A collaborative fault-tolerant tracking control method and system for multi-agent systems based on topology reconstruction

Abstract

The present invention discloses a method and system for collaborative fault-tolerant tracking control of a multi-agent system based on topology reconstruction, which is used to solve the problem of maintaining the performance of a multi-agent system under actuator failure. The method specifically includes the following steps: Step 1, clarifying the description of the multi-agent system under fault conditions; Step 2, constructing the initial topology structure and nominal controller of the multi-agent system under fault-free conditions; Step 3, designing a topology reconstruction strategy to deal with various fault scenarios; Step 4, integrating various topology reconstruction strategies and forming a collaborative fault-tolerant control method. The present invention can ensure the performance of the multi-agent system by adjusting the topology structure according to the fault information when a fault occurs in the actuator of the multi-agent system, thereby weakening the adverse effects of the fault on the multi-agent system and improving the reliability of the multi-agent system.

Description

Technical Field

[0001] The present invention belongs to the technical field of multi-agent system control, and in particular relates to a multi-agent system collaborative fault-tolerant tracking control method and system based on topology reconstruction. Background Art

[0002] In a collaborative multi-agent system, if any agent experiences an actuator failure, it is highly likely that both the failed agent and its neighbors will experience adverse effects such as performance degradation or even instability. If improperly handled, the impact of an actuator failure will propagate throughout the entire multi-agent system through information exchange between agents, leading to even worse consequences. Therefore, research on fault-tolerant control methods for multi-agent systems is essential and valuable.

[0003] At present, most fault-tolerant control methods for multi-agent systems are derived from classical fault-tolerant control technology, and most of them focus on designing controllers with fault-tolerant capabilities for each agent. These controllers are often relatively complex in structure. For example, in CN117687434A, the designed multi-agent system fault-tolerant controller structure includes distributed state observers, adaptive parameters, fuzzy neural network items, etc., which requires extremely high computing power. The scale of the multi-agent system is large, and its huge information interaction network will further increase the complexity of the fault-tolerant controller. In CN118131776A, the multi-agent system actuator failure considered is an additive failure that is easier to handle, and the more typical multiplicative failure is not considered. This greatly restricts the application of multi-agent system fault-tolerant control methods in actual objects.

[0004] Therefore, based on the designable and reconfigurable topology structure of the multi-agent system, the present invention designs a multi-agent system collaborative fault-tolerant tracking control method based on topology reconstruction, which greatly simplifies the design of the controller while ensuring the system's fault tolerance. Summary of the Invention

[0005] Purpose of the invention: In order to solve the problems existing in the above-mentioned prior art, the present invention provides a collaborative fault-tolerant tracking control method for a multi-agent system based on topology reconstruction.

[0006] Technical Solution: In a first aspect, the present invention provides a method for collaborative fault-tolerant tracking control of a multi-agent system based on topology reconstruction, the method comprising:

[0007] S1: Construct a dynamic model of the multi-agent system based on the nonlinear models of multiple agents, and consider the dynamic model of the multi-agent system when the actuator of an agent suffers partial loss of control energy efficiency, and each agent needs to track the reference signal generated by the generator;

[0008] S2: Under no-fault conditions, design an initial topology of the multi-agent system and design distributed nominal controllers for the leader agent and the follower agent using state feedback control techniques, so that the multi-agent system can consistently and asymptotically track the reference signal.

[0009] S3: Design corresponding topology reconstruction strategies for different failure scenarios to ensure that the tracking error of the entire multi-agent system converges to zero asymptotically;

[0010] S4: Integrate the various topology reconstruction strategies designed in step S3 into one, and form a collaborative fault-tolerant control method, so that when the multi-agent system detects a certain actuator failure, the collaborative fault-tolerant control method is activated, thereby performing corresponding topology structure adjustments, and achieving consistent tracking of the time-varying reference signal without changing the original structure and parameters of the nominal controller.

[0011] Further, including:

[0012] The nonlinear model of each agent in step S1 is expressed as:

[0013]

[0014] in, Represent the position state and velocity state of the i-th agent, f(x i ) and g(x i ) is used to describe the nonlinear characteristics of the agent, is the control input of the system;

[0015] If the multi-agent system consists of n agents, its dynamic model can be described as follows:

[0016]

[0017] in, and Represents the position state and velocity state of the multi-agent system, F(x)=[f(x1) T ,…,f(x n ) T ] T ,G(x)=diag{g(x1),…,g(x n )},and

[0018] Assuming that the actuator of the i-th agent suffers partial loss of control energy efficiency, its model becomes the following form:

[0019]

[0020] Among them, ρ i=diag{ρ i1 ,…,ρ im}, where 0<ρ ik ≤1, i=1,…,n, and k=1,…,m,ρ ik represents the residual control energy efficiency of the kth control signal of the i-th agent, and m is the dimension of the input control signal. At this time, the multi-agent system model is expressed as:

[0021]

[0022] Where Γ=diag{I (i-1)m ,…,ρ i ,I (n-i)m};

[0023] And each agent needs to track the reference signal produced by the following generator:

[0024]

[0025] Among them, x r ,v r are the position and velocity states of the reference signal r.

[0026] Further, including:

[0027] In step S2, in the absence of faults, the initial topology of the multi-agent system is designed, and distributed nominal controllers are designed for the leader agent and the follower agent using state feedback control technology, specifically including:

[0028] First, the initial topology of the multi-agent is designed as an undirected spanning tree, whose Laplace matrix is ​​denoted as L, which is specifically expressed as L = diag{d i}-A, where A is the adjacency matrix of the multi-agent system topology structure A=[a ij ] T , if agent i and agent j are neighbors, then their connection weight a ij =1, otherwise, a ij =0, and there is a ii =0,d i is the in-degree of the i-th multi-agent, that is is the set of neighbors of agent i, and each agent is numbered from 1 to n. In addition, each agent must carry its own number information and the layer number to which it belongs;

[0029] For the leader agent, which is numbered 1, its control law is designed as:

[0030]

[0031] Among them, c is a parameter to be designed, which must satisfy c>0, b1 is the traction gain, which must satisfy b1>0; v1 represents the speed state corresponding to the leader intelligent agent, and x1 represents the position state corresponding to the leader intelligent agent. is the set of leaders’ neighbors, It means g(x i )’s inverse matrix;

[0032] For follower agent i, its control law is designed as:

[0033]

[0034] The above parameters c, traction gain b1 and all connection weights a of the Laplace matrix L ij The following two conditions must be met:

[0035]

[0036] in, (L) n-1 The matrix remaining after removing the last row and last column of L, λ min {·} represents the minimum characteristic root of the matrix, N is the dimension of the position state quantity x;

[0037] l iz is a constant that satisfies the following Lipschitz condition: |f z (x i )-f z (y i )|≤l iz |x iz -y iz |, then in the absence of faults, the multi-agent system can consistently and asymptotically track the reference signal x r ,v r ; where x i ,y i are all arbitrary values ​​within the domain of the nonlinear term f(·), f z (·) is the zth element of f(·).

[0038] Further, including:

[0039] In the step S3, corresponding topology reconstruction strategies are designed for different failure scenarios to ensure that the tracking error of the entire multi-agent system converges asymptotically to zero, including: failure of the leader agent;

[0040] If the leader agent has an actuator failure, the traction gain b1 is adjusted to the following form:

[0041]

[0042] Among them, ρ0 is the lower bound of the residual control energy efficiency of the actuator, which can eliminate the impact of actuator failure on system performance.

[0043] Further, including:

[0044] In said step S3, for different failure scenarios, corresponding topology reconstruction strategies are designed to ensure that the tracking error of the entire multi-agent system converges asymptotically to zero, and further includes: failure of the leader grandchild agent;

[0045] If an actuator failure occurs in the leader's grandchild agent, and the maximum tolerable degree of the failure is 1-ρ0, it satisfies the following inequality:

[0046]

[0047] Among them, ρ0 is the lower bound of the residual control energy efficiency of the actuator, h is the number of the faulty agent; represents the set of neighbors of the faulty agent, a ht represents the connection weight between the faulty agent h and its neighbor t;

[0048] The topology reconstruction strategy of the multi-agent system is designed as follows: construct a new directed connection from 1 to h, that is, the leader becomes the neighbor of the faulty agent, and the faulty agent can directly receive information from the leader, and its weight is set to a h1 =2a M , and adjust the weight a th for The system can maintain its original tracking performance.

[0049] Further, including:

[0050] In said step S3, for different failure scenarios, corresponding topology reconstruction strategies are designed to ensure that the tracking error of the entire multi-agent system converges asymptotically to zero, and also include: failure of the leader child node agent;

[0051] If an actuator failure occurs in the leader's child agent, and the maximum tolerable degree of the failure 1-ρ0 satisfies the following inequality:

[0052]

[0053] Among them, ρ0 is the lower bound of the residual control energy efficiency of the actuator, r is the number of the child node corresponding to the faulty agent h, is the set of child nodes of the faulty agent; a rt is the connection weight between the faulty agent child node r and its neighbor t;

[0054] The topology reconstruction strategy of the multi-agent system is designed as follows:

[0055] First, the faulty agent is exchanged with the child node r. The child node r needs to satisfy the following requirements: the number of its child nodes must be At this point, the faulty agent becomes the grandchild of the leader, and its number is updated to r;

[0056] Then, construct a new directed arc from 1 to r, with a weight set to a r1 =2a M , and adjust the weight a rt for Finally, the system can maintain its original tracking performance.

[0057] Further, including:

[0058] In said step S3, for different failure scenarios, corresponding topology reconstruction strategies are designed to ensure that the tracking error of the entire multi-agent system converges asymptotically to zero, and further includes: failure of the remaining agents;

[0059] If an actuator failure occurs in the remaining agents, and the maximum tolerable degree of the failure 1-ρ0 satisfies the following inequality:

[0060]

[0061] Among them, ρ0 is the lower bound of the residual control energy efficiency of the actuator, h is the number of the faulty agent;

[0062] The topology reconstruction strategy of the multi-agent system is designed as follows:

[0063] First, adjust the weights for

[0064] Then, a new directed path (1,h1),(h1,h2)(h f-1 ,h f ), And its weight must meet the following conditions:

[0065]

[0066] This enables the system to maintain its original tracking performance.

[0067] Further, including:

[0068] In step S4, the topology reconstruction strategies in step S3 are integrated to form the following collaborative fault-tolerant control method, including:

[0069] When a multi-agent system detects an actuator failure, if its maximum allowable value satisfies the following inequality:

[0070]

[0071] Where h is the number of the faulty agent, and T represents the layer to which the faulty agent belongs. The collaborative fault-tolerant control method is activated, and the corresponding topology reconstruction strategy in step S3 is called according to the fault information. This achieves consistent tracking of the time-varying reference signal by only adjusting the topology of the multi-agent system without changing the original structure and parameters of the agent nominal controller.

[0072] On the other hand, the present invention also provides a multi-agent system collaborative fault-tolerant tracking control system based on topology reconstruction, the system comprising:

[0073] The model building module is used to build the dynamic model of the multi-agent system based on the nonlinear models of multiple agents. It also considers the dynamic model of the multi-agent system when the actuator of an agent suffers partial loss of control energy efficiency, and each agent needs to track the reference signal produced by the generator;

[0074] a distributed nominal controller design module for designing an initial topology of the multi-agent system in a fault-free state and designing distributed nominal controllers for the leader agent and the follower agent respectively using state feedback control technology so that the multi-agent system can consistently and asymptotically track the reference signal;

[0075] A topology reconstruction strategy building module is used to design corresponding topology reconstruction strategies for different failure scenarios to ensure that the tracking error of the entire multi-agent system converges to zero asymptotically;

[0076] The integration module is used to integrate the designed topology reconstruction strategies into one and form a collaborative fault-tolerant control method. When the multi-agent system detects a certain actuator failure, the collaborative fault-tolerant control method is activated to make corresponding topology adjustments, thereby achieving consistent tracking of the time-varying reference signal without changing the original structure and parameters of the nominal controller.

[0077] Finally, the present invention also provides a computer-readable storage medium, on which is stored a multi-agent system collaborative fault-tolerant tracking control program based on topology reconstruction. When the multi-agent system collaborative fault-tolerant tracking control program based on topology reconstruction is executed by a processor, the steps of the multi-agent system collaborative fault-tolerant tracking control method based on topology reconstruction as described above are implemented.

[0078] Beneficial effects: Compared with the prior art, the present invention has the following advantages:

[0079] In the absence of faults, the present invention designs the initial topology of the multi-agent system and uses state feedback control technology to design distributed nominal controllers for the leader agent and the follower agent respectively, so that the multi-agent system can consistently and asymptotically track the reference signal. The designed nominal controller has a simple structure and low computing power requirements. The implementation of fault-tolerant control only depends on reconstructing the topology of the multi-agent system, rather than designing a controller with a complex structure, which greatly simplifies the design of the controller.

[0080] The present invention designs corresponding topology reconstruction strategies for different fault scenarios to ensure that the tracking error of the entire multi-agent system converges to zero asymptotically. That is, different collaborative fault-tolerant control methods are designed for different fault conditions. It can handle the more typical multiplicative actuator failures in the multi-agent system, and can effectively achieve consistent tracking of the time-varying reference signal by the multi-agent system under fault conditions without the need to accurately estimate or obtain fault information. BRIEF DESCRIPTION OF THE DRAWINGS

[0081] Figure 1 This is a flow chart of the multi-agent system collaborative fault-tolerant tracking control method based on topology reconstruction according to an embodiment of the present invention;

[0082] Figure 2 This is a block diagram of a multi-agent system collaborative fault-tolerant tracking control system based on topology reconstruction according to an embodiment of the present invention. DETAILED DESCRIPTION

[0083] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention and not all of the embodiments. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention without making any creative efforts shall fall within the scope of protection of the present invention.

[0084] The accompanying drawings, which constitute a part of the present invention, are used to provide a further understanding of the present invention. The exemplary embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute improper limitations on the present invention.

[0085] A first aspect of the present invention provides a method for collaborative fault-tolerant tracking control of a multi-agent system based on topology reconstruction, the method comprising:

[0086] S1: Construct a dynamic model of the multi-agent system based on the nonlinear models of multiple agents, and consider the dynamic model of the multi-agent system when the actuator of an agent suffers partial loss of control energy efficiency, and each agent needs to track the reference signal generated by the generator;

[0087] S2: Under no-fault conditions, design an initial topology of the multi-agent system and design distributed nominal controllers for the leader agent and the follower agent using state feedback control techniques, so that the multi-agent system can consistently and asymptotically track the reference signal.

[0088] S3: Design corresponding topology reconstruction strategies for different failure scenarios to ensure that the tracking error of the entire multi-agent system converges to zero asymptotically;

[0089] S4: Integrate the various topology reconstruction strategies designed in step S3 into one, and form a collaborative fault-tolerant control method, so that when the multi-agent system detects a certain actuator failure, the collaborative fault-tolerant control method is activated, thereby performing corresponding topology structure adjustments, and achieving consistent tracking of the time-varying reference signal without changing the original structure and parameters of the nominal controller.

[0090] The nonlinear model of each agent in step S1 is expressed as:

[0091]

[0092] in, Represent the position state and velocity state of the i-th agent, f(x i ) and g(x i ) is used to describe the nonlinear characteristics of the agent, is the control input of the system;

[0093] If the multi-agent system consists of n agents, its dynamic model can be described as follows:

[0094]

[0095] in, and Represents the position state and velocity state of the multi-agent system, F(x)=[f(x1) T ,…,f(x n ) T ] T ,G(x)=diag{g(x1),…,g(x n )},and

[0096] Assuming that the actuator of the i-th agent suffers partial loss of control energy efficiency, its model becomes the following form:

[0097]

[0098] Among them, ρ i =diag{ρ i1 ,…,ρim}, where 0<ρ ik ≤1, i=1,…,n, and k=1,…,m,ρ ik represents the residual control energy efficiency of the kth control signal of the i-th agent, and m is the dimension of the input control signal. At this time, the multi-agent system model is expressed as:

[0099]

[0100] Where Γ=diag{I (i-1)m ,…,ρ i ,I (n-i)m};

[0101] And each agent needs to track the reference signal produced by the following generator:

[0102]

[0103] Among them, x r ,v r are the position and velocity states of the reference signal r.

[0104] In step S2, in the absence of faults, the initial topology of the multi-agent system is designed, and distributed nominal controllers are designed for the leader agent and the follower agent using state feedback control technology, specifically including:

[0105] First, the initial topology of the multi-agent is designed as an undirected spanning tree, whose Laplace matrix is ​​denoted as L, which is specifically expressed as L = diag{d i}-A, where A is the adjacency matrix of the multi-agent system topology structure A=[a ij ] T , if agent i and agent j are neighbors, then their connection weight a ij =1, otherwise, a ij =0, and there is a ii =0,d i is the in-degree of the i-th multi-agent, that is is the set of neighbors of agent i, and each agent is numbered from 1 to n. In addition, each agent must carry its own number information and the layer number to which it belongs;

[0106] For the leader agent, which is numbered 1, its control law is designed as:

[0107]

[0108] Among them, c is a parameter to be designed, which must satisfy c>0, b1 is the traction gain, which must satisfy b1>0; v1 represents the speed state corresponding to the leader intelligent agent, and x1 represents the position state corresponding to the leader intelligent agent. is the set of leaders’ neighbors, It means g(x i )’s inverse matrix;

[0109] For follower agent i, its control law is designed as:

[0110]

[0111] The above parameters c, traction gain b1 and all connection weights a of the Laplace matrix L ij The following two conditions must be met:

[0112]

[0113] in, (L) n-1 The matrix remaining after removing the last row and last column of L, λ min {·} represents the minimum characteristic root of the matrix, N is the dimension of the position state quantity x;

[0114] l iz is a constant that satisfies the following Lipschitz condition: |f z (x i )-f z (y i )|≤l iz |x iz -y iz |, then in the absence of faults, the multi-agent system can consistently and asymptotically track the reference signal x r ,v r ; where x i ,y i are all arbitrary values ​​within the domain of the nonlinear term f(·), f z (·) is the zth element of f(·).

[0115] In the step S3, corresponding topology reconstruction strategies are designed for different failure scenarios to ensure that the tracking error of the entire multi-agent system converges asymptotically to zero, including: failure of the leader agent;

[0116] If the leader agent has an actuator failure, the traction gain b1 is adjusted to the following form:

[0117]

[0118] Among them, ρ0 is the lower bound of the residual control energy efficiency of the actuator, which can eliminate the impact of actuator failure on system performance.

[0119] In said step S3, for different failure scenarios, corresponding topology reconstruction strategies are designed to ensure that the tracking error of the entire multi-agent system converges asymptotically to zero, and further includes: failure of the leader grandchild agent;

[0120] If an actuator failure occurs in the leader's grandchild agent, and the maximum tolerable degree of the failure is 1-ρ0, it satisfies the following inequality:

[0121]

[0122] Among them, ρ0 is the lower bound of the residual control energy efficiency of the actuator, h is the number of the faulty agent; represents the set of neighbors of the faulty agent, a ht represents the connection weight between the faulty agent h and its neighbor t;

[0123] The topology reconstruction strategy of the multi-agent system is designed as follows: construct a new directed connection from 1 to h, that is, the leader becomes the neighbor of the faulty agent, and the faulty agent can directly receive information from the leader, and its weight is set to a h1 =2a M , and adjust the weight a th for The system can maintain its original tracking performance.

[0124] In said step S3, for different failure scenarios, corresponding topology reconstruction strategies are designed to ensure that the tracking error of the entire multi-agent system converges asymptotically to zero, and also include: failure of the leader child node agent;

[0125] If an actuator failure occurs in the leader's child agent, and the maximum tolerable degree of the failure 1-ρ0 satisfies the following inequality:

[0126]

[0127] Among them, ρ0 is the lower bound of the residual control energy efficiency of the actuator, r is the number of the child node corresponding to the faulty agent h, is the set of child nodes of the faulty agent; a rt is the connection weight between the faulty agent child node r and its neighbor t;

[0128] The topology reconstruction strategy of the multi-agent system is designed as follows:

[0129] First, the faulty agent is exchanged with the child node r. The child node r needs to satisfy the following requirements: the number of its child nodes must be At this point, the faulty agent becomes the grandchild of the leader, and its number is updated to r;

[0130] Then, construct a new directed arc from 1 to r, with a weight set to a r1 =2a M , and adjust the weight a rt for Finally, the system can maintain its original tracking performance.

[0131] In said step S3, for different failure scenarios, corresponding topology reconstruction strategies are designed to ensure that the tracking error of the entire multi-agent system converges asymptotically to zero, and further includes: failure of the remaining agents;

[0132] If an actuator failure occurs in the remaining agents, and the maximum tolerable degree of the failure 1-ρ0 satisfies the following inequality:

[0133]

[0134] Among them, ρ0 is the lower bound of the residual control energy efficiency of the actuator, h is the number of the faulty agent;

[0135] The topology reconstruction strategy of the multi-agent system is designed as follows:

[0136] First, adjust the weights for

[0137] Then, a new directed path (1,h1),(h1,h2)(h f-1 ,h f ), And its weight must meet the following conditions:

[0138]

[0139] This enables the system to maintain its original tracking performance.

[0140] Further, including:

[0141] In step S4, the topology reconstruction strategies in step S3 are integrated to form the following collaborative fault-tolerant control method, including:

[0142] When a multi-agent system detects an actuator failure, if its maximum allowable value satisfies the following inequality:

[0143]

[0144] Where h is the number of the faulty agent, and T represents the layer to which the faulty agent belongs. The collaborative fault-tolerant control method is activated, and the corresponding topology reconstruction strategy in step S3 is called according to the fault information. This achieves consistent tracking of the time-varying reference signal by only adjusting the topology of the multi-agent system without changing the original structure and parameters of the agent nominal controller.

[0145] To facilitate understanding of the above embodiments, the present invention provides more detailed solution details, specifically:

[0146] like Figure 1 As shown, the first aspect of this embodiment provides a multi-agent system collaborative fault-tolerant tracking control method based on topology reconstruction, which is specifically:

[0147] Step 1: Define the general dynamic equations of the multi-agent system and the dynamic equations of the system under actuator failure conditions;

[0148] For ease of description, this article uses the following notations: It means that the submatrix with the first w rows and columns is deleted (1≤w≤n-1). and its subsets Indicates removal of a collection back The remaining subset. For a square matrix λ k {B}, λ min {B}} and λ max {B} represents the kth eigenvalue, minimum eigenvalue, and maximum eigenvalue of B, respectively, where k = 1, 2, ..., n. n represents the n×n identity matrix, is an n-dimensional vector whose elements are all 1. Symbol Represents the Kronecker product of matrices. Represents the set of positive integers.

[0149] The nonlinear model of the i-th agent is:

[0150]

[0151] in, Represent the position state and velocity state of the i-th agent, f(x i ) and g(x i ) is used to describe the nonlinear characteristics of the agent, is the control input of the system.

[0152] If the multi-agent system consists of n agents, its dynamic model can be described as

[0153]

[0154] in, and Represents the state of the multi-agent system. F(x)=[f(x1) T ,…,f(x n ) T ] T ,G(x)=diag{g(x1),…,g(x n )},and

[0155] Assuming that the actuator of the i-th agent suffers partial loss of control energy efficiency, its model becomes the following form:

[0156]

[0157] where ρ i =diag{ρ i1 ,…,ρ im}, where 0<ρ ik ≤1, i=1,…,n, and k=1,…,m. ρ ik represents the residual control energy efficiency of the kth control signal of the i-th agent. At this time, the multi-agent system model is:

[0158]

[0159] Where Γ=diag{I (i-1)m ,…,ρ i ,I (n-i)m}.

[0160] Each agent needs to track the reference signal produced by the following generator:

[0161]

[0162] where x r ,v r are the position and velocity states of the reference signal.

[0163] Step 2: Design the initial topology and distributed nominal controller of the multi-agent system under fault-free conditions;

[0164] First, the initial topology of the multi-agent system is designed as an undirected spanning tree, whose Laplacian matrix is ​​denoted as L, and each agent is numbered from 1 to n. In addition, in addition to its own number information, each agent must also carry information such as the number of layers it belongs to.

[0165] (1) For the leader agent (numbered 1), its control law is designed as follows:

[0166]

[0167] Where c is a parameter to be designed, which must satisfy c>0, and b1 is the traction gain, which must satisfy b1>0.

[0168] (2) For follower agent i, its control law is designed as:

[0169]

[0170] Conclusion 1: For the multi-agent system (1) with actuator failure, a distributed nominal controller is designed as shown in Equations (2)-(3). If the controller parameters c, traction gain b1, and all connection weights a of the system Laplace matrix L are ij The following two conditions are met:

[0171]

[0172] in, l ik is a constant that satisfies the following Lipschitz condition: |f k (x i )-f k (y i )|≤l ik |x ik -y ik |, then in the absence of faults, the multi-agent system can consistently and asymptotically track the reference signal x r ,v r .

[0173] Proof: Define the error vector Then the dynamic equation of the multi-agent system can be rewritten as:

[0174]

[0175] Choose the following positive definite matrix:

[0176]

[0177] in,

[0178] make Using the positive definite matrix P, design the following Lyapunov function:

[0179]

[0180] Taking the time derivative of V yields:

[0181]

[0182] in,

[0183] Verifiable cL-pI n +B>0, so qI n -cL-B<0 and rl n -cL-B<0, so If and only if and hour, According to the La Salle invariant set principle, when t→∞, V→0, that is, when t→∞, and Therefore, the multi-agent system can consistently and asymptotically track the reference signal x r ,v r .

[0184] Step 3: Design corresponding topology reconstruction strategies for different failure scenarios;

[0185] First, after an actuator failure occurs, the multi-agent system model can be written as:

[0186]

[0187] Among them, ρ0I Nn ≤Γ Nn , ρ0 is the lower bound of the actuator residual control energy efficiency that can be obtained through fault detection.

[0188] Define a diagonal matrix

[0189] (1) Leader Agent Failure

[0190] Conclusion 2: If the leader agent has an actuator failure, if the traction gain b1 is adjusted to the following form:

[0191]

[0192] Where ρ0 is the lower bound of the residual control energy efficiency of the actuator, which can eliminate the impact of actuator failure on system performance.

[0193] Proof: At this point, the Laplace matrix is ​​rewritten as:

[0194]

[0195] According to a 1j =a j1 , we can get:

[0196]

[0197] Select the following positive definite matrix ​

[0198]

[0199] in,

[0200] Select Lyapunov function Taking its derivative with respect to time, we get:

[0201]

[0202] in Similar to formula (4), we can get And only if and hour, This proves that the consistent tracking error of the entire multi-agent system is and converges asymptotically to zero.

[0203] (2) Leader grandchild agent failure

[0204] Conclusion 3: If an actuator failure occurs in the leader's grandchild agent, and the maximum tolerable degree of the failure 1-ρ0 satisfies the following inequality:

[0205]

[0206] in, h is the number of the faulty agent. If the topology reconstruction strategy of the multi-agent system is designed as: construct a new directed arc from 1 to h, and its weight is set to a h1 =2a M , and adjust the weights for This enables the system to maintain the original tracking performance before the failure.

[0207] Proof: After topological reconstruction according to Conclusion 3, the Laplace matrix is ​​updated as follows:

[0208]

[0209] in And you can get:

[0210]

[0211] Define the following positive definite matrix

[0212]

[0213] Select Lyapunov function After taking its derivative, we can get a form similar to formula (5), so we have And only if and hour, Provable consistent tracking error of multi-agent systems and converges asymptotically to zero.

[0214] (3) Leader subnode agent failure

[0215] Conclusion 4: If an actuator failure occurs in the leader's child agent, and the maximum tolerable degree of the failure 1-ρ0 satisfies the following inequality:

[0216]

[0217] in, h is the number of the faulty agent, is the set of child nodes of the faulty agent. If the topology reconstruction strategy of the multi-agent system is designed as follows: first, the faulty agent and the child node r (the number of child nodes must be At this time, the faulty agent becomes the grandchild of the leader and its number is updated to r. Similar to (2), a new directed arc from 1 to r is constructed, and its weight is set to a r1 =2a M , and adjust the weights for Finally, the system can maintain its original tracking performance.

[0218] Proof: Similar to the second case, so omitted.

[0219] (4) Remaining Agent Failure

[0220] Conclusion 5: If the actuator of the remaining agents fails, and the maximum tolerable degree of the failure 1-ρ0 satisfies the following inequality:

[0221]

[0222] in, h is the number of the faulty agent. If the topology reconstruction strategy of the multi-agent system is designed as follows: first adjust the weight for Then construct a new directed path from the leader to the faulty agent And its weight must meet the following conditions:

[0223]

[0224] This enables the system to maintain its original tracking performance.

[0225] Proof: Here, we only need to prove the convergence of the system when the number of layers to which the faulty agent belongs satisfies k = 4 + 2p (p = 2, 3, ...). The proofs for other cases are similar and will not be repeated here. After topology reconstruction according to Conclusion 5, the Laplace matrix is ​​updated to:

[0226]

[0227] Where, Where h0 represents the leader.

[0228] Define the following positive definite matrix

[0229]

[0230] Select Lyapunov function After taking its derivative, we can get a form similar to formula (5), so we have And only if and hour, By the same token, it can be proved that the consistent tracking error of the entire system converges to zero asymptotically.

[0231] Step 4: Form a collaborative fault-tolerant control method

[0232] Integrate the topology reconstruction strategies in step 3 to form the following collaborative fault-tolerant control method:

[0233] When a multi-agent system detects an actuator failure, if its maximum allowable value satisfies the following inequality:

[0234]

[0235] Where h is the number of the faulty agent and k represents the layer number to which the faulty agent belongs. The collaborative fault-tolerant control method is activated. According to the fault information (including the faulty agent's ID, layer number, fault severity, etc.), the corresponding topology reconstruction strategy in 3 is called. This achieves consistent tracking of the time-varying reference signal by only adjusting the topology of the multi-agent system without changing the original structure and parameters of the agent's nominal controller.

[0236] In a specific implementation, each agent can be equipped with a transmitter and a receiver. Broadcast communication is used, with the transmitter transmitting information such as the agent's ID, status, and fault severity to other agents within its communication range. When an agent fails, other agents within its communication range learn of the failure through the receiver and then employ appropriate topology reconstruction strategies to adjust their own interactions, such as refusing to receive information from the failed agent or adjusting the weight of interactions with the failed agent.

[0237] On the other hand, Figure 2 As shown, the present invention also provides a multi-agent system collaborative fault-tolerant tracking control system based on topology reconstruction, the system comprising:

[0238] The model building module is used to build the dynamic model of the multi-agent system based on the nonlinear models of multiple agents. It also considers the dynamic model of the multi-agent system when the actuator of an agent suffers partial loss of control energy efficiency, and each agent needs to track the reference signal produced by the generator;

[0239] a distributed nominal controller design module for designing an initial topology of the multi-agent system in a fault-free state and designing distributed nominal controllers for the leader agent and the follower agent respectively using state feedback control technology so that the multi-agent system can consistently and asymptotically track the reference signal;

[0240] A topology reconstruction strategy building module is used to design corresponding topology reconstruction strategies for different failure scenarios to ensure that the tracking error of the entire multi-agent system converges to zero asymptotically;

[0241] The integration module is used to integrate the designed topology reconstruction strategies into one and form a collaborative fault-tolerant control method. When the multi-agent system detects a certain actuator failure, the collaborative fault-tolerant control method is activated to make corresponding topology adjustments, thereby achieving consistent tracking of the time-varying reference signal without changing the original structure and parameters of the nominal controller.

[0242] Finally, the present invention also provides a computer-readable storage medium, on which is stored a multi-agent system collaborative fault-tolerant tracking control program based on topology reconstruction. When the multi-agent system collaborative fault-tolerant tracking control program based on topology reconstruction is executed by a processor, the steps of the multi-agent system collaborative fault-tolerant tracking control method based on topology reconstruction as described above are implemented.

[0243] It should be noted that since the storage medium provided in the embodiments of this application is the storage medium used to implement the method of the embodiments of this application, based on the method described in the embodiments of this application, those skilled in the art will be able to understand the specific structure and deformation of the storage medium, and therefore will not be described in detail here. All storage media used in the method of the embodiments of this application fall within the scope of protection to be provided by this application.

[0244] Those skilled in the art will appreciate that embodiments of the present invention may be provided as methods, systems, or computer program products. Thus, the present invention may take the form of an entirely hardware embodiment, an entirely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to magnetic disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0245] The present invention is described with reference to 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, as well as combinations of processes and / or blocks in the flowcharts and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowcharts and / or block diagrams. Figure 1 a process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0246] These computer program instructions may also be stored in a computer readable memory that can direct a computer or other programmable data processing device to work in a specific manner, so that the instructions stored in the computer readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 a process or multiple processes and / or boxes Figure 1 The function specified in one or more boxes.

[0247] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operational steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing the instructions executed on the computer or other programmable device for implementing the process. Figure 1 a process or multiple processes and / or boxes Figure 1 A step that specifies a function in one or more boxes.

[0248] It should be noted that, in the claims, any reference signs placed between parentheses shall not be construed as limiting the claims. The word "comprising" does not exclude the presence of components or steps not listed in the claim. The word "a" or "an" preceding a component does not exclude the presence of a plurality of such components. The invention can be implemented by means of hardware comprising several distinct components and by means of a suitably programmed computer. In a unit claim enumerating several means, several of these means may be embodied by one and the same item of hardware. The use of the words first, second, third etc. does not indicate any order. These words may be interpreted as names.

[0249] Although the preferred embodiments of the present invention have been described, those skilled in the art may make additional changes and modifications to these embodiments once they have learned the basic creative concept. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments and all changes and modifications that fall within the scope of the present invention.

[0250] Obviously, those skilled in the art may make various changes and modifications to the present invention without departing from the spirit and scope of the present invention. Thus, if such changes and modifications fall within the scope of the claims and their equivalents, the present invention is intended to include such changes and modifications.

[0251] The above are only preferred embodiments of the present invention and are not intended to limit the patent scope of the present invention. Any equivalent structure or equivalent process transformation made using the contents of the present invention description and drawings, or directly or indirectly applied in other related technical fields, are also included in the patent protection scope of the present invention.

Claims

1. A method for cooperative fault-tolerant tracking control of a multi-agent system based on topology reconstruction, characterized by: The method includes: S1: Construct a dynamic model of the multi-agent system based on the nonlinear models of multiple agents, and consider the dynamic model of the multi-agent system when the actuator of an agent suffers partial loss of control energy efficiency, and each agent needs to track the reference signal generated by the generator; S2: Under no-fault conditions, design an initial topology of the multi-agent system and design distributed nominal controllers for the leader agent and the follower agent using state feedback control techniques, so that the multi-agent system can consistently and asymptotically track the reference signal. S3: Design corresponding topology reconstruction strategies for different failure scenarios to ensure that the tracking error of the entire multi-agent system converges to zero asymptotically; S4: Integrate the topology reconstruction strategies designed in step S3 into one, and form a collaborative fault-tolerant control method, so that when the multi-agent system detects a certain actuator failure, the collaborative fault-tolerant control method is activated to perform corresponding topology adjustments, thereby achieving consistent tracking of the time-varying reference signal without changing the original structure and parameters of the nominal controller; In step S2, in the absence of faults, the initial topology of the multi-agent system is designed, and distributed nominal controllers are designed for the leader agent and the follower agent using state feedback control technology, specifically including: First, the initial topology of the multi-agent is designed as an undirected spanning tree, and its Laplace matrix is ​​recorded as L , which is specifically expressed as , is the adjacency matrix of the multi-agent system topology , if the agent With the agent If they are neighbors, their connection weight ,otherwise, , and there are , For the The in-degree of multiple agents, that is , For intelligent agents The set of neighbors, and each agent is numbered from 1 to n ,In addition, each agent needs to carry the layer number it belongs to in addition to its own ,number information; For the leader agent, which is numbered 1, its control law is designed as: （6） in, is a parameter to be designed, which must satisfy , To achieve traction gain, ; Indicates the speed state corresponding to the leader agent, Indicates the position state corresponding to the leader agent, is the set of leaders’ neighbors, means The inverse matrix of For follower agents , and its control law is designed as: （7） The above parameters , traction gain and the Laplace matrix All connection weights The following two conditions must be met: （8） （9） in, , , for Remove the remaining matrix from the last row and last column. represents the minimum characteristic root of the matrix, is the position state quantity Dimensions; is a constant that satisfies the following Lipschitz condition: , then in the absence of faults, the multi-agent system can consistently and asymptotically track the reference signal ;in, All are nonlinear terms Any value in the domain, for No. elements; In the step S3, corresponding topology reconstruction strategies are designed for different failure scenarios to ensure that the tracking error of the entire multi-agent system converges asymptotically to zero, including: failure of the leader agent; If the leader agent has an actuator failure, the traction gain Adjust to the following form: （10） in, is the lower bound of the residual control energy efficiency of the actuator, which can eliminate the impact of actuator failure on system performance.

2. The method for cooperative fault-tolerant tracking control of a multi-agent system based on topology reconstruction according to claim 1 is characterized in that: The nonlinear model of each agent in step S1 is expressed as: （1） in, Respectively represent The position state and velocity state of each agent, and Used to describe the nonlinear characteristics of intelligent agents, is the control input of the system; If the multi-agent system consists of n The above intelligent agents are composed of the following, and its dynamic model is described as: （2） in, and represents the position state and velocity state of the multi-agent system, , and ; Assume that If the actuator of an agent suffers partial loss of control energy efficiency, its model becomes the following form: （3） in, ,in, , ,and , Indicates the The first The residual control energy efficiency of the control signal is is the dimension of the input control signal. At this time, the multi-agent system model is expressed as: (4) in, ; And each agent needs to track the reference signal produced by the following generator: （5） in, is the reference signal Position state and speed state.

3. The method for cooperative fault-tolerant tracking control of a multi-agent system based on topology reconstruction according to claim 1, characterized in that: In said step S3, for different failure scenarios, corresponding topology reconstruction strategies are designed to ensure that the tracking error of the entire multi-agent system converges asymptotically to zero, and further includes: failure of the leader grandchild agent; If the leader's grandson node agent has an actuator failure, and the maximum tolerable degree of the failure is The following inequality is satisfied: （11） in, is the lower bound of the residual control energy efficiency of the actuator, , is the number of the faulty agent; represents the set of neighbors of the faulty agent, Representing a faulty agent and neighbors The connection weight between them; the topology reconstruction strategy of the multi-agent system is designed as: construct a new arrive The leader becomes the neighbor of the faulty agent, and the faulty agent can directly receive information from the leader, and its weight is set to , and adjust the weights for , the system can maintain its original tracking performance.

4. The method for cooperative fault-tolerant tracking control of a multi-agent system based on topology reconstruction according to claim 1, characterized in that: In said step S3, for different failure scenarios, corresponding topology reconstruction strategies are designed to ensure that the tracking error of the entire multi-agent system converges asymptotically to zero, and also include: failure of the leader child node agent; If the leader's child node agent has an actuator failure, and the maximum tolerable degree of the failure is The following inequality is satisfied: （12） in, is the lower bound of the residual control energy efficiency of the actuator, , Faulty Agent The number of the corresponding child node, is the set of child nodes of the faulty agent; Fault agent child node With neighbors The connection weight between them; The topology reconstruction strategy of the multi-agent system is designed as follows: First, the faulty agent and the child node To exchange, the child node Need to meet: The number of its child nodes must be At this point, the faulty agent becomes the grandchild of the leader, and its number is updated to ; Then, construct a new arrive The weight of the directed arc is set to , and adjust the weights for , and finally the system can maintain the original tracking performance.

5. The method for cooperative fault-tolerant tracking control of a multi-agent system based on topology reconstruction according to claim 1, characterized in that: In said step S3, for different failure scenarios, corresponding topology reconstruction strategies are designed to ensure that the tracking error of the entire multi-agent system converges asymptotically to zero, and further includes: failure of the remaining agents; If the remaining agents have actuator failures, and the maximum tolerable degree of the failure is The following inequality is satisfied: （13） in, is the lower bound of the residual control energy efficiency of the actuator, , is the number of the faulty agent; The topology reconstruction strategy of the multi-agent system is designed as follows: First, adjust the weights for , Then, a new directed path is constructed from the leader to the faulty agent , and its weight must meet the following conditions: （14） （15） （16） This enables the system to maintain its original tracking performance.

6. The method for cooperative fault-tolerant tracking control of a multi-agent system based on topology reconstruction according to claim 5, characterized in that: In step S4, the topology reconstruction strategies in step S3 are integrated to form the following collaborative fault-tolerant control method, including: When a multi-agent system detects an actuator failure, if its maximum allowable value satisfies the following inequality: （17） in, is the fault agent number, Indicates the layer number to which the faulty agent belongs, the collaborative fault-tolerant control method is activated, and according to the fault information, the corresponding topology reconstruction strategy in step S3 is called, thereby achieving consistent tracking of the time-varying reference signal by only adjusting the topology structure of the multi-agent system without changing the original structure and parameters of the agent nominal controller.

7. A control system implemented by a multi-agent system collaborative fault-tolerant tracking control method based on topology reconstruction, characterized by: The system includes: The model building module is used to build the dynamic model of the multi-agent system based on the nonlinear models of multiple agents. It also considers the dynamic model of the multi-agent system when the actuator of an agent suffers partial loss of control energy efficiency, and each agent needs to track the reference signal produced by the generator; a distributed nominal controller design module for designing an initial topology of the multi-agent system in a fault-free state and designing distributed nominal controllers for the leader agent and the follower agent respectively using state feedback control technology so that the multi-agent system can consistently and asymptotically track the reference signal; A topology reconstruction strategy building module is used to design corresponding topology reconstruction strategies for different failure scenarios to ensure that the tracking error of the entire multi-agent system converges to zero asymptotically; The integration module is used to integrate the designed topology reconstruction strategies into one and form a collaborative fault-tolerant control method. When the multi-agent system detects a certain actuator failure, the collaborative fault-tolerant control method is activated to make corresponding topology adjustments, thereby achieving consistent tracking of the time-varying reference signal without changing the original structure and parameters of the nominal controller.

8. A computer-readable storage medium, characterized in that The computer-readable storage medium stores a multi-agent system collaborative fault-tolerant tracking control program based on topology reconstruction, which, when executed by a processor, implements the steps of the multi-agent system collaborative fault-tolerant tracking control method based on topology reconstruction as described in any one of claims 1 to 6.

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