train cooperative formation under polynomial approximation is constructed. Based on the longitudinal motion dynamics equation of multi-train cooperative formation under polynomial approximation, combined with the real-time displacement tracking error and speed tracking error of adjacent trains in the running direction of the train formation, an adaptive approximate controller for each train in the train formation and its related parameter adaptive law are constructed; The coordinated operation of trains is controlled based on the constructed adaptive approximate controller and its related parameter adaptive law.

[0007] Furthermore, the longitudinal motion dynamics equation of the multi-train cooperative formation is constructed using a single-particle model, wherein the resistance of the train is divided into basic running resistance and additional resistance; the dynamics equation is specifically expressed as follows:

[0008] in, , t , is the total time of coordinated operation of multiple trains, , and They represent the real-time displacement, velocity and acceleration of the i-th train in the running direction of the multi-train cooperative formation respectively; Represents the total weight of the i-th train in the running direction of the multi-train coordinated formation; Represents the control input of the i-th train in the running direction of the multi-train coordinated formation; represents the basic running resistance of the i-th train in the running direction of the multi-train cooperative formation related to the train speed, Represents the additional resistance encountered by the i-th train on a fixed line in the running direction of the multi-train coordinated formation.

[0009] Furthermore, the construction of the longitudinal motion dynamics equation of multiple train cooperative formation under the polynomial approximation is specifically as follows: a polynomial function is used to approximate the additional resistance of trains in the running direction of the multiple train cooperative formation; based on the longitudinal motion dynamics equation of multiple train cooperative formation, combined with the basic running resistance equation and the polynomial function representing the additional resistance, the construction of the longitudinal motion dynamics equation of multiple train cooperative formation under polynomial approximation is realized.

[0010] Furthermore, the longitudinal motion dynamics equation of the multi-train cooperative formation under the polynomial approximation is specifically expressed as follows:

[0011] in, , t , is the total time of coordinated operation of multiple trains, , and They represent the real-time displacement, velocity and acceleration of the i-th train in the running direction of the multi-train cooperative formation respectively; Represents the total weight of the i-th train in the running direction of the multi-train coordinated formation; Represents the control input of the i-th train in the running direction of the multi-train coordinated formation; represents the basic running resistance of the i-th train in the running direction of the multi-train cooperative formation related to the train speed, represents the polynomial coefficient, which is any non-negative real number. , is the polynomial dimension, is a polynomial function of independent variables; is the reconstruction error function.

[0012] Furthermore, for the first train, its adaptive approximation controller is as follows:

[0013]

[0014] in, is the control input of the first train in the direction of multi-train coordinated formation operation, The total weight of the first train in the direction of operation of the multi-train coordinated formation; is the expected acceleration tracking trajectory of the first train in the train running direction; T represents the transpose of the phasor; for The estimated value of , is the Davis coefficient of the first train, and its error term satisfy ; , They represent the 0th, 1st and 2nd powers of the speed of the first train at time t respectively; for The estimated value of , represents the polynomial coefficients; and its error term satisfy ; , represents the 0th, 1st and mth powers of the polynomial independent variable function corresponding to the first train at time t; is a symbolic function; , and is the controller gain to be selected; for The estimated value of is the upper bound of the reconstruction error, and are the displacement tracking error and speed tracking error of the first train in the direction of coordinated operation of the train formation, and are the expected displacement tracking trajectory and expected speed tracking trajectory of the first train in the train formation cooperative operation direction, and They are the real-time displacement and speed of the first train in the direction of coordinated operation of the train formation.

[0015] Furthermore, for the first train, the adaptive law of the relevant parameters corresponding to its adaptive approximation controller is specifically: ; ; ; in, is the normal number to be selected for the first train; , is the positive definite matrix to be selected for the first train.

[0016] Furthermore, for the subsequent train, its adaptive approximation controller is specifically expressed as:

[0017]

[0018] in, represents the control input of the i-th train in the direction of multi-train coordinated formation operation, represents the total weight of the i-th train in the direction of operation of the multi-train coordinated formation, is the expected acceleration tracking trajectory of the i-th train; T represents the transpose of the phasor; for The estimated value of , is the Davis coefficient of the i-th train and its error term, satisfy ; , They represent the 0th, 1st and 2nd powers of the speed of the i-th train at time t respectively; for The estimated value of , represents the polynomial coefficients, and its error term satisfy ; , represents the 0th, 1st and mth powers of the polynomial independent variable function corresponding to the i-th train at time t; is a symbolic function; , and is the controller gain to be selected; for The estimated value of is the upper bound of the reconstruction error, and are the real-time displacement tracking error and speed tracking error of the i-th train in the direction of coordinated operation of the train formation, and are the real-time displacement and speed of the i-1th train in the direction of coordinated operation of the train formation, and are the real-time displacement and speed of the i-th train in the direction of coordinated operation of the train formation, Represents the safe distance between the i-th train and the i-1-th train in the running direction of the train formation system.

[0019] Furthermore, for subsequent trains, the adaptive law of the relevant parameters corresponding to the adaptive approximation controller is specifically: ; ; ; in, is a normal number to be selected for the i-th train; , is the positive definite matrix to be selected for the i-th train.

[0020] Furthermore, for the obtained adaptive approximation controller and its related parameter adaptation law, the Lyapunov function is used to verify the collaborative stability of the multi-train closed-loop control system under multi-train cooperative formation operation.

[0021] According to a second aspect of an embodiment of the present invention, there is provided a high-speed train cooperative control system based on adaptive polynomial approximation, comprising: A dynamic equation construction unit, which is used to construct the longitudinal motion dynamic equation of a multi-train cooperative formation based on the force analysis results of each train in the train formation; A dynamic equation construction unit under polynomial approximation is used to construct the dynamic equation of longitudinal motion of multi-train cooperative formation under polynomial approximation based on the dynamic equation of longitudinal motion of multi-train cooperative formation, using polynomial functions to approximate the unknown additional resistance suffered by multiple trains during operation; An adaptive approximation controller construction unit is used to construct an adaptive approximation controller for each train in the train formation and its related parameter adaptive law based on the longitudinal motion dynamics equation of a multi-train cooperative formation under polynomial approximation and in combination with the real-time displacement tracking error and speed tracking error of adjacent trains in the running direction of the train formation; The system control unit is used to control the coordinated operation of trains based on the constructed adaptive approximation controller and its related parameter adaptive law.

[0022] Compared with the prior art, the present invention has the following beneficial effects: The scheme described in the present invention provides a high-speed train cooperative control method and system based on adaptive polynomial approximation. The scheme uses an adaptive control method to coordinate the high-speed train formation, so as to achieve stable operation of the entire formation while ensuring a safe distance. At the same time, the scheme uses a polynomial algorithm to approximate the additional resistance, and directly designs a feedback controller, which can effectively deal with the uncertainty of the additional resistance during the operation of multiple train cooperative formations, and ensure that the actual speed and displacement of the train can accurately track the preset target.

[0023] Advantages of additional aspects of the present invention will be given in part in the following description, and in part will become obvious from the following description, or will be learned through practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0024] The accompanying drawings in the specification, which constitute a part of the present invention, are used to provide a further understanding of the present invention. The exemplary embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute improper limitations on the present invention.

[0025] Figure 1 It is a flow chart of a high-speed train cooperative control method based on adaptive polynomial approximation described in an embodiment of the present invention; Figure 2 Schematic diagram of displacement error curves of various trains described in the embodiment of the present invention; Figure 3 Schematic diagram of speed error curves of various trains described in an embodiment of the present invention; Figure 4 Schematic diagram of the structure of a high-speed train cooperative control system based on adaptive polynomial approximation according to an embodiment of the present invention; Figure 5 Schematic diagram of the structure of an electronic device described in an embodiment of the present invention. DETAILED DESCRIPTION

[0026] The present invention will be further described below in conjunction with the accompanying drawings and embodiments.

[0027] It should be noted that the following detailed descriptions are exemplary and are intended to provide further explanation of the present invention. Unless otherwise specified, all technical and scientific terms used herein have the same meanings as those commonly understood by those skilled in the art to which the present invention belongs.

[0028] It should be noted that the terms used herein are only for describing specific embodiments and are not intended to limit exemplary embodiments according to the present invention. As used herein, unless the context clearly indicates otherwise, the singular form is also intended to include the plural form. In addition, it should be understood that when the terms "comprising" and / or "including" are used in this specification, it indicates the presence of features, steps, operations, devices, components and / or combinations thereof.

[0029] In the absence of conflict, the embodiments of the present invention and the features of the embodiments may be combined with each other.

[0030] In order to solve the problems existing in the prior art, such as Figure 1 As shown, this embodiment provides a high-speed train cooperative control method based on adaptive polynomial approximation, which specifically includes the following processing procedures: Step 1: Based on the force analysis results of each train in the train formation, the longitudinal motion dynamics equation of multi-train cooperative formation is constructed; The construction of the dynamic equation is based on Newton's second law to analyze the longitudinal motion of each train in the formation, and a single-particle model is used to establish the longitudinal motion dynamic equation of multi-train cooperative formation for the multi-train dynamic system; In a specific implementation, the step 1 includes the following processing steps: The established longitudinal motion dynamics equation of multi-train cooperative formation is: (1) in, , t , is the total time of coordinated operation of multiple trains, , and They represent the real-time displacement, velocity and acceleration of the i-th train at time t in the running direction of the multi-train cooperative formation respectively; Represents the total weight of the i-th train in the direction of operation of the multi-train coordinated formation, including the car body, passengers and their luggage, etc.; represents the control input (traction force / braking force) of the i-th train in the running direction of the multi-train coordinated formation; in actual operation, the resistance of the train is divided into two parts, namely the basic running resistance and the additional resistance. represents the basic running resistance of the i-th train in the running direction of the multi-train cooperative formation related to the train speed, represents the additional resistance of the i-th train on the fixed line in the running direction of the multi-train cooperative formation. The basic running resistance can be described by the Davis equation as follows: (2) in, , , is the basic running resistance coefficient of the i-th train in the running direction of the multi-train cooperative formation, that is, the Davis coefficient, which can be obtained through wind tunnel test.

[0031] Step 2: Based on the longitudinal motion dynamics equation of multi-train cooperative formation, the polynomial function is used to approximate the unknown additional resistance of multiple trains during operation, and the longitudinal motion dynamics equation of multi-train cooperative formation under polynomial approximation is constructed; In a specific implementation, step 2 includes the following processing steps: Step 201: Using a polynomial function Approximate the additional resistance of the i-th train in the direction of operation of the multi-train cooperative formation as follows: (3) in, About of Polynomial of degree, represents the polynomial coefficient, which is any non-negative real number. , is the polynomial dimension, is a polynomial function of independent variables; is the reconstruction error, and satisfies (4) in, Reconstruction error The upper bound of .

[0032] Step 202: Combining formulas (1) to (4), the longitudinal motion dynamics equation of each train in the multi-train coordinated formation operation under polynomial approximation is obtained: (5) Step 3: Based on the longitudinal motion dynamics equation of multi-train cooperative formation under polynomial approximation, combined with the real-time displacement tracking error and speed tracking error of adjacent trains in the running direction of the train formation, an adaptive approximation controller for each train in the train formation and its related parameter adaptive law are constructed; In a specific implementation, step 3 includes the following processing steps: Step 301: The first train in the formation is the basis of the entire formation, and the subsequent trains must operate in coordination with the first train under the premise of safe and stable operation. Therefore, the real-time displacement tracking error of the first train (i=1) in the running direction of the train formation is first designed. and velocity tracking error : (6) in, and It is the expected displacement tracking trajectory and expected speed tracking trajectory of the first train in the cooperative operation direction of the train formation.

[0033] Step 302: Construct the first train in the direction of the train formation cooperative operation ( i =1) is: (7) in, is the expected acceleration tracking trajectory of the first train in the train direction; T represents the transpose of the phasor; for The estimated value of , is the Davis coefficient of the first train, and its error term satisfy ; , They represent the 0th, 1st and 2nd powers of the speed of the first train at time t respectively; for The estimated value of , represents the polynomial coefficients; And its error term satisfy ; , represents the 0th, 1st and mth powers of the polynomial independent variable function corresponding to the first train at time t; represents a symbolic function; , and is the controller gain to be selected; for The estimated value of .

[0034] Step 303: Design the adaptive law of the parameters of the first train (i=1) in the direction of the multi-train formation coordinated operation as follows: (8) (9) (10) in, is a normal number to be selected; , is the positive definite matrix to be selected.

[0035] Step 304: Design the real-time displacement tracking error of the subsequent train (i=2,3,…,n) with the adjacent previous train as the tracking target during the multi-train coordinated formation operation and velocity tracking error : (11) in, Represents the safe distance between the i-th train and the i-1-th train in the running direction of the multi-train coordinated formation.

[0036] Step 305: During the process of constructing a multi-train formation for coordinated operation, the subsequent trains ( i =2,3,…, n ) is: (12) in, for The estimated value of , is the Davis coefficient of the i-th train and its error term, satisfy ; , They represent the 0th, 1st and 2nd powers of the speed of the i-th train at time t respectively; for The estimated value of , represents the polynomial coefficients, and its error term satisfy ; , represents the 0th, 1st and mth powers of the polynomial independent variable function corresponding to the i-th train at time t; is a symbolic function; , and is the controller gain to be selected; for The estimated value of .

[0037] Step 306: Design the subsequent trains in the direction of the multi-train formation coordinated operation ( i =2,3,…, n ) The adaptive law of relevant parameters is as follows: (13) (14) (15) in, is a normal number to be selected; , is the positive definite matrix to be selected.

[0038] Step 4: Control the coordinated operation of trains based on the constructed adaptive approximate controller and its related parameter adaptive laws.

[0039] In the specific implementation, the method also needs to prove the collaborative stability of the closed-loop control system of multiple trains under the collaborative formation operation of multiple trains through the Lyapunov function, and further use the designed adaptive law and controller to control the collaborative operation of trains. Under the premise of ensuring the safe distance between adjacent trains, the first train approaches the expected trajectory, and the subsequent trains operate collaboratively under the constraints of the safe distance and speed limit curve.

[0040] In a specific implementation, step 4 includes the following processing steps: Step 401: Construct the Lyapunov function Vi(t) of the i-th train as follows: (16) Step 402: Deriving the Lyapunov function Vi(t) in combination with step S41, constructing the overall Lyapunov function under the multi-train adaptive approximation cooperative formation operation as follows: (17) Arranged Through Lyapunov stability theory, the stability of the closed-loop cooperative control system of high-speed trains under adaptive polynomial approximation can be verified, that is, under the adaptive approximation cooperative driving strategy, the multi-train cooperative formation control system has good displacement and speed tracking characteristics, and two adjacent trains can stably cooperate while maintaining a safe distance.

[0041] In order to verify the feasibility and effectiveness of the method described in this embodiment, the following experimental verification was carried out: Considering the resistance caused by curve resistance, slope resistance, tunnel resistance and unmodeled factors during the operation of multi-train coordinated formation, the effectiveness of the control method is verified through simulation experiments. In the simulation experiment, the train running time is 2000 seconds and the total mass is 500 tons. The center angle of the multi-train running curve is 120° and the slope angle is , the tunnel length is 1,500 meters.

[0042] Based on the above simulation conditions, simulation experiments were carried out on four trains to obtain the displacement and speed response curves of each train under the proposed adaptive approximate cooperative driving strategy, as shown in Figure 2. Figure 2 and Figure 3 As shown, Figure 2 and Figure 3 The displacement tracking error and speed tracking error of each vehicle under the condition of multi-train cooperative formation operation are described respectively. Combined with the simulation results, it is concluded that during the operation of multi-train formation, each train can obtain good displacement tracking performance and speed tracking performance under the adaptive approximate cooperative driving strategy, and the entire train formation operates stably under the premise of ensuring a safe distance, achieving the expected cooperative operation effect, proving the effectiveness of the control method adopted in this embodiment.

[0043] In one or more embodiments, corresponding to the above method, such as Figure 4 As shown, this embodiment provides a high-speed train cooperative control system based on adaptive polynomial approximation, including: A dynamic equation construction unit, which is used to construct the longitudinal motion dynamic equation of a multi-train cooperative formation based on the force analysis results of each train in the train formation; A dynamic equation construction unit under polynomial approximation is used to construct the dynamic equation of longitudinal motion of multi-train cooperative formation under polynomial approximation based on the dynamic equation of longitudinal motion of multi-train cooperative formation, using polynomial functions to approximate the unknown additional resistance suffered by multiple trains during operation; An adaptive approximation controller construction unit is used to construct an adaptive approximation controller for each train in the train formation and its related parameter adaptive law based on the longitudinal motion dynamics equation of a multi-train cooperative formation under polynomial approximation and in combination with the real-time displacement tracking error and speed tracking error of adjacent trains in the running direction of the train formation; The system control unit is used to control the coordinated operation of trains based on the constructed adaptive approximation controller and its related parameter adaptive law.

[0044] It can be understood that the system described in this embodiment corresponds to the method in the above embodiment, and its technical details are described in detail in Embodiment 1, so they are not repeated here.

[0045] In further embodiments, there is also provided: An electronic device, such as Figure 5 As shown, the electronic device includes an input unit, a memory, a processor, a feedback device and an output unit; wherein the memory is used to store computer programs; the processor is used to implement the above-mentioned high-speed train collaborative control method based on adaptive polynomial approximation when executing the computer program stored in the memory.

[0046] The above-mentioned memory may include a random access memory (RAM) or a non-volatile memory, such as at least one disk memory. Optionally, the memory may also be at least one storage device located away from the above-mentioned processor.

[0047] The above-mentioned processor can be a general-purpose processor, including a central processing unit (CPU), a network processor (NP), etc.; it can also be a digital signal processor (DSP), an application specific integrated circuit (ASIC), a field programmable gate array (FPGA) or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components.

[0048] A computer-readable storage medium stores instructions, which, when executed on a computer, enable the computer to execute any of the methods described in the above embodiments.

[0049] A computer program product comprising instructions, when running on a computer, enables the computer to execute any of the methods described in the above embodiments.

[0050] In the above embodiments, it can be implemented in whole or in part by software, hardware, firmware or any combination thereof. When implemented using software, it can be implemented in whole or in part in the form of a computer program product. The computer program product includes one or more computer instructions. When the computer program instructions are loaded and executed on a computer, the process or function described in the embodiment of the present application is generated in whole or in part. The computer may be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The computer instructions may be stored in a computer-readable storage medium, or transmitted from one computer-readable storage medium to another computer-readable storage medium. For example, the computer instructions may be transmitted from a website site, computer, server or data center to another website site, computer, server or data center by wired (e.g., coaxial cable, optical fiber, digital subscriber line) or wireless (e.g., infrared, wireless, microwave, etc.) means. The computer-readable storage medium may be any available medium that a computer can access or a data storage device such as a server or data center that includes one or more available media integrated. The available medium may be a magnetic medium (e.g., a floppy disk, a hard disk, a tape), an optical medium (e.g., a DVD), or a semiconductor medium (e.g., a solid-state hard disk SolidState Disk), etc.

[0051] The above description is only a preferred embodiment of the present application and is not intended to limit the protection scope of the present application. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present application are included in the protection scope of the present application.

[0052] The above description is only a specific implementation of the present application, so that those skilled in the art can understand or implement the present application. Various modifications to these embodiments will be apparent to those skilled in the art, and the general principles defined herein can be implemented in other embodiments without departing from the spirit or scope of the present application. Therefore, the present application will not be limited to the embodiments shown herein, but will conform to the widest range consistent with the principles and novel features applied for herein.

Claims

1. A high-speed train cooperative control method based on adaptive polynomial approximation, characterized in that: include: Based on the force analysis results of each train in the train formation, the longitudinal motion dynamics equation of multi-train cooperative formation is constructed; Based on the longitudinal motion dynamics equation of multi-train cooperative formation, the polynomial function is used to approximate the unknown additional resistance of multiple trains during operation, and the longitudinal motion dynamics equation of multi-train cooperative formation under polynomial approximation is constructed. Based on the longitudinal motion dynamics equation of multi-train cooperative formation under polynomial approximation, combined with the real-time displacement tracking error and speed tracking error of adjacent trains in the running direction of the train formation, an adaptive approximate controller for each train in the train formation and its related parameter adaptive law are constructed; The coordinated operation of trains is controlled based on the constructed adaptive approximate controller and its related parameter adaptive law.

2. The high-speed train cooperative control method based on adaptive polynomial approximation according to claim 1, characterized in that: The longitudinal motion dynamics equation of the multi-train cooperative formation is constructed using a single-particle model, wherein the resistance of the train is divided into basic running resistance and additional resistance; the dynamics equation is specifically expressed as follows: ； in, , t , is the total time of coordinated operation of multiple trains, , and They represent the real-time displacement, velocity and acceleration of the i-th train in the running direction of the multi-train cooperative formation respectively; Represents the total weight of the i-th train in the running direction of the multi-train coordinated formation; Represents the control input of the i-th train in the running direction of the multi-train coordinated formation; represents the basic running resistance of the i-th train in the running direction of the multi-train cooperative formation related to the train speed, Represents the additional resistance encountered by the i-th train on a fixed line in the running direction of the multi-train coordinated formation.

3. The high-speed train cooperative control method based on adaptive polynomial approximation according to claim 1, characterized in that: The construction of the longitudinal motion dynamics equation of multiple train cooperative formation under the polynomial approximation is specifically as follows: a polynomial function is used to approximate the additional resistance of trains in the running direction of the multiple train cooperative formation; based on the longitudinal motion dynamics equation of multiple train cooperative formation, combined with the basic running resistance equation and the polynomial function representing the additional resistance, the construction of the longitudinal motion dynamics equation of multiple train cooperative formation under polynomial approximation is realized.

4. The high-speed train cooperative control method based on adaptive polynomial approximation according to claim 1, characterized in that: The longitudinal motion dynamics equation of the multi-train cooperative formation under the polynomial approximation is specifically expressed as follows: ； in, , t , is the total time of coordinated operation of multiple trains, , and They represent the real-time displacement, velocity and acceleration of the i-th train in the running direction of the multi-train cooperative formation respectively; Represents the total weight of the i-th train in the running direction of the multi-train coordinated formation; Represents the control input of the i-th train in the running direction of the multi-train coordinated formation; represents the basic running resistance of the i-th train in the running direction of the multi-train cooperative formation related to the train speed, represents the polynomial coefficients, , is the polynomial dimension, is a polynomial function of independent variables; is the function of the reconstruction error.

5. The high-speed train cooperative control method based on adaptive polynomial approximation according to claim 1, characterized in that: For the first train, its adaptive approximation controller is as follows: ； ； in, is the control input of the first train in the direction of multi-train coordinated formation operation, The total weight of the first train in the direction of operation of the multi-train coordinated formation; is the expected acceleration tracking trajectory of the first train in the train running direction; T represents the transpose of the phasor; for The estimated value of , is the Davis coefficient of the first train, and its error term satisfy ; , They represent the 0th, 1st and 2nd powers of the speed of the first train at time t respectively; for The estimated value of , represents the polynomial coefficients; and its error term satisfy ; , represents the 0th, 1st and mth powers of the polynomial independent variable function corresponding to the first train at time t; is a symbolic function; , and is the controller gain to be selected; for The estimated value of is the upper bound of the reconstruction error, and are the displacement tracking error and speed tracking error of the first train in the direction of coordinated operation of the train formation, and are the expected displacement tracking trajectory and expected speed tracking trajectory of the first train in the direction of coordinated operation of the train formation, and They are the real-time displacement and speed of the first train in the direction of coordinated operation of the train formation.

6. The high-speed train cooperative control method based on adaptive polynomial approximation according to claim 5, characterized in that: For the first train, the adaptive law of the relevant parameters corresponding to its adaptive approximation controller is as follows: ； ； ； in, is the normal number to be selected for the first train; , is the positive definite matrix to be selected for the first train.

7. The high-speed train cooperative control method based on adaptive polynomial approximation according to claim 1, characterized in that: For the subsequent train, its adaptive approximation controller is specifically expressed as: ； ； in, represents the control input of the i-th train in the direction of multi-train coordinated formation operation, represents the total weight of the i-th train in the direction of operation of the multi-train coordinated formation, is the expected acceleration tracking trajectory of the i-th train; T represents the transpose of the phasor; for The estimated value of , is the Davis coefficient of the i-th train and its error term, satisfy ; , They represent the 0th, 1st and 2nd powers of the speed of the i-th train at time t respectively; for The estimated value of , represents the polynomial coefficients, and its error term satisfy ; , represents the 0th, 1st, and mth powers of the polynomial independent variable function corresponding to the i-th train at time t, is a symbolic function; , and is the controller gain to be selected; for The estimated value of is the upper bound of the reconstruction error, and are the real-time displacement tracking error and speed tracking error of the i-th train in the direction of coordinated operation of the train formation, and are the real-time displacement and speed of the i-1th train in the direction of coordinated operation of the train formation, and are the real-time displacement and speed of the i-th train in the direction of coordinated operation of the train formation, Represents the safe distance between the i-th train and the i-1-th train in the running direction of the train formation system.

8. The high-speed train cooperative control method based on adaptive polynomial approximation according to claim 7, characterized in that: For subsequent trains, the adaptive law of the relevant parameters corresponding to the adaptive approximation controller is as follows: ； ； ； in, is a normal number to be selected for the i-th train; , is the positive definite matrix to be selected for the i-th train.

9. The high-speed train cooperative control method based on adaptive polynomial approximation according to claim 1, characterized in that: For the obtained adaptive approximation controller and its related parameter adaptation law, the Lyapunov function is used to verify the collaborative stability of the multi-train closed-loop control system under multi-train cooperative formation operation.

10. High-speed train cooperative control system based on adaptive polynomial approximation, characterized in that: include: A dynamic equation construction unit, which is used to construct the longitudinal motion dynamic equation of a multi-train cooperative formation based on the force analysis results of each train in the train formation; A dynamic equation construction unit under polynomial approximation is used to construct the dynamic equation of longitudinal motion of multi-train cooperative formation under polynomial approximation based on the dynamic equation of longitudinal motion of multi-train cooperative formation, using polynomial functions to approximate the unknown additional resistance suffered by multiple trains during operation; An adaptive approximation controller construction unit is used to construct an adaptive approximation controller for each train in the train formation and its related parameter adaptive law based on the longitudinal motion dynamics equation of a multi-train cooperative formation under polynomial approximation and in combination with the real-time displacement tracking error and speed tracking error of adjacent trains in the running direction of the train formation; The system control unit is used to control the coordinated operation of trains based on the constructed adaptive approximation controller and its related parameter adaptive law.

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