Multi-objective optimization adaptive adhesion tracking control method for virtual marshalling train

Abstract

This invention belongs to the field of high-speed train control technology and proposes a multi-objective optimization adaptive adhesion tracking control method for virtual train formations. The method includes the following steps: constructing a dynamic model of the virtual train formation; establishing a multi-objective optimization tracking controller based on the dynamic model; the multi-objective optimization tracking controller constructs a high-order state-space model containing errors, sets a multi-objective cost function including tracking error, operating energy consumption, and passenger comfort, and solves for the feedback gain based on this function to form the core control law; establishing an adaptive law based on the train's adhesion state to tune the control weight matrix parameters of the multi-objective optimization tracking controller in real time; and generating control commands using the multi-objective optimization tracking controller based on the train's initial operating state and target distance. This method achieves real-time coordination and balance of multiple performance indicators, including safety, efficiency, energy consumption, and comfort.

Description

Technical Field

[0001] This invention belongs to the field of high-speed train control technology and relates to a multi-objective optimization adaptive adhesion tracking control method for virtual train formations. Background Technology

[0002] With the increasing demand for intelligent and flexible rail transit, virtual train formation technology enables flexible scheduling and control of trains through dynamic formation, breaking through the limitations of traditional physical formation. It can dynamically reorganize trains in real time according to passenger flow, line load, and other conditions, adapting to diversified transportation needs, significantly reducing empty load rate and energy consumption, and solving problems such as resource waste, limited capacity, and low efficiency of manual scheduling in traditional rail transit. It can improve the utilization rate of rail lines and vehicle systems under limited cost conditions.

[0003] Cooperative tracking control of trains is crucial for realizing virtual train formation and requires further research and development. Traditional tracking control methods struggle to adapt to changes in wheel-rail adhesion when trains operate in complex environments, easily leading to wheel slippage or coasting and threatening operational safety. Furthermore, traditional tracking control often focuses on a single objective, lacking coordinated optimization for multiple objectives such as operating energy consumption and comfort, thus limiting the intelligence level of virtual train formations. For example, Chinese patent application CN118859734A discloses an improved active disturbance rejection control method for high-speed train virtual formations based on the GRO algorithm. Its core idea is to use active disturbance rejection control (ADRC) to handle internal and external disturbances and introduce the GRO intelligent optimization algorithm to offline tune five key parameters of the ADRC controller. However, in this method, the GRO algorithm optimizes parameters before the controller operates, obtaining a fixed set of optimal parameters. Once track conditions such as adhesion change drastically, this set of preset parameters may no longer be optimal, making real-time dynamic adjustment impossible and limiting adaptability. For example, Chinese patent application CN119941063A discloses a carbon emission-based virtual train formation cooperative operation control method for high-speed railways. Its core idea is to use a Model Predictive Control (MPC) framework, taking energy consumption as a core optimization objective and refining the impact of gradients, curves, and tunnels on the desired tracking distance. While this method considers additional track resistance, it does not address the microscopic adhesion dynamics at the wheel-rail contact level, such as creep rate and adhesion coefficient. Therefore, it cannot prevent or address the specific safety issue of wheel slippage or coasting caused by insufficient adhesion. Another example is Chinese patent application CN 119428800A, which discloses a wheel-rail adhesion cooperative control method for heavy-haul train formations. This method explicitly combines adhesion control with group operation control, designing different adhesion control strategies for the lead and follower trains and introducing logic switches to coordinate the two. The system uses a logical decision value Log (0 or 1) to choose between group operation control and adhesion control. When Log=0 (slippage), group control is turned off and only adhesion control is executed. This poses a risk of control interruption and impact. It does not have a unified framework for real-time and uninterrupted trade-offs and optimization of multiple objectives such as safety, tracking accuracy, energy consumption, and comfort.

[0004] In view of the above problems, there is an urgent need in this field for a multi-objective collaborative optimization adaptive adhesion tracking control method that considers safety, efficiency, energy consumption, and comfort, so as to ensure the efficient and stable operation of virtual train formations under different environmental conditions. Summary of the Invention

[0005] This invention proposes a multi-objective optimization adaptive adhesion tracking control method for virtual train formations. Under the premise of ensuring safety, this method achieves coordinated optimization of efficiency, tracking accuracy, energy saving and ride comfort during the tracking process.

[0006] The technical solution of this invention is implemented as follows:

[0007] A multi-objective optimization adaptive adhesion tracking control method for virtual train formations includes the following steps:

[0008] S1. Construct a dynamic model of a virtual train formation, wherein the virtual train formation includes one lead power unit and at least one follower power unit;

[0009] S2. Based on the dynamic model, a multi-objective optimization tracking controller is established. The multi-objective optimization tracking controller constructs a high-order state-space model containing errors, sets a multi-objective cost function that includes tracking error, operating energy consumption and ride comfort, and solves the feedback gain based on the function to form the core control law.

[0010] S3. Establish an adaptive law based on the train adhesion state to adjust the control weight matrix parameters of the multi-objective optimized tracking controller in real time;

[0011] S4. Calculate the current state error based on the initial running state of the train and the target distance, and input it into the multi-target optimized tracking controller to generate control commands.

[0012] As a preferred embodiment of the present invention, the dynamic model of the virtual train power unit in step S1 includes a basic dynamic model, a unit resistance calculation model, and a motor-side transmission dynamic model.

[0013] The basic dynamic model is as follows:

[0014]

[0015] In the formula:

[0016] For the mass of the power unit of the virtual train formation, For the acceleration of the power unit of the virtual train formation, The adhesive force acting on the power unit of the virtual train formation. The running resistance experienced by the power unit of the virtual train formation. This refers to the wheel-rail adhesion coefficient during the operation of the virtual train power unit. The basic resistance per unit force experienced by the power unit of a virtual train formation. The additional resistance per unit curve experienced by the power unit of the virtual train formation. The additional resistance per unit gradient experienced by the power unit of the virtual train formation. Additional tunnel resistance per unit area experienced by the power unit of the virtual train formation.

[0017] As a preferred embodiment of the present invention, the unit resistance calculation model is as follows:

[0018] ;

[0019] In the formula: , , This is an empirical coefficient representing the unit basic resistance experienced by the power unit of a virtual train formation. For the car body speed of the power unit of the virtual train formation, The curve radius of the track traversed by the power unit of the virtual train formation. The gradient of the ramp traversed by the power unit of the virtual train formation. The length of the tunnel traversed by the power unit of the virtual train formation.

[0020] As a preferred embodiment of the present invention, the motor-side transmission dynamics model is as follows:

[0021]

[0022] In the formula: The total moment of inertia of the motor shaft of the power unit in a virtual train formation. For the rotational inertia of the motor in the power unit of the virtual train formation, For the rotational inertia of the wheelset of the power unit in a virtual train formation, This refers to the gearbox transmission ratio. For the angular velocity of the motor in the power unit of the virtual train formation, For the output torque of the motor of the power unit of the virtual train formation, For the load torque of the power unit of the virtual train formation, This refers to the wheelset radius of the power unit in a virtual train formation.

[0023] As a preferred embodiment of the present invention, the high-order state-space model containing errors is constructed by transforming the position, velocity, and acceleration states of each power unit into error states relative to the navigation unit. The specific form of the high-order state-space model containing errors is as follows:

[0024]

[0025] In the formula, Let be the error state matrix of the i-th virtual train power unit. This is the system matrix after the state model transformation. and The input matrix after the state model transformation. Let be the distance error of the power unit of the i-th virtual train formation. Let be the speed error of the power unit of the i-th virtual train formation. Let be the acceleration error of the power unit of the i-th virtual train formation. This represents the target distance between the power units of two virtual train formations. Let be the rate of change of acceleration of the i-th virtual train power unit. Let be the rate of acceleration change of the power unit of the (i-1)th virtual train formation, which is the rate of acceleration change of the previous power unit. Let be the travel position of the power unit of the i-th virtual train formation. This represents the travel position of the (i-1)th virtual train power unit, i.e., the travel position of the previous power unit. Let be the speed of the i-th virtual train power unit. Let be the car body speed of the (i-1)th virtual train power unit, which is the car body speed of the previous power unit. Let be the acceleration of the i-th virtual train power unit. This is the acceleration of the (i-1)th virtual train power unit, which is the acceleration of the previous power unit.

[0026] In a preferred embodiment of the present invention, the multi-objective cost function is:

[0027]

[0028] In the formula, Let be the error weight matrix of the i-th virtual train power unit. Let be the input weight matrix for the power unit of the i-th virtual train formation. Let be the distance error weighting coefficient for the i-th virtual train power unit. Let be the speed error weighting coefficient of the i-th virtual train power unit. Let be the acceleration error weighting coefficient of the i-th virtual train power unit. Let be the energy consumption weighting coefficient of the i-th virtual train power unit. Let be the comfort weighting coefficient of the power unit of the i-th virtual train formation.

[0029] In a preferred embodiment of the present invention, the feedback gain is obtained through the following steps:

[0030] Solving the continuous-time algebraic Riccati equation yields a unique symmetric positive definite solution matrix containing all optimality information of the system. The algebraic Riccati equation is as follows: ;

[0031] The optimal feedback gain matrix is ​​obtained by using the unique symmetric positive definite solution matrix:

[0032] ;

[0033] In the formula, Let be the unique symmetric positive definite solution matrix of the Riccati equations corresponding to the power unit of the i-th virtual train formation. Let be the feedback gain matrix of the power unit of the i-th virtual train formation. Let be the distance error feedback gain of the i-th virtual train power unit. Let the speed error feedback gain be the speed error of the i-th virtual train power unit. Let be the acceleration error feedback gain of the i-th virtual train power unit. Let be the energy consumption feedback gain of the power unit of the i-th virtual train formation.

[0034] As a preferred embodiment of the present invention, the core control law is as follows:

[0035]

[0036] In the formula, Let be the rate of change of acceleration of the i-th virtual train power unit.

[0037] As a preferred embodiment of the present invention, the core control law further includes feedforward compensation for the acceleration disturbance of the preceding vehicle, specifically:

[0038] ;

[0039] In the formula, Let acceleration be the final control input for the power unit of the i-th virtual train formation. For the time step of virtual train formation tracking and control, This is the acceleration of the (i-1)th virtual train power unit, which is the acceleration of the previous power unit.

[0040] In a preferred embodiment of the present invention, the train adhesion state is calculated as follows:

[0041] ;

[0042] In the formula, Let be the adhesion quality index of the i-th virtual train power unit. , which is the adhesive stability index of the power unit of the i-th virtual train formation; Let be the creep rate of the power unit of the i-th virtual train formation; Let be the wheel-rail adhesion coefficient during the operation of the i-th virtual train power unit.

[0043] In a preferred embodiment of the present invention, the creep rate of the virtual train power unit is calculated as follows:

[0044]

[0045] In the formula, Let be the creep speed of the i-th virtual train power unit. Let be the wheel-to-wheel angular velocity of the i-th virtual train power unit. This refers to the wheelset radius of the power unit in a virtual train formation.

[0046] In a preferred embodiment of the present invention, the wheel-rail adhesion coefficient of the virtual train power unit is calculated using the Polach model:

[0047]

[0048] In the formula, To achieve the maximum wheel-rail adhesion coefficient, The train wheel-rail adhesion saturation coefficient. This is the train wheel-rail adhesion attenuation coefficient.

[0049] As a preferred embodiment of the present invention, the adaptive law is as follows:

[0050]

[0051] In the formula, To adjust based on adhesion quality index , , The weighting coefficients, To adjust based on adhesive stability index , , The weighting coefficients, To adjust based on adhesion quality index and The weighting coefficients, To adjust based on adhesive stability index and The weighting coefficients, , These are the growth rate coefficients of the monotonic mapping functions for the adhesion quality index and the adhesion stability index, respectively. , These are the theoretical maximum values ​​for the adhesion quality index and the adhesion stability index, respectively. The baseline value for the distance error weighting coefficient is... The baseline value for the speed error weighting coefficient is... The baseline value for the acceleration error weighting coefficient is... This is the baseline value for the energy consumption weighting coefficient. This is the baseline value for the comfort weighting coefficient.

[0052] The beneficial effects of the present invention using the above technical solution are as follows:

[0053] The multi-objective optimized adaptive adhesion tracking control method for virtual train formations provided in this invention achieves synergistic optimization of operating efficiency, tracking accuracy, energy saving, and ride comfort by setting a cost function that includes multiple objectives such as error, energy consumption, and comfort, thereby improving the overall performance of virtual train formations. An adaptive law is established based on the train adhesion state, and the controller parameters are dynamically tuned using this law to enhance the system's robustness and adaptability to complex environments, effectively preventing wheel slippage and coasting, and ensuring driving safety. A high-order state-space model and optimal control law are employed, combined with feedforward compensation and saturation constraints, to ensure that the virtual train formations quickly converge to the target distance during dynamic tracking, reducing overshoot and oscillation, and improving control accuracy and stability. Simulation verification shows that this method performs excellently in key indicators such as settling time, overshoot, energy consumption, and comfort, completing the tracking task in a shorter time and with higher efficiency while maintaining a stable distance. It can also flexibly adapt to different operating conditions, adjusting parameters in real time according to the train wheel-rail adhesion, achieving tracking control with lower train energy consumption and better comfort. Attached Figure Description

[0054] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.

[0055] Figure 1 This is a flowchart of the multi-objective optimization adaptive adhesion tracking control method for virtual train formations according to the present invention.

[0056] Figure 2 This is a dynamic analysis diagram of the power unit of the virtual train formation according to the present invention.

[0057] Figure 3 This is a schematic diagram of the virtual train formation dynamics model of the present invention.

[0058] Figure 4 This is a flowchart illustrating the adaptive wheel-rail adhesion tuning parameters of the present invention.

[0059] Figure 5 This is a flowchart of the multi-objective optimization adaptive adhesion tracking control process for virtual train formation according to the present invention.

[0060] Figure 6 The following diagram shows the simulation results of the collaborative tracking control of the power unit 1 according to the present invention. In the diagram, a is the curve of tracking distance changing with time, b is the curve of tracking speed changing with time, c is the curve of tracking acceleration changing with time, d is the curve of acceleration rate changing with time, e is the curve of adhesion coefficient changing with time, and f is the curve of operating energy consumption changing with time.

[0061] Figure 7The following diagram shows the simulation results of the collaborative tracking control of the power unit 2 according to the present invention. In the diagram, a is the curve of tracking distance changing with time, b is the curve of tracking speed changing with time, c is the curve of tracking acceleration changing with time, d is the curve of acceleration rate changing with time, e is the curve of adhesion coefficient changing with time, and f is the curve of operating energy consumption changing with time. Detailed Implementation

[0062] The technical solutions of the present invention will be clearly and completely described below with reference to the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0063] Example 1

[0064] like Figure 1 The diagram shows a flowchart of the multi-objective optimization adaptive adhesion tracking control method for virtual train formations according to the present invention. The basic building block of the virtual train formation is the power unit. First, a dynamic model of a single power unit is established. Then, based on the dynamic model of the single power unit, the lead power unit and all following power units are integrated through the vehicle-to-vehicle wireless communication information exchange mechanism to form a power unit formation, thus constructing the dynamic model of the entire virtual train formation. Each power unit transmits operating status information such as position, speed, and acceleration in real time through vehicle-to-vehicle wireless communication technology, forming a dynamically coordinated formation system.

[0065] Each following power unit sets a tracking target, taking the immediately preceding power unit as the tracking object, and clearly defines the preset target distance;

[0066] By acquiring the real-time operating status of each power unit, including key parameters such as position, velocity, and acceleration, and combining this with the preset target spacing, the distance error, velocity error, and acceleration error of each following power unit relative to the preceding power unit are calculated, forming a state error input signal.

[0067] The state error is input to the multi-target optimization tracking controller, which outputs control commands to each following power unit. Each power unit adjusts its own operating state according to the control commands to achieve accurate tracking of the preceding power unit while maintaining a stable target distance. The tracking controller adopts a real-time feedback mechanism to continuously collect the train wheel-rail adhesion state and adjust the control weight matrix parameters of the controller in real time, so that the tracking controller outputs control commands that are updated in real time and dynamically adapt to changes in adhesion state.

[0068] This invention provides a multi-objective optimization adaptive adhesion tracking control method for virtual train formations, comprising the following steps:

[0069] S1. Establish a dynamic model of a virtual train formation, which includes one virtual train formation pilot power unit and two virtual train formation follower power units;

[0070] S2. Based on the dynamic model, a multi-objective optimization tracking controller is established. The multi-objective optimization tracking controller constructs a high-order state-space model containing errors, sets a multi-objective cost function that includes tracking error, operating energy consumption and ride comfort, and solves the feedback gain based on the function to form the core control law.

[0071] S3. Establish an adaptive law based on the train adhesion state to adjust the control weight matrix parameters of the multi-objective optimized tracking controller in real time;

[0072] S4. Based on the initial running state of the train and the target distance, the multi-target optimized tracking controller generates control commands to adjust the train state in real time and complete the tracking task.

[0073] I. Specifically, in step S1, a dynamic analysis is performed on a single-section virtual train formation to establish a dynamic model of the virtual train formation:

[0074] (1) Considering that the overall system of the virtual train is relatively complex and has a high degree of nonlinear response, and that the tracking control behavior is mainly concentrated in the running gear, i.e., wheelsets, a modeling analysis of the dynamic state of the simplified virtual train power unit is performed. Lateral and vertical degrees of freedom motion is ignored, and track surface irregularities and differences in vertical force on wheelsets are not considered. It is assumed that the loads of the car body and the primary and secondary suspensions are uniformly applied to multiple single wheelsets that bear the weight of the entire car.

[0075] The virtual train power unit is treated as a single-mass system. Based on fundamental principles of dynamics, the forces acting on the virtual train power unit during operation are analyzed. These forces include viscous force and total resistance, with the total resistance comprising basic resistance and additional resistance. The simplified dynamic analysis of the virtual train power unit is as follows: Figure 2 As shown.

[0076] The basic dynamic model of the virtual train power unit is shown below:

[0077]

[0078] In the formula:

[0079] This refers to the mass of the power unit of the virtual train, i.e., the mass of a single car body in the virtual train. For the acceleration of the power unit of the virtual train formation, The adhesive force acting on the power unit of the virtual train formation. The running resistance experienced by the power unit of the virtual train formation. This refers to the wheel-rail adhesion coefficient during the operation of the virtual train power unit. The basic resistance per unit force experienced by the power unit of a virtual train formation. The additional resistance per unit curve experienced by the power unit of the virtual train formation. The additional resistance per unit gradient experienced by the power unit of the virtual train formation. Additional tunnel resistance per unit area experienced by the power unit of the virtual train formation.

[0080] (2) The basic resistance is mainly caused by friction between the wheel and rail and air resistance, and it always exists. The magnitude of the resistance can be determined by empirical formulas. Additional resistance includes curve additional resistance, gradient additional resistance and tunnel additional resistance, the magnitude of which is related to the environment in which the virtual train power unit operates.

[0081] The expressions for various unit resistances experienced by the power unit of a virtual train formation are as follows:

[0082]

[0083] In the formula: , , These are the empirical coefficients for the unit basic resistance experienced by the power unit of the virtual train formation. For the car body speed of the power unit of the virtual train formation, The curve radius of the track traversed by the power unit of the virtual train formation. The gradient of the roadway traversed by the power unit of the virtual train formation. The length of the tunnel traversed by the power unit of the virtual train formation.

[0084] (3) Model and analyze the transmission of the power unit of the virtual train. The motor torque is first transmitted to the wheel axle through the gear, and then from the wheel axle to the wheel. Under adhesion conditions, the train wheelset can realize the transmission from driving torque to adhesion traction force.

[0085] The dynamic expression of the motor-side transmission of the power unit in a virtual train formation is shown below:

[0086]

[0087] In the formula: The total moment of inertia of the motor shaft of the power unit in a virtual train formation. The moment of inertia of the motor in the power unit of the virtual train formation. For the rotational inertia of the wheelset of the power unit in a virtual train formation, This refers to the gearbox transmission ratio. For the angular velocity of the motor in the power unit of the virtual train formation, For the output torque of the motor of the power unit of the virtual train formation, For the load torque of the power unit of the virtual train formation, This refers to the wheelset radius of the power unit in a virtual train formation.

[0088] In this embodiment, considering that the empirical coefficient of the basic resistance per unit and the gearbox transmission ratio of the virtual train power unit are closely related to the train model and specific characteristics, in order to reduce the uncertainty in operation control, the power units of each virtual train are set to be of the same model and the relevant parameters are kept consistent. In addition, in order to focus on the core control issues and facilitate the analysis of control performance, the train travels on a straight line at all times, so there is no curve radius R, and the slope and tunnel conditions remain unchanged.

[0089] In this embodiment, the parameters of the dynamic model of the virtual train power unit are determined based on the CRH2 type train. The relevant parameters are shown in Table 1.

[0090] Table 1 Parameter Table of Dynamic Model

[0091] ;

[0092] (4) Subsequently, based on the basic dynamic model of a single-car virtual train formation, a virtual train formation dynamic model containing multiple independent power units is established, including one virtual train formation lead power unit and two virtual train formation follower power units. Information is transmitted and exchanged between the power units via vehicle-to-vehicle wireless communication technology to ensure real-time communication, and they are arranged in a small-interval formation according to actual transportation needs. The resulting virtual train formation dynamic model is as follows: Figure 3 As shown, the lead power unit transmits its real-time operating status (position, velocity, acceleration) to the first follower power unit; the first follower power unit transmits its real-time status to the second follower power unit.

[0093] Second, in step S2, based on the aforementioned dynamic model, a multi-objective optimized tracking controller is established. This controller constructs a high-order state-space model containing errors, sets a multi-objective cost function encompassing tracking error, operating energy consumption, and ride comfort, and solves for the feedback gain based on this function to form the core control law. The process includes the following steps:

[0094] 1. Construct a high-order state-space model for virtual train formations.

[0095] (1) Constructing state equations

[0096] Each virtual train power unit is an independent dynamic system. The analysis is based on the point mass model, taking into account the changes in the speed and acceleration of each power unit during the tracking control process. A third-order integrator is used to construct a high-order state space model of the virtual train.

[0097] The high-order state-space model of the virtual train formation is shown below:

[0098] ;

[0099] , ;

[0100] In the formula, Let i be the state matrix of the i-th virtual train power unit. For the system matrix, Let be the input matrix for the power unit of the i-th virtual train formation. Let be the rate of change of acceleration of the i-th virtual train power unit. Let be the travel position of the power unit of the i-th virtual train formation. Let be the speed of the i-th virtual train power unit. Let be the acceleration of the power unit of the i-th virtual train formation.

[0101] (2) Convert to a state-space model containing errors

[0102] The tracking reference target of the virtual train power unit is the previous power unit. The original global state space model is augmented and transformed into a newly defined error-containing state space model. Simultaneously, considering the natural decay characteristics of acceleration and acceleration error caused by air resistance, mechanical friction, and communication delays during train operation, a damping coefficient is introduced into the system matrix to make the model more accurately reflect the actual tracking situation of the train.

[0103] The resulting high-order state-space model containing the error is shown below:

[0104]

[0105] , ,

[0106] In the formula, Let i be the state matrix including errors for the power unit of the i-th virtual train formation. This is the system matrix after the state model transformation. and All of these are input matrices after the state model transformation. Let be the rate of change of acceleration of the i-th virtual train power unit. Let be the rate of acceleration change of the power unit of the (i-1)th virtual train formation, which is the rate of acceleration change of the previous power unit. Let be the distance error of the power unit of the i-th virtual train formation. Let be the speed error of the power unit of the i-th virtual train formation. Let be the acceleration error of the power unit of the i-th virtual train formation. This represents the travel position of the (i-1)th virtual train power unit, i.e., the travel position of the previous power unit. Let be the car body speed of the (i-1)th virtual train power unit, which is the car body speed of the previous power unit. Let be the acceleration of the (i-1)th virtual train power unit, i.e., the acceleration of the previous power unit. This represents the target distance between the power units of two virtual train formations. The acceleration error damping coefficient of the power unit of the virtual train formation. This is the acceleration damping coefficient of the power unit of the virtual train formation.

[0107] In this embodiment, , .

[0108] 2. Define the multi-objective cost function

[0109] To achieve optimal balance between operational efficiency, tracking accuracy, train energy consumption, and passenger comfort, and to realize collaborative optimization, a cost function containing multiple objectives is set.

[0110] The cost function containing multiple objectives is as follows:

[0111]

[0112] This cost function achieves efficient and accurate tracking by penalizing the train's distance, speed, and acceleration errors. Considering that traction energy consumption during train tracking is primarily used to overcome inertia and running resistance for acceleration, the square of the acceleration is penalized to suppress high acceleration values ​​and reduce energy consumption. The ride comfort during train operation is directly related to the rate of change of acceleration; therefore, the square of the rate of change of acceleration is penalized to suppress abrupt acceleration changes and improve ride comfort.

[0113] At the same time, a corresponding control weight matrix is ​​designed. The weights are initialized randomly, and the various weight parameters can be adjusted in real time to adapt to various operating conditions and control strategies.

[0114] The control weight matrix is ​​as follows:

[0115]

[0116] In the formula, Let be the error weight matrix of the i-th virtual train power unit. Let be the input weight matrix for the power unit of the i-th virtual train formation. Let be the distance error weighting coefficient for the i-th virtual train power unit. Let be the speed error weighting coefficient of the i-th virtual train power unit. Let be the acceleration error weighting coefficient of the i-th virtual train power unit. Let be the energy consumption weighting coefficient of the i-th virtual train power unit. Let be the comfort weighting coefficient of the power unit of the i-th virtual train formation.

[0117] 3. Based on the above model and cost function, find the unique optimal control command that minimizes the cost function J:

[0118] (1) Solve the continuous-time algebraic Riccati equation to obtain a unique symmetric positive definite solution matrix containing all optimality information of the system. ;

[0119] Algebraic Riccati equations:

[0120] (2) Using the unique symmetric positive definite solution matrix, the optimal feedback gain matrix is ​​calculated:

[0121]

[0122] (3) Obtain the core control law:

[0123]

[0124] 4. Based on vehicle-to-vehicle communication, the real-time status of all virtual train power units is acquired. Feedforward compensation is then integrated, and the acceleration disturbance of the previous power unit is superimposed onto the control input to offset the disturbance's impact, improving tracking accuracy. Furthermore, the core control law is obtained:

[0125]

[0126] in, Let be the unique symmetric positive definite solution matrix of the Riccati equations corresponding to the power unit of the i-th virtual train formation. Let be the feedback gain matrix of the power unit of the i-th virtual train formation. Let be the distance error feedback gain of the i-th virtual train power unit. Let the speed error feedback gain be the speed error of the i-th virtual train power unit. Let be the acceleration error feedback gain of the i-th virtual train power unit. Let be the energy consumption feedback gain of the i-th virtual train power unit. Let be the rate of change of acceleration of the i-th virtual train power unit. The final control input acceleration for the i-th virtual train power unit is the final generated control command. The time step for tracking and controlling virtual train formations.

[0127] Considering the limitations on the maximum acceleration and deceleration capabilities of virtual train formations during traction and braking in actual engineering projects, saturation constraints are incorporated. An acceleration threshold is set, which is the maximum absolute value of acceleration allowed by the power unit's traction system. Similarly, an acceleration rate threshold is set, which is the maximum absolute value of the acceleration rate allowed by the power unit's traction system. These constraints limit the acceleration and acceleration rate of the power unit, ensuring the safe operation of the virtual train formation and preventing excessive traction energy consumption and poor passenger experience. In this embodiment, the acceleration threshold is 1.0 m / s². 2 The threshold for the rate of change of acceleration is 2.0 m / s². 3 .

[0128] After completing the above steps, a virtual train formation multi-target optimization tracking controller can be constructed. It can sense the precise position, speed, and acceleration of the tracked target in real time, and balance and coordinate multiple control objectives such as control safety, operating efficiency, tracking accuracy, energy saving, and passenger comfort. Based on this, control commands are generated to smoothly and quickly adjust the power output of the following power unit to cope with various tracking situations such as target acceleration, deceleration, and cruising. This allows the physically decoupled virtual train formation to dynamically track the running status of the leading train safely, accurately, and efficiently, just like a rigid connection, and strictly maintain the actual distance between the two power units near the preset target spacing.

[0129] Third, step S3 involves establishing an adaptive law based on the train's adhesion state to tune the control weight matrix parameters of the multi-objective optimized tracking controller in real time. This specifically includes the following steps:

[0130] 1. Calculate the adhesion coefficient and creep rate between the wheel and rail.

[0131] When a virtual train is traveling at high speed, due to the load of the vehicle weight, the wheel-rail contact area remains in a relatively stationary adhesive state. Simultaneously, due to the driving torque, the wheelset rolls forward, causing relative motion or a tendency for relative motion in the wheel-rail contact area, resulting in relative slippage. Because both adhesive and creep exist simultaneously, the vehicle's speed differs from the circumferential speed of the wheel-rail rolling motion; this speed difference is called the creep speed, and the ratio of the creep speed to the vehicle's speed is called the creep ratio.

[0132] The train creep calculation model is shown below:

[0133]

[0134] In the formula, Let be the creep speed of the i-th virtual train power unit. Let be the speed of the i-th virtual train power unit. Let be the wheel-to-wheel angular velocity of the i-th virtual train power unit. Let be the creep rate of the power unit of the i-th virtual train formation. This refers to the wheelset radius of the power unit in a virtual train formation.

[0135] Considering the complexity of the adhesion contact state between the wheels and rails of virtual train formations, and the fact that it is subject to various influencing factors, the adhesion coefficient is used as a numerical indicator to quantify it, and the Polach model is used for estimation.

[0136] The expression for the adhesion coefficient of the Polach model is as follows:

[0137]

[0138] In the formula, Let be the wheel-rail adhesion coefficient during the operation of the i-th virtual train power unit. To achieve the maximum wheel-rail adhesion coefficient, The train wheel-rail adhesion saturation coefficient. This is the train wheel-rail adhesion attenuation coefficient.

[0139] In this embodiment, , , The calculation frequency and control cycle of creep rate and adhesion coefficient are synchronized.

[0140] Using this model, the adhesion characteristic curve can be well fitted, and the adhesion state between the wheels and rails of the virtual train can be perceived in real time, providing accurate input for subsequent adaptive tracking control.

[0141] 2. Dynamic parameter tuning based on adaptive laws

[0142] Based on the real-time adhesion state, the weight parameters of the multi-objective optimization controller in step two are automatically adjusted.

[0143] To prevent measurement noise from causing significant interference and to avoid the limitations of directly using the adhesion coefficient and creep rate as adaptive law inputs, a more explicit control orientation is established. An adhesion state evaluation model is built, and the adhesion coefficient and creep rate are nonlinearly transformed to obtain two indices for describing the adhesion state between the wheel and rail.

[0144] The train adhesion state evaluation model is shown below:

[0145]

[0146] In the formula, Let be the adhesion quality index of the i-th virtual train power unit. is the adhesive stability index of the power unit of the i-th virtual train formation.

[0147] Adhesion quality index assesses the control potential under current operating conditions from the perspective of energy conversion efficiency, reflecting the actual effectiveness of wheel-rail contact. Stability index quantifies the power unit's ability to resist instability and slippage. These two indices, through nonlinear transformation, retain the original physical characteristics while highlighting the sensitivity to different indices, providing a suitable basis for subsequent parameter adjustments in the tracking controller.

[0148] In the virtual train multi-objective optimization tracking controller, there are 5 parameters to be tuned, namely: , , , and These parameters are all parameters in the control weight matrix. Among them, the error weight coefficients, especially the distance error weight coefficient, mainly affect the response speed of the tracking control system. The larger the weight, the larger the input to the tracking controller, and the faster the power unit completes the tracking task. However, in the actual virtual train tracking process, factors such as wheel-rail adhesion must also be considered to prevent safety accidents and repeated oscillations. Simultaneously, to reasonably achieve multi-objective optimization, the weight settings of energy consumption and comfort terms must be carefully considered to ensure the overall performance during train tracking. The tuning process for each undetermined parameter is as follows: Figure 4 As shown.

[0149] With two adhesion state indices as inputs and the parameter values ​​to be tuned as outputs, an adaptive law is set so that the system automatically pursues higher tracking efficiency when the adhesion state is good, and prioritizes energy saving and comfort of train operation when the adhesion state deteriorates. The adaptive law adopts a hierarchical hybrid structure, combining exponential smoothing characteristics with linear weighting, which can avoid sudden changes in controller parameters and ensure smooth changes in parameters when the indices change.

[0150] The adaptive law expression is set as follows:

[0151]

[0152] In the formula, To adjust based on adhesion quality index , , The weighting coefficients, To adjust based on adhesive stability index , , The weighting coefficients, To adjust based on adhesion quality index and The weighting coefficients, To adjust based on adhesive stability index and The weighting coefficients, , These are the growth rate coefficients of the monotonic mapping functions for the adhesion quality index and the adhesion stability index, respectively. , These are the theoretical maximum values ​​for the adhesion quality index and the adhesion stability index, respectively. The baseline value for the distance error weighting coefficient is... The baseline value for the speed error weighting coefficient is... The baseline value for the acceleration error weighting coefficient is... This is the baseline value for the energy consumption weighting coefficient. This is the baseline value for the comfort weighting coefficient.

[0153] The parameters in the adaptive law can be initially set based on engineering experience, and then finally determined after adjustment and optimization based on simulation experimental results. The values ​​of each parameter in the adaptive law are shown in Table 2.

[0154] Table 2 Adaptive Law Parameter Table

[0155] ;

[0156] Through the aforementioned adaptive law, different operating conditions can be flexibly adapted to, and the parameters to be determined can be adjusted in a relatively smooth manner to complete the adaptive tracking control of the wheel-rail adhesion of the virtual train. When the adhesion quality and adhesion stability indices are large, the weight of distance error is increased and the weight of other indices is decreased, allowing the power unit to track with greater acceleration and converge to the target distance as quickly as possible. When the adhesion quality and adhesion stability indices are small, the weight of distance error is decreased and the weight of other indices is increased, prioritizing driving safety, limiting the control input amplitude, and avoiding slippage. This allows the power unit to complete the tracking task with lower energy consumption and higher comfort, achieving stable and efficient tracking. The tracking control process of the virtual train after parameter tuning is as follows: Figure 5 As shown.

[0157] The new weight parameters are immediately updated into the cost function of the multi-objective optimization tracking controller in step two. Based on the new weights, the controller re-solves the core control law and generates control commands that match the current wheel-rail adhesion capability.

[0158] IV. Step S4 includes the following steps:

[0159] The initial operating state of each power unit of the virtual train formation is set, including travel speed, acceleration, and actual spacing information. At the same time, the target spacing for tracking control is given, the current state error is calculated and input into the multi-objective optimized adaptive adhesive tracking controller. The control command is then obtained to adjust the train state in real time and complete the tracking task.

[0160] The initial state and related parameter settings of this embodiment are shown in Table 3.

[0161] Table 3 Initial State and Related Parameters

[0162] ;

[0163] In this embodiment, the first virtual formation power unit following the lead power unit is designated as the following power unit 1, and its initial distance from the lead power unit is the initial distance 1. The second virtual formation power unit following the lead power unit is designated as the following power unit 2, and its initial distance from the following power unit 1 is the initial distance 2. Simultaneously, the acceleration of each power unit is zero at the initial moment.

[0164] Based on the aforementioned condition parameters and initial state, this invention utilizes the method to conduct control simulation experiments, completing a virtual train formation cooperative tracking task. The simulation results are then compared with those of PID fixed-parameter control to demonstrate the superior overall performance of the method provided by this invention. The simulation results are as follows: Figure 6 and Figure 7 As shown in Table 4, the tracking control performance indicators are as follows.

[0165] Table 4 Tracking Control Performance Indicators

[0166] ;

[0167] Figure 6 shows the simulation results of the cooperative tracking control of the following power unit 1. In the figure, a represents the tracking distance versus time, b represents the tracking speed versus time, c represents the tracking acceleration versus time, d represents the rate of change of acceleration versus time, e represents the adhesion coefficient versus time, and f represents the operating energy consumption versus time. Combining these sub-figures, the significant advantages of the multi-objective adaptive control method of this invention compared to PID fixed-parameter control are clearly evident. A detailed analysis follows:

[0168] Figure 6 -a is a graph showing the tracking distance changing over time, visually illustrating the dynamic change in distance between the following power unit 1 and the pilot power unit. Initially, the distance between them is 60m, and the target distance is 50m. Both control methods initiate tracking to reduce the distance error. Under PID fixed parameter control, the distance decreases with slight fluctuations, gradually stabilizing only after a small overshoot during tracking, eventually settling near the target distance. In contrast, under the multi-target adaptive control of this invention, the distance decreases smoothly without significant fluctuations or overshoot, and converges stably to the target distance of 50m in approximately 14.6s, a 2.6s reduction compared to the 17.2s adjustment time of PID fixed parameter control, demonstrating superior tracking accuracy and rapid response capability.

[0169] Figure 6-b shows the tracking speed variation over time, reflecting the speed adjustment process of the following power unit 1. Initially, both power unit 1 and the navigator unit have a speed of 50 m / s. In the initial tracking phase, to reduce the distance, both control methods control power unit 1 to increase its speed. Under PID fixed parameter control, the speed reaches a maximum of 51.433 m / s, with slight oscillations during the speed increase. Under the multi-objective adaptive control of this invention, the maximum speed is only 51.177 m / s, the speed increase is smoother, and there are no oscillations. After the distance stabilizes, it quickly returns to the same speed as the navigator unit, ensuring tracking efficiency while avoiding additional resistance and energy consumption caused by excessive speed.

[0170] Figure 6-c shows the tracking acceleration over time, illustrating the acceleration regulation characteristics of power unit 1. In the initial tracking phase, both control methods output large accelerations to quickly reduce the distance. However, the acceleration curve of the PID fixed-parameter control exhibits significant fluctuations, with a higher peak value and a slower decay rate, resulting in minor acceleration fluctuations in the later stages. The multi-objective adaptive control of this invention produces an acceleration curve with a lower peak value and smoother decay, avoiding the impact of sudden acceleration changes on ride comfort and equipment wear, while also laying the foundation for energy reduction.

[0171] Figure 6-d shows the acceleration rate of change curve over time. The figure shows that under PID fixed parameter control, the acceleration rate of change fluctuates more, with a root mean square value of 0.032 m / s³. In contrast, the acceleration rate of change curve of the multi-objective adaptive control of this invention is much smoother, with a root mean square value of only 0.027 m / s³, which is significantly lower than that of PID control. This effectively suppresses sudden acceleration changes, greatly improves ride comfort, and meets the comfort requirements in multi-objective optimization.

[0172] Figure 6-e shows the adhesion coefficient variation over time, reflecting the stability of the wheel-rail adhesion state. During the tracking process, the adhesion coefficient of the multi-objective adaptive control method of this invention fluctuated less, indicating that the method can effectively adapt to the wheel-rail adhesion state, prevent wheel slippage or coasting, and ensure driving safety. In contrast, the adhesion coefficient of the PID fixed parameter control fluctuated relatively more, showing a slight decrease at key nodes of speed and acceleration adjustment, which poses certain safety hazards.

[0173] Figure 6-f shows the energy consumption curve over time, illustrating the energy consumption during the tracking process. Under PID fixed parameter control, the power curve fluctuates significantly, with an average power of 0.224 MW. The power curve of the multi-objective adaptive control of this invention is much smoother, with an average power of only 0.217 MW. This advantage stems from the smooth speed and acceleration regulation, avoiding additional energy loss caused by excessive speed and acceleration fluctuations, thus achieving a synergy between energy saving and efficient tracking.

[0174] In summary, the data in each subplot of Figure 6 fully demonstrate that when the multi-objective adaptive control method of the present invention is applied to the following power unit 1, it is superior to PID fixed parameter control in terms of adjustment time, overshoot, speed control, acceleration stability, adhesion coefficient maintenance and energy consumption control. The adjustment effect is smoother and more stable, and the tracking task can be completed in a shorter time and with higher efficiency, while taking into account safety and comfort.

[0175] Figure 7 shows the simulation results of the cooperative tracking control of the following power unit 2. The types of its sub-graphs are the same as those in Figure 6. Since the tracking target of the following power unit 2 is the following power unit 1, and the following power unit 1 is in a dynamic adjustment state, the tracking process of the following power unit 2 is more complex. However, the multi-objective adaptive control method of the present invention still shows significant advantages, which are analyzed in detail below:

[0176] Figure 7 -a is a graph showing the tracking distance changing over time. This graph shows that the initial distance of the following power unit 2 is 60m, and the target distance is 50m. Due to the dynamic adjustment of the following power unit 1 in the initial period, the adjustment time of the following power unit 2 is longer than that of the following power unit 1 under both control methods. However, the adjustment time of the multi-objective adaptive control of this invention is 15.8s, which is still shorter than the 18.2s of the PID fixed parameter control. The spacing curve of the PID fixed parameter control fluctuates more significantly, with an overshoot of 1.099%; while the spacing curve of the multi-objective adaptive control of this invention decreases smoothly, with an overshoot of only 0.012%, and the tracking accuracy is significantly better than that of PID control.

[0177] Figure 7-b shows the tracking speed versus time curve. It indicates that under PID fixed-parameter control, the maximum speed of the following power unit 2 reaches 52.790 m / s, significantly higher than the 52.319 m / s achieved by the multi-objective adaptive control of this invention. Excessive speed leads to a substantial increase in the basic resistance experienced by power unit 2 during operation, reducing energy efficiency and increasing the equipment's operating load. In contrast, the multi-objective adaptive control of this invention, through precise speed adjustment, minimizes peak speed while maintaining tracking efficiency, making speed changes more aligned with the dynamic adjustments of the preceding power unit and avoiding ineffective high-speed driving.

[0178] Figure 7-c shows the tracking acceleration curve over time. The figure shows that the acceleration curve of the PID fixed parameter control fluctuates more violently, with a higher peak value and a longer duration, resulting in poor operation stability of the following power unit 2. Although the acceleration curve of the multi-target adaptive control of the present invention has a certain adjustment process due to the dynamic adjustment of the tracking target, the overall decay is smoother and it stabilizes quickly in the later stage of tracking. This avoids the increase in energy consumption and decrease in comfort caused by repeated acceleration fluctuations, demonstrating stronger dynamic adaptability.

[0179] Figure 7-d shows the acceleration rate of change over time. The figure shows that the acceleration rate of change under PID fixed parameter control fluctuates more, with a root mean square value of 0.045 m / s³, resulting in poor ride comfort. The multi-objective adaptive control of this invention has a root mean square value of 0.037 m / s³ for acceleration, and the curve is smoother, effectively reducing the jolt caused by sudden acceleration changes. Even when the target being tracked is unstable, it can still ensure good ride comfort.

[0180] Figure 7-e shows the adhesion coefficient as a function of time. The figure shows that the adhesion coefficient of the multi-objective adaptive control of the present invention remains at a high level with minimal fluctuations, ensuring good adhesion between the wheel and rail and effectively preventing wheel spin or skidding. In contrast, the adhesion coefficient of the PID fixed parameter control fluctuates significantly when the speed and acceleration are adjusted greatly, and the adhesion coefficient is lower than that of the present invention in some periods, which poses certain safety risks. This safety advantage is even more prominent in complex working conditions where the target is being tracked dynamically.

[0181] Figure 7-f shows the energy consumption variation curve over time. The figure indicates that the power curve of PID fixed-parameter control exhibits large fluctuations and high peak values, with an average power of 0.247 MW. In contrast, the average power of the multi-objective adaptive control method of this invention is only 0.238 MW, saving 3.64% of energy compared to PID control. This result stems from the method's precise control of speed and acceleration, avoiding additional energy consumption caused by excessive speed and acceleration fluctuations. Furthermore, the combination of adaptive laws for dynamic adaptation to the adhesion state further optimizes energy consumption performance, achieving energy-saving operation under complex conditions.

[0182] In summary, the data in Figure 7 show that although the following power unit 2 faces the complex situation of initial instability in the target being tracked, it still outperforms PID fixed parameter control in terms of settling time, overshoot, maximum speed control, comfort, adhesion stability, and energy consumption under the multi-objective adaptive control method of this invention. While the tracking time of power unit 2 is slightly longer than that of power unit 1 under both control methods, the overall performance advantage of the method of this invention remains significant, fully verifying the effectiveness and adaptability of this method in multi-power unit cooperative tracking scenarios.

[0183] Comprehensive analysis of the tracking control performance indicators shows that, under the control method of this invention, the settling time and overshoot of the two following power units are both small, reflecting the stability and efficiency of the control system. The maximum speed and average energy consumption of following power unit 2 are slightly larger than those of following power unit 1, but still within a reasonable range. The root mean square of the acceleration change rate of both following power units is very small, indicating that both have good comfort. Compared with existing technologies, the multi-objective optimized adaptive adhesion tracking control method provided by this invention shortens the settling time by 14.12%, reduces the overshoot by 2.27%, saves energy by 3.40%, and improves comfort by 16.88%. Simultaneously, it maintains a higher adhesion coefficient during acceleration tracking, preventing wheel spin or coasting and ensuring driving safety, demonstrating superior performance in many aspects.

[0184] Step S3 is omitted from the method of this invention, i.e., an adaptive law is not established based on the train adhesion state to adjust the control weight matrix parameters of the multi-objective optimized tracking controller in real time. A comparative simulation test is conducted based on the above condition parameters and initial state, and the results are compared with the control simulation test results of the method of this invention. The results show that compared with the method that omits the adaptive law, the method of this invention has better performance in terms of energy consumption, safety and comfort during accelerated tracking.

[0185] This invention's multi-objective optimization adaptive adhesion tracking control method effectively copes with external disturbances and adapts to changes in wheel-rail adhesion. By setting various error weights and the core control law, it ensures rapid convergence and reduces overshoot. Simultaneously, multi-objective optimization reduces train traction energy consumption and improves passenger comfort. It exhibits superior performance in terms of settling time, overshoot, maximum speed, average energy consumption, and root mean square value of jerk, verifying its advanced nature. This demonstrates that the control method can excellently meet various needs in practical engineering, stably, efficiently, and with low carbon footprint, completing tracking control tasks with superior overall performance.

[0186] The above are merely preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A multi-objective optimization adaptive adhesion tracking control method for virtual consist trains, characterized in that, The method comprises the following steps: S1, constructing a dynamics model of a virtual marshalling train, the virtual marshalling train comprising 1 leading power unit and at least 1 following power unit; S2, based on the dynamics model, establishing a multi-objective optimization tracking controller, the multi-objective optimization tracking controller being configured to set a multi-objective cost function comprising a tracking error, an operation energy consumption and a ride comfort by constructing a high-order state space model containing an error, and to solve a feedback gain based on the function to form a core control law; S3, establishing an adaptive law according to a train adhesion state to real-time adjust a control weight matrix parameter of the multi-objective optimization tracking controller; S4, calculating a current state error according to an initial operation state and a target distance of the train and inputting the state error to the multi-objective optimization tracking controller to generate a control instruction; The train adhesion state is calculated as follows: ； wherein, is the adhesion quality index of the i-th virtual marshaled train power unit, is the adhesion stability index of the i-th virtual marshaled train power unit; is the creep rate of the i-th virtual marshaled train power unit; is the wheel-rail adhesion coefficient when the i-th virtual marshaled train power unit is running. The adaptive law is shown as follows: ； wherein is a weight coefficient adjusted based on the adhesion quality index , , , is a weight coefficient adjusted based on the adhesion stability index , , , is a weight coefficient adjusted based on the adhesion quality index and , is a weight coefficient adjusted based on the adhesion stability index and , , are respectively a monotonic mapping function growth rate coefficient of the adhesion quality index and the adhesion stability index, , are respectively a theoretical maximum value of the adhesion quality index and the adhesion stability index, is a distance error weight coefficient reference value, is a speed error weight coefficient reference value, is an acceleration error weight coefficient reference value, is an energy consumption weight coefficient reference value, is a comfort weight coefficient reference value.

2. The multi-objective optimization adaptive traction control method for virtual consist trains according to claim 1, wherein, The high-order state space model containing the error is constructed by converting a position, a speed and an acceleration state of each power unit into an error state relative to a tracking target, and a specific form of the high-order state space model containing the error is as follows: ； wherein, is the state matrix of the ith virtual consist power unit with error, is the system matrix of the state model after conversion, and is the input matrix of the state model after conversion, is the distance error of the ith virtual consist power unit, is the speed error of the ith virtual consist power unit, is the acceleration error of the ith virtual consist power unit, is the target distance between two virtual consist power units, is the acceleration change rate of the ith virtual consist power unit, is the acceleration change rate of the ith-1 virtual consist power unit, i.e. the acceleration change rate of the previous power unit, is the travel position of the ith virtual consist power unit, is the travel position of the ith-1 virtual consist power unit, i.e. the travel position of the previous power unit, is the car body speed of the ith virtual consist power unit, is the car body speed of the ith-1 virtual consist power unit, i.e. the car body speed of the previous power unit, is the acceleration of the ith virtual consist power unit, is the acceleration of the ith-1 virtual consist power unit, i.e. the acceleration of the previous power unit.

3. The multi-objective optimization adaptive traction control method for virtual consist trains according to claim 2, characterized in that, The multi-objective cost function is as follows: ； wherein, is an error weight matrix of the ith virtual marshaled train power unit, is an input weight matrix of the ith virtual marshaled train power unit, is a distance error weight coefficient of the ith virtual marshaled train power unit, is a speed error weight coefficient of the ith virtual marshaled train power unit, is an acceleration error weight coefficient of the ith virtual marshaled train power unit, is an energy consumption weight coefficient of the ith virtual marshaled train power unit, is a comfort weight coefficient of the ith virtual marshaled train power unit.

4. The multi-objective optimization adaptive traction control method for virtual consist trains according to claim 3, wherein, The feedback gain is obtained by the following steps: Solving the continuous-time algebraic Riccati equation to obtain the unique symmetric positive definite solution matrix containing all the optimal information of the system, the algebraic Riccati equation: ; An optimal feedback gain matrix is calculated by using a unique symmetric positive definite solution matrix: ； wherein, is the unique symmetric positive definite solution matrix of the Riccati equation for the i-th virtual marshalling train power unit, is the feedback gain matrix of the i-th virtual marshalling train power unit, is the distance error feedback gain of the i-th virtual marshalling train power unit, is the speed error feedback gain of the i-th virtual marshalling train power unit, is the acceleration error feedback gain of the i-th virtual marshalling train power unit, is the energy consumption feedback gain of the i-th virtual marshalling train power unit.

5. The multi-objective optimization adaptive traction control method for virtual consist trains according to claim 4, wherein, The core control law is as follows: ； In the formula, is the acceleration rate of change of the i-th virtual marshalling train power unit.

6. The multi-objective optimization adaptive traction control method for virtual consist trains according to claim 5, wherein, The core control law further comprises a feedforward compensation for an acceleration disturbance of a preceding vehicle, and is specifically as follows: ； wherein is the final control input acceleration for the i-th virtual consist power unit, is the time step for virtual consist tracking control.

7. The multi-objective optimization adaptive traction control method for virtual consist trains according to claim 1, wherein, A creep rate of the power unit of the virtual marshalling train is calculated as follows: ； wherein is the creep speed of the i-th virtual consist power unit, is the carbody speed of the i-th virtual consist power unit, is the wheelset angular speed of the i-th virtual consist power unit, is the wheelset radius of the virtual consist power unit.

8. The multi-objective optimization adaptive traction control method for virtual consist trains according to claim 1, wherein, A calculation of a wheel-rail adhesion coefficient of the power unit of the virtual marshalling train adopts a Polach model. ； wherein is the creep speed of the i-th virtual consist power unit, is the maximum wheel-rail adhesion coefficient, is the train wheel-rail adhesion saturation coefficient, is the train wheel-rail adhesion decay coefficient.

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