Multi-train formation fault-tolerant control method under switching topology

Abstract

The invention relates to a multi-train formation fault-tolerant control method under switching topology, and the method comprises the steps: designing a position reset performance function, carrying out the nonlinear transformation of a formation position tracking error signal and the position reset performance function, and carrying out the calculation to obtain a position coupling preset performance constraint error variable of an ith train; designing a speed reset performance function, performing nonlinear transformation on the formation speed tracking error signal and the speed reset performance function, and calculating to obtain a speed coupling preset performance constraint error variable of the ith train; and based on the position coupling preset performance constraint error variable, designing a virtual control law of the ith train, and based on the position coupling preset performance constraint error variable, the speed coupling preset performance constraint error variable and the virtual control law, carrying out multi-train formation fault-tolerant control under the switching topology. Therefore, the tracking precision and the safe operation of the formation train can be ensured under the condition that the actuator breaks down and the communication topological structure is switched.

Description

Technical Field

[0001] The present invention relates to the technical field of high - speed train operation control, and particularly to a multi - train formation fault - tolerant control method under switched topologies. Background Art

[0002] In order to improve the efficiency and reliability of railway transportation, train formation operation control has become a research hotspot in recent years. Through effective formation control, trains can achieve precise distance maintenance and speed synchronization, thereby improving the safety and efficiency of train operation. However, train formation operation control faces various challenges. One of them is that the actuators of trains may fail, which will directly affect the operation state of trains and the safety of the formation.

[0003] To ensure the safety of train formations, control algorithms need to ensure that the intervals between trains are strictly within a safe range. In this case, preset performance control has become an effective method. Preset performance control can limit the error response of the system by setting preset performance boundaries, ensuring the safe intervals between trains and maintaining the stability of train formations even when actuators fail. However, in actual operation, train control systems also face the challenge of communication topology switching. During operation, due to the possible differences in the coverage range and signal strength of communication networks in different geographical areas that trains pass through, or due to poor communication network quality, the tracking error of trains will jump, resulting in the failure of train state safety constraints and thus the existence of singularities in the system. This will make it difficult to guarantee the convergence of tracking errors and may affect the operation safety of trains. Although certain progress has been made in train safety and protection control based on preset performance, there is currently no mature theoretical system for high - precision formation control considering variable topology switching.

[0004] In summary, it is very necessary to study a multi - train formation fault - tolerant control method under switched topologies to achieve high - precision formation control and safe and stable operation of trains under variable communication topologies. Summary of the Invention

[0005] (1) Technical Problems to be Solved

[0006] In view of the above - mentioned shortcomings and deficiencies of the prior art, the present invention provides a multi - train formation fault - tolerant control method under switched topologies, which solves the technical problem in the prior art of how to achieve high - precision formation control and safe and stable operation of trains under variable communication topologies.

[0007] (2) Technical Solutions

[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 formation fault - tolerant control method under a switching topology, including: establishing a longitudinal dynamics model of the i - th train in a multi - train formation considering that the trains in the multi - train formation are subject to running resistance and actuator failures; wherein the longitudinal dynamics model includes the real - time position and the real - time speed of the i - th train; calculating a formation position tracking error signal of the i - th train based on a given known formation target reference curve and the real - time position of the i - th train, designing a position reset performance function with pulse performance for the formation position tracking error signal, and performing a non - linear transformation on the formation position tracking error signal and the position reset performance function to calculate a position - coupled preset performance constraint error variable of the i - th train; calculating a formation speed tracking error signal of the i - th train based on a given known formation target reference curve and the real - time speed of the i - th train, designing a speed reset performance function with pulse performance according to the formation position tracking error signal, the position reset performance function, and the formation speed tracking error signal, and performing a non - linear transformation on the formation speed tracking error signal and the speed reset performance function to calculate a speed - coupled preset performance constraint error variable of the i - th train; designing a virtual control law for the i - th train based on the position - coupled preset performance constraint error variable, and performing multi - train formation fault - tolerant control of the i - th train under a switching topology based on the position - coupled preset performance constraint error variable, the speed - coupled preset performance constraint error variable, and the virtual control law.

[0010] In a possible embodiment, the calculation expression of the formation position tracking error signal is:

[0011]

[0012] In the formula, represents the formation position tracking error signal at time t; a i，0 (t) represents whether the i - th train can receive the known formation target reference curve at time t; p i (t) represents the real - time position of the i - th train at time t; p d，i (t) represents the reference position of the i - th train at time t, and the reference position is determined based on the given known formation target reference curve; S d，i represents the expected distance difference between the real - time position and the reference position of the i - th train; n represents the number of all trains in the multi - train formation; a i，j (t) represents whether there is a communication connection 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 time t; S i，j represents the expected distance difference between the i - th train and the j - th train.

[0013] In a possible embodiment, the calculation expression of the position reset performance function is as follows:

[0014]

[0015] In the formula, represents the derivative of the position reset performance function q p，i (t); both x1 and x2 are positive constants; represents the design parameter of the position reset performance function of the i-th train, and it is a positive constant; t k represents the k-th topology switching moment; Δq p，i (k) represents the jump variable of the position reset performance function of the i-th train at the moment when the topology switches at t = t k ; is a positive number greater than 1; Δe p，i (k) represents the mutation value of the formation position tracking error signal of the i-th train.

[0016] In a possible embodiment, the calculation expression of the formation speed tracking error signal is as follows:

[0017]

[0018] In the formula, represents the formation speed tracking error signal at time t; a i，0 (t) represents whether the i-th train can receive the known formation target reference curve at time t; v i (t) represents the real-time speed of the i-th train at time t; v d，i (t) represents the reference speed of the i-th train at time t, and the reference speed is determined based on the given known formation target reference curve; n represents the number of all trains in the multi-train formation; a i，j (t) represents whether there is a communication connection between the i-th train and the j-th train in the multi-train formation; 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.

[0019] In a possible embodiment, the calculation expression of the speed reset performance function is as follows:

[0020]

[0021] In the formula, represents the derivative of the speed reset performance function q v，i (t); x3 is a positive constant; represents the design parameter of the speed reset performance function of the i-th train, and it is a positive constant; Denote the formation position tracking error signal at time t; q p，i (t) denote the position reset performance function; Δq v，i (k) denote the jump variable of the speed reset performance function of the i-th train at the moment when the topology switches at t = t k ; is a positive number greater than 1; Δe v，i (k) denote the mutation value of the formation speed tracking error signal of the i-th train.

[0022] In a possible embodiment, the calculation expression of the virtual control law of the i-th train is:

[0023] α i (t)= -k1(ψ p，i 3 (t)+ψ p，i (t));

[0024] In the formula, α i (t) denote the virtual control law of the i-th train; k1 is a positive constant; ψ p，i (t) denote the position coupling preset performance constraint error variable of the i-th train at time t.

[0025] In a possible embodiment, the multi-train formation fault-tolerant control under switched topology for the i-th train is performed through the following formula:

[0026]

[0027] In the formula, τ i (t) denote the multi-train formation fault-tolerant controller for switched topology; is the estimated value of the first unknown parameter μ i (t), and the first unknown parameter μ i (t) satisfies: And μ i And are both positive constants; k2 is a positive constant; is the estimated value of the second unknown parameter m 1，i (t), and the second unknown parameter m 1，i (t) satisfies: And m 1，i And are both positive constants; is the estimated value of the third unknown parameter m2,i(t), and the third unknown parameter m2,i(t) satisfies: And m 2，i And are both positive constants; ψ v，i(t) represents the speed coupling preset performance constraint error variable; a i，j (t) represents whether there is a communication connection between the i-th train and the j-th train in the multi-train formation; a i，0 (t) represents whether the i-th train can receive the known formation target reference curve at time t; B i (t) represents the running resistance suffered by the i-th train during operation at time t; represents v j The derivative of (t); represents v d，i The derivative of (t).

[0028] In a possible embodiment, The adaptive parameter update law of The calculation expression is as follows:

[0029]

[0030] In the formula, represents projecting onto within the range of; g1 and σ i are both positive constants; represents the formation speed tracking error signal at time t; q v，i (t) represents the speed reset performance function.

[0031] In a possible embodiment, The adaptive parameter update law of is:

[0032]

[0033] In the formula, represents projecting onto within the range of; g2 is a positive constant.

[0034] In a possible embodiment, The adaptive parameter update law of is:

[0035]

[0036] In the formula, g3 is a positive constant.

[0037] Second, the embodiments of the present application provide a storage medium, on which a computer program is stored, and 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.

[0038] In a third aspect, an embodiment of the present application provides 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, the method described in the first aspect or any optional implementation manner of the first aspect is executed.

[0039] In a fourth aspect, the present application provides a computer program product. When the computer program product runs on a computer, the computer is enabled to execute the method in the first aspect or any possible implementation manner of the first aspect.

[0040] (III) Beneficial effects

[0041] The beneficial effects of the present invention are as follows:

[0042] An embodiment of the present application provides a multi-train formation fault-tolerant control method under a switching topology. This method considers the possible actuator failures and switching of communication topologies during the operation of the train formation. According to the state information of the train and the state information of adjacent trains obtained through the communication topology structure, the update of unknown fault parameters is dynamically updated in real time, and a position and speed reset performance function with pulse performance is designed to keep the preset performance boundary of the train within the allowable safety range at all times, ensuring the safety of the train during formation operation. By using the non-linear error conversion technology, the tracking error of the train is constrained within the preset reset performance function boundary, which can ensure the tracking accuracy and safe operation of the formation trains in the case of actuator failures and switching of communication topology structures.

[0043] To make the above objects, features, and advantages to be achieved by the embodiments of the present application more obvious and understandable, the following specifically enumerates preferred embodiments and, in conjunction with the accompanying drawings, makes a detailed description as follows. Description of the drawings

[0044] 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 related drawings can also be obtained based on these drawings.

[0045] Figure 1 Shows a flowchart of a multi-train formation fault-tolerant control method under a switching topology provided by an embodiment of the present application;

[0046] Figure 2 Shows a possible communication topology structure diagram of a train formation provided by an embodiment of the present application;

[0047] Figure 3 A schematic diagram of a communication topology switching signal provided by an embodiment of the present application is shown;

[0048] Figure 4 A schematic diagram of the position tracking error of each train in a formation provided by an embodiment of the present application is shown;

[0049] Figure 5 A schematic diagram of the position tracking error of each train in a formation provided by an embodiment of the present application is shown. Detailed implementation manners

[0050] To better explain the present invention for easy understanding, the present invention will be described in detail below in conjunction with the accompanying drawings through specific implementation manners.

[0051] An embodiment of the present application provides a fault-tolerant control method for multi-train formation under switched topologies, designs a reset performance boundary based on impulsive dynamics, when the tracking error jumps due to the switching of the train communication topology, immediately increases the preset boundary according to the jump value of the tracking error, so that the tracking error can also be constrained within the preset performance range at the topology switching moment, avoiding system instability. Obtain the state information of adjacent trains according to the communication topology structure, and use nonlinear transformation to keep the state tracking error of the constrained train within the reset performance boundary. Under the preset performance control design framework, a fault-tolerant control strategy based on reset performance is designed for each train to estimate and compensate for the time-varying actuator faults, so as to ensure the stable and safe operation of the train formation under the conditions of communication topology switching and actuator faults.

[0052] To better understand the above 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 described 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.

[0053] Please refer to Figure 1 , Figure 1 , which shows a flowchart of a fault-tolerant control method for multi-train formation under switched topologies provided by an embodiment of the present application. It should be understood that the fault-tolerant control method for multi-train formation under switched 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 fault-tolerant control method for multi-train formation under switched topologies includes:

[0054] Step S110, establish a longitudinal dynamics model of the \(i\)-th train in a multi-train formation considering that the trains in the multi-train formation are subject to running resistance and there are actuator failures. Among them, the longitudinal dynamics model includes the real-time position and the real-time speed of the \(i\)-th train.

[0055] Specifically, consider \(n\) trains running in formation on a line. The first train in the running direction is the leading train, and the subsequent trains are numbered as the 2nd, 3rd, \(\cdots\), \(n\)-th trains in sequence. For a train formation system composed of \(n\) trains with a time-varying communication topology, the communication topology structure between trains switches among all possible topology sets \(Q\), that is, \(\{G\) q : \(q\in Q\}\), where \(q\in N\) + is the \(q\)-th possible communication topology structure, and \(N\) represents natural numbers. Based on the knowledge of topological graph theory, use a time-varying undirected graph \(G\) σ(t) \(=\{V, E\) σ(t) , \(A\) ζ(t) \} to describe the communication relationship among the \(n\) trains in the formation. Among them, the \(i\)-th node in \(V = \{1, 2, \cdots, n\}\) represents the \(i\)-th train; \(E\) σ(t) \(= V\times V\) is the set of edges \((i, j)\) in the time-varying undirected graph \(G\) σ(t) . \(i\) and \(j\) respectively represent the \(i\)-th node and the \(j\)-th node, and the edge \((i, j)\in G\) σ(t) means that the \(i\)-th train can communicate with the \(j\)-th train at time \(t\); represents the adjacency matrix of the topological graph \(G\) σ(t) , and \(\sigma(t): [0, \infty)\to Q\) is the topology switching signal, and \(a\) i，j (t) represents whether there is a communication connection 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 \((i, j)\in G\) σ(t) , \(a\) i,j (t) is equal to 1, otherwise \(a\) i,j (t) = 0, and \(a\) i，i (t) = 0. And, at time \(t\), the Laplacian matrix corresponding to \(A\) σ(t) is \(L\) σ(t) \(=[l\) i，j (t)]\in R\) n× \(^{n\times n}\), where \(l\) i，j (t) represents the element in the \(i\)-th row and \(j\)-th column of the Laplacian matrix, and the value rule of this \(l\) i，j (t) is: when \(i\neq j\), \(l\) i，j (t)= -a\) i，j (t), otherwise, Define the set of adjacent trains of the \(i\)-th train at time \(t\) as \(B\) i(t) = {i: (i, j) ∈ G σ(t) , j = 1, 2,..., n}. If there is a continuous edge (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 , k represents the serial number of a certain train with a communication connection to the i-th train, i i,k , k = 1, 2,..., n is a constant and i i,k = 1, 2,..., n, then there is said to be a path between the i-th train and the j-th train. If there is a path between any two trains in the formation at time t, then the time-varying undirected graph G σ(t) is connected. Also, 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 of whether the trains in the formation can receive the known formation target reference curve, diag represents the diagonal matrix, a n，0 (t) represents whether the n-th train in the formation can receive the known formation target reference curve, a i，0 (t) = 1 means that the i-th train can receive the known formation target reference curve at time t, otherwise, a i,0 (t) = 0.

[0056] Considering the case where the trains in the formation are subject to running resistance and there are actuator failures, according to the communication topology relationship in the above steps, considering that the actuator of the i-th train is subject to partial actuator failure and bias fault, the longitudinal dynamic model of the i-th train in the formation is constructed as follows:

[0057]

[0058] In the formula, pi(t) represents the real-time position of the i-th train at time t; represents the derivative of pi(t); v i (t) represents the real-time speed of the i-th train at time t; represents the derivative of v i (t); is the actual output of the actuator of the i-th train under the fault at time t. Due to the actuator failure, there is a deviation between the desired control signal τ i (t) to be designed and . The relationship between τ i (t) and can be expressed by the following formula:

[0059]

[0060] Wherein, k i is the actuator failure factor of the i-th train, and κ i ∈ [0, 1); β i is the unknown bias fault factor of the actuator of the i-th train;

[0061] And, B i (t) is the running resistance suffered by the i-th train during operation at time t, and its expression is:

[0062] B i (t) = b0 + b1v i (t) + b2v i 2 (t).

[0063] Wherein, b0, b1 and b2 are known Davis equation coefficients.

[0064] Step S120: Based on the given known formation target reference curve and the real-time position of the i-th train, calculate the formation position tracking error signal of the i-th train, and design a position reset performance function with pulse performance for the formation position tracking error signal, and perform a non-linear transformation on the formation position tracking error signal and the position reset performance function to calculate the position coupling preset performance constraint error variable of the i-th train.

[0065] Specifically, according to the above communication topology relationship and the longitudinal dynamics model of the i-th train, based on the given known formation target reference curve and the real-time position of the i-th train, calculate the formation position tracking error signal of the i-th train as follows:

[0066]

[0067] Wherein, represents the formation position tracking error signal at time t; a i，0 (t) represents whether the i-th train can receive the known formation target reference curve at time t; p i (t) represents the real-time position of the i-th train at time t; p d，i (t) represents the reference position of the i-th train at time t, and the reference position is determined based on the given known formation target reference curve; S d，i represents the expected distance difference between the real-time position and the reference position of the i-th train; n represents the number of all trains in the multi-train formation; a i，j (t) represents whether there is a communication connection 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 time t; S i，j represents the expected distance difference between the i-th train and the j-th train.

[0068] Also, assume that the communication topology between trains only switches at time t = t k (i.e., the k-th communication topology switching moment), then the time sequence of topology switching is τ1, τ2,..., τ k ,.... Also, in the following time intervals [t0, t1), [t1, t2),..., [t k , t k+1 ), … the communication topology between trains remains unchanged, where k ∈ Z is the k-th communication topology switching, and t0 = 0, Z represents the set of integers. Let be the topology residence time, and assume that the topology switching time of the train satisfies:

[0069] At time t = t k , the communication topology between trains switches, resulting in a mutation of the formation position tracking error signal of the i-th train, and define the mutation value of the formation position tracking error signal of the i-th train as:

[0070]

[0071] In the formula, Δe p，i (k) represents the mutation value of the formation position tracking error signal of the i-th train; represents the value at time t - . Among them, the mathematical meaning of t - is the left limit at time t.

[0072] Furthermore, design a position reset performance function q p，i (t) with pulse performance for the i-th train as follows:

[0073]

[0074] In the formula, represents the derivative of the position reset performance function q p，i (t); both x1 and X2 are positive constants; represents the design parameter of the position reset performance function of the i-th train, and it is also a positive constant; t k represents the k-th topology switching moment; Δq p，i (k) represents the jump variable of the position reset performance function of the i-th train at the moment when the topology switches at t = t k ; is a positive number greater than 1; Δe p，i (k) represents the mutation value of the formation position tracking error signal of the i-th train.

[0075] Furthermore, for the formation position tracking error signal and the position reset performance function q p，i (t), a non-linear transformation is performed to obtain the position-coupled preset performance constraint error variable of the i-th train, specifically:

[0076]

[0077] In the formula, ψ p，i (t) represents the position-coupled preset performance constraint error variable of the i-th train at time t.

[0078] Step S130: Based on the given known formation target reference curve and the real-time speed of the i-th train, calculate the formation speed tracking error signal of the i-th train, and design a speed reset performance function with pulse performance according to the formation position tracking error signal, the position reset performance function, and the formation speed tracking error signal, and perform a non-linear transformation on the formation speed tracking error signal and the speed reset performance function to calculate the speed-coupled preset performance constraint error variable of the i-th train.

[0079] Specifically, according to the above communication topology relationship and the longitudinal dynamics model of the i-th train, based on the given known formation target reference curve and the real-time speed of the i-th train, calculate the formation speed tracking error signal of the i-th train as follows:

[0080]

[0081] In the formula, represents the formation speed tracking error signal at time t; a i，0 (t) represents whether the i-th train can receive the known formation target reference curve at time t; v i (t) represents the real-time speed of the i-th train at time t; v d，i (t) represents the reference speed of the i-th train at time t, and the reference speed is determined based on the given known formation target reference curve; n represents the number of all trains in the multi-train formation; a i，j (t) represents whether there is a communication connection between the i-th train and the j-th train in the multi-train formation; v j (t) represents the real-time speed of the, -th train at time t; α in this formula i (t) represents the virtual control law to be designed for the i-th train at time t.

[0082] And, assuming that the communication topology between trains only switches at \(t = t\) k moment (i.e., the \(k\)-th communication topology switching moment), then the time series of topology switching is \(t_1, t_2, \cdots, t\) k , \(\cdots\). And, in the following time intervals \([t_0, t_1)\), \([t_1, t_2)\), \(\cdots\), \([t\) k , \(t\) k+1 ), \(\cdots\) the communication topology between trains remains unchanged, where \(k\in Z\) is the \(k\)-th communication topology switch, and \(t_0 = 0\), \(Z\) represents the set of integers. Let be the topology residence time. Assuming that the topology switching time of the train satisfies:

[0083] At \(t = t\) k moment, the communication topology between trains switches, resulting in a mutation of the formation speed tracking error signal of the \(i\)-th train, and define the mutation value of the formation speed tracking error signal of the \(i\)-th train as:

[0084]

[0085] where \(\Delta e\) v，i (k) represents the mutation value of the formation speed tracking error signal of the \(i\)-th train; represents the value at \(t\) - moment.

[0086] Furthermore, design a speed reset performance function \(q\) v，i (t) with pulse performance for the \(i\)-th train as follows:

[0087]

[0088] where represents the derivative of the speed reset performance function \(q\) v，i (t); \(x_3\) is a positive constant; represents the design parameter of the speed reset performance function of the \(i\)-th train, and it is also a positive constant; represents the formation position tracking error signal at \(t\) moment; \(q\) p，i (t) represents the position reset performance function; \(\Delta q\) v，i (k) represents the jump variable of the speed reset performance function of the \(i\)-th train at the moment when the topology switches at \(t = t\) k ; is a positive number greater than 1; \(\Delta e\) v，i (k) represents the mutation value of the formation speed tracking error signal of the \(i\)-th train.

[0089] Furthermore, for the formation speed tracking error signal and the speed reset performance function q v，i (t) are non-linearly transformed to calculate the speed coupling preset performance constraint error variable of the i-th train, specifically:

[0090]

[0091] where ψ v，i (t) represents the speed coupling preset performance constraint error variable.

[0092] Step S140: Based on the position coupling preset performance constraint error variable, design the virtual control law of the i-th train, and based on the position coupling preset performance constraint error variable, the speed coupling preset performance constraint error variable, and the virtual control law, perform multi-train formation fault-tolerant control for the i-th train under switched topologies.

[0093] Specifically, the virtual control law for the i-th train is as follows:

[0094] α i (t) = -k1(ψ p，i 3 (t) + ψ p，i (t));

[0095] where α i (t) represents the virtual control law of the i-th train; k1 is a positive constant; ψ p，i (t) represents the position coupling preset performance constraint error variable of the i-th train at time t.

[0096] Furthermore, the i-th train is subjected to multi-train formation fault-tolerant control under switched topologies through the following formula, specifically:

[0097]

[0098] where τ i (t) represents the multi-train formation fault-tolerant controller for switched topologies; is the estimated value of the first unknown parameter μ i (t), and the first unknown parameter μ i (t) satisfies: and μ i and are both positive constants; k2 is a positive constant; is the estimated value of the second unknown parameter m 1，i (t), and the second unknown parameter m 1，i (t) satisfies: and m1，i and are both positive constants; is the third unknown parameter m 2，i the estimated value of (t), and the third unknown parameter m 2,i (t) satisfies: and m 2，i and are both positive constants; ψ v，i (t) represents the speed coupling preset performance constraint error variable; a i,j (t) represents whether there is a communication connection between the i-th train and the j-th train in the multi-train formation; a i,0 (t) represents whether the i-th train can receive the known formation target reference curve at time t; B i (t) represents the running resistance suffered by the i-th train during operation at time t; represents the derivative of v j (t); represents the derivative of v d,i (t).

[0099] And, the adaptive parameter update law is as follows:

[0100]

[0101] In the formula, represents projecting onto the range; g1 and σ i are both positive constants; represents the formation speed tracking error signal at time t; q v，i (t) represents the speed reset performance function.

[0102] Furthermore, the adaptive parameter update law is:

[0103]

[0104] In the formula, represents projecting onto the range; g2 is a positive constant.

[0105] Furthermore, the adaptive parameter update law is:

[0106]

[0107] In the formula, g3 is a positive constant.

[0108] It should be noted here that the parameters involved in this application can be set according to actual needs, and the embodiments of this application are not limited thereto.

[0109] For example, the parameters x1, x2, p，i of the position reset performance function q and in (t) can all be set according to actual needs, and the embodiments of this application are not limited thereto; the parameters x3, v,i and of the speed reset performance function q in (t) can also all be set according to actual needs, and the embodiments of this application are not limited thereto; the parameter k1 of the virtual control law α i in (t) can also be set according to actual needs, and the embodiments of this application are not limited thereto; the parameters k2, g1, g2, g3 and σ i of the multi - train formation fault - tolerant controller τ i in (t) can also all be set according to actual needs, and the embodiments of this application are not limited thereto.

[0110] Therefore, by means of the above - mentioned technical solution, this method considers the possible actuator faults and the switching of communication topologies during the train formation operation, obtains the state information of adjacent trains according to the state information of the train and through the communication topology structure, updates the unknown fault parameters in real - time dynamically, and designs the position and speed reset performance functions with pulse performance to keep the preset performance boundary of the train within the allowable safety range all the time, ensuring the safety of the train during the formation operation. Using the nonlinear error conversion technology, the tracking error of the train is constrained within the preset reset performance function boundary, which can ensure the tracking accuracy and safe operation of the formation trains in the case of actuator faults and the switching of communication topology structures.

[0111] To facilitate the understanding of the embodiments of this application, the following will be described through specific embodiments.

[0112] Specifically, the train formation system provided in this embodiment consists of a train formation composed of n trains. Considering the longitudinal dynamic model under the actuator faults of the trains in the formation and the time - varying train formation communication topology, a multi - train formation fault - tolerant control method under switching topology is designed, so that the formation position and speed tracking errors of the trains are both limited within the safety range, ensuring the tracking accuracy and safe operation of the formation trains.

[0113] In practical applications, the parameters x1, x2, p，i of the position reset performance function q and Set to 0.5, 2.15, 2, and 0.03; the parameters x3 of the speed reset performance function q v，i (t) can also be and Set to 1, 2, and 0.3; the parameter k1 of the virtual control law α i (t) can be set to 0.4; the parameters k2, g1, g2, g3, and σ of the multi - train formation fault - tolerant controller τ i (t) can be i Set to 1.5, 0.0001, 0.0005, 0.01, and 0.5.

[0114] Based on the above - given parameters, the multi - train formation fault - tolerant control method under switching topology in this embodiment is simulated and verified, and the results are as shown in Figure 2 、 Figure 3 、 Figure 4 and Figure 5 . Among them, Figure 2 shows a possible communication topology structure diagram of a train formation provided by an embodiment of the present application, Figure 3 shows a schematic diagram of a communication topology switching signal provided by an embodiment of the present application, Figure 4 shows a schematic diagram of the position tracking error of each train in a formation provided by an embodiment of the present application, Figure 5 shows a schematic diagram of the position tracking error of each train in a formation provided by an embodiment of the present application. Combining Figures 2 to 5 it can be seen that this control method can constrain the error of the train within the range of the preset reset performance function.

[0115] It should be understood that the above - mentioned multi - train formation fault - tolerant control method under switching topology is only exemplary. Those skilled in the art can make various deformations according to the above - mentioned method, and the deformed solutions also fall within the protection scope of the present application.

[0116] Those skilled in the art should understand that the embodiments of the present invention can be provided as methods, systems, or computer program products. 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 memories, CD - ROMs, optical memories, etc.) containing computer - usable program codes.

[0117] The present invention is described with reference to the flowcharts and / or block diagrams of methods, devices (systems), and computer program products according to 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.

[0118] It should be noted that in the claims, any reference signs placed between parentheses shall not be construed as limiting the claim. The word "comprising" does not exclude the presence of elements or steps not listed in the claim. The word "a" or "an" preceding an element does not exclude the presence of a plurality of such elements. The present invention can be implemented by means of hardware including several different elements and by means of a suitably programmed computer. In a claim listing several means, several of these means can be embodied by the same hardware. The use of the terms first, second, third, etc. is for convenience only and does not denote any order. These terms can be construed as part of the element name.

[0119] In addition, it should be noted that in the description of this specification, the description of terms such as "one embodiment", "some embodiments", "embodiment", "example", "specific example" or "some examples", etc. means 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.

[0120] 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 concept. Therefore, the claims should be construed to include the preferred embodiments as well as all changes and modifications falling within the scope of the present invention.

[0121] 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 claims of the present invention and their equivalent technologies, the present invention should also include these modifications and variations.

Claims

1. A fault-tolerant control method for multi-train formation under switching topology, characterized in that: include: Under the condition that the trains in the multi-train formation are subject to running resistance and there is an actuator failure, a longitudinal dynamic model of the i-th train in the multi-train formation is established; wherein the longitudinal dynamic model includes the real-time position of the i-th train and the real-time speed of the i-th train; Based on a given known formation target reference curve and the real-time position of the i-th train, a formation position tracking error signal of the i-th train is calculated, and a position reset performance function with pulse performance is designed for the formation position tracking error signal, and a nonlinear transformation is performed on the formation position tracking error signal and the position reset performance function to calculate a position coupling preset performance constraint error variable of the i-th train; Based on the given known formation target reference curve and the real-time speed of the i-th train, a formation speed tracking error signal of the i-th train is calculated, and according to the formation position tracking error signal, the position reset performance function and the formation speed tracking error signal, a speed reset performance function with pulse performance is designed, and the formation speed tracking error signal and the speed reset performance function are nonlinearly transformed to calculate a speed coupling preset performance constraint error variable of the i-th train; Based on the position-coupled preset performance constraint error variable, a virtual control law of the i-th train is designed, and based on the position-coupled preset performance constraint error variable, the speed-coupled preset performance constraint error variable and the virtual control law, fault-tolerant control of a multi-train formation under a switching topology is performed on the i-th train.

2. The fault-tolerant control method for multi-train formation under switching topology according to claim 1 is characterized in that: The calculation expression of the formation position tracking error signal is: In the formula, represents the formation position tracking error signal at time t; a i，0 (t) indicates whether the i-th train can receive the known formation target reference curve at the time t; p i (t) represents the real-time position of the i-th train at the time t; p d，i (t) represents the reference position of the i-th train at the time t, and the reference position is determined based on the given known formation target reference curve; s d，i represents the expected distance difference between the real-time position of the i-th train and the reference position; n represents the number of all trains in the multi-train formation; a i，j (t) indicates whether there is a communication connection 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; s i，j represents the expected distance difference between the i-th train and the j-th train.

3. The fault-tolerant control method for multi-train formation under switching topology according to claim 2 is characterized in that: The calculation expression of the position reset performance function is: In the formula, The position reset performance function q is represented by p，i The derivative of (t); x1 and x2 are both positive constants; represents the design parameter of the position resetting performance function of the i-th train, and is a positive constant; t k represents the kth topology switching time; Δq p，i (k) means that at t = t k The jump variable of the position reset performance function of the i-th train at the time when the topology switching occurs; is a positive number greater than 1; Δe p，i (k) represents the mutation value of the formation position tracking error signal of the i-th train.

4. The fault-tolerant control method for multi-train formation under switching topology according to claim 1 is characterized in that: The calculation expression of the formation speed tracking error signal is as follows: In the formula, represents the formation speed tracking error signal at time t; a i，0 (t) indicates whether the i-th train can receive the known formation target reference curve at the time t; v i (t) represents the real-time speed of the i-th train at the time t; v d，i (t) represents the reference speed of the i-th train at the time t, and the reference speed is determined based on the given known formation target reference curve; n represents the number of all trains in the multi-train formation; a i，j (t) indicates whether there is a communication connection between the i-th train and the j-th train in the multi-train formation; v j (t) represents the real-time speed of the j-th train at the time t; α in this formula i (t) represents the virtual control law to be designed for the i-th train at the time t.

5. The fault-tolerant control method for multi-train formation under switching topology according to claim 4 is characterized in that: The calculation expression of the speed reset performance function is: In the formula, The speed reset performance function q is represented by v，i The derivative of (t); x3 is a positive constant; represents the design parameter of the speed reset performance function of the i-th train, and is a positive constant; represents the formation position tracking error signal at time t; q p，i (t) represents the position reset performance function; Δq v，i (k) means that at t = t k The jump variable of the speed reset performance function of the i-th train at the time when the topology switching occurs; is a positive number greater than 1; Δe v，i (k) represents the mutation value of the formation speed tracking error signal of the i-th train.

6. The fault-tolerant control method for multi-train formation under switching topology according to claim 1 is characterized in that: The calculation expression of the virtual control law of the i-th train is: a i (t)=-k(ψ p,i 3 (t)+ψ p，i (t)); In this formula, α i (t) represents the virtual control law of the i-th train; k1 is a positive constant; ψ p，i (t) represents the position coupling preset performance constraint error variable of the i-th train at the time t.

7. The fault-tolerant control method for multi-train formation under switching topology according to claim 6 is characterized in that: The multi-train formation fault-tolerant control under the switching topology is performed on the i-th train by the following formula: In the formula, τ i (t) represents a fault-tolerant controller for multi-train formation under switching topology; is the first unknown parameter μ i (t), and the first unknown parameter μ i (t)Satisfy: and μ i and are all normal numbers; k2 is a normal number; is the second unknown parameter m 1，i (t), and the second unknown parameter m 1，i (t)Satisfy: And m 1 ，i and All are normal numbers; is the third unknown parameter m 2，i (t), and the third unknown parameter m 2，i (t)Satisfy: and m 2，i and are all positive numbers; v，i (t) represents the speed coupling preset performance constraint error variable; a i，j (t) indicates whether there is a communication connection between the i-th train and the j-th train in the multi-train formation; a i，0 (t) indicates whether the i-th train can receive the known formation target reference curve at the time t; B i (t) represents the running resistance encountered by the i-th train during its running at the time t; Indicates v j The derivative of (t); Indicates v d，i The derivative of (t).

8. The fault-tolerant control method for multi-train formation under switching topology according to claim 7 is characterized in that: Said Adaptive parameter update law The calculation expression is as follows: In the formula, Indicates that the Projection to the In the range of g1 and σ i All are normal numbers; represents the formation speed tracking error signal at time t; q v，i (t) represents the speed reset performance function.

9. The fault-tolerant control method for multi-train formation under switching topology according to claim 8, characterized in that: Said Adaptive parameter update law for: In the formula, Indicates that the Projection to the In the range of; g2 is a positive constant.

10. The fault-tolerant control method for multi-train formation under switching topology according to claim 9, characterized in that: Said The adaptive parameter update law of for: In the formula, g3 is a positive constant.

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