Group consensus control method for multi-agent systems based on impulse control

Abstract

The present invention belongs to the field of intelligent information processing, and in particular relates to a multi-agent system group consistency control method based on pulse control, the method comprising: constructing a topological structure of a nonlinear multi-agent system; grouping the agents in the system according to the topological structure; designing a pulse control protocol; at a pulse moment, each agent receives the position information of a neighboring agent, and processes the received position information through a pulse control protocol to obtain a weighted position result of an agent that sends information and an agent that receives the information; updating its own state according to the weighted position result to complete group consistency; analyzing the influence of control parameters on the system achieving group consistency; the present invention adopts pulse control to achieve group consistency, controls the agent to receive information from neighboring nodes at the pulse moment, and updates its own state, which can reduce network loss and enhance system robustness.

Description

Technical Field

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

[0002] In recent years, inspired by the clustering behavior in organisms, the consistency research of multi-agent systems has been widely used in many fields such as computer science, drone formations, cluster spacecraft detection and wireless sensors, and has become a research boom in the field of automatic control. However, due to the increasing complexity of the actual environment, people have higher and higher requirements for the reliability and diversity of multi-agent systems. Multi-agent systems generally consider two situations, namely, the leader situation and the leaderless situation. In the leaderless situation, a distributed controller is designed for each agent so that the agents in the system eventually converge to a common value; in a system with a leader, the followers usually remain in the same state as the leader.

[0003] At present, most research focuses on achieving consistency in multi-agent systems, that is, the agents in the system achieve a common state. However, in real applications, the state of consistency will 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. Group consistency means that in the system, the agents are divided into multiple groups, the same group achieves the same state, and different groups achieve different states, so that the system can achieve multiple different states. In the study of multi-agent group consistency, the continuous control method is mainly used; however, the continuous control method is difficult to operate and has large transmission loss; therefore, a non-continuously controlled agent system group consistency control method is urgently needed. Summary of the invention

[0004] In order to solve the above problems in the prior art, the present invention proposes a multi-agent system group consistency control method based on impulse control, the method comprising:

[0005] S1. Construct the topological structure of the multi-agent system;

[0006] S2, grouping the agents in the system according to the topological structure;

[0007] S3, design pulse control protocol;

[0008] S4. At the pulse time, each agent in the same group receives the location information of the neighboring agent, and processes the received location information through the pulse control protocol to obtain the weighted location result of the agent sending the information and the agent receiving the information;

[0009] S5. Update its own status according to the weighted position to complete the grouping consistency.

[0010] Preferably, the process of constructing the topological structure of the 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.

[0011] Furthermore, each node in the multi-agent system includes a leader node and a follower node; each leader node is connected to at least one follower node to form a group.

[0012] Furthermore, the dynamic model of the leader node is:

[0013]

[0014] The dynamic model of the follower node is:

[0015]

[0016] in, Represents the leader node σ i The position change, φ(.) represents a nonlinear function, Represents the leader node σ i The position state at time t, Ξ represents the constant matrix, and p represents the number of leader nodes; Indicates the position change of following node i, x i (t) represents the position state of the follower node i at time t, m represents the number of agents in the system, and n represents the number of follower nodes.

[0017] Preferably, the designed pulse control protocol is:

[0018]

[0019] in, represents the position change of the following node i, φ(.) represents the nonlinear function, x i (t) represents the position state of the following node i at time t, Ξ represents the constant matrix, u i (t) represents the designed pulse control protocol, δ(tt k ) indicates that at t k The unit impulse function at time t k represents the pulse control time, b k represents the pulse gain, j represents node j, N i represents the set of neighbor nodes of node i, a ij Indicates whether node i and node j exchange information. If a ij≥0 means there is information exchange between node i and node j. ij <0 means that there is no information exchange between node i and node j, x j (t) represents the position state of the following node j at time t, l ij represents the Laplace matrix element between node i and node j, that is, Represents the leader node σ j The position state at time t, Represents the leader node σ i Position state at time t.

[0020] Preferably, when the agent receives the location information of the neighboring agent, the agent is controlled by a pulse control protocol to receive the location information sent by the neighboring agent at the pulse time.

[0021] Preferably, the process of processing the received location information through the pulse control protocol includes: receiving information from neighboring nodes at the pulse time, and updating its own location status in combination with the information of the neighboring nodes under the control of the control protocol.

[0022] Preferably, the conditions for the agents in the system to meet group consistency are:

[0023]

[0024] 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 leader node, m represents the number of agents in the system, and p represents the number of leader nodes.

[0025] Advantages of the present invention:

[0026] 1) The present invention adopts pulse control to achieve group consistency, and controls the intelligent agent to receive information from neighboring nodes at the pulse time and update its own state, which can not only reduce network loss but also enhance the robustness of the system.

[0027] 2) Consider nonlinear systems, break through the limitations of linear system applications, make the system more practical, and apply it to a wider range of scenarios. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] Figure 1 It is a topological structure diagram of the multi-agent system of the present invention;

[0029] Figure 2 It is the algorithm flow chart of the present invention;

[0030] Figure 3is a comparison diagram of the state errors between the follower and the leader of the present invention;

[0031] Figure 4 is the state diagram of the intelligent agent of the present invention;

[0032] Figure 5 This is a graph showing the effect of pulse gain on system convergence in the present invention. DETAILED DESCRIPTION

[0033] 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.

[0034] A group consensus control method for multi-agent systems based on impulse control, such as Figure 2 As shown, the method includes: constructing the topological structure of the multi-agent system; grouping the agents in the system according to the topological structure; designing a pulse control protocol; at the pulse control moment, each agent receives the position information of the neighboring agent, and processes the received position information through the pulse control protocol to obtain the weighted position result of the agent sending the information and the agent receiving the information; updating its own state according to the weighted position result to achieve group consistency; analyzing the influence of control parameters on the system to achieve group consistency.

[0035] 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.

[0036] 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 = [v 1 ,v 2 ,…,v n ],v n Represents the nth agent, and 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 eji ∈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 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.

[0037] All agents share a common state space The state of agent i is defined as x i , and x=(x 1 ,…,x n ) T .

[0038] Let L = DA be the Laplacian matrix of the graph G, where D is the degree matrix, expressed as D = diag(d 1 ,d 2 ,…,d n ), is the degree of agent i, then L = [l ij ] n×n The elements of are:

[0039]

[0040] Where D represents the degree matrix, diag(.) represents the diagonal matrix, and d n represents the degree of the nth node, L represents the Laplacian matrix, l ij represents the elements of the Laplacian matrix, N i Represents the set of neighbor nodes of node i.

[0041] Each node in the multi-agent system includes a leader node and a follower node; each leader node is connected to at least one follower node to form a group.

[0042] Preferably, the multi-agent system contains m agents, among which there are p leaders and n followers. Then there are agents with a first-order structure that satisfy:

[0043]

[0044] in, are the position state and input control of agent i, Represents the position change of agent i.

[0045] In the system, the dynamic model of the leader node is:

[0046]

[0047] The dynamic model of the follower node is:

[0048]

[0049] in, Represents the leader node σ i The position change, φ(.) represents a nonlinear function, Represents the leader node σ i The position state at time t, Ξ represents the constant matrix, and p represents the number of leader nodes; Indicates the position change of following node i, x i (t) represents the position state of the follower node i at time t, m represents the number of agents in the system, and n represents the number of follower nodes.

[0050] If the continuous nonlinear function φ: Satisfies the Lipschitz condition |φ(x 1 )-φ(x 2 )|≤l|x 1 -x 2 |, then all the results obtained in one-dimensional space can be generalized to n-dimensional space using Kronecker product. If the graph G contains a directed spanning tree, that is, there is at least one root node that can access other nodes; and the graph G is disconnected: it can be separated into multiple groups, each separated group is either a single node or contains a spanning tree.

[0051] In the same group, each agent receives the location information of neighboring agents and processes the received location information through the pulse control protocol to obtain the weighted location result of the agent that sent the information and the agent that received the information. The specific process includes:

[0052] 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:

[0053]

[0054] in, represents the position change of the following node i, φ(.) represents a nonlinear function, x i (t) represents the position state of the following node i at time t, Ξ represents the constant matrix, ui (t) represents the designed pulse control protocol, δ(tt k )express That is, at t k The unit impulse function at time t k represents the pulse control time, b k represents the pulse gain, j represents node j, N i represents the set of neighbor nodes of node i, a ij Indicates whether node i and node j have information interaction. If a ij ≥0 means there is information exchange between node i and node j. ij <0 means that there is no information exchange between node i and node j, x j (t) represents the position state of the following node j at time t, l ij represents the Laplace matrix element between node i and node j, that is, Represents the leader node σ j The position state at time t, Represents the leader node σ i The position state at time t. δ(t) is the Dirac function, and b k <0 is the pulse gain, t k is the pulse time, and the state of the dynamic leader of each group is set to

[0055] When t = t k When , the change of the agent's position state at the pulse moment is:

[0056]

[0057] in h is the pulse interval, Δx i (t k ) represents the agent i at the pulse time t k This means that agent i can change its state at t based on the state information of its neighbors. k Update your status suddenly from time to time.

[0058] like Then x i (t) is left continuous, that is Time series {t k}satisfy

[0059] If the continuous nonlinear function φ: Satisfies the Lipschitz condition |φ(x 1 )-φ(x 2 )|≤l|x1 -x 2 |, the graph G contains a directed spanning tree, and there exists a constant ξ>1 that satisfies the following conditions:

[0060] T a (λ Ξ +2l)+ln(λ k ξ)<0

[0061] Among them, T a =t k -t k - 1 =h is the pulse interval. And λ Ξ and λ k They are (Ξ+Ξ T ) and [(L+I m )b k -I m ] T [(L+I m )b k -I m ], l is the Lipschitz constant, I m Represents an m-order identity matrix, then the system can achieve group consistency according to the pulse control protocol.

[0062] A specific implementation of a multi-agent system with a directed fixed topology, such as Figure 1 As shown, there are 8 agents in the system, which are divided into two groups G1 and G2. Agents 1, 3, 4, and 5 belong to G1, and agents 2, 6, 7, and 8 belong to G2, and agents 1 and 2 are leaders.

[0063] If the elements of the adjacency matrix between all nodes are 1, then the adjacency matrix is ​​A; the Laplacian matrix is ​​L; that is:

[0064]

[0065]

[0066] Assume ξ = 1.01, the position state change of agent i is expressed as And φ(x i (t),t)=x i (t)sin(t 2 ), the known matrix Ξ=I m , we can calculate λ Ξ =1,λ k =5.8034. The initial state of the agent is x 1 (0) = 1, x 2 (0) = -2, x 3 (0) = 2, x4 (0) = -1, x 5 (0) = -1.5, x 6 (0) = 1.5, x 7 (0) = 3, x 8 (0) = -1.5.

[0067] Assume b k =-0.4, respectively for continuous control, pulse interval h 1 =0.001s,h 2 =0.002s is used for simulation to analyze the influence of pulse control on the system grouping consistency and the influence of different pulse intervals on the grouping consistency, that is, the influence on the convergence time of the system.

[0068] Depend on Figure 3 Figure (a), Figure (b) and Figure 4 From Figure (a) and Figure (b), we can see that the convergence time of pulse control is longer than that of continuous control. This is because continuous control controls the system continuously, while pulse control only controls the system at the pulse moment. Although this reduces the loss of the network and improves the robustness of the system, it also prolongs the convergence time of the system.

[0069] Depend on Figure 3 As shown in Figure (b) and Figure (c), the state error between the follower and the leader eventually approaches zero, indicating that group consistency is achieved, where δ 31 represents the position difference between follower 3 and leader 1. From these two figures, we can see that h 1 = 0.001s, the convergence time is about 0.015s, and h 2 = 0.002s, the convergence time difference is about 0.02s, from which we can conclude that: the larger the pulse interval, the fewer pulses in the same time, the longer the time for the state error to approach 0, and the longer the system convergence time. Similarly, Figure 4 As can be seen from Figure (b) and Figure (c), the state of the agent is finally consistent with the state of the leader. Combining the two figures, it can be concluded that the longer the pulse interval is, the longer the convergence time of the agent is.

[0070] Assume the pulse interval is h1 = 0.001s, and control the gain of different pulses respectively. Simulation is performed to analyze the effect of pulse control gain on the system convergence time.

[0071] Depend on Figure 5 It can be seen from Figure (a) and Figure (b) that when h is constant, b k The larger the value, the weaker the control over the system and the longer the final convergence time of the system. k The smaller it is, the shorter the convergence time of the system.

[0072] The system can achieve group consistency of the multi-agent system under the action of the pulse control protocol. When the pulse interval is larger, the number of pulses in the same time is smaller, and the system convergence time is longer. When the pulse gain is small, the control of the system is greater, and the system convergence time is shorter.

[0073] 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 multi-agent system group consistency control method based on impulse control, characterized in that: include: S1. Construct the topological structure of the multi-agent system; S2, grouping the agents in the system according to the topological structure; S3, design pulse control protocol; S4. At the pulse moment, each agent in the same group receives the location information of the neighboring agent, and processes the received location information through the pulse control protocol to obtain the weighted location result of the agent sending the information and the agent receiving the information; specifically including: 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: in, represents the position change of the following node i, φ(.) represents the nonlinear function, xi(t) represents the position state of the following node i at time t, Ξ represents the constant matrix, ui(t) represents the designed pulse control protocol, δ(t-tk) represents the unit impulse function at time tk, tk represents the pulse control time, bk represents the pulse gain, j represents the node j, N i represents the set of neighbor nodes of node i, a ij Indicates whether node i and node j have information interaction, x j (t) represents the position state of the following node j at time t, l ij represents the Laplace matrix element between node i and node j, represents the position state of the leader node σj at time t, represents the position state of the leader node σi at time t, δ(t) is the Dirac function, bk<0 is the pulse gain, tk is the pulse time, and the state of the dynamic leader of each group is σi=1,…,p; When t = tk, the change of the agent's position state at the pulse time is: in h is the pulse interval, Δxi(tk) represents the pulse time of agent i. tk Status changes; S5. Update the state of the agent receiving the information according to the weighted position to achieve group consistency; specifically including: like Then xi(t) is left continuous, that is The time series {tk} satisfies If the continuous nonlinear function φ: The Lipschitz condition |φ(x1)-φ(x2)|≤l|x1-x2| is satisfied. The graph G contains a directed spanning tree and there exists a constant ξ>1 satisfying the following conditions: Ta(λ Ξ +2l)+ln(λkξ)<0 Where, Ta = tk-tk-1 = h is the pulse interval, λ Ξ and λk are (Ξ+Ξ T )and [(L+Im)bk-Im] T The maximum eigenvalue of [(L+Im)bk-Im], l is the Lipschitz constant, Im represents an m-order unit matrix, and the system achieves group consistency according to the pulse control protocol.

2. According to the method of claim 1, the method is characterized in that: 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.

3. The method for controlling group consistency of a multi-agent system based on impulse control according to claim 2, characterized in that: Each node in the multi-agent system includes a leader node and a follower node; each leader node is connected to at least one follower node to form a group.

4. The method for controlling group consistency of a multi-agent system based on impulse control according to claim 3, characterized in that: The dynamic model of the leader node is: The dynamic model of the follower node is: in, represents the position change of the leader node σi, φ(.) represents a nonlinear function, represents the position state of the leader node σi at time t, Ξ represents the constant matrix, and p represents the number of leader nodes; represents the position change of the follower node i, xi(t) represents the position state of the follower node i at time t, m represents the number of agents in the system, and n represents the number of follower nodes.

5. The method for controlling group consistency of a multi-agent system based on impulse control according to claim 1, characterized in that: When the agent receives the location information of the neighboring agent, the pulse control protocol is used to control the agent to receive the location information sent by the neighboring agent at the pulse time.

6. The method for controlling group consistency of a multi-agent system based on impulse control according to claim 1, characterized in that: The process of processing the received location information through the pulse control protocol includes: receiving information from neighbor nodes at the pulse time, and updating its own location status in combination with the information of the neighbor nodes under the control of the control protocol.

7. The method for controlling group consistency of a multi-agent system based on impulse control according to claim 1, characterized in that: The conditions for the agents in the system to meet group consistency are: 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 leader node, m represents the number of agents in the system, and p represents the number of leader nodes.

Images