A group consensus control method for multi-agent systems with switching topology based on impulse control

Abstract

The present invention belongs to the field of intelligent information control, and in particular relates to a group consistency control method for a multi-agent system with a switching topology structure based on pulse control, the method comprising: constructing a multi-agent system with a switching topology structure; grouping the constructed multi-agent system; designing a pulse control protocol and a non-pulse control protocol; the agent receives status information from neighboring agents at pulse moments and non-pulse moments respectively; updates the neighboring agent status information at pulse moments through the pulse control protocol; updates the neighboring agent status information received at non-pulse moments through the non-pulse control protocol; and completes group consistency; the present invention adopts a method combining pulse control and non-pulse control to control the agent to receive status information of neighbor nodes and update its own status, which not only reduces network loss and enhances system robustness, but also accelerates the convergence time of the system.

Description

Technical Field

[0001] The invention belongs to the field of intelligent information control, and in particular relates to a group consistency control method of a multi-agent system with a switching topology structure based on pulse control. Background Art

[0002] In recent years, multi-agent systems have received extensive attention due to their potential applications in computer science, drones, etc. In multi-agent systems, the consistency problem is the most critical. Consistency means that the agents in the system receive information from surrounding individuals and communicate with their neighbors, and finally converge to a common state.

[0003] At present, the focus of research on multi-agent systems is to achieve the consistency of multi-agent systems, that is, the agents in the system achieve a common state. However, in real applications, the state of consistency may change with changes in the environment, situation, task and time. Therefore, group consistency is proposed, that is, all agents in the system can achieve multiple different states. In the study of group consistency of multi-agent systems, the continuous control method is mainly used. However, compared with continuous control, discontinuous control has the advantages of stronger robustness and easy operation. Therefore, it is necessary and feasible to introduce discontinuous control into multi-agent systems. At the same time, in the study of multi-agent systems, it is more practical to consider systems with switching topology structures, making the system more flexible.

[0004] However, only using the pulse method to achieve the group consistency of the system improves the robustness of the system, but at the same time increases the convergence time of the system. Therefore, there is an urgent need for a control method that combines pulse control and non-pulse control to achieve fast group consistency of the system. Summary of the invention

[0005] In order to solve the above problems in the prior art, the present invention proposes a group consistency control method of a multi-agent system with a switching topology structure based on pulse control, the method comprising:

[0006] S1: Construct a multi-agent system with a switching topology structure, obtain the topology of the multi-agent system at the pulse time and the topology of the multi-agent system at the non-pulse time;

[0007] S2: Grouping the agents in the constructed multi-agent system according to the topological structure of the multi-agent system at the pulse moment and the topological structure of the multi-agent system at the non-pulse moment;

[0008] S3: Design a control protocol, the set control protocol includes a pulse control protocol and a non-pulse control protocol;

[0009] S4: The agent receives the state information from the neighboring agent at the pulse time, and updates the state information of the neighboring agent received at the pulse time through the pulse control protocol;

[0010] S5: After updating the state information at the pulse time, the agent receives the state information from the neighboring agent at the non-pulse time, and uses the non-pulse control protocol to update the state information of the neighboring agent received at the non-pulse time;

[0011] S6: Use Lyapunov’s stability theorem and graph theory knowledge to verify the agent after state update and complete group consistency.

[0012] Preferably, the process of obtaining the topological structure of the multi-agent system includes: taking each agent in the agent system as a node, obtaining a topological graph of the system, and taking each edge in the graph as information interaction between adjacent nodes.

[0013] Furthermore, the process of obtaining the topological graph includes: obtaining each node in the system and grouping the nodes into a set V = [v1, v2, ..., v n ],v n represents the nth agent; according to the node set, the set of edges between nodes is Let e ij =(v i , v j ), that is, node v j Able to receive data from node v i Information; let the adjacency matrix be A = (a ij ) n×n , and a ij ≥0, if e ji ∈ε, then a ij >0; if Then a ij =0; where a ij Represents the topological connection weight between agent i and agent j; constructs a topological graph G = (V, ε, A) according to the node set, edge set and adjacency matrix, where V represents the set of nodes in the multi-agent network, ε represents the set of edges between nodes, and A represents the adjacency matrix.

[0014] Preferably, grouping the agents includes: dividing each node in the agent system into a virtual leader node and a follower node, each virtual leader node is connected to at least one follower node to form a grouping node.

[0015] Preferably, the designed control protocol is:

[0016]

[0017] Among them, t∈(t k-1 ,t k ] represents the non-pulse time, t = t k Indicates that at the pulse time, represents the position change of node i at the non-pulse moment, N i represents the set of neighbor nodes of node i at the non-pulse time, a ij represents the information interaction between node i and node j at the non-pulse moment, x i (t) represents the position state of node i at time t, l ij represents the element of the Laplace matrix L at the non-pulse time, t k represents the pulse time, Δx i (t) represents the state change of agent i at time t at the pulse moment, d ij represents the information interaction between node i and node j at the pulse time, N′ i represents the set of neighbor nodes of node i at the pulse time, l′ ij represents the element of the Laplace matrix L′ at the pulse time, Represents grouping σ j The state that the agent expects to achieve, that is, the state of the virtual leader.

[0018] Preferably, the conditions for satisfying group consistency in each group of agents are:

[0019]

[0020] Among them, x i (t) represents the position state of the following node i at time t, x j (t) represents the position state of the following node j at time t, σ i represents the virtual leader node, m represents the number of agents in the system, and p represents the number of virtual leader nodes.

[0021] Advantages of the present invention:

[0022] 1) The present invention adopts a method combining pulse control and non-pulse control to achieve group consistency. The control agent receives information from neighboring nodes at pulse time and non-pulse time respectively, and updates its own state. This can not only reduce network loss and enhance the robustness of the system, but also reduce the convergence time of the system.

[0023] 2) Consider multi-agent systems with switching topologies to make the system more practical and flexible. BRIEF DESCRIPTION OF THE DRAWINGS

[0024] Figure 1 A topological diagram of a multi-agent system of the present invention;

[0025] Figure 2 It is the algorithm flow chart of the present invention;

[0026] Figure 3 It is a relationship diagram between time and topology diagram of the present invention. DETAILED DESCRIPTION

[0027] 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.

[0028] A group consensus control method for multi-agent systems with switching topology based on impulse control, such as Figure 2 Said method comprises:

[0029] S1: Construct a multi-agent system with a switching topology structure, obtain the topology of the multi-agent system at the pulse time and the topology of the multi-agent system at the non-pulse time;

[0030] The topological graph constructed by the inventor is first divided into two groups, and then each group has a virtual leader, corresponding to L1 and L2 in the topological graph, and each virtual leader is connected to at least one follower intelligent agent; at the pulse moment and the non-pulse moment, it is a different topological graph, that is, the connection method between the intelligent agents is different, but the number of intelligent agents is the same.

[0031] S2: Grouping the agents in the constructed multi-agent system according to the topological structure of the multi-agent system at the pulse moment and the topological structure of the multi-agent system at the non-pulse moment;

[0032] S3: Design a control protocol, the set control protocol includes a pulse control protocol and a non-pulse control protocol;

[0033] S4: The agent receives the state information from the neighboring agent at the pulse time, and updates the state information of the neighboring agent received at the pulse time through the pulse control protocol;

[0034] S5: After updating the state information at the pulse time, the agent receives the state information from the neighboring agent at the non-pulse time, and uses the non-pulse control protocol to update the state information of the neighboring agent received at the non-pulse time;

[0035] S6: Use Lyapunov’s stability theorem and graph theory knowledge to verify the agent after state update and complete group consistency.

[0036] The process of obtaining the topological structure of a multi-agent system includes: treating each agent in the agent network as a node, connecting two adjacent nodes to form a topological graph; each edge in the graph represents the information interaction between adjacent agents.

[0037] In a multi-agent network, its topology is G = (V, ε, A), where V represents the set of nodes in the multi-agent network, ε represents the set of edges between nodes, and A represents the adjacency matrix. The node set is V = [v1, v2, …, v n ],v n Represents the nth agent, and the set of edges between nodes is (graph G has no self-loop); let e ij =(v i , v j ), that is, node v j Able to receive data from node v i Information; let the adjacency matrix be A = (a ij ) n×n , and a ij ≥0, if e ji ∈ε, then a ij >0; if Then a ij =0; where a ij represents the topological connection weight between agent i and agent j. If in the adjacency matrix A of graph G, there exists a ij =a ji , then the graph G is an undirected graph, and its adjacency matrix A is a symmetric matrix. The graph G corresponds to a multi-agent network, and node i corresponds to an agent in the multi-agent network. The neighbor set of agent i is N i = {v j ∈V:(v i ,v j )∈ε}. In a directed graph, if there is at least one directed path between a node and any other node, then the graph is said to have a directed spanning tree.

[0038] For simplicity, agents that keep exchanging information with an agent for a period of time are called regular neighbors of the agent, and agents that keep exchanging information during the pulse time are called pulse neighbors of the agent. The set of regular neighbors of an agent is N i = {v j ∈V:(v i ,v j )∈ε}, then the pulse neighbor set of the system is defined as: N′ i = {v j ∈V:(v i ,v j )∈ε}.

[0039] All agents share a common state space The state of agent i is defined as x i , and x=(x1,…,x n ) T .

[0040] When t≠t k When , the out-degree of agent i is The in-degree is Let D be the diagonal matrix of the out-degree of each node on the diagonal, so the Laplacian matrix L associated with the directed graph G is defined as L = DA, and its elements are expressed as:

[0041]

[0042] Where D represents the degree matrix at the non-pulse time, diag(.) represents the diagonal matrix, L represents the Laplace matrix at the non-pulse time, l ij represents the element of the Laplace matrix at the non-pulse time, N i Represents the set of neighbor nodes of node i at non-pulse time.

[0043] When t = t k When , the out-degree of agent i is The in-degree is Laplace matrix L′=[l′ ij ] n×n At pulse time t k The definition is as follows:

[0044]

[0045] Where diag(.) represents the diagonal matrix, L′ represents the Laplace matrix at the pulse time, l′ ij represents the element of the Laplace matrix at the pulse time, N′ i represents the set of neighbor nodes of node i at the pulse time. Assume d ij ≥0, And define D′=IL′.

[0046] The average pulse interval of the pulse sequence ξ={t1,t2,…,} is equal to T a , if there exists a positive integer N0 and a positive number T a , so that Where N ξ is the number of pulses of the pulse sequence ξ on the interval (t0, t).

[0047] Let G = (V, ε, A) be a weighted directed graph. Let is the set of reverse edges of graph G, which is obtained by reversing the order of all nodes in ε. Therefore, the mirror image of graph G is defined as and has the same set of nodes as G, The edge set of The adjacency matrix is Elements are

[0048] Node v of the directed graph G = (V, ε, A) i is balanced if and only if the in-degree of the node is equal to its out-degree. A graph G is called balanced if and only if all its nodes are balanced.

[0049] Let G be a directed graph, the adjacency matrix be A = adj(G), and the Laplacian matrix be L = L(G). yes A is a valid Laplacian matrix if and only if G is balanced.

[0050] Each node in the multi-agent system includes a virtual leader node and a follower node; each virtual leader node is connected to at least one follower node to form a group.

[0051] All the results obtained in one-dimensional space can be extended to n-dimensional space using Kronecker product. If the graph G contains a directed spanning tree, there is at least one root node that can access other nodes.

[0052] In the system, each agent receives the location information of neighboring agents and processes the received location information through the pulse control protocol and the non-pulse control protocol to obtain the weighted location results of the agent that sends the information and the agent that receives the information. The specific process includes:

[0053] According to the information interaction between neighboring nodes and the nature of impulse control, the impulse control protocol for any node i is designed as follows:

[0054]

[0055] Among them, t∈(t k-1 ,t k ] represents the non-pulse time, t = t k Indicates that at the pulse time, represents the position change of node i at the non-pulse moment, N i represents the set of neighbor nodes of node i at the non-pulse time, a ij represents the information interaction between node i and node j at the non-pulse moment, x i (t) represents the position state of node i at time t, l ijrepresents the element of the Laplace matrix L at the non-pulse time, t k represents the pulse time, Δx i (t) represents the state change of agent i at time t at the pulse moment, where h is the pulse interval, d is ij represents the information interaction between node i and node j at the pulse time, N′ i represents the set of neighbor nodes of node i at the pulse time, l′ ij represents the element of the Laplace matrix L′ at the pulse time, Represents grouping σ j The state that the agent expects to achieve is the state of the virtual leader. Then x i (t) is left continuous, that is Time series {t k}satisfy

[0056] Simplify the control protocol:

[0057]

[0058] in represents the change of position state, L is the Laplace matrix at the non-pulse moment, x(t) represents the state of position, N i represents the set of neighbor nodes of node i at the non-pulse time, l ij represents the elements of the Laplace matrix L at the non-pulse moment, Represents grouping σ j The state that the agent expects to achieve, that is, the state of the virtual leader. i (t) represents the state change of agent i at time t at the pulse moment, L′ represents the Laplace matrix at the pulse moment, N′ i represents the set of neighbor nodes of node i at the pulse time, l′ ij represents the element of the Laplace matrix L′ at the pulse time.

[0059] For the designed control protocol, if there exists a constant 0<α<1 such that (1-α)I-2L′+L′ T L′≤0, where the graph corresponding to matrix L is balanced, and the graphs corresponding to matrix L and matrix L′ each contain a spanning tree. Then, for the designed control protocol, the multi-agent system can be exponentially The speed of group consistency is achieved. a is the average pulse interval of the pulse sequence ξ={t1,t2,…,}, for The second smallest eigenvalue of

[0060] The process of verifying the agent after state update using Lyapunov stability theorem and graph theory knowledge includes: is the state error function at the non-pulse moment, is the state error function at the pulse time, and The state of the static virtual leader of each group is set to

[0061] Let δ=(δ1,…,δ n ) T is the error function of the system, then the simplified control protocol is transformed into the state error equation:

[0062]

[0063] in, represents the change of the error function, L is the Laplace matrix at the non-pulse moment, δ(t) represents the error function, t k is the pulse time, Represents the error after pulse control, I n represents the n-order identity matrix, the Laplace matrix of L′ pulse time, δ(t k ) represents the error before pulse control.

[0064] The function of Lyapunov's stability theorem is:

[0065] V(δ)=δ T δ (6)

[0066] When t∈(t k-1 ,t k ], the function of Lyapunov's stability theorem is differentiated to obtain:

[0067]

[0068] Integrating the derived function yields:

[0069]

[0070] When t = t k-1 When , according to the function of Lyapunov's stability theorem, we can get:

[0071]

[0072] According to formula (8) and formula (9), we can get:

[0073]

[0074] The average pulse interval of the pulse sequence ξ={t1,t2,…,} is equal to T a , if there exists a positive integer N0 and a positive number T a , so that Where N ξ is the number of pulses of the pulse sequence ξ on the interval (t0, t). Simplifying formula (10), we get:

[0075]

[0076] Since V(δ)=δ T δ, then so However, multi-agent systems can be exponentially Group consistency is achieved at the speed of .

[0077] A specific implementation of a multi-agent system with two topological structures, such as Figure 1 As shown in the figure, there are 5 agents and 2 virtual leaders in the system, which are divided into two groups G1 and G2. Agents 1, 2, and 3 belong to G1, 4 and 5 belong to G2, and L1 and L2 are virtual leaders. The two topologies have the same agents, but the relationships between the agents are different. Figure 1 (a) represents the topological diagram at the pulse time, Figure 1 (b) shows the topological diagram at non-pulse time.

[0078] In the present invention, the relationship between the two topological structures and time is as follows: Figure 3 As shown, in the gray area, it is a non-pulse moment, and the topology of the system is Figure 1 (b) in the above. At t1,…,t k The time is the pulse time, and the corresponding topological diagram is Figure 1 (a) in .

[0079] The above embodiments further illustrate the purpose, technical solutions and advantages of the present invention in detail. It should be understood that the above embodiments are only preferred implementation modes of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made to the present invention within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A group consensus control method for a multi-agent system with a switching topology based on impulse control. It is characterized in that include: S1: Construct a multi-agent system with a switching topology structure, obtain the topology of the multi-agent system at the pulse time and the topology of the multi-agent system at the non-pulse time; S2: Grouping the agents in the constructed multi-agent system according to the topological structure of the multi-agent system at the pulse moment and the topological structure of the multi-agent system at the non-pulse moment; S3: Design the control protocol. The control protocol to be set includes pulse control protocol and non-pulse control protocol. The control protocol is: Among them, t∈(t k-1 ,t k ] represents the non-pulse time, t = t k Indicates that at the pulse time, represents the position change of node i at the non-pulse moment, N i represents the set of neighbor nodes of node i at the non-pulse time, a ij represents the information interaction between node i and node j at the non-pulse moment, x i (t) represents the position state of node i at time t, l ij represents the element of the Laplace matrix L at the non-pulse time, t k represents the pulse time, Δx i (t) represents the state change of agent i at time t at the pulse moment, d ij represents the information interaction between node i and node j at the pulse time, N′ i represents the set of neighbor nodes of node i at the pulse time, l′ ij represents the element of the Laplace matrix L′ at the pulse time, Represents grouping σ j The state that the agent expects to achieve; S4: The agent receives the state information from the neighboring agent at the pulse time, and updates the state information of the neighboring agent received at the pulse time through the pulse control protocol; S5: After updating the state information at the pulse time, the agent receives the state information from the neighboring agent at the non-pulse time, and uses the non-pulse control protocol to update the state information of the neighboring agent received at the non-pulse time; S6: Use Lyapunov's stability theorem and graph theory knowledge to verify the agents after state update and complete group consistency; the conditions for group consistency in each group of agents are: Among them, x i (t) represents the position state of the following node i at time t, xj(t) represents the position state of the following node j at time t, σ i represents the virtual leader node, m represents the number of agents in the system, and p represents the number of virtual leader nodes.

2. According to claim 1, a group consistency control method for a multi-agent system with a switching topology structure based on pulse control, It is characterized in that The process of obtaining the topological structure of a multi-agent system includes: treating each agent in the agent system as a node, obtaining a topological graph of the system, and treating each edge in the graph as information interaction between adjacent nodes.

3. A group consistency control method for a multi-agent system with a switching topology structure based on pulse control according to claim 2, It is characterized in that The process of obtaining the topology graph includes: obtaining each node in the system and grouping the nodes into V = [v 1 ,v 2 ,…,v n ],v n represents the nth agent; according to the node set, the set of edges between nodes is Let e ij =(v i , v j ), that is, node v j Able to receive information from node vi; let the adjacency matrix be A = (a ij ) n×n , and a ij ≥0, if e ji ∈ε, then a ij >0; if Then a ij =0; where a ij Represents the topological connection weight between agent i and agent j; constructs a topological graph G = (V, ε, A) according to the node set, edge set and adjacency matrix, where V represents the set of nodes in the multi-agent network, ε represents the set of edges between nodes, and A represents the adjacency matrix.

4. According to claim 1, a group consistency control method for a multi-agent system with a switching topology structure based on pulse control, It is characterized in that The grouping of intelligent agents includes: dividing each node in the intelligent agent system into a virtual leader node and a follower node, and each virtual leader node is connected to at least one follower node to form a grouping node.

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