Method for improving MAS consistency convergence rate through improved edge reconnection operation

Abstract

The invention discloses a method for improving the MAS consistency convergence rate through improved edge reconnection operation, and relates to the technical field of multi-agent system communication topological optimization, and the method comprises the steps: building a communication topological graph based on a multi-agent system comprising n agents, obtaining a Laplacian matrix through employing an adjacent matrix and a degree matrix of the graph, and obtaining the MAS consistency convergence rate through the Laplacian matrix; calculating a second small eigenvalue of the Laplacian matrix and a Fiedler vector of the second small eigenvalue; according to the absolute value of the difference of the components of the Fiedler vector, determining the deleted and inserted edges, recalculating the Laplacian matrix eigenvalue of the topological graph of the deleted and inserted edges, and regarding the graph with the increased second small eigenvalue of the Laplacian matrix as a new communication topological structure graph of the multi-agent system; verifying the effectiveness of the improved edge reconnection operation method; according to the improved edge reconnection operation, necessary conditions for increasing the algebraic connectivity are increased, the increase amplitude of the algebraic connectivity is maximized, the number of iterations of the algorithm is reduced, and consumption of computing resources is reduced.

Description

Technical Field

[0001] The present invention relates to the technical field of multi-agent system communication topology optimization, and in particular to a method for improving the consistency convergence rate of a MAS by using an improved edge reconnection operation. Background Art

[0002] In recent years, with the continuous development of science and technology such as computers, communications, and control, multi-agent systems (MAS) have been widely used in many fields such as sensor networks, smart grids, intelligent transportation, data networks, and distributed computing. In practical applications, the higher the convergence rate of a multi-agent system, the more sensitive the system will be in terms of perception, execution, and flexibility. For systems with high real-time performance and rapid response requirements, such as drone swarm combat systems and smart grids, the consistency convergence rate of the system is the key to determining whether the task is successfully executed. Therefore, it is crucial to improve the consistency convergence rate of the multi-agent system.

[0003] The consensus convergence rate of a multi-agent system (MAS) quantifies how fast the system reaches consensus from the initial state under a certain consensus protocol. Currently, in order to improve the consensus convergence rate of a multi-agent system, research is usually conducted from two aspects: designing and improving the consensus protocol and optimizing the communication topology. In terms of designing and improving system consensus protocols, early consensus protocols converged asymptotically. In order to improve the convergence rate of a multi-agent system to reach consensus, a large number of scholars have conducted in-depth research on consensus protocols and made continuous improvements, and designed consensus protocols that converge in finite time and specified time.

[0004] In terms of optimizing communication topology, research shows that when the consensus protocol of a multi-agent system is given (such as a continuous consensus protocol, a periodic sampling consensus protocol, and an event-triggered consensus protocol), the convergence rate of the multi-agent system is determined by the eigenvalue of its communication topology graph: the greater the algebraic connectivity, the faster the consistency convergence rate of the system, so that the agents can reach consensus more quickly. The algebraic connectivity here is the second smallest eigenvalue of the Laplace matrix corresponding to the communication topology graph of the multi-agent system. Currently, commonly used methods for optimizing communication topology include adding edges, edge rotations, edge swaps, and edge reconnections. These edge operations can be used to construct a greedy algorithm to iteratively optimize the structure of the communication topology, thereby improving the algebraic connectivity. However, constructing a greedy algorithm and performing iterative optimization will consume a lot of computing resources and time.

[0005] Based on this, the purpose of the present invention is to provide a method for improving the MAS consistency convergence rate by using an improved edge reconnection operation, updating the algorithm in the communication topology optimization, and reducing the number of iterations and computing resources. Summary of the invention

[0006] In order to make up for the shortcomings of the prior art problems, the present invention provides a method for improving the consistency convergence rate of MAS by using an improved edge reconnection operation. It proposes a new idea for an improved edge reconnection operation. On the basis of the original edge reconnection operation, it adds the necessary conditions for increasing the algebraic connectivity, so that the increase in algebraic connectivity is maximized, thereby effectively reducing the number of iterations of the algorithm and reducing the consumption of computing resources.

[0007] To achieve the above object, the present invention provides the following technical solutions:

[0008] A method for improving the MAS consistency convergence rate by using an improved edge reconnection operation comprises the following steps:

[0009] (1) Based on a multi-agent system consisting of n agents, its communication topology is modeled using a simple undirected graph in graph theory, and then the communication topology graph of the multi-agent system is constructed;

[0010] (2) Based on the communication topology graph of the multi-agent system established in step (1), the Laplace matrix is ​​obtained using the adjacency matrix and degree matrix of the graph, and the second smallest eigenvalue of the Laplace matrix and its Fiedler vector are calculated;

[0011] (3) Determine the edges to be deleted and inserted in the communication topology graph according to the absolute value of the difference between the components of the Fiedler vector, recalculate the Laplace matrix eigenvalues ​​of the topology graphs of the deleted and inserted edges, and regard the graph with the increased second smallest eigenvalue of the Laplace matrix as the new communication topology graph of the multi-agent system;

[0012] (4) Verify the effectiveness of the improved edge reconnection operation method.

[0013] In the present invention, the communication topology diagram of the multi-agent system is constructed as follows:

[0014] Let the communication topology of the multi-agent system be G = (V(G), E(G)), where V(G) = {v1,...,v n} represents the vertex set of graph G, E(G) represents the edge set in graph G; the initial state of agent i is represented by its position coordinates, speed, yaw angle and other physical quantities that change with time t, denoted by vector σ i (t), i = 1, ..., n; if the agent i is regarded as a particle moving on a plane, its state is described by the position coordinates, that is, σ i (t) = [x i (t),y i (t)] T , where x i (t) represents the horizontal coordinate of agent i, y i (t) represents the vertical coordinate of agent i.

[0015] In the present invention, the calculation process of the Fiedler vector in step (2) is as follows:

[0016] The communication topology of the multi-agent system established in step (1) is G = (V(G), E(G)), and its adjacency matrix A(G) = [a ij ]∈R n×n Defined as: If (v i ,v j )∈E(G), then a ij =1, otherwise a ij = 0; the degree matrix D(G) of graph G is an n-dimensional diagonal matrix, and the elements on its main diagonal are the number of neighbors of each vertex;

[0017] The Laplacian matrix of graph G is L(G)=D(G)-A(G);

[0018] Calculate the eigenvalues ​​of the Laplace matrix L(G) and arrange the eigenvalues ​​in non-decreasing order: λ1(G)≤λ2(G)≤…≤λ n (G), where the second smallest eigenvalue λ2(G) is called algebraic connectivity; the larger λ2(G) is, the faster the consistency convergence rate of the system is, that is, the system reaches consistency in less time;

[0019] Calculate the eigenvector corresponding to the eigenvalue λ2(G), denoted as u (2) (G)=[u1 (2) (G),...,u n (2) (G)] T , which is also called the Fiedler vector.

[0020] In the present invention, the steps for obtaining the communication topology diagram of the new multi-agent system in step (3) are as follows:

[0021] 1) According to the Fiedler vector obtained in step (2), select an edge to be deleted from the communication topology graph (v i ,v j ), satisfying |u i (2) (G)-u j (2) (G)| has the smallest value, and its minimum value is recorded as e min ; If there are multiple items, select one of them;

[0022] 2) Find a set of non-adjacent vertex pairs in the communication topology graph, where any vertex v s and v t All meet e min <|u s(2) (G)-u t (2) (G)|, let this vertex pair set be V(D);

[0023] 3) Delete edge (v i ,v j ) is denoted as Gv i v j , according to Figure Gv i v j The corresponding Laplace matrix calculates the second smallest eigenvalue λ2(Gv i v j ) and its corresponding eigenvector u (2) (Gv i v j ); At this time, in the set V(D), find the k (2) (Gv i v j )-u l (2) (Gv i v j )|The maximum value of non-adjacent vertex pair {v k ,v l}, insert edge (v k ,v l ), the resulting graph is denoted as G'; if there are multiple edges with the largest value, select any one of them;

[0024] 4) According to the Laplace matrix corresponding to the graph G', calculate the eigenvalues ​​of the matrix, where the second smallest eigenvalue λ2(G') is the new key performance indicator; if λ2(G')>λ2(G), then the edge reconnection operation maximizes the increase of the key performance indicator λ2(G), and the graph G' is regarded as the communication topology structure diagram of the new multi-agent system; if λ2(G')≤λ2(G), re-execute step 1).

[0025] In the present invention, the effectiveness of the improved edge reconnection operation method is verified in step (4), as follows:

[0026] Define the system error function when the system reaches consensus

[0027] Among them, the vector σ i (t) represents the state of agent i at time t, and x* represents the state of the agent when the system reaches consensus, which is usually the average of the initial states in the system;

[0028] By using Matlab to draw the curve corresponding to the system error function, we can intuitively reflect how the system error changes with time before and after the communication topology of the multi-agent system changes. It is a decreasing function with time t, and the function value tends to zero. Each vertex on the curve can represent the error of the system at a certain moment, and the faster the function value tends to zero, the less time the system takes to reach consensus.

[0029] Compared with the prior art, the present invention has the following beneficial effects:

[0030] The present invention proposes an improved edge rewiring operation, which uses a graph in graph theory for modeling, regards each intelligent agent as a vertex in the graph, and regards the communication between intelligent agents as an edge in the graph theory. It deletes and adds edges based on Fiedler vectors to increase the algebraic connectivity of the communication topology graph. Compared with the traditional edge rewiring operation method, the present invention adds the necessary conditions for increasing the algebraic connectivity, so that the increase in algebraic connectivity is maximized, thereby effectively reducing the number of algorithm iterations and reducing the consumption of computing resources. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] Figure 1 The present invention is a flow chart of the method.

[0032] Figure 2 Schematic diagram of the communication topology optimization process of the multi-agent system of the present invention.

[0033] Figure 3 This is a comparison diagram of the error curves of the multi-agent system of the present invention.

[0034] Figure 4 This is a flow chart of the improved edge reconnection operation of the present invention. DETAILED DESCRIPTION

[0035] 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.

[0036] Combination Figure 1-4 The present invention is specifically described. The present invention proposes a method for improving the consistency convergence rate of a multi-agent system based on edge reconnection operation, such as Figure 1 As shown, the specific steps include:

[0037] Step 1: Based on the given communication topology of the multi-agent system, use a simple undirected graph in graph theory to model it, and then construct the communication topology graph of the multi-agent system.

[0038] The present invention takes a multi-agent system containing 6 agents as an example, and its communication topology diagram is as follows: Figure 2 G a As shown in Figure G a The vertex v in i Represents agent i, graph G a The undirected edges in represent the communication relationship between agents. Now we use the graph in graph theory to model it. Let the graph G a G a =(V(G a ), E(G a )), where V(G a )={v1,...,v6} represents the graph G a The vertex set E(G a ) represents the graph G a The set of edges, namely E(G a )={(v1, v2), (v1, v3), (v1, v4), (v2, v3), (v4, v5), (v4, v6)}. Figure G a Undirected edge (v i , v j ) represents the communication between agents i and j, for example, the undirected edge (v2, v3) represents the communication between agents 2 and 3; a The non-adjacent edges {v s , v t} represents that agents s and t do not communicate with each other. For example, the non-adjacent edge {v3, v5} represents that agents 3 and 5 do not communicate with each other. Assume that the state of agent i (1≤i≤6) is represented by its corresponding two-dimensional coordinates. Now assume that the initial states of the six agents are shown in the following table:

[0039] Agent 1 Agent 2 Agent 3 Agent 4 Agent 5 Agent 6 Horizontal axis 1 0 1 3 5 5 Vertical axis 2 0 -2 -2 -2 2

[0040] That is, the initial values ​​of the six agents in the horizontal direction are recorded as x(0)=(x i (0)) T =(1,0,1,3,5,5) T , i = 1, 2, ..., 6, the initial value in the vertical direction is denoted as y(0) = (y i (0)) T =(2,0,-2,-2,-2,2) T , i=1,...,6.

[0041] Step 2: Based on the communication topology of the multi-agent system established in step 1, the communication topology G is a The corresponding D(G a ) and A(Ga ) are:

[0042] Here D(G a ) is the element in the i-th row and i-th column that corresponds to the vertex v i The number of adjacent vertices (i.e., the number of agents communicating with agent i). For example, the element in row 3 and column 3 indicates that the number of adjacent vertices to v3 is 2 (i.e., the number of agents communicating with agent 3 is 2). If A(G a ) is 1, which means that vertex v i and vertex v j There is an edge between them, that is, they are adjacent; if A(G a ) is 0, which means that vertex v i and vertex v j There is no edge between them, that is, they are not adjacent. If the element in the 1st row and 2nd column is 1, it means that there is an edge between vertex v1 and vertex v2 (that is, agent 1 and agent 2 communicate); if the element in the 1st row and 5th column is 0, it means that there is no edge between vertex v1 and vertex v5 (that is, agent 1 and agent 5 do not communicate). Then the communication topology graph G a The corresponding Laplace matrix L(G a )for:

[0043] Since the Laplace matrix L(G a ) is a semi-positive definite real symmetric matrix. The Laplace matrix L(G a ) and arrange the eigenvalues ​​in non-decreasing order as follows:

[0044] λ1(G a )=0<λ2(G a )=0.4384<λ3(G a )=1<λ4(G a )=3≤λ5(G a )=3<λ6(G a )=4.5616, here, the second smallest eigenvalue λ2(G a )=0.4384 is the algebraic connectivity, which is regarded as the key performance indicator of the system. Through Matlab calculation, it can be obtained that the eigenvalue λ2(G a ) corresponds to the eigenvector u (2) (G a ) = [-0.2610, -0.4647, -0.4647, 0.2610, 0.4647, 0.4647] T . Vector u (2) (G a ) at agent i is shown in the following table:

[0045] Agent 1 Agent 2 Agent 3 Agent 4 Agent 5 Agent 6 <![CDATA[u1 (2) (G a )]]> <![CDATA[u2 (2) (G a )]]> <![CDATA[u3 (2) (G a )]]> <![CDATA[u4 (2) (G a )]]> <![CDATA[u5 (2) (G a )]]> <![CDATA[u6 (2) (G a )]]> -0.2610 -0.4647 -0.4647 0.2610 0.4647 0.4647

[0046] Step 3: Based on step 2, find the key performance indicator λ2(G a )=0.4384. By changing the communication topology of the system through the improved edge reconnection operation, the aim is to maximize the improvement of λ2(G a ), thereby accelerating the consistency convergence rate and making the system converge faster. The specific steps are as follows:

[0047] (1)|u i (2) (G a )-u j (2) (G a )|is the vector u (2) (G a ) is the absolute value of the difference between the components at the adjacent agent i and agent j. From the communication topology graph G a The edge set E(G a )={(v1, v2), (v1, v3), (v1, v4), (v2, v3), (v4, v5), (v4, v6)}, select an edge to be deleted (v i , v j ), satisfying |u i (2) (G a )-u j (2) (G a )| has the smallest value, and its minimum value is recorded as e min If there are multiple items, select any one of them. Through example calculation, we get the following table:

[0048] <![CDATA[(v1,v2)]]> <![CDATA[(v1,v3)]]> <![CDATA[(v1,v4)]]> <![CDATA[(v2,v3)]]> <![CDATA[(v4,v5)]]> <![CDATA[(v4,v6)]]> <![CDATA[|u i (2) (G a )-u j (2) (G a )|]]> 0.2037 0.2037 0.5220 0 0.2037 0.2037

[0049] From the above table, we can see that due to e min =|u2 (2) (G a )-u3 (2) (G a )|=0, so the edge (v2, v3) is selected as the edge to be deleted, that is, the communication between agent 2 and agent 3 is to be disconnected.

[0050] (2)|u s (2) (G a )-u t (2) (G a )|is the vector u (2) (G a) is the absolute value of the difference between the components at non-adjacent agents s and t. Find a set of non-adjacent vertex pairs in the communication topology graph, where any vertex pair {v s , v t} all satisfy e min =0<|u s (2) (G a )-u t (2) (G a )|, let this vertex set be V(D).

[0051] <![CDATA[{v1,v6}]]> <![CDATA[{v1,v5}]]> <![CDATA[{v2,v6}]]> <![CDATA[{v2,v5}]]> <![CDATA[{v2,v4}]]> <![CDATA[{v3,v4}]]> <![CDATA[{v3,v5}]]> <![CDATA[{v3,v6]]]> <![CDATA[{v5,v6}]]> <![CDATA[u s (2) (G a )-u t (2) (G a )]]> 0.725 0.7257 0.9294 0.9294 0.7257 0.7257 0.9294 0.9294 0

[0052] Through the above calculation, e min =0<|u s (2) (G a )-u t (2) (G a )| is V(D) = {{v1, v6}, {v1, v5}, {v2, v6}, {v2, v5}, {v2, v4}, {v3, v4}, {v3, v5}, {v3, v6}}.

[0053] (3) The graph obtained after deleting the edge (v2, v3) is denoted as G a -v2v3, even if Agent 2 and Agent 3 lose communication, such as Figure 2 G a -v2v3. From the definition of degree matrix and adjacency matrix in the previous article, we can get graph G a -v2v3 corresponding degree matrix D(G a -v2v3) and the adjacency matrix A(G a -v2v3) are:

[0054]

[0055] Then figure G a -v2v3 corresponding Laplace matrix L(G a -v2v3) is:

[0056]

[0057] Since the Laplace matrix L(G a -v2v3) is a semi-positive definite real symmetric matrix, and the Laplace matrix L(G a -v2v3), arrange the eigenvalues ​​in non-decreasing order as follows:

[0058] λ1(G a -v2v3)=0<λ2(G a -v2v3)=0.4384<λ3(G a -v2v3)=1<λ4(G a -v2v3)=1<λ5(G a -v2v3)=3<λ6(G a -v2v3)=4.5616.

[0059] Through Matlab calculation, we can get the second smallest eigenvalue λ2(G a )=0.4384The corresponding eigenvector is u (2) (G a -v2v3)=[-0.2610,-0.4647,-0.4647,0.2610,0.4647,0.4647] T . Vector u (2) (G a -v2v3) components at agent i are shown in the following table:

[0060] Agent 1 Agent 2 Agent 3 Agent 4 Agent 5 Agent 6 <![CDATA[u1 (2) (G a -v2v3)]]> <![CDATA[u2 (2) (G a -v2v3)]]> <![CDATA[u3 (2) (G a -v2v3)]]> <![CDATA[u4 (2) (G a -v2v3)]]> <![CDATA[u5 (2) (G a -v2v3)]]> <![CDATA[u6 (2) (G a -v2v3)]]> -0.2610 -0.4647 -0.4647 0.2610 0.4647 0.4647

[0061] Now find in the set V(D) that |u k (2) (G a -v2v3)-u l (2) (G a -v2v3)|The largest non-adjacent vertex pair {v k , v l}.

[0062]

[0063] From the above table, we can see that there are multiple non-adjacent vertex pairs that satisfy |u k (2) (G a -v2v3)-u l (2) (G a -v2v3)| has the largest value, that is, {v2, v6}, {v2, v5}, {v3, v5} and {v3, v6}. Now we arbitrarily select non-adjacent vertex pairs {v3, v5} to connect, even if Agent 3 and Agent 5 communicate with each other, the resulting graph is denoted by G b ,like Figure 2 At this point, the edge (v3, v5) that can maximize the increase in the key performance indicator is inserted.

[0064] (5) Based on Figure 2 G b, and from the definition of degree matrix and adjacency matrix in the previous text, we can know that graph G b The corresponding degree matrix D(G b ) and the adjacency matrix A(G b ) are: Then figure G b The corresponding Laplace matrix L(G b )for:

[0065] Since the Laplace matrix L(G b ) is a semi-positive definite real symmetric matrix. The Laplace matrix L(G b ) and arrange the eigenvalues ​​in non-decreasing order as follows:

[0066] λ1(G b )=0<λ2(G b )=0.6571<λ3(G b )=1<λ4(G b )=2.5293<λ5(G b )=3<λ6(G b )=4.8136.

[0067] G b The key indicator λ2(G b )=0.6571, and λ2(G a )=0.4384<λ2(G b )=0.6571. Through the specific practice of the improved edge reconnection operation, the edge (v2, v3) is deleted and the edge (v3, v5) is added in the communication topology graph. Even if agent 2 and agent 3 are disconnected from each other, agent 3 and agent 5 communicate with each other, and the algebraic connectivity of the communication topology graph of the multi-agent system increases the most. The communication topology graph of the multi-agent system after the change is shown in Figure 2 G b shown.

[0068] Step 4: In order to verify the effectiveness of the improved edge reconnection operation method, define the system error function when the system reaches consistency where the vector σ i (t) represents the state of agent i at time t, and x* represents the state when the system reaches consensus, which is usually the average of the initial states. When the system reaches consensus, the final coordinates of all agents are (x*, y*), where

[0069] x*=(x*,y*) T . Define the system error function In the process of the system reaching consensus, the error Error(t)→0. If Error(t)=0 when t>T, the system reaches consensus at time T. By drawing the function graph through Matlab, the function graph can intuitively reflect the curve of the system error changing with time before and after the communication topology structure of the multi-agent system changes, such as Figure 3 As shown. Note that Figure 3 The red solid line and the blue dashed line respectively show the communication topology diagram G a and G b By comparison, it can be seen that the system error after optimization approaches 0 faster than the system error before optimization. In particular, when the communication time is 3 seconds, G b The system error is about G a of It shows that the communication topology graph corresponding to the multi-agent system is in G b There is a higher consistency convergence rate.

[0070] What has been described above are only preferred specific implementations of the present invention, but the protection scope of the present invention is not limited thereto. Any technician familiar with the technical field, within the technical scope disclosed by the present invention, can make equivalent replacements or changes based on the technical solutions and inventive concepts of the present invention, which should be covered by the protection scope of the present invention.

Claims

1. A method for improving the MAS consistency convergence rate by using an improved edge reconnection operation, characterized in that: The following steps are involved: (1) Based on a multi-agent system consisting of n agents, its communication topology is modeled using a simple undirected graph in graph theory, and then the communication topology graph of the multi-agent system is constructed; (2) Based on the communication topology graph of the multi-agent system established in step (1), the Laplace matrix is ​​obtained using the adjacency matrix and degree matrix of the graph, and the second smallest eigenvalue of the Laplace matrix and its Fiedler vector are calculated; (3) Determine the edges to be deleted and inserted in the communication topology graph according to the absolute value of the difference between the components of the Fiedler vector, recalculate the Laplace matrix eigenvalues ​​of the topology graphs of the deleted and inserted edges, and regard the graph with the increased second smallest eigenvalue of the Laplace matrix as the new communication topology graph of the multi-agent system; (4) Verify the effectiveness of the improved edge reconnection operation method.

2. The method for improving the MAS consistency convergence rate by using the improved edge reconnection operation according to claim 1, characterized in that: The communication topology diagram for constructing a multi-agent system is as follows: Let the communication topology of the multi-agent system be G = (V(G), E(G)), where V(G) = {v1,…,v n } represents the vertex set of graph G, E(G) represents the edge set in graph G; the initial state of agent i is represented by its position coordinates, speed, yaw angle and other physical quantities that change with time t, denoted by vector σ i (t), i = 1, ..., n; if the agent i is regarded as a particle moving on a plane, its state is described by the position coordinates, that is, σ i (t) = [x i (t),y i (t)] T , where x i (t) represents the horizontal coordinate of agent i, y i (t) represents the vertical coordinate of agent i.

3. The method for improving the MAS consistency convergence rate by using the improved edge reconnection operation according to claim 1, characterized in that: The calculation process of the Fiedler vector in step (2) is as follows: The communication topology of the multi-agent system established in step (1) is G = (V(G), E(G)), and its adjacency matrix A(G) = [a ij ]∈R n×n Defined as: If (v i ,v j )∈E(G), then a ij =1, otherwise a ij = 0; the degree matrix D(G) of graph G is an n-dimensional diagonal matrix, and the elements on its main diagonal are the number of neighbors of each vertex; The Laplacian matrix of graph G is L(G)=D(G)-A(G); Calculate the eigenvalues ​​of the Laplace matrix L(G) and arrange the eigenvalues ​​in non-decreasing order as follows: λ1(G)≤λ2(G)≤…≤λ n (G), where the second smallest eigenvalue λ2(G) is called algebraic connectivity; the larger λ2(G) is, the faster the consistency convergence rate of the system is, that is, the system reaches consistency in less time; Calculate the eigenvector corresponding to the eigenvalue λ2(G), denoted as u (2) (G)=[u1 (2) (G),...,u n (2) (G)] T , which is also called the Fiedler vector.

4. The method for improving the MAS consistency convergence rate by using the improved edge reconnection operation according to claim 1, characterized in that: The steps for obtaining the communication topology diagram of the new multi-agent system in step (3) are as follows: 1) According to the Fiedler vector obtained in step (2), select an edge to be deleted from the communication topology graph (v i ,v j ), satisfying |u i (2) (G)-u j (2) (G)| has the smallest value, and its minimum value is recorded as e min ; If there are multiple items, select one of them; 2) Find a set of non-adjacent vertex pairs in the communication topology graph, where any vertex v s and v t All meet e min <|u s (2) (G)-u t (2) (G)|, let this vertex pair set be V(D); 3) Delete edge (v i ,v j ) is denoted as Gv i v j , according to Figure Gv i v j The corresponding Laplace matrix calculates the second smallest eigenvalue λ2(Gv i v j ) and its corresponding eigenvector u (2) (Gv i v j ); At this time, in the set V(D), find the k (2) (Gv i v j )-u l (2) (Gv i v j )|The maximum value of non-adjacent vertex pair {v k ,v l }, insert edge (v k ,v l ), the resulting graph is denoted as G'; if there are multiple edges with the largest value, select any one of them; 4) According to the Laplace matrix corresponding to the graph G', calculate the eigenvalues ​​of the matrix, where the second smallest eigenvalue λ2(G') is the new key performance indicator; if λ2(G')>λ2(G), then the edge reconnection operation maximizes the increase of the key performance indicator λ2(G), and the graph G' is regarded as the communication topology structure diagram of the new multi-agent system; if λ2(G')≤λ2(G), re-execute step 1).

5. The method for improving the MAS consistency convergence rate by using the improved edge reconnection operation according to claim 2, characterized in that: In step (4), the effectiveness of the improved edge reconnection operation method is verified as follows: Define the system error function when the system reaches consensus Among them, the vector σ i (t) represents the state of agent i at time t, and x* represents the state of the agent when the system reaches consensus, which is usually the average of the initial states in the system; By using Matlab to draw the curve corresponding to the system error function, we can intuitively reflect how the system error changes with time before and after the communication topology of the multi-agent system changes. It is a decreasing function with time t, and the function value tends to zero. Each vertex on the curve can represent the error of the system at a certain moment, and the faster the function value tends to zero, the less time the system takes to reach consensus.

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