Multi-agent system cooperative fault-tolerant tracking control method and system based on topology reconstruction

Abstract

The invention discloses a multi-agent system cooperative fault-tolerant tracking control method and system based on topology reconstruction, which are used for solving the problem of performance maintenance of a multi-agent system under an actuator fault. The method specifically comprises the following steps: step 1, determining description of a multi-agent system under a fault condition; 2, constructing an initial topological structure and a nominal controller of the multi-agent system under the fault-free condition; 3, designing a topology reconstruction strategy for coping with each fault scene; and step 4, integrating each topology reconstruction strategy and forming a cooperative fault-tolerant control method. According to the method, when the actuator of the multi-agent system breaks down, the performance of the multi-agent system can be ensured by adjusting the topological structure according to the fault information, so that the adverse effect of the fault on the multi-agent system is weakened, and the reliability of the multi-agent system is improved.

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] For multi-agent system collaboration, if any agent has an actuator failure, the faulty agent and its neighbors are likely to suffer adverse effects such as performance degradation or even instability. If not handled properly, the impact of actuator failure will spread to the entire multi-agent system through information interaction between agents, leading to worse consequences. Therefore, the research on fault-tolerant control methods for multi-agent systems is necessary and meaningful.

[0003] At present, most of the 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 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 multi-agent systems is large, and their huge information interaction network will further increase the complexity of fault-tolerant controllers. 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 of the present invention, a method for coordinated fault-tolerant tracking control of a multi-agent system based on topology reconstruction is provided, the method comprising:

[0007] S1: Construct the 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 a certain 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 use 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;

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

[0010] 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 structure adjustments, thereby 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 ith agent, respectively, f(x i ) and g(x i ) is used to describe the nonlinear characteristics of the agent. It is the control input of the system;

[0015] If the multi-agent system is composed 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 the distributed nominal controllers are designed for the leader agent and the follower agent respectively using the 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 by L, which is specifically expressed as L = diag{d i}-A, where A is the adjacency matrix of the multi-agent system topology A=[a ij ] T , if agents i and 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 ith 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 needs to carry the layer number in addition to its own number information;

[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 needs to satisfy c>0, b1 is the traction gain, which needs to satisfy b1>0; v1 represents the speed state corresponding to the leader agent, and x1 represents the position state corresponding to the leader 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, the pulling gain b1 and all the 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(·), z (·) is the zth element of f(·).

[0038] Further, including:

[0039] In the 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, including: leader agent failure;

[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 the 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 grandchild node agent;

[0045] If the leader's grandchild agent has an actuator failure, and the maximum tolerable degree of the failure 1-ρ0 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, 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 the 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: leader subnode agent failure;

[0051] If an actuator failure occurs in the leader's child node 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:

[0055] First, the faulty agent is exchanged with the child node r, and the child node r needs to satisfy: the number of its child nodes needs to be The least, at this time, 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 the original tracking performance.

[0057] Further, including:

[0058] In the 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 includes: failure of the remaining agents;

[0059] If the remaining agents have actuator failures, 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:

[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 will enable 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 the 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, T represents the layer to which the faulty agent belongs, and the collaborative fault-tolerant control method is activated. 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 topological structure 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, and consider the dynamic model of the multi-agent system when the actuator of a certain agent suffers partial loss of control energy efficiency, and each agent needs to track the reference signal generated by the generator;

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

[0075] The topology reconstruction strategy building module is used to design corresponding topology reconstruction strategies for different fault 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, so that when the multi-agent system detects a certain actuator failure, the collaborative fault-tolerant control method is activated to make corresponding topology structure 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] Under fault-free conditions, the present invention designs the initial topological structure 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 realization of fault-tolerant control only relies on reconstructing the topological structure of the multi-agent system, rather than designing a complex controller, 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 faults without the need to accurately estimate or obtain fault information. BRIEF DESCRIPTION OF THE DRAWINGS

[0081] Figure 1 A flow chart of a method for cooperative fault-tolerant tracking control of a multi-agent system 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 described in an embodiment of the present invention. DETAILED DESCRIPTION

[0083] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are 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 multi-agent system collaborative fault-tolerant tracking control method based on topology reconstruction, the method comprising:

[0086] S1: Construct the 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 a certain 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 use 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;

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

[0089] 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 structure adjustments, thereby 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 ith agent, respectively, f(x i ) and g(x i ) is used to describe the nonlinear characteristics of the agent. It is the control input of the system;

[0093] If the multi-agent system is composed 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 the distributed nominal controllers are designed for the leader agent and the follower agent respectively using the 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 by L, which is specifically expressed as L = diag{d i}-A, where A is the adjacency matrix of the multi-agent system topology A=[a ij ] T , if agents i and 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 ith 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 needs to carry the layer number in addition to its own number information;

[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 needs to satisfy c>0, b1 is the traction gain, which needs to satisfy b1>0; v1 represents the speed state corresponding to the leader agent, and x1 represents the position state corresponding to the leader 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, the pulling gain b1 and all the 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, 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, including: leader agent failure;

[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 the 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 grandchild node agent;

[0120] If the leader's grandchild agent has an actuator failure, and the maximum tolerable degree of the failure 1-ρ0 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, 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 the 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: leader subnode agent failure;

[0125] If an actuator failure occurs in the leader's child node 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:

[0129] First, the faulty agent is exchanged with the child node r, and the child node r needs to satisfy: the number of its child nodes needs to be The least, at this time, 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 the original tracking performance.

[0131] In the 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 includes: failure of the remaining agents;

[0132] If the remaining agents have actuator failures, 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:

[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 will enable 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 the 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, T represents the layer to which the faulty agent belongs, and the collaborative fault-tolerant control method is activated. 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 topological structure of the multi-agent system without changing the original structure and parameters of the agent nominal controller.

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

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

[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 symbols: It means that the submatrix with the first w rows and columns deleted (1≤w≤n-1). For a non-empty set and its subsets Represents 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, the minimum eigenvalue, and the 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 ith agent, respectively, 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 keep track of the reference signal produced by the following generators:

[0161]

[0162] where x r ,v r are the position state and velocity state 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 is designed as an undirected spanning tree, whose Laplace 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 also needs to 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:

[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 parameter c, the traction gain b1, and all the 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 the 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 the leader's grandchild agent has an actuator failure, 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 the Lyapunov function After taking the 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 the leader's child node agent has an actuator failure, 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 the original tracking performance.

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

[0219] (4) Remaining Agent Failure

[0220] Conclusion 5: If the remaining agents have actuator failures, 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 will enable the system to maintain its original tracking performance.

[0225] Proof: Here, we only need to prove that the system converges 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] In the formula, Where h0 represents the leader.

[0228] Define the following positive definite matrix

[0229]

[0230] Select the Lyapunov function After taking the 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 the multi-agent system detects an actuator failure, if its maximum allowable value satisfies the following inequality:

[0234]

[0235] Among them, h is the number of the faulty agent, k represents the number of layers to which the faulty agent belongs, then the collaborative fault-tolerant control method is activated, and according to the fault information (including the ID of the faulty agent, the number of layers, the fault severity, etc.), the corresponding topology reconstruction strategy in 3 is called, thereby achieving consistent tracking of the time-varying reference signal by only adjusting the topological structure of the multi-agent system without changing the original structure and parameters of the agent nominal controller.

[0236] In the specific implementation, each agent can be equipped with a transmitter and a receiver, and a broadcast communication method is adopted to inform other agents within its communication range of the agent's own ID, status, fault severity and other information through the transmitter. When an agent fails, other agents within its communication range learn about the fault through the receiver, and then call the corresponding topology reconstruction strategy to adjust their own interaction mode, such as refusing to receive information from the faulty agent or adjusting the weight of interaction with the faulty 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, and consider the dynamic model of the multi-agent system when the actuator of a certain agent suffers partial loss of control energy efficiency, and each agent needs to track the reference signal generated by the generator;

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

[0240] The topology reconstruction strategy building module is used to design corresponding topology reconstruction strategies for different fault 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, so that when the multi-agent system detects a certain actuator failure, the collaborative fault-tolerant control method is activated to make corresponding topology structure 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 embodiment of the present application is the storage medium used to implement the method of the embodiment of the present application, based on the method introduced in the embodiment of the present application, the person skilled in the art can understand the specific structure and deformation of the storage medium, so it is not repeated here. All storage media used in the method of the embodiment of the present application belong to the scope of protection of this application.

[0244] It will be appreciated by those skilled in the art that embodiments of the present invention may be provided as methods, systems or computer program products. Therefore, the present invention may take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware. 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 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 flowchart and / or block diagram, as well as the combination of processes and / or blocks in the flowchart and / or block diagram, 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 flowchart and / or block diagram. 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 capable of directing a computer or other programmable data processing device to operate 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 A 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 operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process. Figure 1 A process or multiple processes and / or boxes Figure 1 The steps for the functions specified 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 may be implemented by means of hardware comprising several different 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, and 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 can make various changes and modifications 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 equivalents, the present invention is also intended to include these modifications and variations.

[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 specification 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 multi-agent system collaborative fault-tolerant tracking control method based on topology reconstruction, characterized by: The method includes: S1: Construct the 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 a certain 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 use 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; S3: Design corresponding topology reconstruction strategies for different fault 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 structure adjustments, thereby achieving consistent tracking of the time-varying reference signal without changing the original structure and parameters of the nominal controller.

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: in, represent the position state and velocity state of the ith agent, respectively, f(x i ) and g(x i ) is used to describe the nonlinear characteristics of the agent. It is the control input of the system; If the multi-agent system is composed of n agents, its dynamic model can be described as follows: 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 Assuming that the actuator of the i-th agent suffers partial loss of control energy efficiency, its model becomes the following form: 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: where Γ = diag{I (i-1)m , …, ρ i , I (n-i)m}; And each agent needs to track the reference signal produced by the following generator: Among them, x r ,v r are the position and velocity states of the reference signal r.

3. According to the method of claim 2, the method is characterized by: In step S2, in the absence of faults, the initial topology of the multi-agent system is designed, and the distributed nominal controllers are designed for the leader agent and the follower agent respectively using the state feedback control technology, specifically including: First, the initial topology of the multi-agent is designed as an undirected spanning tree, whose Laplace matrix is ​​denoted by L, which is specifically expressed as L = diag{d i }-A, where A is the adjacency matrix of the multi-agent system topology A=[a ij ] T , if agents i and 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 ith 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 needs to carry the layer number in addition to its own number information; For the leader agent, which is numbered 1, its control law is designed as: Among them, c is a parameter to be designed, which needs to satisfy c>0, b1 is the traction gain, which needs to satisfy b1>0; v1 represents the speed state corresponding to the leader agent, and x1 represents the position state corresponding to the leader agent. is the set of leaders’ neighbors, means g(x i )’s inverse matrix; For follower agent i, its control law is designed as: The above parameters c, the pulling gain b1 and all the connection weights a of the Laplace matrix L ij The following two conditions must be met: 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; 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(·), z (·) is the zth element of f(·).

4. The method for cooperative fault-tolerant tracking control of a multi-agent system based on topology reconstruction according to claim 3 is characterized in that: In the 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, including: leader agent failure; If the leader agent has an actuator failure, the traction gain b1 is adjusted to the following form: 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.

5. The method for cooperative fault-tolerant tracking control of a multi-agent system based on topology reconstruction according to claim 3 is characterized in that: In the 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 grandchild node agent; If the leader's grandchild agent has an actuator failure, and the maximum tolerable degree of the failure 1-ρ0 satisfies the following inequality: 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; 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, 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.

6. The method for cooperative fault-tolerant tracking control of a multi-agent system based on topology reconstruction according to claim 3 is characterized in that: In the 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: leader subnode agent failure; If an actuator failure occurs in the leader's child node agent, and the maximum tolerable degree of the failure 1-ρ0 satisfies the following inequality: 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; The topology reconstruction strategy of the multi-agent system is designed as: First, the faulty agent is exchanged with the child node r, and the child node r needs to satisfy: the number of its child nodes needs to be The least, at this time, the faulty agent becomes the grandchild of the leader, and its number is updated to r; 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 the original tracking performance.

7. The method for cooperative fault-tolerant tracking control of a multi-agent system based on topology reconstruction according to claim 3 is characterized by: In the 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 includes: failure of the remaining agents; If the remaining agents have actuator failures, and the maximum tolerable degree of the failure 1-ρ0 satisfies the following inequality: Among them, ρ0 is the lower bound of the residual control energy efficiency of the actuator, h is the number of the faulty agent; The topology reconstruction strategy of the multi-agent system is designed as: First, adjust the weights for Then, a new directed path (1,h1),(h1,h2)(h f-1 ,h f ), And its weight must meet the following conditions: This will enable the system to maintain its original tracking performance.

8. The method for cooperative fault-tolerant tracking control of a multi-agent system based on topology reconstruction according to claim 7 is 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 the multi-agent system detects an actuator failure, if its maximum allowable value satisfies the following inequality: Where h is the number of the faulty agent, T represents the layer to which the faulty agent belongs, and the collaborative fault-tolerant control method is activated. 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 topological structure of the multi-agent system without changing the original structure and parameters of the agent nominal controller.

9. A multi-agent system cooperative fault-tolerant tracking control system based on topology reconstruction, characterized in that: 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, and consider the dynamic model of the multi-agent system when the actuator of a certain agent suffers partial loss of control energy efficiency, and each agent needs to track the reference signal generated by the generator; A distributed nominal controller design module is used to design an initial topology of the multi-agent system in a fault-free state, and to design distributed nominal controllers for the leader agent and the follower agent respectively by using a state feedback control technique, so that the multi-agent system can consistently and asymptotically track the reference signal; The topology reconstruction strategy building module is used to design corresponding topology reconstruction strategies for different fault 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, so that when the multi-agent system detects a certain actuator failure, the collaborative fault-tolerant control method is activated to make corresponding topology structure adjustments, thereby achieving consistent tracking of the time-varying reference signal without changing the original structure and parameters of the nominal controller.

10. 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, and 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 in any one of claims 1 to 8 are implemented.

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