Multi-train cooperative strengthening performance control method under switching topology

Abstract

The invention relates to a multi-train cooperative strengthening performance control method under switching topology, which comprises the following steps of: performing nonlinear transformation on a position tracking error and a speed tracking error, and obtaining a position error variable and a speed error variable of coupling safety constraint of an ith train according to a position reset performance function and a speed reset performance function; constructing a strengthening performance expansion position error according to the position tracking error and the position error variable, constructing a strengthening performance expansion speed error according to the speed tracking error and the speed error variable, and constructing a strengthening performance expansion speed error according to the strengthening performance expansion position error and the strengthening performance expansion speed error. And performing multi-train cooperative strengthening performance control on the ith train under the switching topology, thereby improving the tracking performance while ensuring the safe cooperative operation of the multiple trains.

Description

Technical Field

[0001] The present invention relates to the technical field of high-speed train operation control, and in particular to a method for controlling the coordinated performance enhancement of multiple trains under a switching topology. Background Art

[0002] Railway transportation is one of the fastest growing modes of transportation in the world and has experienced rapid development in recent years. However, despite the steady growth of railway operating mileage and the increasing density of the road network, there is still a significant gap between railway transportation capacity and demand. Therefore, improving the efficiency of railway transportation has become a key issue that needs to be addressed. With the advancement of information technology and automation, train cooperative control is considered to be an effective way to improve railway emergency response capabilities and operating efficiency, which has attracted widespread attention.

[0003] In addition, ensuring the safe operation of trains is the basis of the problem of train cooperative control. In the actual cooperative operation of multiple trains, the tracking distance between trains must be greater than the safety distance to avoid train collisions and bring safety hazards. To this end, based on the preset performance control method, the expected performance boundary is designed to constrain the train tracking performance. By converting the tracking error signal of the train subject to safety constraints into a new unconstrained variable, the train position and speed can be ensured to be within the safe range. However, the environment in the process of cooperative operation of multiple trains is complex and changeable. When the train runs to different communication network coverage areas or encounters extreme climate, in order to ensure that the information between multiple trains can be transmitted, the communication network topology will switch, resulting in a sudden change in the train tracking error signal. In addition, due to the characteristics of the preset performance control method, the boundary of the tracking error does not directly depend on the control gain, which means that in the event of unexpected situations, such as sensor errors or measurement noise, the system's tracking error will also exceed the preset performance boundary, resulting in singularities or completely uncontrollable problems, thereby endangering the operation safety of the train.

[0004] In summary, how to achieve high-precision multi-train coordinated operation while ensuring safety constraints under dynamically changing communication network conditions is an urgent problem to be solved in multi-train coordinated control. Therefore, it is very necessary to propose a multi-train coordinated enhanced performance control method under switching topology. Summary of the invention

[0005] 1. Technical issues to be resolved

[0006] In view of the above-mentioned shortcomings and deficiencies of the prior art, the present invention provides a method for controlling the collaborative performance enhancement of multiple trains under a switching topology, which solves the technical problem existing in the prior art of how to achieve high-precision collaborative operation of multiple trains.

[0007] (II) Technical solution

[0008] To achieve the above object, the main technical solutions adopted by the present invention include:

[0009] In a first aspect, an embodiment of the present invention provides a multi-train collaborative enhanced performance control method under a switched topology, including: considering the collaborative operation of n trains on the same railway line, establishing a second-order nonlinear dynamic model of the i-th train; where the i-th train is any one of the n trains; based on the second-order nonlinear dynamic model and the preset collaborative reference position-velocity curve of the i-th train, calculating the position tracking error and the velocity tracking error of the i-th train respectively, and according to the position tracking error and the velocity tracking error, calculating the position mutation amount of the position tracking error and the velocity mutation amount of the velocity tracking error of the i-th train at the k-th communication topology switching moment, and according to the position mutation amount, defining the update law of the position reset performance function with a reset function of the i-th train, and according to the velocity mutation amount, defining the update law of the velocity reset performance function with a reset function of the i-th train; performing a nonlinear transformation on the position tracking error and the velocity tracking error, and according to the position reset performance function and the velocity reset performance function, obtaining the position error variable and the velocity error variable of the coupled safety constraint of the i-th train; constructing an enhanced performance extended position error according to the position tracking error and the position error variable, and constructing an enhanced performance extended velocity error according to the velocity tracking error and the velocity error variable, and performing multi-train collaborative enhanced performance control of the i-th train under a switched topology according to the enhanced performance extended position error and the enhanced performance extended velocity error.

[0010] In a possible embodiment, the collaborative reference position-velocity curve includes collaborative reference position curve information; the calculation expression of the position tracking error is as follows:

[0011]

[0012] In the formula, represents the position tracking error at time t; a i，0 (t) represents whether the i-th train can receive the known collaborative target position and velocity curve at time t; p i (t) represents the real-time position of the i-th train at time t; p r，i (t) represents the collaborative reference position curve information of the i-th train at time t; Q r，i represents the distance error variable between the i-th train and the collaborative reference position curve information; j represents the j-th train; n represents the number of trains in the formation; a i，j (t) represents whether there is information interaction between the i-th train and the j-th train in the multi-train formation at time t; p j (t) represents the real-time position of the j-th train at time t; Q i，jRepresents the speed error variable of the i-th train and the coordinated reference speed curve information.

[0013] In a possible embodiment, the coordinated reference position speed curve includes coordinated reference speed curve information; the calculation expression of the speed tracking error is as follows:

[0014]

[0015] In the formula, Represents the speed tracking error at time t; v i (t) represents the real-time speed of the i-th train at time t; v r，i (t) represents the coordinated reference speed curve information of the i-th train at time t; v j (t) represents the real-time speed of the j-th train at time t; α i (t) represents the virtual control law to be designed for the i-th train at time t.

[0016] In a possible embodiment, the calculation expression of the position mutation amount is:

[0017]

[0018] In the formula, Δz p，i (k) represents the position mutation amount; Represents The value at t - Moment;

[0019] And, the calculation expression of the speed mutation amount is:

[0020]

[0021] In the formula, Δz v，i (k) represents the speed mutation amount; Represents The value at t - Moment.

[0022] In a possible embodiment, the calculation expression of the update law of the position reset performance function is:

[0023]

[0024] In the formula, Represents the derivative of the update law of the position reset performance function r pi (t); y1 represents the first positive constant; Represents the position reset performance design parameter with a reset function for the i-th train; y2 represents the second positive constant; Δr p，i (k) represents at t = t kThe variation of the position reset performance function of the i-th train at time; w p，i Represents a first positive number greater than 1;

[0025] Moreover, the calculation expression of the update law of the speed reset performance function is:

[0026]

[0027] In the formula, Represents the derivative of the update law of the speed reset performance function r vi (t); y3 represents a third positive constant; Represents the speed reset performance design parameter with a reset function for the i-th train; Δr v，i (k) represents the variation of the speed reset performance function of the i-th train at t = t k ; w v，i Represents a second positive number greater than 1.

[0028] In a possible embodiment, the calculation expression of the position error variable is:

[0029]

[0030] In the formula, Represents the position error variable at time t;

[0031] Moreover, the calculation expression of the speed error variable is:

[0032]

[0033] In the formula, Represents the speed error variable at time t.

[0034] In a possible embodiment, the calculation expression of the enhanced performance extended position error is:

[0035]

[0036] In the formula, ∈ p，i (t) represents the enhanced performance extended position error.

[0037] In a possible embodiment, the calculation expression of the enhanced performance extended speed error is:

[0038]

[0039] In the formula, ∈ v,i (t) represents the enhanced performance extended speed error.

[0040] In a possible embodiment, the method for multi-train collaborative enhanced performance control under switched topologies for the i-th train by enhancing the position error of performance expansion and the speed error of performance expansion is as follows:

[0041] α i (t) = -s1∈ p，i (t);

[0042]

[0043] In the formula, α i (t) represents the virtual control law to be designed for the i-th train at time t; s1 represents the fourth positive constant; u i (t) represents the control signal output by the train actuator to be designed at time t; s2 represents the fifth positive constant; a i，j (t) represents whether there is information interaction between the i-th train and the j-th train in the multi-train formation; a i，0 (t) represents that the i-th train can receive the collaborative reference position and speed curve.

[0044] Second, the embodiments of the present application provide a storage medium on which a computer program is stored. When the computer program is run by a processor, it executes the method described in the first aspect or any optional implementation manner of the first aspect.

[0045] Third, the embodiments of the present application provide an electronic device, including: a processor, a memory, and a bus. The memory stores machine-readable instructions executable by the processor. When the electronic device runs, the processor communicates with the memory through the bus. When the machine-readable instructions are executed by the processor, they execute the method described in the first aspect or any optional implementation manner of the first aspect.

[0046] Fourth, the present application provides a computer program product. When the computer program product runs on a computer, it causes the computer to execute the method in the first aspect or any possible implementation manner of the first aspect.

[0047] (III) Beneficial effects

[0048] The beneficial effects of the present invention are:

[0049] The embodiment of the present application provides a multi - train collaborative enhanced performance control method under switching topologies. The present application considers the situation where the tracking error jumps due to the switching of the communication topology structure during the collaborative operation of trains. According to the communication topology structure, a position reset performance function with a reset function is designed, and a multi - train collaborative enhanced performance control method under switching topologies is proposed, so that the position and speed tracking errors of multiple trains are constrained within the pre - designed reset performance function with a reset function, and the tracking performance of multiple trains can be further enhanced by adjusting the controller parameters.

[0050] To make the above - mentioned objects, features, and advantages of the embodiments of the present application more obvious and understandable, the following specifically gives preferred embodiments and, in conjunction with the accompanying drawings, makes a detailed description as follows. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] To more clearly illustrate the technical solutions of the embodiments of the present application, the following briefly introduces the drawings required to be used in the embodiments of the present application. It should be understood that the following drawings only show some embodiments of the present application, and therefore should not be regarded as limiting the scope. For those of ordinary skill in the art, without creative efforts, other relevant drawings can also be obtained based on these drawings.

[0052] Figure 1 Shows the flowchart of a multi - train collaborative enhanced performance control method under switching topologies provided by the embodiment of the present application;

[0053] Figure 2 Shows the schematic diagrams of all communication topologies of a multi - train provided by the embodiment of the present application;

[0054] Figure 3 Shows the schematic diagram of a multi - train communication topology switching signal provided by the embodiment of the present application;

[0055] Figure 4 Shows the schematic diagram of the position tracking error of all trains provided by the embodiment of the present application;

[0056] Figure 5 Shows the schematic diagram of the speed tracking error of all trains provided by the embodiment of the present application. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0057] To better explain the present invention for easy understanding, the following makes a detailed description of the present invention through specific embodiments in conjunction with the accompanying drawings.

[0058] An embodiment of the present application proposes a multi - train cooperative enhanced performance control method under switching topologies. By introducing impulsive dynamics, a reset performance boundary is designed to ensure that even in the case of sudden error mutations caused by topology switching, a preset boundary is immediately increased to absorb the suddenly increased tracking error and prevent the system from entering an unstable state. Based on the state information of adjacent trains, the position tracking error and speed tracking error of trains under safety constraints are transformed into unconstrained new variables. A multi - train enhanced performance control method is designed so that while the tracking performance of trains is constrained within the designed reset performance boundary, the tracking error can also be adjusted to arbitrarily small by selecting appropriate control gains. Therefore, it can ensure that the positions and speeds of multiple trains are within a safe range under topology switching, realizing the active safety protection function of trains and further improving the cooperative tracking performance of trains on this basis.

[0059] To better understand the above - mentioned technical solution, the exemplary embodiments of the present invention will be described in more detail below with reference to the accompanying drawings. Although the exemplary embodiments of the present invention are shown in the drawings, it should be understood that the present invention can be implemented in various forms and should not be limited by the embodiments set forth herein. On the contrary, these embodiments are provided to enable a more clear and thorough understanding of the present invention and to fully convey the scope of the present invention to those skilled in the art.

[0060] Please refer to Figure 1 , Figure 1 , which shows a flowchart of a multi - train cooperative enhanced performance control method under switching topologies provided by an embodiment of the present application. It should be understood that the multi - train cooperative enhanced performance control method under switching topologies can be executed by an electronic device, and the specific device of the electronic device can be set according to actual needs, and the embodiments of the present application are not limited thereto. For example, the electronic device can be a train control device, etc. Specifically, the multi - train cooperative enhanced performance control method under switching topologies includes:

[0061] Step S110, considering the case where n trains run cooperatively on the same railway line, establish a second - order nonlinear dynamic model of the i - th train. Wherein, the i - th train is any one of the n trains.

[0062] Specifically, considering n trains running cooperatively on the same railway line, taking the first train in the running direction as the leading train, and sequentially numbering the subsequent trains as the 2nd, 3rd,..., nth trains. Considering that the communication topology structure among the n trains running cooperatively is time - varying and switching, and all possible topology sets are S, then the s - th possible topology graph G s satisfies {G s : s ∈ S}. According to the knowledge of topology graph theory, a time - varying undirected graph G σ(t) ={V, E σ(t) , A σ(t)}, which represents the communication topology relationship among n trains running in coordination. Among them, the nodes in V = {1, 2,..., n} are the trains numbered i; E σ(t) = V×V represents the set of edges (i, j) in the topology graph G σ(t) at time t, where i and j respectively represent the i-th train and the j-th train, and the edge (i, j) ∈ G σ(t) means that the i-th train can communicate with the j-th train at time t; A σ(t) = [a i，j (t)] ∈ R n×n represents the adjacency matrix of the topology graph G σ(t) , and σ(t): [0, ∞) → S represents the communication topology switching signal between trains, and a i，j (t) represents whether there is information interaction between the i-th train and the j-th train in the multi-train formation, and the value rule of a i，j (t) is: when (i, j) ∈ G σ(t) , a i，j (t) is equal to 1, otherwise a i，j (t) is equal to 0, and a i，i (t) = 0. Among them, a i，i (t) represents its own communication topology loop, and a i，i (t) is defined as 0. And, at time t, the Laplacian matrix corresponding to A σ(t) is L σ(t) = [l i，j (t)] ∈ R n×n , where l i，j (t) represents the element in the i-th row and j-th column of the L σ(t) matrix, and the value rule of this l i，j (t) is: when i ≠ j, l i，j (t) = -a i，j (t), otherwise, at time t, the set of adjacent trains with information transmission to the i-th train is N i (t) = {i: (i, j) ∈ G σ(t) , j = 1, 2,..., n}. If there are consecutive edges (i, i i，1 ), (i i，2 , i i，3 ),..., (j i，1 , j) between the i-th train and the j-th train, where i i，k represents the train number that has information interaction with the i-th train in the formation, k = 1, 2,..., n, then there is a path between the i-th train and the j-th train. When there is at least one path between any two trains at time t, then the topology graph G σ(t)is connected. And, define M σ(t) = diag{a 1，0 (t), a 2，0 (t),..., a n，0 (t)}, where M σ(t) represents the matrix set indicating whether the trains in the formation can receive the known cooperative reference position - speed curve, diag represents the diagonal matrix, and a n，0 (t) indicates that the nth train can receive the cooperative reference position - speed curve, and a i，0 (t)= 1 means that the ith train can receive the known cooperative target position and speed curve at time t, otherwise, a i，0 (t)= 0.

[0063] Among them, the cooperative reference position - speed curve can also be called the cooperative reference curve.

[0064] And, based on the preset cooperative reference position - speed curve of the ith train, the real - time speed of the ith train, the real - time position of the ith train, the output control signal of the train actuator to be designed, and the undirected graph G of the communication topology structure among multiple trains obtained above σ(t) , establish the second - order nonlinear dynamic model of the ith train, and the specific form of this second - order nonlinear dynamic model is as follows:

[0065]

[0066] In the formula, represents the derivative of p i (t), and p i (t) represents the real - time position of the ith train collected by the sensor at time t; v i (t) represents the real - time speed of the ith train collected by the sensor at time t; represents the derivative of v i (t); u i (t) represents the output control signal of the train actuator to be designed at time t; κ i (t) represents the running resistance suffered by the ith train at time t, and its expression is:

[0067] κ i (t)= c0 + c1v i (t)+ c2v i 2 (t);

[0068] In the formula, c0 represents the first known Davis resistance parameter coefficient; c1 represents the second known Davis resistance parameter coefficient; c2 represents the third known Davis resistance parameter coefficient.

[0069] Step S120: Based on the second-order nonlinear dynamics model and the preset cooperative reference position-velocity curve of the \(i\)-th train, calculate the position tracking error and velocity tracking error of the \(i\)-th train respectively. According to the position tracking error and velocity tracking error, calculate the position mutation of the position tracking error and the velocity mutation of the velocity tracking error of the \(i\)-th train at the \(k\)-th communication topology switching moment. And according to the position mutation, define the update law of the position reset performance function with a reset function for the \(i\)-th train, and according to the velocity mutation, define the update law of the velocity reset performance function with a reset function for the \(i\)-th train.

[0070] Specifically, the calculation expression of the position tracking error is as follows:

[0071]

[0072] In the formula, represents the position tracking error at time \(t\); \(a\) i，0 (t) represents whether the \(i\)-th train can receive the known cooperative target position and velocity curve at time \(t\); \(p\) i (t) represents the real-time position of the \(i\)-th train at time \(t\); \(p\) r，i (t) represents the cooperative reference position curve information of the \(i\)-th train at time \(t\); \(Q\) r，i represents the expected distance between the \(i\)-th train and the cooperative reference position curve information; \(j\) represents the \(j\)-th train; \(n\) represents the number of trains in the formation; \(a\) i，j (t) represents whether there is information interaction between the \(i\)-th train and the \(j\)-th train in the multi-train formation at time \(t\); \(p\) j (t) represents the real-time position of the \(j\)-th train at time \(t\); \(Q\) i，j represents the expected distance between the \(i\)-th train and the cooperative reference velocity curve information.

[0073] And the calculation expression of the velocity tracking error is as follows:

[0074]

[0075] In the formula, represents the velocity tracking error at time \(t\); \(v\) i (t) represents the real-time velocity of the \(i\)-th train at time \(t\); \(v\) r，i (t) represents the cooperative reference velocity curve information of the \(i\)-th train at time \(t\); \(v\) j (t) represents the real-time velocity of the \(j\)-th train at time \(t\); \(\alpha\) i (t) represents the virtual control law to be designed for the \(i\)-th train at time \(t\).

[0076] Assume that the communication topology structure of the multi-trains only changes at \(t = t\) kSwitch at the moment (i.e., the k-th communication topology switching moment), where k ∈ Z represents the k-th communication topology switching, to obtain the time series t1, t2,..., t k ,.... Among them, Z represents the set of integers. In the following time intervals [t0, t1], [t1, t2),..., [t k , t k+1 ),..., the communication topology structure remains unchanged, and t0 = 0. Define τ to represent the topology residence time, and the communication topology switching times satisfy the following inequality relationship: t k+1 - t k > τ.

[0077] Furthermore, define the position jump variable of the position tracking error and the speed jump variable of the speed tracking error of the i-th train at the k-th communication topology switching moment t k as follows:

[0078]

[0079]

[0080] In the formula, Δz p，i (k) represents the position jump variable; represents at the value at t - ; Δz v，i (k) represents the speed jump variable; represents at the value at t - . Among them, the mathematical meaning of t - is the left limit at time t.

[0081] Furthermore, define the update law of the position reset performance function with a reset function for the i-th train as follows:

[0082]

[0083] In the formula, represents the derivative of the update law of the position reset performance function r pi (t); y1 represents the first positive constant; represents the position reset performance design parameter with a reset function for the i-th train, and it is a positive constant; y2 represents the second positive constant; Δr p，i (k) represents the change in the position reset performance function of the i-th train at t = t k , and Δr p，i (k) = r p，i (t) - r p，i (t - ), r p，i (t- ) represents r pi (t) at time t - ; w p，i represents the first positive number greater than 1.

[0084] Furthermore, the update law of the speed reset performance function with a reset function for the i-th train is defined as follows:

[0085]

[0086] where represents the derivative of the update law of the speed reset performance function r vi (t); y3 represents the third positive constant; represents the design parameter of the speed reset performance with a reset function for the i-th train, and it is a positive constant; Δr v，i (k) represents the change in the speed reset performance function of the i-th train at t = t k , and Δr v，i (k) = r v，i (t) - r v，i (t - ), r v，i (t - ) represents the value of r vi (t) at time t - ; w v，i represents the second positive number greater than 1.

[0087] Step S130: Perform a non-linear transformation on the position tracking error and the speed tracking error, and obtain the position error variable and the speed error variable of the coupled safety constraint of the i-th train according to the position reset performance function and the speed reset performance function.

[0088] Specifically, the calculation expression of this position error variable is:

[0089]

[0090] where represents the position error variable at time t;

[0091] And, the calculation expression of this speed error variable is:

[0092]

[0093] where represents the speed error variable at time t.

[0094] Step S140: Construct an enhanced performance extended position error based on the position tracking error and the position error variable, construct an enhanced performance extended speed error based on the speed tracking error and the speed error variable, and perform multi-train cooperative enhanced performance control with switched topologies for the i-th train according to the enhanced performance extended position error and the enhanced performance extended speed error.

[0095] Specifically, based on the position tracking error, the position error variable, the speed tracking error, and the speed error variable, in order to constrain the tracking performance of the train within the designed reset performance boundary and also adjust the tracking error to arbitrarily small by selecting appropriate control gains, the enhanced performance extended position error and the enhanced performance extended speed error are constructed as follows:

[0096]

[0097] In the formula, ∈ p，i (t) represents the enhanced performance extended position error; ∈ v，i (t) represents the enhanced performance extended speed error.

[0098] And the method for performing multi-train cooperative enhanced performance control with switched topologies for the i-th train through the enhanced performance extended position error and the enhanced performance extended speed error is as follows:

[0099] α i (t) = -s1 ∈ p,i (t);

[0100]

[0101] In the formula, α i (t) represents the virtual control law to be designed for the i-th train at time t; S1 represents the fourth positive constant; u i (t) represents the control signal output by the train actuator to be designed at time t; s2 represents the fifth positive constant; a i，j (t) represents whether there is information interaction between the i-th train and the j-th train in the multi-train formation at time t; a i，0 (t) represents whether the i-th train can receive the known cooperative target position and speed curve at time t.

[0102] Subsequently, the designed signal u i (t) can be applied to the train actuator to perform cooperative control on multiple trains to ensure the safe operation of multiple trains.

[0103] It should be understood that the parameters involved in this application can be set according to actual needs, and the embodiments of this application are not limited thereto.

[0104] For example, the design parameters y1, y2, and w in the position reset performance function r pi (t) with a reset function for the i-th train p,i and the parameters y3, w in the speed reset performance function r vi (t) v，i and the parameters s1 of the virtual control law α i (t) and the parameter s2 of the design signal u i (t) are all set according to actual requirements, and the embodiments of the present application are not limited thereto.

[0105] Therefore, by means of the above technical solutions, the present application considers the situation where the tracking error jumps due to the switching of the communication topology structure during the cooperative operation of trains, designs a position reset performance function with a reset function according to the communication topology structure, and proposes a multi-train cooperative reinforcement performance control method under the switched topology, so that the position and speed tracking errors of multiple trains are both constrained within the pre-designed reset performance function with a reset function, and the tracking performance of multiple trains can be further enhanced by adjusting the controller parameters.

[0106] To facilitate the understanding of the embodiments of the present application, the following will be described through specific embodiments.

[0107] Specifically, in order to verify the effectiveness of the multi-train cooperative reinforcement performance control method under the switched topology provided in this embodiment, MATLAB is used for simulation experiments to verify, and the following detailed description is made:

[0108] The system provided in this embodiment, which consists of n trains, considers the time-varying characteristics of the communication topology structure between trains, constructs the enhanced performance extended position and speed errors, and designs a multi-train cooperative reinforcement performance control method under the switched topology, so that while the position and speed tracking errors of the trains are both constrained within the range of the pre-designed reset performance function, the tracking error can be further enhanced by adjusting the controller parameters, ensuring the safe cooperative operation of multiple trains while improving the tracking performance.

[0109] In practical applications, the design parameters y1, y2, and w in the position reset performance function r pi (t) with a reset function for the i-th train p，i and can be set to 0.5, 2.15, 2, and 0.03. Moreover, the parameters y3, w vi in the speed reset performance function r v，i and can be set to 1, 2, and 0.3 respectively. Moreover, the parameter S1 of the virtual control law α i (t) can be set to 0.4. Moreover, the design signal ui The parameter S2 of (t) is set to 1.5.

[0110] Based on the above given parameters, the multi - train collaborative enhanced performance control method under the switching topology in this embodiment is simulated and verified. Among them, Figure 2 shows all the communication topology structure diagrams of a multi - train provided by the embodiment of the present application, Figure 3 shows a schematic diagram of the communication topology switching signal of a multi - train provided by the embodiment of the present application, Figure 4 shows a schematic diagram of the position tracking error of all trains provided by the embodiment of the present application, Figure 5 shows a schematic diagram of the speed tracking error of all trains provided by the embodiment of the present application. Combining with Figure 2 , Figure 3 , Figure 4 and Figure 5 it can be seen that the method of the present application can constrain the position and speed of the train within the range of the pre - designed reset performance function.

[0111] It should be understood that the above - mentioned multi - train collaborative enhanced performance control method under the switching topology is only exemplary. Those skilled in the art can make various deformations according to the above - mentioned method, and the deformed scheme also belongs to the protection scope of the present application.

[0112] Those skilled in the art should understand that the embodiments of the present invention can be provided as a method, a system or a computer program product. Therefore, the present invention can adopt the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware aspects. Moreover, the present invention can adopt the form of a computer program product implemented on one or more computer - usable storage media (including but not limited to disk memory, CD - ROM, optical memory, etc.) containing computer - usable program code.

[0113] The present invention is described with reference to the flowcharts and / or block diagrams of methods, devices (systems) and computer program products according to the embodiments of the present invention. It should be understood that each process and / or block in the flowcharts and / or block diagrams, and the combination of processes and / or blocks in the flowcharts and / or block diagrams can be implemented by computer program instructions.

[0114] It should be noted that the word "a" or "an" before a component does not exclude the existence of a plurality of such components. The present invention can be implemented by means of hardware including several different components and by means of a properly programmed computer. Among the several devices listed, several of these devices can be embodied by the same hardware. The use of the words first, second, third, etc. is only for the convenience of expression and does not represent any order. These words can be understood as part of the component name.

[0115] In addition, it should be noted that in the description of this specification, the descriptions of terms such as "one embodiment", "some embodiments", "embodiment", "example", "specific example" or "some examples" mean that the specific features, structures, materials or characteristics described in connection with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic representations of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described can be combined in any one or more embodiments or examples in a suitable manner. In addition, without contradiction, those skilled in the art can combine and combine the different embodiments or examples described in this specification and the features of different embodiments or examples.

[0116] Although the preferred embodiments of the present invention have been described, those skilled in the art can make additional changes and modifications after learning the basic creative concepts. Therefore, the technical solutions should be construed as including the preferred embodiments and all changes and modifications falling within the scope of the present invention.

[0117] Obviously, those skilled in the art can make various modifications and variations to the present invention without departing from the spirit and scope of the present invention. Thus, if these modifications and variations of the present invention fall within the scope of the technical solutions of the present invention and their equivalent technologies, the present invention should also include these modifications and variations.

Claims

1. A multi - train collaborative enhanced performance control method under a switching topology, characterized in that, Including: When considering the coordinated operation of n trains on the same railway line, establish a second-order nonlinear dynamic model for the i-th train; where the i-th train is any one of the n trains; Based on the second-order nonlinear dynamic model and the preset coordinated reference position-velocity curve of the i-th train, calculate the position tracking error and the velocity tracking error of the i-th train respectively, and according to the position tracking error and the velocity tracking error, calculate the position mutation of the position tracking error and the velocity mutation of the velocity tracking error of the i-th train at the k-th communication topology switching moment, and according to the position mutation, define the update law of the position reset performance function with a reset function for the i-th train, and according to the velocity mutation, define the update law of the velocity reset performance function with a reset function for the i-th train; Perform a nonlinear transformation on the position tracking error and the velocity tracking error, and according to the position reset performance function and the velocity reset performance function, obtain the position error variable and the velocity error variable of the coupled safety constraint of the i-th train; According to the position tracking error and the position error variable, construct an enhanced performance extended position error, and according to the velocity tracking error and the velocity error variable, construct an enhanced performance extended velocity error, and perform multi-train coordinated enhanced performance control for the i-th train under the switching topology according to the enhanced performance extended position error and the enhanced performance extended velocity error.

2. The multi-train collaborative enhanced performance control method under the switching topology according to claim 1, wherein The coordinated reference position-velocity curve includes coordinated reference position curve information; the calculation expression of the position tracking error is as follows: Wherein, represents the position tracking error at time t; a i，0 (t) represents whether the i-th train can receive the known cooperative target position and speed curve at the time t; p i (t) represents the real-time position of the i-th train at the time t; p r,i (t) represents the cooperative reference position curve information of the i-th train at the time t; Q r,i represents the distance error variable between the i-th train and the cooperative reference position curve information; j represents the j-th train; n represents the number of trains in the formation; q i，j (t) represents whether there is information interaction between the i-th train and the j-th train in the multi-train formation; p j (t) represents the real-time position of the j-th train at the time t; Q i，j represents the speed error variable between the i-th train and the cooperative reference speed curve information.

3. The multi - train collaborative enhanced performance control method under the switching topology according to claim 2, characterized in that, The coordinated reference position-velocity curve includes coordinated reference velocity curve information; the calculation expression of the velocity tracking error is as follows: wherein, represents the speed tracking error at the t-th moment; v i (t) represents the real-time speed of the i-th train at the t-th moment; v r，i (t) represents the cooperative reference speed curve information of the i-th train at the t-th moment; v j (t) represents the real-time speed of the j-th train at the t-th moment; α in this formula i (t) represents the virtual control law to be designed for the i-th train at the t-th moment.

4. The multi - train collaborative reinforcement performance control method under the switching topology according to claim 3, characterized in that, The calculation expression of the position mutation is: where Δz p,i (k) represents the mutation amount of the position; represents the said value at time t - ; And, the calculation expression of the velocity mutation is: where, Δz v，i (k) represents the sudden change in the speed; represents the value at time t - .

5. The multi-train collaborative enhanced performance control method under the switching topology according to claim 4, characterized in that The calculation expression of the update law of the position reset performance function is: In the formula, represents the derivative of the update law of the position reset performance function r pi (t); y1 represents the first positive constant; represents the position reset performance design parameter with a reset function for the i-th train; y2 represents the second positive constant; Δr p，i (k) represents the change in the position reset performance function of the i-th train at t = t k ; w p，i represents a first positive number greater than 1; And, the calculation expression of the update law of the velocity reset performance function is: wherein, represents the derivative of the update law of the speed reset performance function r vi (t); y3 represents the third positive constant; represents the speed reset performance design parameter with a reset function of the i-th train; Δr v，i (k) represents the change in the speed reset performance function of the i-th train at t = t k ; w v，i represents the second positive number greater than 1.

6. The method for multi - train collaborative enhanced performance control under the switching topology according to claim 5, characterized in that The calculation expression of the position error variable is: wherein, represents the position error variable at the time t; And, the calculation expression of the velocity error variable is: wherein, represents the velocity error variable at the time t.

7. The method for multi-train collaborative enhanced performance control under the switching topology according to claim 6, characterized in that The calculation expression of the enhanced performance extended position error is: wherein, ∈ p，i (t) represents the enhanced performance expansion position error.

8. The multi-train collaborative enhanced performance control method under the switching topology according to claim 7, characterized in that The calculation expression of the enhanced performance extended velocity error is: where ∈ v，i (t) represents the enhanced performance expansion speed error.

9. The multi-train collaborative enhanced performance control method under the switching topology according to claim 8, characterized in that The method for performing multi-train coordinated enhanced performance control for the i-th train under the switching topology through the enhanced performance extended position error and the enhanced performance extended velocity error is as follows: where α in this formula i (t) represents the virtual control law to be designed for the i-th train at the t-th moment; s1 represents the fourth positive constant; u i (t) represents the control signal output by the train actuator to be designed at the t-th moment; s2 represents the fifth positive constant; a i，j (t) represents whether there is information interaction between the i-th train and the j-th train in the multi-train formation; a i，0 (t) represents that the i-th train can receive the cooperative reference position and speed curve.

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