A high-speed train optimal traction coordination method based on dynamic average consistency

Abstract

This invention relates to a dynamic average consistency-based optimal traction coordination method for high-speed trains, belonging to the field of high-speed train operation control. The method includes: considering a high-speed train with at least two traction power units, establishing a traction power coordination optimization problem for the high-speed train based on the operating state of each traction power unit; then, utilizing the characteristics of the optimal solution, transforming the traction power coordination optimization problem into a dynamic average consistency problem; and using a coordination optimization algorithm based on elastic fixed-time dynamic average consistency to distribute and obtain the optimal traction force for each traction power unit of the high-speed train. This invention eliminates the need for global information collection and processing at the control center, avoiding single-node failures at the control center; it can track the optimal solution within a preset fixed time, meeting the requirements for fast and high-precision train control performance; and it can operate normally under network attacks, ensuring the safe and stable operation of high-speed trains.

Description

Technical Field

[0001] This invention belongs to the field of high-speed train operation control and relates to an optimal traction coordination method for high-speed trains based on dynamic average consistency. Background Technology

[0002] To meet the higher performance requirements of railway transportation, such as safety, comfort, energy efficiency, and punctuality, high-speed trains must be equipped with advanced operation control systems to control traction and braking. Train traction power is mainly divided into two types: centralized traction power mode and distributed traction power mode. Because high-speed train operation requires powerful propulsion, high-speed trains generally adopt a distributed traction power mode, where multiple traction power units are distributed across multiple carriages. Existing train operation control systems utilize a control center to coordinate, optimize, and control the distributed traction power. This centralized coordination method has drawbacks such as single-node failures, heavy communication burden on the control center, and poor scalability, making it difficult to guarantee the future high-speed, high-density, and commuter-style operation needs of high-speed trains.

[0003] To overcome the drawbacks of centralized coordination optimization and control in high-speed trains, academia and industry have recently proposed distributed coordinated control methods for high-speed trains based on multi-agent system consistency. For example, patent application number 201910588591.1 proposes a distributed control method for multiple power units in high-speed trains; patent application number 201810557997.9 proposes a train stopping consistency control method based on multi-agent systems; and the paper "Distributed adaptive fault-tolerant control for high-speed trains using multi-agent system model," published in IEEE Transactions on Vehicular Technology, proposes a distributed adaptive fault-tolerant control method for high-speed trains.

[0004] The aforementioned high-speed train distributed coordinated control scheme mainly addresses the control issues of train position and speed, while neglecting the optimal coordinated allocation of traction power. This prevents high-speed trains from achieving low-cost operation under distributed control. Secondly, existing high-speed train distributed coordinated control schemes only achieve asymptotic convergence, making it difficult to guarantee rapid and high-precision train control. Furthermore, existing high-speed train distributed coordinated control schemes consider ideal communication scenarios, while actual communication networks are highly vulnerable to cyberattacks, thus affecting the safe operation of trains. Summary of the Invention

[0005] In view of this, the purpose of this invention is to provide a high-speed train optimal traction coordination method based on dynamic average consistency. This method addresses the problem of optimal coordination and allocation of high-speed train traction power under the control input of adversary network attacks. Based on a distributed optimization algorithm with elastic fixed-time dynamic average consistency, it achieves safe, fast and optimal allocation of distributed traction power of high-speed trains in the absence of a control center.

[0006] To achieve the above objectives, the present invention provides the following technical solution: A method for optimal traction coordination of high-speed trains based on dynamic average consistency is proposed. The method includes: considering a high-speed train with no less than two traction power units, establishing a traction power coordination optimization problem for the high-speed train based on the operating status of each traction power unit; transforming the traction power coordination optimization problem into a dynamic average consistency problem using the characteristics of the optimal solution; and distributively obtaining the optimal traction force for each traction power unit of the high-speed train based on a coordination optimization algorithm with elastic fixed-time dynamic average consistency.

[0007] Furthermore, establishing the traction power coordination optimization problem for high-speed trains includes: Establishing a cost function that needs to be optimized for high-speed train traction power coordination:

[0008] In the formula, This represents the total cost function with respect to traction force. , Indicates the first i The traction force provided by each traction power unit Indicates the first i The cost function of a traction power unit n This indicates the total number of traction power units.

[0009] Establish the constraints that must be satisfied to minimize this cost function, including the traction-resistance balance constraint, expressed as:

[0010] In the formula, The time-varying total resistance experienced by the high-speed train, and the upper and lower limits of the traction force, are represented as:

[0011] In the formula, Indicates the first i The lower limit of the traction force of each traction power unit Indicates the first i The upper limit of traction force of each traction power unit.

[0012] By employing a smooth penalty function, the traction power coordination optimization problem with both equality and inequality constraints is transformed into a traction power coordination optimization problem with only equality constraints:

[0013] st

[0014] In the formula, This represents the total cost function with penalty costs. Indicates the first i A cost function for each traction power unit with penalty costs;

[0015]

[0016] In the formula, For the first i Penalty parameters for the coordination optimization problem of a traction power unit.

[0017] Furthermore, based on the aforementioned traction power coordination optimization problem with only equality constraints, and according to the characteristics of the optimal solution of this coordination optimization problem, the traction power coordination optimization problem is transformed into a dynamic average consistency problem. Specifically, in the aforementioned traction power coordination optimization problem with only equality constraints, If the function is quadratically continuously differentiable and strongly convex, then the optimal solution to the coordination optimization problem is the stationary point of the Lagrange function; where the Lagrange function is expressed as:

[0018] In the formula, Representing Lagrange multipliers for equality constraints; According to the Newton-Raphson method, the Lagrange function... L The stationary points can be obtained from the following equation:

[0019] In the formula, , , and Represent the Lagrange function respectively exist Given the gradient and Hessian matrix at a given point; then, according to the above equation, the expression for the lumped optimal solution can be obtained as follows:

[0020]

[0021] In the formula, Indicates the first iThe optimal traction power value for each traction power unit. According to the optimal solution expression, the key to solving the traction power coordination optimization problem in a distributed manner is how to obtain the time-varying values ​​in a distributed manner using a dynamic average consensus algorithm. Specifically, a coordination optimization algorithm based on elastic fixed-time dynamic average consistency can be used to obtain time-varying values ​​in a distributed manner. and optimal traction power value .

[0022] Furthermore, a coordinated optimization algorithm based on elastic fixed-time dynamic average consistency is used to estimate the optimal traction power value of each traction power unit in a distributed manner. :

[0023] In the formula, The estimated first i The optimal traction power value for each traction power unit; and Indicates the first i Auxiliary variables for the coordinated optimization algorithm of traction power units, used for estimation .

[0024] Updated respectively using the following formulas and :

[0025]

[0026] In the formula, Indicates the first i The communication neighbor set of each traction power unit Represents the communication weight coefficient, if the first... The and the first Each traction power unit can obtain information from the others through communication connections. and ,otherwise and The communication topology between traction power units satisfies the conditions of being undirected and connected; and Indicates the first i The state variables of the coordinated optimization algorithm for each traction power unit and It is the first State variables of the coordinated optimization algorithm for each traction power unit; Indicates assignment to the first The virtual time-varying resistance of the coordinated optimization algorithm for each traction power unit is continuously differentiable and satisfies the following conditions: .

[0027] Update the state variables respectively using the following formulas and :

[0028]

[0029] In the formula, and The initial value is any bounded real value; and Indicates the first i The control input for the coordinated optimization algorithm of the traction power unit and These represent the network attacker's actions against the first... i Control input of the traction power unit coordination optimization algorithm and The multiplicative attack component applied, and The attackers were respectively targeting the first i Control input of the traction power unit coordination optimization algorithm and The applied additive attack component. The multiplicative attack component is time-varying and unknown, satisfying the following conditions: and , and It is a known bounded positive constant; the additive attack component is also time-varying and unknown, satisfying... and , and It is a known bounded positive constant.

[0030] Among them, the i Control input of the traction power unit coordination optimization algorithm and They are represented as follows:

[0031]

[0032] In the formula, , , , , , Indicates a positive control gain. Indicates control parameters, The preset fixed convergence time parameter for the controller, and Indicates the first Consistency error of auxiliary variables in the coordinated optimization algorithm of traction power units Represented as ,in It is an absolute value function.

[0033] The proposed coordinated optimization algorithm based on elastic fixed-time dynamic average consistency can ensure that the estimated optimal traction force value is obtained. Within a preset fixed convergence time Then, accurately track the time-varying optimal traction power. .

[0034] The beneficial effects of this invention are as follows: (1) The high-speed train traction power optimization and coordination method proposed in this invention is distributed, which does not require global information collection and processing by the control center, avoids single-node failure of the control center, reduces the communication and computing burden of the controller, and helps to improve the reliability of the train control operation system.

[0035] (2) The high-speed train traction power optimization and coordination method proposed in this invention tracks the optimal solution within a preset fixed time. Its convergence rate within the fixed time can be directly adjusted by the controller parameters. The preset fixed time convergence characteristic is conducive to meeting the fast and high-precision control performance requirements of high-speed trains with high speed, high density and public transportation operation.

[0036] (3) The high-speed train traction power optimization and coordination method proposed in this invention can operate normally even under the control input of the network attack controller, which is conducive to ensuring the safe and stable operation of high-speed trains.

[0037] Other advantages, objectives, and features of the invention will be set forth in part in the description which follows, and in part will be apparent to those skilled in the art from the following examination, or may be learned from practice of the invention. The objectives and other advantages of the invention can be realized and obtained through the following description. Attached Figure Description

[0038] To make the objectives, technical solutions, and advantages of the present invention clearer, the preferred embodiments of the present invention will be described in detail below with reference to the accompanying drawings, wherein: Figure 1 This is a flowchart illustrating the optimal traction coordination method for high-speed trains based on dynamic average consistency as described in this invention. Figure 2 This is a topology diagram of the communication connections between traction power units. Detailed Implementation

[0039] The following specific examples illustrate the implementation of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and various details in this specification can be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that the illustrations provided in the following embodiments are only schematic representations of the basic concept of the present invention. Unless otherwise specified, the following embodiments and features can be combined with each other.

[0040] This invention addresses the problem of optimal coordination and allocation of traction power for high-speed trains under the control input of adversary network attacks. It proposes a distributed optimization algorithm based on elastic fixed-time dynamic average consistency, which achieves safe, fast and optimal allocation of distributed traction power for high-speed trains in the absence of a control center.

[0041] like Figure 1 As shown, the method proposed in this invention mainly includes: considering a high-speed train has ( There are (two or more integers) traction power units. First, based on the operating state of each traction power unit, a traction power coordination optimization problem for high-speed trains is established. Second, using the characteristics of the optimal solution, the traction power coordination optimization problem is transformed into a dynamic average consistency problem. Finally, the optimal traction force of each traction power unit is obtained based on the elastic fixed-time dynamic average consistency algorithm.

[0042] This invention provides a detailed description of the method proposed in this invention, using a high-speed train comprising six traction power units as an example. The communication connections between the traction power units are as follows: Figure 2 As shown.

[0043] Specifically, the method includes: 1. First, based on the operating status of the six traction power units, a traction power coordination optimization problem for high-speed trains is established. Specifically, the cost function to be optimized for high-speed train traction power coordination is established:

[0044] in, This represents the total cost function with respect to traction force. , Indicates the first i The traction force provided by each traction power unit Indicates the first i The cost function of a traction power unit is quadratically differentiable and strongly convex. The cost parameters are... , , , and the upper and lower limits of traction force. , As shown in Table 1: Table 1

[0045] The constraints that must be satisfied to minimize the cost function include: 1) Traction-resistance balance constraint:

[0046] in, This represents the time-varying total resistance experienced by the high-speed train.

[0047] 2) Upper and lower limits of traction force of the traction power unit:

[0048] Then, a smooth penalty function is used to transform the proposed traction power coordination optimization problem with both equality and inequality constraints into a traction power coordination optimization problem with only equality constraints, as shown in the following equation:

[0049] st

[0050] in, This represents the total cost function with penalty costs. Indicates the first i The cost function of a traction power unit with penalty cost is expressed as:

[0051] in, For the first i Penalty parameters for the coordinated optimization problem of a single traction power unit; , .

[0052] 2. Secondly, by utilizing the characteristics of the optimal solution, the traction power coordination optimization problem is transformed into a dynamic average consistency problem.

[0053] In the aforementioned traction power coordination optimization problem with only equality constraints, due to It is strongly convex; therefore, the optimal solution to the coordination optimization problem is the Lagrangian function. The outposts, among which For equality-bound Lagrange multipliers.

[0054] According to the Newton-Raphson method, the Lagrange function... L The stationary point can be obtained by the following formula:

[0055]

[0056]

[0057] in, and These are the Lagrange functions. exist The gradient and Hessian matrix at point 1. From the above equation, the following expression for the lumped optimal solution can be obtained:

[0058]

[0059] in, Indicates the first i The optimal traction power value for each traction power unit. As shown in the above equation, the key to solving the traction power coordination optimization problem in a distributed manner is how to use a dynamic average consensus algorithm to obtain the time-varying values ​​in a distributed manner. .

[0060] 3. The optimal traction force of the six traction power units is obtained in a distributed manner based on the elastic fixed-time dynamic average consensus algorithm.

[0061] A coordinated optimization algorithm based on elastic fixed-time dynamic average consistency is used to estimate the optimal traction power value of each traction power unit in a distributed manner.

[0062] in, For the estimated first i The optimal traction power value for each traction power unit; and For the first i Auxiliary variables for the coordinated optimization algorithm of traction power units, used for estimation .

[0063] and Updated using the following formulas respectively:

[0064]

[0065] in, For the first i The communication neighbor set of each traction power unit The communication weighting coefficient (its values ​​are shown in Table 2). and For the first iThe state variables of the coordinated optimization algorithm for each traction power unit and For the first j The state variables of the coordinated optimization algorithm for each traction power unit.

[0066] Table 2

[0067] To be assigned to the i The virtual time-varying resistance of the coordinated optimization algorithm for each traction power unit has the following values:

[0068]

[0069]

[0070]

[0071]

[0072]

[0073] State variables and Update using the following formulas respectively:

[0074]

[0075] in, and The initial value is 0. and For the first i The control input for the coordinated optimization algorithm of the traction power unit , The attackers were respectively targeting the first i Control input of the traction power unit coordination optimization algorithm , The multiplicative attack component applied, , The attackers were respectively targeting the first i Control input of the traction power unit coordination optimization algorithm , The additive attack component applied.

[0076] Cyber ​​attackers control input and The multiplicative attack component applied and its lower bound. and As shown in Table 3, for control input and The additive attack component applied and its upper bound. and As shown in Table 4.

[0077] Table 3

[0078] Table 4

[0079] No. i Control input of the traction power unit coordination optimization algorithm and Represented as:

[0080]

[0081] in, , , , , , A positive control gain For control parameters, The preset fixed convergence time parameter for the controller, and For the first Consistency error of auxiliary variables in the coordinated optimization algorithm of traction power units Represented as ,in It is an absolute value function.

[0082] The proposed traction power unit coordination optimization algorithm based on elastic fixed-time dynamic average consistency can ensure that the estimated optimal traction power value is obtained. At the preset time Then, accurately track the time-varying optimal solution. .

[0083] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A high-speed train optimal traction coordination method based on dynamic average consistency, characterized in that: Consider a high-speed train with no less than two traction power units. Based on the operating status of each traction power unit, establish a traction power coordination optimization problem for the high-speed train. By utilizing the characteristics of the optimal solution, the traction power coordination optimization problem is transformed into a dynamic average consistency problem; A coordinated optimization algorithm based on elastic fixed-time dynamic average consistency is used to distribute and obtain the optimal traction force for each traction power unit of a high-speed train. The aforementioned problem of coordinating and optimizing the traction power of high-speed trains includes: Establishing a cost function that needs to be optimized for high-speed train traction power coordination: wherein denotes the total cost function with respect to the tractive force, , denotes the tractive force provided by the i-th tractive power unit, i denotes the tractive force provided by the i-th tractive power unit, denotes the cost function of the i-th tractive power unit, i denotes the cost function of the i-th tractive power unit, n denotes the total number of tractive power units; Establish the constraints that must be satisfied to minimize the cost function, including the traction-drag balance constraint. and upper and lower limits of traction force constraints ;in, This represents the time-varying total resistance experienced by the high-speed train. and They represent the first i The lower limit and upper limit of traction force of each traction power unit; By employing a smooth penalty function, the traction power coordination optimization problem with both equality and inequality constraints is transformed into a traction power coordination optimization problem with only equality constraints: s.t. In the formula, This represents the total cost function with penalty costs. Indicates the first i A cost function for each traction power unit with penalty costs; In the formula, Indicates the first i Penalty parameters for the coordination optimization problem of a traction power unit.

2. The method according to claim 1, characterized in that: Based on the aforementioned traction power coordination optimization problem with only equality constraints, and according to the characteristics of the optimal solution of this coordination optimization problem, the traction power coordination optimization problem is transformed into a dynamic average consistency problem; wherein, in the aforementioned traction power coordination optimization problem with only equality constraints, If the function is quadratically continuously differentiable and strongly convex, then the optimal solution to the coordination optimization problem is the stationary point of the Lagrange function; where the Lagrange function is expressed as: In the formula, Representing Lagrange multipliers for equality constraints; According to the Newton-Raphson method, the Lagrange function L The stationary point is obtained by the following formula: In the formula, , , and Represent the Lagrange function respectively exist Given the gradient and Hessian matrix at a given point; then, according to the above equation, the expression for the lumped optimal solution is: In the formula, Indicates the first i The optimal traction power value of each traction power unit; based on the optimal traction power value The key to the distributed solution of the optimal traction force value is to obtain the time-varying expression in a distributed manner. A coordination optimization algorithm based on elastic fixed-time dynamic average consistency is used to obtain time-varying values ​​in a distributed manner. and .

3. The method according to claim 2, characterized in that: A coordinated optimization algorithm based on elastic fixed-time dynamic average consistency estimates the optimal traction power value of each traction power unit in a distributed manner. : In the formula, The estimated first i The optimal traction power value for each traction power unit; and Indicates the first i Auxiliary variables for the coordinated optimization algorithm of traction power units, used for estimation ; Updated respectively using the following formulas and : In the formula, Indicates the first i The communication neighbor set of each traction power unit; Represents the communication weight coefficient, if the first... The and the first Each traction power unit can obtain information from the others through communication connections. and ,otherwise and The communication topology between traction power units satisfies the conditions of being undirected and connected; and Indicates the first i State variables of the coordinated optimization algorithm for each traction power unit; Indicates assignment to the first Virtual time-varying resistance of a coordinated optimization algorithm for a single traction power unit Continuously differentiable and satisfying ; Among them, state variables and Updated using the following formulas respectively: In the formula, and Indicates the first i Control inputs for the coordinated optimization algorithm of each traction power unit; and These represent the network attacker's actions against the first... i Control input of the traction power unit coordination optimization algorithm and The applied multiplicative attack component, which is time-varying and unknown, satisfies... and , and It is a known bounded positive constant; and These represent the network attacker's actions against the first... i Control input of the traction power unit coordination optimization algorithm and The applied additive attack component, which is time-varying and unknown, satisfies... and , and It is a known bounded positive constant; The control input and They are represented as follows: In the formula, , , , , , Indicates a positive control gain. Indicates control parameters, This indicates the controller's preset fixed convergence time parameter. and Indicates the first Consistency error of auxiliary variables in the coordinated optimization algorithm of traction power units express ,in It is an absolute value function.

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