Multi-train cooperative tracking control method under relative braking protection constraint

Abstract

The invention discloses a multi-train cooperative tracking control method under relative braking protection constraint. The method comprises the following steps: constructing an optimization model; cooperative tracking control; the step of constructing the optimization model specifically comprises train dynamic model establishment, train operation constraint and optimization control problem; the cooperative tracking control specifically comprises model reconstruction based on an augmented Lagrangian method, solution by adopting a trust region method, and design of a multi-train cooperative tracking control algorithm under relative braking protection constraint. According to the solution algorithm based on the trust region method, efficient solution of the multi-train cooperative tracking control strategy under the relative braking distance is achieved. The cooperative control strategy designed by the invention is solved through a trust region method, so that the control force of the high-speed train can be adjusted at each decision moment. By means of the adjustment, the actual train distance can be rapidly converged to the expected train distance, and the efficiency and safety of train operation are guaranteed.

Description

Technical Field

[0001] The present invention relates to the field of train operation cooperative tracking operation control, and in particular to a multi-train cooperative tracking control method under relative braking protection constraints. Background Art

[0002] Nowadays, railway has become one of the most popular modes of passenger transportation due to its significant advantages in terms of speed, punctuality and energy efficiency. In order to further improve transportation efficiency and flexibility, many emerging train control technologies are being studied, such as the latest train operation control system based on train-to-train communication and virtual marshaling train operation control scheme. With the increase in train density, the distance between trains is getting smaller and smaller. How to ensure the safe distance between adjacent trains under high train density and tight tracking conditions and design tracking controllers for multiple trains is of great significance in theoretical and practical engineering fields.

[0003] In existing train control systems, the absolute braking spacing method is usually used to calculate the safety margin. This method assumes that the train ahead is stationary, so the protection interval between adjacent trains increases accordingly. To further improve efficiency, the spacing protection method based on relative braking has received increasing attention. In this method, both the position information and speed information of the train ahead are taken into account. Compared with the absolute braking spacing method, the relative braking spacing method significantly reduces the distance between adjacent trains, thereby increasing the line capacity. Summary of the invention

[0004] In order to solve the problems of the prior art, the present invention proposes a multi-train cooperative tracking control method under relative braking protection constraints, the method comprising: Build optimization models; Collaborative tracking control; The construction of the optimization model specifically includes the establishment of a train dynamic model, train operation constraints, and optimization control issues; The cooperative tracking control specifically includes: model reconstruction based on the augmented Lagrangian method, solving by the trust region method, and designing a multi-train cooperative tracking control algorithm under relative braking protection constraints.

[0005] Furthermore, the train dynamic model is established, specifically including: During the operation, the train is subject to traction / braking force, basic resistance, external disturbance and additional resistance composed of ramp and curve resistance. Its dynamic equation is expressed as: ; in, and Separately for the moment train position, control and speed, For trains Quality, and Train At the moment Basic resistance, additional resistance and external disturbance; In order to ensure that the actual motion of the train can track the reference curve, a and Train The reference position and speed; further introduce the deviation variable and Respectively represent the deviation of the actual train position, speed and control force relative to the reference value; Equation (1) is sampled at every time interval Sampling, getting the train The discrete-time state error equation is: ; in, and is the basic drag coefficient. To simplify the description, the matrix is ​​introduced Refactoring equation (2) rewrites the constraint into the following compact form: ; in, .

[0006] Furthermore, the train operation constraints specifically include: To ensure the safe operation of adjacent trains, the train and train The distance between them should meet the minimum spacing constraint; the calculation of the safety spacing is divided into absolute braking distance and relative braking distance; The absolute braking distance calculation method ignores the movement of the front train and assumes that the speed is zero. The safety distance constraint is expressed as: ; in For trains The maximum braking force, Indicates train Length, It is the minimum distance to ensure the safety of train operation; The relative braking distance calculation method fully considers the position and speed information of the front train, and the spacing constraint based on the relative braking distance is expressed as: ; in For trains Maximum braking force; The actual control force input is limited by the actual train actuator and has the following control constraints: ; in and Respectively represent trains The actual speed of the train is limited by the maximum permissible speed, which is expressed as follows: ; Maximum allowed speed Determined by route conditions, weather conditions and temporary speed restrictions.

[0007] Furthermore, the optimization control problem specifically includes: An optimized control model is constructed to accurately track the reference speed curve while achieving relative braking distance protection, as shown below: ; ; In the optimization control problem, represents the number of online trains, and Represent the initial time and the end time respectively. and is the corresponding weight coefficient, the purpose is to find a balance between punctuality and energy efficiency; specifically, by minimizing the tracking speed deviation in the objective function and tracking position deviation , so that the actual position-speed curve of the train on the line is close to the desired speed-position curve; by reducing the third term in the objective function , that is, the error between the actual input and the reference control force, reducing energy consumption and achieving smooth driving; the train state transfer equation is given by formula (3), and (6) represents the interval constraint relative to the braking distance; the train state and control constraints are given by formulas (7) and (8); the initial speed and terminal speed are given by formula (9); Based on the model predictive control MPC framework, the objective function of the original problem (9) is reconstructed as follows: ; in, is a finite prediction horizon; therefore, the original optimal tracking control problem is It is formulated as the following optimization problem: ; ; ; ; .

[0008] Furthermore, the model reconstruction based on the augmented Lagrangian method specifically includes: Transform the optimization control problem (11) and constraints (12)-(15) into an unconstrained optimization problem; The augmented Lagrangian method is introduced to reformulate the original optimization problem. The constructed optimization control problem contains equality constraints and inequality constraints. For the equality constraint (12), the Lagrangian multiplier is introduced. and penalty parameters The following items are obtained: ; For the relative braking distance inequality constraint (13), the reconstructed expression is as follows: ; in, is the Lagrange multiplier; The velocity constraint (14) is considered to consist of two inequalities, which are obtained by introducing the Lagrange multiplier and , its enhanced form is expressed as follows: ; Similarly, the enhanced form of the control force constraint (15) is as follows: ; in, and is the Lagrange multiplier; In order to simplify the transformation process, the original problem (11) is rewritten into the following compact form: ; in, is the objective function defined in (10), is the vector of control variables, represents the set of equation constraints including the train position and speed state transfer equations (12), represents the inequality constraint set, including the train head distance constraint (13), the train speed constraint (14) and the train control force constraint (15), and are the index sets of equality and inequality constraints respectively; By using the enhanced Lagrangian method, the constrained optimization control problem (20) is equivalently transformed into the following unconstrained form: ; in, and are the Lagrange multiplier vectors for equality and inequality constraints, respectively, is the penalty parameter, which will be imposed when the constraint is violated during the iteration; is a slack variable, which is equal to zero when the constraint is satisfied and has no effect on the control force in the objective function when the constraint is violated. Specifically, the constrained optimization control problem (11) and the constraints (12)-(15) are equivalently transformed into the following unconstrained optimization problem: ; in, is the unconstrained problem after transformation, is the decision variable, and is the Lagrange multiplier matrix for the equality and inequality constraints.

[0009] Furthermore, the solution using the trust region method specifically includes: After obtaining the unconstrained problem (22) at each sampling time, the trust region method is used to solve it; the basic idea of ​​the trust region method is to construct a trust region subproblem within a given trust region radius, which is regarded as a quadratic approximation of the transformed problem (22); To facilitate the construction of the trust region subproblem, we first calculate the gradient matrix of the optimization problem (22): and the Hessian matrix The calculation of is as follows: ; ; No. The trust region subproblem of the iteration The expression is as follows: ; in is the decision variable of subproblem (24), is the trust region radius and satisfies ,and is an arbitrary vector norm, usually taken as Norm or norm; By solving the quadratic programming subproblem (24), we obtain the decision variables , also known as the trial step size; in order to check whether the trial step size should be accepted, a new variable is introduced , which represents the ratio of the actual decline value to the predicted decline value, is defined as follows: ; in and They are the actual drop value and predicted drop value of the objective function after applying the trial step size; the actual drop value is expressed as follows: ; The predicted decline value is defined as follows: ; If the trial step size performed can reduce the value of the objective function (22) to a sufficient extent, that is, , then the trial step is accepted and used to construct a new initial vector for the next subproblem; otherwise, the trial step needs to be rejected; the iterative process is expressed as follows: ; It is worth noting that, from (28), the update of the trust region radius also depends on The value of , then the radius needs to be reduced in the next iteration because no progress is made at the current radius; if , it means that the trial step size is well approximated, and the trust region radius is increased to allow a larger step size; if , then the trust region radius will be adjusted; the adjustment of the trust region radius is summarized as follows: ; in It is The trust region radius of the iteration, is the upper bound of the trust region radius, is a positive constant parameter that satisfies ; Experience, Set as ; After updating the decision vector for a new round of iteration, it is necessary to determine whether the termination condition is met. The condition is set as follows: ; in is an acceptable termination threshold; if this condition is met, the optimal solution is obtained, otherwise, the subproblem is reconstructed using the updated information; Based on the above description, the trust region solution method for the unconstrained cooperative tracking control problem (22) is summarized in the following Algorithm 1; Algorithm 1: Solution based on trust region enter: Unconstrained Problem ; Initial point ; Initial Parameters ; Output: Optimal solution and the optimal value ; step: set up arrive ; calculate and ; if ,but get and And terminate the algorithm otherwise, Constructor Problem , and solve calculate ; renew ; if ,but ; otherwise, ; renew ; End the loop The input of Algorithm 1 includes the initial vector , initial trust region radius , acceptable termination threshold , and the unconstrained tracking control problem (22); by constructing and solving the trust region subproblem in each iteration, the trial step size is obtained And used to update subsequent iteration variables and the trust region radius Update according to (28) and (29) respectively; this process will be repeated until the iteration termination condition (30) is met; after meeting this condition, the solution of the unconstrained optimization problem (22) is obtained, thereby providing the optimal control input at each decision moment.

[0010] Furthermore, the design of the multi-train cooperative tracking control algorithm under relative braking protection constraints specifically includes, based on model reconstruction and trust region algorithm, proposing that the multi-train cooperative tracking control under relative braking protection constraints is divided into a two-layer structure. The outer structure uses the augmented Lagrangian method to transform the original problem into an unconstrained optimal control problem, and the inner structure uses the trust region method to efficiently solve the equivalent problem. The overall framework is shown in Algorithm 2: Algorithm 2: Multi-train cooperative tracking control algorithm under relative braking protection constraints enter: The MPC problem at each sampling moment (11) Initial Parameters ; Output: Optimal control force error ; External structure: set up arrive ; Reframing the Unconstrained Problem ; Internal structure: Will Input to Algorithm 1 get and Value End of internal structure calculate Value if ,but set up and ; from Obtained ; Break out of the loop otherwise, Update Lagrange multipliers and penalty factors renew

[0011] End the loop End External Structure The input of the outer structure is the original optimal control problem (1); by introducing Lagrange multipliers and penalty parameters, the relative braking margin and other relevant operating constraints are added to the objective function, resulting in the unconstrained problem (22); in each iteration of the outer layer, Algorithm 1 is triggered to solve the unconstrained problem (22) and introduces a new variable , used to check whether the termination condition is met, and is calculated as follows: ; Then the termination criterion is expressed as: ; in, is an acceptable termination threshold; if constraint (32) holds, the optimal solution to the unconstrained problem is obtained and the iteration is terminated; otherwise, the penalty parameter should be updated according to (33) for the next iteration: ; in is a constant set empirically; accordingly, the Lagrange multipliers used for the equality and inequality constraints (12)-(15) should be updated as follows: ; ; During the iterative interaction between the internal and external structures, the external structure reconstructs the original optimization problem and outputs an unconstrained problem at each iteration. The unconstrained problem is then passed as input to the internal structure. The internal structure returns the solution of the unconstrained problem and gives it to the external structure. The external structure uses the solution to check the termination condition and update the unconstrained problem. If the termination condition (32) is met, the current solution is regarded as the global optimal solution, otherwise a new unconstrained problem needs to be reconstructed for the next iteration.

[0012] In another aspect, the present invention further provides an electronic device, The invention comprises a memory and a processor, and computer instructions stored in the memory and executed on the processor. When the computer instructions are executed by the processor, the above method is implemented.

[0013] On the other hand, the present invention further provides a computer-readable storage medium for storing computer instructions, wherein when the computer instructions are executed by a processor, the above method is performed.

[0014] Beneficial effects of the present invention: 1. The present invention proposes a solution algorithm based on the trust region method, which realizes the efficient solution of the multi-train cooperative tracking control strategy under relative braking distance.

[0015] 2. The cooperative control strategy designed by the present invention is solved by the trust region method, so that the high-speed train can adjust the control force at each decision moment. This adjustment enables the actual inter-vehicle distance to converge quickly to the expected inter-vehicle distance, ensuring the efficiency and safety of train operation. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] The present invention has the following accompanying drawings: Figure 1 Train spacing based on absolute braking distance; Figure 2 Train spacing based on relative braking distances; Figure 3 Train reference speed curve; Figure 4 Time-space diagram of trains under relative braking control; Figure 5 The distance between adjacent trains. DETAILED DESCRIPTION

[0017] The following is combined with Figure 1-5 The present invention is described in further detail.

[0018] 1. Optimizing model construction In this section, the dynamic operation model of the train is first described and the mechanism of relative braking distance is explained. Then, under the objective of minimizing the tracking error, the optimization model of the cooperative tracking control problem is constructed based on the relative braking distance constraint.

[0019] A. Train Dynamic Model During the operation of the train, the train is subject to traction / braking force, basic resistance, external disturbance and additional resistance composed of ramp and curve resistance. Its dynamic equation can be expressed as: ; in, Separately for the moment train position, control and speed, For trains Quality, Train At the moment basic resistance, additional resistance and external disturbance.

[0020] In order to ensure that the actual motion of the train can track the reference curve, a and Train The reference position and speed. Further introducing the deviation variable Respectively represent the deviation of the actual train position, speed and control force relative to the reference value. Sample equation (1) at every time interval Sampling, getting the train The discrete-time state error equation is: ; in, and is the basic drag coefficient. To simplify the description, the matrix Restructuring equation (2) allows the constraint to be rewritten in the following compact form: ; in, ; B. Train operation constraints To ensure the safe operation of adjacent trains, the train and train The distance between the two vehicles should meet the minimum spacing constraint. Generally, the calculation of safety spacing can be divided into two types: absolute braking distance and relative braking distance.

[0021] For the absolute braking distance calculation method, such as Figure 1 As shown in Figure 2, the motion of the train ahead is ignored and its speed is assumed to be zero. The safety distance constraint can be expressed as: ; in For trains The maximum braking force, Indicates train Length, It is the minimum distance to ensure the safety of train operation.

[0022] like Figure 2 As shown in the figure, the relative braking distance calculation method fully considers the position and speed information of the train ahead, and the spacing constraint based on the relative braking distance is expressed as: ; in For trains By comparison Figure 1 and Figure 2 It can be clearly seen that the safety spacing based on the relative braking distance can shorten the minimum distance between adjacent trains, thereby improving the tracking efficiency.

[0023] By comparing equation (5) and equation (6), it can be found that the spacing constraint based on the relative braking distance can shorten the tracking interval between trains while ensuring safety. The present invention adopts equation (6) to protect train safety.

[0024] In addition, the actual control force input is limited by the actual train actuators and has the following control constraints: ; in and Respectively represent trains The actual speed of the train is also limited by the maximum allowed speed, expressed as follows: ; Maximum allowed speed Determined by route conditions, weather conditions and temporary speed restrictions.

[0025] C. Optimization control problem Based on the above analysis, an optimization control model is constructed as shown in formula (9), aiming to achieve accurate tracking of the reference speed curve under relative braking distance protection, as shown below: ; ; In the optimization control problem, represents the number of online trains, and Represent the initial time and the end time respectively. and is the corresponding weight coefficient, the purpose is to find a balance between punctuality and energy efficiency. Specifically, by minimizing the tracking speed deviation in the objective function and tracking position deviation , so that the actual position-speed curve of the train on the line is as close as possible to the expected speed-position curve, thereby improving safety and punctuality. By reducing the third term in the objective function , which is the error between the actual input and the reference control force, reduces energy consumption and achieves smooth driving. The train state transfer equation is given by formula (3), while (6) represents the interval constraint relative to the braking distance. In addition, the state and control constraints of the train are given by formulas (7) and (8). The initial speed and terminal speed are given by formula (9).

[0026] Furthermore, based on the model predictive control (MPC) framework, the objective function of the original problem (9) is restructured as follows: ; in, is a finite prediction horizon. Therefore, the original optimal tracking control problem is It can be formulated as the following optimization problem: ; ; ; ; ; However, it is noted that formula (13) is a complex constraint containing quadratic terms and coupled with adjacent trains, which makes it difficult to solve the MPC problem directly by conventional methods. In order to solve this difficulty, the present invention proposes a cooperative control strategy solution algorithm based on the trust region method, and the specific content will be described in detail below.

[0027] 2. Trust Region Method In this section, in order to efficiently handle complex relative braking distance constraints and meet the real-time requirements of train operation, a novel cooperative tracking control strategy is proposed based on the trust region method. First, the original problem is transformed into an unconstrained problem using the augmented Lagrangian method, and then the equivalent unconstrained problem is efficiently solved using the trust region method.

[0028] A. Reconstruct the model based on the augmented Lagrangian method Traditionally, the trust region method is used to deal with unconstrained optimization problems. In order to apply the trust region method to the train optimization control problem, it is necessary to transform the optimization control problem (11) and its constraints (12)-(15) into an unconstrained optimization problem.

[0029] Here, the augmented Lagrangian method is introduced to reformulate the original optimization problem. It can be found that the constructed optimization control problem contains equality constraints and inequality constraints. For the equality constraint (12), the Lagrangian multiplier is introduced and penalty parameters , we get the following items: ; For the relative braking distance inequality constraint (13), the reconstructed expression is as follows: ; in, is the Lagrange multiplier.

[0030] The velocity constraint (14) can be viewed as consisting of two inequalities, which are solved by introducing the Lagrange multiplier and , its enhanced form is expressed as follows: ; Similarly, the enhanced form of the control force constraint (15) is as follows: ; in, and is the Lagrange multiplier.

[0031] To simplify the transformation process, the original problem (11) can be rewritten into the following compact form: ; in, is the objective function defined in (10), is the vector of control variables, represents the set of equation constraints including the train position and speed state transfer equations (12), represents the inequality constraint set, including the train head distance constraint (13), the train speed constraint (14) and the train control force constraint (15), and are the index sets of equality and inequality constraints respectively.

[0032] By using the enhanced Lagrangian method, the above constrained optimization control problem (20) can be equivalently transformed into the following unconstrained form: ; in, and are the Lagrange multiplier vectors for equality and inequality constraints, respectively, is the penalty parameter that is applied when the constraint is violated during the iteration.

[0033] is a slack variable, which is equal to zero when the constraint is satisfied and has no effect on the control force in the objective function when the constraint is violated. Specifically, the constrained optimization control problem (11) and the constraints (12)-(15) can be equivalently transformed into the following unconstrained optimization problem: ; in, is the unconstrained problem after transformation, is the decision variable, and is the Lagrange multiplier matrix for the equality and inequality constraints.

[0034] B. Trust Region Algorithm After obtaining the unconstrained problem (22) at each sampling time, the trust region method is used to solve it. The basic idea of ​​the trust region method is to construct a trust region subproblem within a given trust region radius, which can be regarded as a quadratic approximation of the transformed problem (22).

[0035] To facilitate the construction of the trust region subproblem, we first calculate the gradient matrix of the optimization problem (22): and the Hessian matrix The calculation of is as follows: ; ; No. The trust region subproblem of the iteration The expression is as follows: ; in is the decision variable of subproblem (24), is the trust region radius and satisfies ,and is an arbitrary vector norm, usually taken as Norm or Norm.

[0036] By solving the quadratic programming subproblem (24), we obtain the decision variables , which is also called the trial step size. In order to check whether the trial step size should be accepted, a new variable is introduced , which represents the ratio of the actual decline value to the predicted decline value, is defined as follows: ; in and are the actual decrease value and predicted decrease value of the objective function after applying the trial step size. The actual decrease value is expressed as follows: ; The predicted decline value is defined as follows: ; If the trial step size performed can reduce the value of the objective function (22) to a sufficient extent, that is, , then the trial step is accepted and used to construct a new initial vector for the next subproblem. Otherwise, the trial step needs to be rejected. The iterative process can be expressed as follows: ; It is worth noting that from (28) we can see that the update of the trust region radius also depends on If , then the radius needs to be reduced in the next iteration because no progress is made at the current radius. , it means that the trial step size is well approximated and the trust region radius can be increased to allow a larger step size. , then the trust region radius may be slightly adjusted. The adjustment of the trust region radius is summarized as follows: ; in It is The trust region radius of the iteration, is the upper bound of the trust region radius, is a positive constant parameter that satisfies . From experience, Set as .

[0037] In addition, after updating the decision vector for a new round of iteration, it is necessary to determine whether the termination condition is met. The condition is set as follows: ; in is an acceptable termination threshold. If this condition is met, the optimal solution is obtained, otherwise, the subproblem is reconstructed using the updated information.

[0038] Based on the above description, the trust region solution method for the unconstrained cooperative tracking control problem (22) is summarized in the following Algorithm 1.

[0039] Algorithm 1: Solution based on trust region enter: Unconstrained Problem ; Initial point ; Initial Parameters ; Output: Optimal solution and the optimal value ; step: set up arrive .

[0040] calculate and .

[0041] if ,but get and And terminate the algorithm.

[0042] otherwise, Constructor Problem , and solve calculate ; renew ; if ,but ; otherwise ; renew ; End the loop The input of Algorithm 1 includes the initial vector , initial trust region radius , acceptable termination threshold , and the unconstrained tracking control problem (22). By constructing and solving the trust region subproblem in each iteration, the trial step size is obtained And used to update subsequent iteration variables and the trust region radius Update according to (28) and (29) respectively. This process is repeated until the iteration termination condition (30) is met. After satisfying this condition, we can obtain the solution of the unconstrained optimization problem (22), thereby providing the optimal control input at each decision moment.

[0043] C. Design of multi-train cooperative tracking control algorithm under relative braking protection constraints Based on model reconstruction and trust region algorithm, the multi-train cooperative tracking control under relative braking protection constraints proposed in this paper can be divided into two layers. The outer layer uses the augmented Lagrangian method to transform the original problem into an unconstrained optimal control problem, and the inner layer uses the trust region method to efficiently solve the equivalent problem. The overall framework is shown in Algorithm 2.

[0044] Algorithm 2: Multi-train cooperative tracking control algorithm under relative braking protection constraints enter: The MPC problem at each sampling time is (11).

[0045] Initial Parameters .

[0046] Output: Optimal control force error .

[0047] External structure: set up arrive .

[0048] Reframing the Unconstrained Problem .

[0049] Internal structure: Will Input to Algorithm 1.

[0050] get and The value of .

[0051] End of internal structure calculate The value of .

[0052] if ,but set up and ; from Obtained .

[0053] Break out of the loop otherwise, Update the Lagrange multipliers and penalty factors.

[0054] renew ; End the loop End External Structure The input of the outer structure is the original optimal control problem (1). By introducing Lagrange multipliers and penalty parameters, the relative braking margin and other relevant operating constraints are added to the objective function, resulting in the unconstrained problem (22). In each iteration of the outer layer, Algorithm 1 is triggered to solve the unconstrained problem (22) and introduces a new variable , used to check whether the termination condition is met, and is calculated as follows: ; Then the termination criterion is expressed as: ; in, is an acceptable termination threshold. If the constraint (32) holds, the optimal solution to the unconstrained problem is obtained and the iteration is terminated. Otherwise, the penalty parameter should be updated according to (33) for the next iteration: ; in is a constant, set empirically. Accordingly, the Lagrange multipliers used for the equality and inequality constraints (12)-(15) should be updated as follows: ; ; In the iterative interaction between the internal and external structures, the external structure reconstructs the original optimization problem and outputs an unconstrained problem at each iteration, which is then passed as input to the internal structure. The internal structure returns the solution of the unconstrained problem and gives it to the external structure, which uses the solution to check the termination condition and update the unconstrained problem. If the termination condition (32) is met, the current solution is considered to be the global optimal solution, otherwise a new unconstrained problem needs to be reconstructed for the next iteration.

[0055] pass Figure 4 and Figure 5 Numerical experiments are performed to illustrate the performance of the tracking strategy.

[0056] In the numerical example, real data of China's Beijing-Shanghai High-Speed ​​Railway was selected to verify the effectiveness and efficiency of the proposed collaborative control strategy. Actual operation data of high-speed trains from Tianjin South Railway Station to Beijing South Railway Station were selected. The distance between the two stations is about 122 kilometers, and the travel time is about 30 minutes. In the simulation experiment, 6 high-speed trains running from Tianjin South Railway Station to Beijing South Railway Station were considered. The length of each train is 210 meters, and the minimum safe vehicle spacing between trains is Set to 1200 meters. In addition, other parameters of the high-speed train are set as follows: Set to Set to , Set to Set to Set to . Weight coefficient are all set to 0.1. In our experiments, it is assumed that each train follows the same reference speed curve but departs at different times. The initial positions of the trains are 0, 1310, 2522, 3730, 5010, and 6130 meters, respectively. This results in the initial inter-vehicle spacing between adjacent trains being 1310, 1212, 1208, 1280, and 1120 meters, respectively. The reference speed curve is derived from actual operating data, such as Figure 3 As shown. In order to verify the performance of the proposed method, disturbances are introduced for each train at the first sampling moment. Based on the above data, three sets of simulation experiments are designed to illustrate the effectiveness and performance of the proposed cooperative tracking strategy.

[0057] Figure 4 The space-time trajectories of the six trains under relative braking distances are shown. By applying the proposed cooperative control strategy, Figure 4 It can be clearly seen that by properly adjusting the distance between trains during operation, all trains can follow the train in front more closely while maintaining a safe relative braking distance, demonstrating the effectiveness of the proposed strategy. Figure 5 The actual inter-vehicle spacing curve and the reference inter-vehicle spacing curve of each train are shown as a function of time. Figure 5 As shown in the figure, although the initial inter-vehicle spacing between adjacent trains does not reach the expected distance due to the initial position of each train, by implementing the proposed strategy, the train can dynamically adjust the inter-vehicle spacing between adjacent trains to reach the expected value. Subsequently, the required safe inter-vehicle spacing is maintained until the train arrives at the station. For each train, the actual tracking curve closely follows the reference curve and is always above it, which confirms that the proposed strategy effectively ensures the safety of train operation.

[0058] like Figure 4 and Figure 5 As shown in the figure, although the initial position of the train causes the inter-vehicle distance to have a positive or negative deviation from the expected value, the designed cooperative control strategy is solved by the trust region method, enabling the high-speed train to adjust the control force at each decision moment. This adjustment enables the actual inter-vehicle distance to converge quickly to the expected inter-vehicle distance, ensuring the efficiency and safety of train operation.

[0059] The above implementation modes are only used to illustrate the present invention, but not to limit the present invention. Ordinary technicians in the relevant technical field can make various changes and deformations without departing from the essence and scope of the present invention. Therefore, all equivalent technical solutions also belong to the scope of the present invention. The scope of patent protection of the present invention should be limited by the claims.

[0060] The contents not described in detail in this specification belong to the prior art known to professional and technical personnel in this field.

Claims

1. A multi-train cooperative tracking control method under relative braking protection constraints, characterized in that: The method comprises: Build optimization models; Collaborative tracking control; The construction of the optimization model specifically includes the establishment of a train dynamic model, train operation constraints, and optimization control issues; The cooperative tracking control specifically includes: model reconstruction based on the augmented Lagrangian method, solving by the trust region method, and designing a multi-train cooperative tracking control algorithm under relative braking protection constraints.

2. The method for controlling multi-train cooperative tracking under relative braking protection constraints as claimed in claim 1, characterized in that: The train dynamic model is established, specifically including: During the operation, the train is subject to traction / braking force, basic resistance, external disturbance and additional resistance composed of ramp and curve resistance. Its dynamic equation is expressed as: ; in, , and Separately for the moment train position, control and speed, For trains Quality, and Train At the moment Basic resistance, additional resistance and external disturbance; In order to ensure that the actual motion of the train can track the reference curve, a and Train The reference position and speed; further introduce the deviation variable , and Respectively represent the deviation of the actual train position, speed and control force relative to the reference value; Equation (1) is sampled at every time interval Sampling, getting the train The discrete-time state error equation is: ; in, and is the basic drag coefficient. To simplify the description, the matrix is ​​introduced Refactoring equation (2) rewrites the constraint into the following compact form: ; in, 。 3. The method for controlling multi-train cooperative tracking under relative braking protection constraints as claimed in claim 2, characterized in that: The train operation constraints specifically include: To ensure the safe operation of adjacent trains, the train and train The distance between them should meet the minimum spacing constraint; the calculation of the safety spacing is divided into absolute braking distance and relative braking distance; The absolute braking distance calculation method ignores the movement of the front train and assumes that the speed is zero. The safety distance constraint is expressed as: ; in For trains The maximum braking force, Indicates train Length, It is the minimum distance to ensure the safety of train operation; The relative braking distance calculation method fully considers the position and speed information of the front train, and the spacing constraint based on the relative braking distance is expressed as: ; in For trains Maximum braking force; The actual control force input is limited by the actual train actuator and has the following control constraints: ; in and Respectively represent trains The actual speed of the train is limited by the maximum permissible speed, which is expressed as follows: ; Maximum allowed speed Determined by route conditions, weather conditions and temporary speed restrictions.

4. The method for controlling multi-train cooperative tracking under relative braking protection constraints as claimed in claim 3, characterized in that: The optimization control problem specifically includes: An optimized control model is constructed to accurately track the reference speed curve while achieving relative braking distance protection, as shown below: ; ; In the optimization control problem, represents the number of online trains, and Represent the initial time and the end time respectively. and is the corresponding weight coefficient, the purpose is to find a balance between punctuality and energy efficiency; Specifically, by minimizing the tracking speed deviation in the objective function and tracking position deviation , so that the actual position-speed curve of the train on the line is close to the expected speed-position curve; By reducing the third term in the objective function , that is, the error between the actual input and the reference control force, reducing energy consumption and achieving smooth driving; the train state transfer equation is given by formula (3), and (6) represents the interval constraint relative to the braking distance; the train state and control constraints are given by formulas (7) and (8); the initial speed and terminal speed are given by formula (9); Based on the model predictive control MPC framework, the objective function of the original problem (9) is reconstructed as follows: ; in, is a finite prediction horizon; therefore, the original optimal tracking control problem is It is formulated as the following optimization problem: ; ; ; ; 。 5. The method for controlling multi-train cooperative tracking under relative braking protection constraints as claimed in claim 4, characterized in that: The model reconstruction based on the augmented Lagrangian method specifically includes: Transform the optimization control problem (11) and constraints (12)-(15) into an unconstrained optimization problem; The augmented Lagrangian method is introduced to reformulate the original optimization problem. The constructed optimization control problem contains equality constraints and inequality constraints. For the equality constraint (12), the Lagrangian multiplier is introduced. and penalty parameters , we get the following items: ; For the relative braking distance inequality constraint (13), the reconstructed expression is as follows: ; in, is the Lagrange multiplier; The velocity constraint (14) is considered to consist of two inequalities, which are obtained by introducing the Lagrange multiplier and , its enhanced form is expressed as follows: ; Similarly, the enhanced form of the control force constraint (15) is as follows: ; in, and is the Lagrange multiplier; In order to simplify the transformation process, the original problem (11) is rewritten into the following compact form: ; in, is the objective function defined in (10), is the vector of control variables, represents the set of equation constraints including the train position and speed state transfer equations (12), represents the inequality constraint set, including the train head distance constraint (13), the train speed constraint (14) and the train control force constraint (15), and are the index sets of equality and inequality constraints respectively; By using the enhanced Lagrangian method, the constrained optimization control problem (20) is equivalently transformed into the following unconstrained form: ; in, and are the Lagrange multiplier vectors for equality and inequality constraints, respectively, is the penalty parameter, which will be imposed when the constraint is violated during the iteration; is a slack variable, which is equal to zero when the constraint is satisfied and has no effect on the control force in the objective function when the constraint is violated. Specifically, the constrained optimization control problem (11) and the constraints (12)-(15) are equivalently transformed into the following unconstrained optimization problem: ; in, is the unconstrained problem after transformation, Decision variables, and is the Lagrange multiplier matrix for the equality and inequality constraints.

6. The method for controlling multi-train cooperative tracking under relative braking protection constraints as claimed in claim 5, characterized in that: The solution using the trust region method specifically includes: After obtaining the unconstrained problem (22) at each sampling time, the trust region method is used to solve it; the basic idea of ​​the trust region method is to construct a trust region subproblem within a given trust region radius, which is regarded as a quadratic approximation of the transformed problem (22); To facilitate the construction of the trust region subproblem, we first calculate the gradient matrix of the optimization problem (22): and the Hessian matrix The calculation of is as follows: ; ; No. The trust region subproblem of the iteration The expression is as follows: ; in is the decision variable of subproblem (24), is the trust region radius and satisfies ,and is an arbitrary vector norm, usually taken as Norm or norm; By solving the quadratic programming subproblem (24), we obtain the decision variables , also known as the trial step size; in order to check whether the trial step size should be accepted, a new variable is introduced , which represents the ratio of the actual decline value to the predicted decline value, is defined as follows: ; in and They are the actual drop value and predicted drop value of the objective function after applying the trial step size; the actual drop value is expressed as follows: ; The predicted decline value is defined as follows: ; If the trial step size performed can reduce the value of the objective function (22) to a sufficient extent, that is, , then the trial step is accepted and used to construct a new initial vector for the next subproblem; otherwise, the trial step needs to be rejected; the iterative process is expressed as follows: ; It is worth noting that, from (28), the update of the trust region radius also depends on The value of , then the radius needs to be reduced in the next iteration because no progress is made at the current radius; if , it means that the trial step size is well approximated, and the trust region radius is increased to allow a larger step size; if , then the trust region radius will be adjusted; the adjustment of the trust region radius is summarized as follows: ; in It is The trust region radius of the iteration, is the upper bound of the trust region radius, is a positive constant parameter that satisfies ; Experience, Set as ; After updating the decision vector for a new round of iteration, it is necessary to determine whether the termination condition is met. The condition is set as follows: ; in is an acceptable termination threshold; if this condition is met, the optimal solution is obtained, otherwise, the subproblem is reconstructed using the updated information; Based on the above description, the trust region solution method for the unconstrained cooperative tracking control problem (22) is summarized in the following Algorithm 1; Algorithm 1: Solution based on trust region enter: Unconstrained Problem ; Initial point ; Initial Parameters ; Output: Optimal solution and the optimal value ; step: set up arrive ; calculate and ; if ,but get And terminate the algorithm otherwise, Constructor Problem , and solve calculate ; renew ; if ,but ; otherwise, ; renew ; End the loop The input of Algorithm 1 includes the initial vector , initial trust region radius , acceptable termination threshold , and the unconstrained tracking control problem (22); by constructing and solving the trust region subproblem in each iteration, the trial step size is obtained And used to update subsequent iteration variables and the trust region radius Update according to (28) and (29) respectively; this process will be repeated until the iteration termination condition (30) is met; after meeting this condition, the solution of the unconstrained optimization problem (22) is obtained, thereby providing the optimal control input at each decision moment.

7. The method for controlling multi-train cooperative tracking under relative braking protection constraints as claimed in claim 6, characterized in that: The design of the multi-train cooperative tracking control algorithm under the relative braking protection constraint specifically includes: Based on model reconstruction and trust region algorithm, it is proposed that the multi-train cooperative tracking control under relative braking protection constraints is divided into two layers. The outer layer uses the augmented Lagrangian method to transform the original problem into an unconstrained optimal control problem, and the inner layer uses the trust region method to efficiently solve the equivalent problem. The overall framework is shown in Algorithm 2: Algorithm 2: Multi-train cooperative tracking control algorithm under relative braking protection constraints enter: The MPC problem at each sampling moment (11) Initial Parameters ; Output: Optimal control force error ; External structure: set up arrive ; Reframing the Unconstrained Problem ; Internal structure: Will Input to Algorithm 1 get and Value End of internal structure calculate Value if ,but set up ; from Obtained ; Break out of the loop otherwise, Update Lagrange multipliers and penalty factors renew ; End the loop End External Structure The input of the outer structure is the original optimal control problem (1); by introducing Lagrange multipliers and penalty parameters, the relative braking margin and other relevant operating constraints are added to the objective function, resulting in the unconstrained problem (22); in each iteration of the outer layer, Algorithm 1 is triggered to solve the unconstrained problem (22) and introduces a new variable , used to check whether the termination condition is met, and is calculated as follows: ； Then the termination criterion is expressed as: ； in, is an acceptable termination threshold; if constraint (32) holds, the optimal solution to the unconstrained problem is obtained and the iteration is terminated; otherwise, the penalty parameter should be updated according to (33) for the next iteration: ； in is a constant set empirically; accordingly, the Lagrange multipliers used for the equality and inequality constraints (12)-(15) should be updated as follows: ； ； During the iterative interaction between the internal and external structures, the external structure reconstructs the original optimization problem and outputs an unconstrained problem at each iteration. The unconstrained problem is then passed as input to the internal structure. The internal structure returns the solution to the unconstrained problem and gives it to the external structure. The external structure uses the solution to check the termination condition and update the unconstrained problem. If the termination condition (32) is met, the current solution is regarded as the global optimal solution, otherwise a new unconstrained problem needs to be reconstructed for the next iteration.

8. An electronic device, characterized in that: The method comprises a memory and a processor and computer instructions stored in the memory and executed on the processor, wherein when the computer instructions are executed by the processor, the method according to any one of claims 1 to 7 is completed.

9. A computer-readable storage medium, characterized in that: Used to store computer instructions, which, when executed by a processor, complete the method described in any one of claims 1 to 7.

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