Speed-limited open multi-intelligent-system cooperative control method

Abstract

The invention discloses a speed-limited open multi-intelligent system cooperative control method, which comprises the following steps of: acquiring intelligent agent information, and constructing an undirected graph topological structure based on the intelligent agent information; based on the undirected graph topological structure, constructing an open multi-agent system model; based on the open multi-agent system model, introducing a Filter variable and an auxiliary variable depicting agent deletion, and constructing a control algorithm of the open multi-agent system; and an agent cooperative control condition is preset, and cooperative control of the open multi-agent system is realized when the control algorithm of the open multi-agent system meets the agent cooperative control condition. According to the method, the open multi-intelligent system model with the topological structure being the undirected graph is constructed, the adding and deleting conditions of the intelligent agents are considered, when the control method is designed, auxiliary variables are introduced, the influence of intelligent agent deleting on the system is eliminated, and therefore all the intelligent agents cooperatively complete a target task on the undirected graph.

Description

Technical Field

[0001] The present invention belongs to the field of intelligent control technology, and in particular relates to a speed-constrained open multi-intelligent system collaborative control method. Background Art

[0002] Due to the rapid development of mobile Internet, the advancement of sensor technology and the improvement of computing power, research on multi-agent systems has received widespread attention. A multi-agent system consists of multiple agents that interact with neighboring agents within their own perception range to jointly complete specific tasks. Generally, multi-agent systems have typical characteristics such as autonomy, intelligence, reliability and scalability. The application fields of multi-agent systems are wide, covering civil and military fields such as intelligent logistics, intelligent manufacturing, and national defense.

[0003] In practical applications, agents can usually be added or removed flexibly to cope with dynamic demands. For example, in a drone formation, as the search area expands or shrinks, the number of drones participating in the formation also increases or decreases. Similarly, in smart grids, smart devices constantly switch on and off, resulting in changes in the number of active devices. That is, the dimension of the system's state space changes over time. Generally, multi-agent systems with this characteristic are called open multi-agent systems, which poses a huge challenge to the analysis and control methods of traditional multi-agent systems. Most of the existing methods for studying the collaborative control of multi-agent systems assume that the number of agents is fixed, so they cannot be directly applied to open systems.

[0004] Most existing studies are based on first-order system modeling, ignoring the high-order, uncertain and incomplete characteristics of the system, which makes it impossible to accurately describe the dynamic characteristics of the system, thus seriously restricting the application of the above research results in engineering. Therefore, it is of theoretical and practical significance to conduct research on second-order open multi-agent systems. In addition, in practical applications, due to technical limitations and environmental disturbances, the speed of the agent is not easy to obtain.

[0005] Therefore, in view of the above problems in the prior art, it is urgent to propose a speed-constrained open multi-intelligent system collaborative control method. Summary of the invention

[0006] In order to solve the above technical problems, the present invention proposes a speed-constrained open multi-intelligent system collaborative control method, which overcomes the impact of agent deletion on the system and takes into account the situation where the agent is constrained by speed information, so as to solve the problems existing in the above-mentioned prior art.

[0007] To achieve the above object, the present invention provides a speed-constrained open multi-intelligence system collaborative control method, comprising the following steps:

[0008] Acquire agent information, and construct an undirected graph topology structure based on the agent information;

[0009] Based on the undirected graph topology structure, an open multi-agent system model is constructed;

[0010] Based on the open multi-agent system model, a filter variable for estimating speed information and an auxiliary variable for describing agent deletion are introduced to construct a control algorithm for the open multi-agent system;

[0011] The agent collaborative control condition is preset, and the control algorithm of the open multi-agent system realizes the collaborative control of the open multi-agent system when the agent collaborative control condition is met.

[0012] Optionally, the expression of the undirected graph topology is as follows:

[0013]

[0014] in, represents the agent index set, ε(k) represents the edge set, and A(k) represents the undirected graph The derived adjacency matrix.

[0015] Optionally, based on the undirected graph topology structure, the process of constructing an open multi-agent system model includes:

[0016] Under the undirected graph topology, a second-order discrete multi-agent system model is constructed based on the position state, speed state and control input of the agent; in the second-order discrete multi-agent system model, a Filter variable that estimates the speed information is introduced to update the control input of the agent, and an open multi-agent system model is constructed by considering the joining or leaving state of the agent.

[0017] Optionally, the expression of the open multi-agent system model is as follows:

[0018]

[0019] in, and They represent the initial position state and speed state of the i-th agent when it joins or activates the network, ξ i (k) and ζ i (k) are the current position and velocity states of the ith agent, respectively, and ζ i (m) represents the speed state of agent i at the mth moment, u i (k) is the control input of the ith agent, ω i (k),θ i (k) represents a Boolean variable.

[0020] Optionally, the state update expression of the Filter variable of the estimated speed information is as follows:

[0021]

[0022] in, represents the Filter state of the current i-th agent, u i (k) is the control input of the ith agent, ω i (k) is a Boolean variable and γ is a positive number.

[0023] Alternatively, the control algorithm of the open multi-agent system is expressed as follows:

[0024]

[0025] Among them, ξ ij (k) = ζ j (k)-ξ i (k) ξ j (k) and They represent the position state and Filter state of agent j at time k respectively. represents the set of neighboring agents of agent i, represents the set of remaining agents, represents the set of deleted agents, y ij (k) represents the auxiliary variable that describes the deletion of the agent, a ij (k) represents the weight of the information received by agent i from agent j, and α and β represent positive numbers.

[0026] Optionally, the state update expression that describes the auxiliary variables deleted by the agent is as follows:

[0027]

[0028] Among them, y ij (k) represents the auxiliary variable that depicts the deletion of the agent at time k, ω i (k),ω j (k) represents a Boolean variable.

[0029] Optionally, the expression of the agent cooperative control condition is as follows:

[0030]

[0031] in, represents the set of agents in the network at time k, and They represent the initial position state and speed state of the i-th agent when it joins or activates the network, ξ i (k) and ζ i (k) are the current position state and velocity state of the i-th agent respectively.

[0032] The present invention also provides a computer device, comprising a memory, a processor and a computer program stored in the memory, wherein the processor executes the computer program to implement the steps of the method.

[0033] The present invention also provides a computer-readable storage medium on which a computer program is stored. When the computer program is executed by a processor, the steps of the method are implemented.

[0034] Compared with the prior art, the present invention has the following advantages and technical effects:

[0035] The present invention constructs an undirected graph topology structure according to agent information, and establishes an open multi-agent system model based on the topology structure; presets the control method, filter variables and auxiliary variables of the open multi-agent system; based on the open multi-agent system model, the control method and the auxiliary variables, under the preset conditions, realizes the collaborative control of the open multi-agent system. The present invention constructs an open multi-agent system model with an undirected graph topology structure, takes into account the addition and deletion of agents, introduces auxiliary variables when designing the control method, eliminates the impact of agent deletion on the system, so that all agents can collaboratively complete the target task on the undirected graph. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] The drawings constituting a part of the present application are used to provide a further understanding of the present application. The illustrative embodiments and descriptions of the present application are used to explain the present application and do not constitute an improper limitation on the present application. In the drawings:

[0037] Figure 1 Schematic diagram of the undirected communication topology of an embodiment of the present invention; wherein (a) is the initial communication topology diagram, (b) is the communication topology diagram when UAV5 and UAV6 leave when k=100, and (c) is the communication topology diagram when UAV6 rejoins when k=200;

[0038] Figure 2 A UAV position trajectory diagram based on an undirected graph in the case of UAV joining and leaving according to an embodiment of the present invention;

[0039] Figure 3 A UAV velocity trajectory diagram based on an undirected graph in the case of UAV joining and leaving according to an embodiment of the present invention;

[0040] Figure 4A Filter variable trajectory diagram of a UAV based on an undirected graph when a UAV joins and leaves an embodiment of the present invention;

[0041] Figure 5 It is a UAV motion trajectory diagram based on an undirected graph when a UAV joins and leaves according to an embodiment of the present invention. DETAILED DESCRIPTION

[0042] It should be noted that, in the absence of conflict, the embodiments and features in the embodiments of the present application can be combined with each other. The present application will be described in detail below with reference to the accompanying drawings and in combination with the embodiments.

[0043] It should be noted that the steps shown in the flowcharts of the accompanying drawings can be executed in a computer system such as a set of computer executable instructions, and that, although a logical order is shown in the flowcharts, in some cases, the steps shown or described can be executed in an order different from that shown here.

[0044] Embodiment 1

[0045] This embodiment provides a speed-constrained open multi-intelligence system collaborative control method, including the following steps:

[0046] Acquire agent information, and construct an undirected graph topology structure based on the agent information;

[0047] Based on the undirected graph topology structure, an open multi-agent system model is constructed;

[0048] Based on the open multi-agent system model, a filter variable for estimating speed information and an auxiliary variable for describing agent deletion are introduced to construct a control algorithm for the open multi-agent system;

[0049] The agent collaborative control condition is preset, and the control algorithm of the open multi-agent system realizes the collaborative control of the open multi-agent system when the agent collaborative control condition is met.

[0050] As a specific implementable method, the present embodiment proposes a method for collaborative control of an open multi-agent system based on speed constraints. The technical solution adopted is to construct a speed-constrained open discrete second-order system on an undirected graph. When designing a distributed consensus protocol, a distributed filter and auxiliary variables that characterize agent deletion are added. First, the open system is modeled, and then a collaborative control algorithm for the system is proposed on this basis, and then the conditions for collaborative control of agents are studied. Finally, MATLAB simulation is used to verify the effectiveness of the proposed algorithm, which specifically includes the following steps:

[0051] Construct an undirected graph topology structure based on the agent information, and further establish an open multi-agent system model:

[0052] In this embodiment, the topological structure is established based on the agent information as an undirected graph. in represents the agent indicator set, is the edge set, A represents an undirected graph The adjacency matrix derived from this is an ordered pair (i, j)∈ε, where (i, j) indicates that agent j can directly receive information sent by agent i. In an undirected graph, agent i can also directly receive information sent by agent j. This embodiment uses a finite sequence (i, e 1 ),(e 1 ,e 2 ),…,(e l ,j) represents the graph There is a directed path between any agent i and j in the graph. If there is a directed path between any two different nodes in Here, this embodiment does not consider self-loops.

[0053] In this embodiment, it is assumed that the undirected graph At every k moment, it is connected, where and represents the number of agents activated at time k. Represents the neighbor set of agent i. It is a picture The multi-agent system model of obtains the adjacency matrix of the corresponding received information, where a ij (k) represents the weight of information received by agent i from agent j. Then a ij (k)>0; if Then a ij (k) = 0. represents the degree of agent i at time k. Then, for k, we have represents the set of remaining agents; Represents the set of newly added agents; Represents a collection of deleted agents; For simplicity, let

[0054] Furthermore, in this embodiment, establishing an open multi-intelligence system model whose topology is an undirected graph includes:

[0055] Construct the considered second-order discrete multi-agent system:

[0056]

[0057] Among them, ξ i(k) is the position state of the i-th agent, ζ i (k) is the speed state of the i-th agent, u i (k) is the control input of the i-th agent.

[0058]

[0059] Among them, the control gains α and β are positive numbers.

[0060] However, in actual engineering, due to the limitations of measurement equipment and sensor capabilities, it is difficult to obtain the speed information of the interactive agent. So that the system can achieve cooperative control. Therefore, the control input (2) can be rewritten as:

[0061]

[0062] Among them, the Filter variable The state update equation is:

[0063]

[0064] Among them, 0<γ<1.

[0065] Since agents can join and leave flexibly, we will consider building an open multi-agent system. and Respectively represent the initial position and speed of the agent. Similarly, this embodiment uses the Boolean variable θ i (k) and ω i (k) indicates whether the agent joins or stays in the network:

[0066]

[0067] Consider an open multi-agent system:

[0068]

[0069] This system shows that: when the agent θ i (k) = 1, then and When the intelligent ω i (k) = 1, and in represents the remaining set of agents, Represents the set of newly added agents.

[0070] Preset the control protocol, filter variables and auxiliary variables of the open multi-intelligent system;

[0071] Furthermore, in this embodiment, the following control algorithm based on the open multi-agent system is designed:

[0072] Formula (3) can be rewritten as:

[0073]

[0074] Among them, ξ ij (k) = ξ j (k)-ξ i (k)

[0075] Formula (4) Filter variable The update rule can be rewritten as:

[0076]

[0077] in, Auxiliary variables that characterize agent deletion, y ij The (k+1) update equation is

[0078]

[0079] like or Then y ij (k+1)=0.

[0080] Based on the open multi-agent system model and preset variables, the collaborative control of the open multi-agent system is realized under the preset conditions.

[0081] Furthermore, in this embodiment, the conditions for studying the coordinated control of intelligent agents include:

[0082] Theorem 1: If is an undirected graph, then consider the open multi-intelligence system (5) and the control protocol (6), the filter variable (7) and the auxiliary variable (8), for k ≥ 0, the following equation holds

[0083]

[0084]

[0085] Under the preset conditions, for k ≥ k * , there exists k * , so that If M(k * ) has a double eigenvalue of 1, and the other eigenvalues ​​are inside the unit circle, then the system can achieve cooperative control.

[0086] As an implementable method, the specific analysis process is mainly divided into two steps.

[0087] First, prove that (9b) holds. When k = 0, we can get Therefore, when k = 0, (9b) holds. Next, we prove that it also holds for k + 1. ω i (k) = 1. Therefore, in this embodiment, it can be obtained that:

[0088]

[0089] in, represents the last time the agent joined / activated before k+1.

[0090] By construction, all items and Therefore, for get:

[0091]

[0092] because and ij (k+1)=0, so (10) holds.

[0093] in accordance with This embodiment obtains:

[0094]

[0095] Then, by construction, this embodiment has Therefore (9b) holds.

[0096] Next, prove that (9a) holds. Obviously, when k = 0, (9a) holds. For k + 1 and i∈ You can get:

[0097]

[0098] In addition, for because and ij (k+1)=0, then we can get:

[0099]

[0100] in accordance with This embodiment obtains:

[0101]

[0102] Then, by using (9b), By construction, this embodiment has Therefore (9a) holds.

[0103] Theorem 2: If is an undirected graph, then consider the open multi-intelligence system (5) and control protocol (6), filter variables (7) and auxiliary variables (8), for k ≥ k * , there exists k * , so that like If there is a double eigenvalue of 1 and the other eigenvalues ​​are inside the unit circle, the system achieves cooperative control, that is, when k→+∞,

[0104] Specifically, we first introduce three lemmas:

[0105] Lemma 1: Consider an undirected graph with n nodes 1 n and are the right and left eigenvectors corresponding to the zero eigenvalue of the Laplacian matrix L, respectively.

[0106] Lemma 2: The Laplacian matrix L has an eigenvalue of weight s if and only if the matrix M has an eigenvalue of weight 1 of weight 2s and an eigenvalue of weight γ of weight s.

[0107] Specifically, considering the case of a fixed network, the system and control protocol are:

[0108]

[0109] Rewrite (11) as: Φ(k+1)=MΦ(k), where and Let λ be an eigenvalue of the matrix M, μ i is the eigenvalue of the Laplacian matrix L, then:

[0110]

[0111] Therefore, when μ i = 0 with s weight, equation (λ-1) 2 The roots of (λ-γ)=0 are λ=1 (multiplicity is 2s), λ=γ (multiplicity is s). The proof is complete.

[0112] Lemma 3: Consider an undirected graph with n nodes (11) The necessary and sufficient condition for achieving cooperative control is that M has a double eigenvalue of 1 and a single eigenvalue of γ (0<γ<1), and the remaining eigenvalues ​​are located inside the unit circle, that is, when k→+∞,

[0113] Specifically, this embodiment first proves the sufficiency: Note that 1 is the double eigenvalue of the matrix M, select For the right eigenvector and right generalized eigenvector of the matrix M corresponding to the 1 eigenvalue, choose are the left generalized eigenvector and left eigenvector of the matrix M corresponding to the 1 eigenvalue. According to Lemma 1, is the left eigenvector corresponding to the zero eigenvalue of the Laplacian matrix L, so let Therefore, there exists a non-singular matrix So that:

[0114]

[0115] Among them, 0 and 0 T Represents vector 0 respectively 3n-3 and is a Jordan block matrix, whose eigenvalues ​​are all within the unit circle. When k→+∞,

[0116]

[0117] Since 0<γ<1, all eigenvalues ​​of the matrix M except eigenvalue 1 are inside the unit circle, so and Therefore, when k→+∞,

[0118]

[0119] Prove the necessity again: Assume that the condition does not hold, that is, assume that the algebraic multiplicity of the eigenvalue 1 of M is greater than 2, or assume that there is an eigenvalue greater than 1. Assume that the algebraic multiplicity of the eigenvalue 1 of M is greater than 2, then The rank of is greater than 2. However, when k→+∞, and This shows that in order to achieve collaborative control, The rank of must be 2. This is consistent with the assumption The rank of is greater than 2, which is a contradiction, so we get the first contradiction. Suppose there is an eigenvalue greater than 1, then It does not exist. This contradicts the stability requirement of the system, so the second contradiction is obtained. The proof is complete.

[0120] Next, we will analyze Theorem 2 in detail:

[0121] because That is, when k ≥ k * When , no agent is deleted or added. At this time, ω i (k) = 1, therefore, and Based on this, formulas (5), (6) and (7) can be expressed as:

[0122]

[0123] Re-state (12) as: Φ(k+1)=M(k)Φ(k), where Without loss of generality, assume The number of the agents in the table corresponds to the previous Number. T (k) is decomposed into Φ T (k) = [Θ T (k) Σ T (k)], where Θ(k) is selected from the previous The relevant variables of the agents, Σ(k) selects the relevant variables of the remaining agents. This embodiment only considers the agent in In the case of

[0124]

[0125] in

[0126] By construction, 1 is the matrix The double eigenvalue of , and the remaining eigenvalues ​​are all inside the unit circle. According to Lemma 3, the system (13) realizes cooperative control, that is,

[0127] Numerical example:

[0128] Through MATLAB simulation, the validity of the theoretical research results is verified. Assuming that the number of UAVs at the beginning is n max =6, Figure 1 Shown is an undirected communication topology diagram. Figure 1 (a) shows the initial communication topology diagram, and the corresponding Laplacian matrix is:

[0129]

[0130] Set initial conditions and parameters α=0.1,β=0.25,γ=0.95. When k=100, UAV5 and 6 are deleted, and their related speed, position and filter information are removed. When k=200, UAV6 is re-added, and its initial information is set to So Figure 1 (b) and Figure 1 (c) The corresponding Laplacian matrices are:

[0131]

[0132] Figure 2-Figure 4 The figure shows the trajectory of UAV position, velocity, and filter variables based on an undirected graph when UAVs are added and deleted. Figure 5 The figure shows the UAV motion trajectory diagram based on the undirected graph when UAV is added and deleted. The topology diagram is shown in Figure 1 shown. Figure 2-Figure 5 It shows that despite the addition and removal of UAVs, the system still achieves cooperative control. Compared with the traditional speed-constrained multi-agent cooperative control, the cooperative performance is affected by the addition and removal of agents. Therefore, the proposed method extends the traditional cooperative control results to a certain extent.

[0133] Compared with traditional speed-constrained multi-agent systems, the algorithm design of this embodiment is more challenging, mainly in terms of how to characterize the deletion of agents. On an undirected graph, the results show that the sum of the positions of agent i is only related to its initial position, speed, and step size k. The sum of the speeds of agent i remains unchanged. Therefore, the derived theoretical results extend most of the existing work, and more importantly, the research methods of traditional speed-constrained systems cannot be directly applied to the current problem.

[0134] Therefore, the method proposed in this embodiment takes into account the situations of adding and deleting intelligent agents, which is more complex and challenging than the existing technologies.

[0135] Embodiment 2

[0136] This embodiment further provides a computer device, including a memory, a processor, and a computer program stored in the memory, wherein the processor executes the computer program to implement the steps of the method.

[0137] Embodiment 3

[0138] This embodiment also provides a computer-readable storage medium on which a computer program is stored. When the computer program is executed by a processor, the steps of the method are implemented.

[0139] The above are only preferred specific implementations of the present application, but the protection scope of the present application is not limited thereto. Any changes or substitutions that can be easily thought of by a person skilled in the art within the technical scope disclosed in the present application should be included in the protection scope of the present application. Therefore, the protection scope of the present application should be based on the protection scope of the claims.

Claims

1. A speed-constrained open multi-intelligence system collaborative control method, characterized in that: The following steps are involved: Acquire agent information, and construct an undirected graph topology structure based on the agent information; Based on the undirected graph topology structure, an open multi-agent system model is constructed; Based on the open multi-agent system model, a filter variable for estimating speed information and an auxiliary variable for describing agent deletion are introduced to construct a control algorithm for the open multi-agent system; The agent collaborative control condition is preset, and the control algorithm of the open multi-agent system realizes the collaborative control of the open multi-agent system when the agent collaborative control condition is met.

2. The method according to claim 1, characterized in that The expression of the undirected graph topology is as follows: in, represents the agent index set, ε(k) represents the edge set, and A(k) represents the undirected graph The derived adjacency matrix.

3. The method according to claim 1, characterized in that Based on the undirected graph topology, the process of constructing an open multi-agent system model includes: Under the undirected graph topology, a second-order discrete multi-agent system model is constructed based on the position state, speed state and control input of the agent; in the second-order discrete multi-agent system model, a Filter variable that estimates the speed information is introduced to update the control input of the agent, and an open multi-agent system model is constructed by considering the joining or leaving state of the agent.

4. The method according to claim 3, characterized in that The expression of the open multi-agent system model is as follows: in, and They represent the initial position state and speed state of the i-th agent when it joins or activates the network, ξ i (k) and ζ i (k) are the current position and velocity states of the ith agent, ζ i (m) represents the speed state of agent i at the mth moment, u i (k) is the control input of the ith agent, ω i (k),θ i (k) represents a Boolean variable.

5. The method according to claim 3, characterized in that: The state update expression of the Filter variable of the estimated speed information is as follows: in, represents the Filter state of the current i-th agent, u i (k) is the control input of the ith agent, ω i (k) is a Boolean variable and γ is a positive number.

6. The method according to claim 1, characterized in that The expression of the control algorithm of the open multi-agent system is as follows: Among them, ξ ij (k) = ξ j (k)-ξ i (k) ξ j (k) and They represent the position state and Filter state of agent j at time k respectively. represents the set of neighboring agents of agent i, represents the set of remaining agents, represents the set of deleted agents, y ij (k) represents the auxiliary variable that describes the deletion of the agent, a ij (k) represents the weight of the information received by agent i from agent j, and α and β represent positive numbers.

7. The method according to claim 6, characterized in that The state update expression that describes the auxiliary variables deleted by the agent is as follows: Among them, y ij (k) represents the auxiliary variable that depicts the deletion of the agent at time k, ω i (k),ω j (k) represents a Boolean variable.

8. The method according to claim 1, characterized in that The expression of the agent cooperative control condition is as follows: in, represents the set of agents in the network at time k, and They represent the initial position state and speed state of the i-th agent when it joins or activates the network, ξ i (k) and ζ i (k) are the current position state and velocity state of the i-th agent respectively.

9. A computer device comprising a memory, a processor and a computer program stored in the memory, characterized in that: The processor executes the computer program to implement the steps of the method according to any one of claims 1 to 8.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the method according to any one of claims 1 to 8 are implemented.

Images