Second-order multi-agent system topology identification method for unmeasurable condition of partial agents, computer system, readable storage medium and program product

Abstract

The invention belongs to the field of multi-agent system topology structure identification, and relates to a second-order multi-agent system topology identification method for unmeasurable conditions of partial agents, which comprises the following steps: step 1, according to whether the state of each agent in a multi-agent system is measurable or not, renumbering each agent, converting a system model at the same time, and determining whether the state of each agent in the multi-agent system is measurable or not; decoupling of the known topology and the unknown topology is achieved through matrix partitioning; 2, estimating the state of an unmeasurable agent according to a sampling signal of the state of the measurable agent by using the number obtained in the step 1 and a model conversion result; and step 3, based on the state estimation result of the unmeasurable agent in the step 2, constructing a measurement matrix and a sampling signal so as to solve the topological structure of the unmeasurable agent. Under the condition of long-term missing of partial agent states in a complex environment, the method can still accurately identify the unknown topological structure of the system, and shows good applicability and robustness.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of multi-agent system topology identification, and more particularly, relates to a second-order multi-agent system topology identification method for a partially observable agent, a computer system, a readable storage medium and a program product, which is suitable for topology structure identification of a multi-agent system satisfying a position-velocity second-order dynamic model. BACKGROUND

[0002] Swarm intelligence is one of the major strategic development directions. The New Generation Artificial Intelligence Development Plan clearly proposes eight basic theories, many of which directly point to the core of swarm intelligence. As a typical application, swarm autonomous unmanned systems are gradually demonstrating their potential in multiple fields, such as maritime search and rescue, marine environment monitoring, disaster emergency rescue, maritime traffic control and intelligent ocean engineering, etc. Among them, unmanned vehicle swarm is becoming an important direction to promote the development of intelligent ocean and smart traffic due to its ability to cover a large area, respond quickly and self-organize and cooperate.

[0003] From the perspective of system modeling, unmanned vehicle swarm can be abstracted as a second-order multi-agent system, whose dynamics state is described by position and velocity, and consistency and cooperative control are achieved through local neighbor interaction between individuals. Complex network theory provides a unified modeling framework for multi-agent systems: individuals correspond to nodes in the network, communication and cooperation correspond to edges in the network, and the topology structure formed thereby is not only the "skeleton" of swarm intelligence, but also the key to group situation awareness and autonomous decision-making. Topology structure directly determines the information propagation efficiency, resource allocation effect and collaborative operation capability of multi-agent systems. In the theory of consistency control and cooperative decision-making, topology structure is the basis for maintaining formation, changing formation and stabilizing swarm. At the same time, topology can also reflect the intention of the system. For example, in the anti-submarine task at sea, the encirclement intention of the enemy's unmanned underwater vehicle swarm is often exposed in advance through the modes of topology contraction, information aggregation and node dominance enhancement. Therefore, accurate identification and tracking of topology structure is of great significance to the situation awareness, cooperative control and adversarial game of unmanned vehicle swarm.

[0004] However, the complex and changeable marine environment brings great challenges to topology identification. Wind and waves and salt spray can cause random interruption of communication links, surges and sea fog blockage can cause sensor perception failure, and body failure can cause long-term absence of state information of part of the unmanned boat. Such situations correspond to the problem of unobservable nodes in second-order multi-agent systems, that is, there are unobservable nodes, and their neighbor interaction relationships are difficult to obtain directly. Once the topology relationship of these missing nodes cannot be quickly inferred, it may cause information islands and disintegration of the formation, seriously threatening the safety of the task. In this case, the topology relationship of unobservable nodes needs to be inferred using the information of observable nodes. Considering the limited storage and communication bandwidth of unmanned boats, a low-sampling and low-computing topology reconstruction scheme is urgently needed. Among many topology identification methods, the method based on compressed sensing can accurately reconstruct sparse topology structure with less sampling data, and is particularly suitable for topology identification of multi-agent systems. Therefore, studying the topology identification method of second-order multi-agent systems based on compressed sensing under the condition that part of the agents is unobservable not only promotes the cross-research of complex networks and multi-agent systems in theory, but also has important significance in practice to improve the autonomy, robustness and confrontation ability of unmanned boat clusters.

[0005] Reference [1] (Dai J, Huang K, Liu Y, et al. Global Reconstruction of Complex Network Topology via Structured Compressive Sensing[J]. IEEE Systems Journal, 2021, 15(2): 1959-1969) proposes a complex network global topology reconstruction method based on structured compressed sensing, which significantly reduces the dependence on large-scale sampling data and prior knowledge. However, this method requires all node states to be observable, and cannot handle the case where part of the agents is unobservable, so there are still application limitations in actual multi-agent systems.

[0006] Document [2] (Chen M, Zhang Y, Zhang Z, et al. Inferring network structure with unobservable nodes from time series data[J]. Chaos: An Interdisciplinary Journal of Nonlinear Science, 2022, 32(1): 013126) is based on deep learning and graph neural network framework, which jointly models observable and unobservable nodes and edges, and realizes the synchronous inference of network topology and missing node state through end-to-end training. However, this method requires a large amount of data, has high training cost, and lacks interpretability, so its scalability and robustness in real-world scenarios still need to be improved.

[0007] Document [3] (Xiufeng Zhang, Gang Wang, Tao Cai, Jian Sun. Network topology identification under the multi-agent agreement protocol[J]. Journal of the Franklin Institute, 2021, 358(13): 6759-6774) is based on graph theory and system identification theory, which classifies observable and unobservable agents, combines controllability and observability theory, and uses agent measurement data to identify system topology. However, this method requires relatively high information and is highly dependent on system controllability and observability, which has certain limitations in practical applications.

[0008] Current research on topology identification of multi-agent systems mainly uses Granger causality analysis, deep learning and other data-driven methods and graph theory methods. Among them, the graph theory-based method requires higher controllability and observability of the multi-agent system and needs more prior knowledge, which limits its application scenarios. In contrast, data-driven methods do not require accurate mathematical models and can effectively deal with nonlinear dynamics and complex interactions of the system, making them more flexible and widely applicable. However, Granger causality analysis and deep learning methods usually rely on a large number of high-frequency and high-precision state samples, and the cost of obtaining these data in practical applications is often high.

[0009] Generally, the existing methods commonly rely on the measurability of all agent states in the system, and have high requirements for the amount of data; and a few studies on unmeasurable agents usually rely on the system having strong controllability and observability, and need a large amount of prior knowledge support. In the face of the demand for resource-limited and real-time response in the multi-agent system, new topology identification methods are needed. SUMMARY

[0010] In view of the above defects or improvement needs of the prior art, the present application provides a second-order multi-agent system topology identification method for the case of partial agent unmeasurability, a computer system, a readable storage medium and a program product, which aims to solve the technical problem of the demand for resource-limited and real-time response in the multi-agent system.

[0011] To achieve the above-mentioned purpose, according to one aspect of the present application, a second-order multi-agent system topology identification method for the case of partial agent unmeasurability is provided, comprising the following steps: Step 1: Agent renumbering and model conversion According to whether the state of each agent in the multi-agent system is measurable, each agent is renumbered, and the system model is converted, and the decoupling of the known topology and the unknown topology is realized by matrix block; Step 2: State estimation of unmeasurable agents Using the numbering and model conversion result obtained in step 1, the state of the unmeasurable agent is estimated according to the sampling signal of the measurable agent state; Step 3: Topology identification of unmeasurable agents Based on the state estimation result of the unmeasurable agent in step 2, the measurement matrix and the sampling signal are constructed, so as to solve the topology structure of the unmeasurable agent.

[0012] Further, the step 1 comprises: Step 1.1: Traverse all agents, and renumber the agent whose state is measurable as , and number the agent whose state is unmeasurable as ; Step 1.2: Construct the position vector and the velocity vector of the agent system, and obtain the matrix representation of the dynamics of the entire system, as shown in formula (1): (1) Wherein, is the position vector of the system at k time, is the velocity vector of the system at k time, k+1 represents the next time of k, represents the sampling period, respectively represents the gain parameters of the position and the velocity, is an identity matrix, The Laplacian matrix of the topology graph of the agent system, which can be decoupled from the known topology and the unknown topology by matrix block according to formula (1); Step 1.3: decoupling the known topology and the unknown topology to obtain the dynamic matrix representation of the measurable agent and the unmeasurable agent respectively.

[0013] Further, the step 2 comprises: Step 2.1: transforming the dynamic matrix representation of the measurable agent to obtain the expression as shown in formula (2): (2) Wherein,

[0014]

[0015] represents the displacement state of the M measurable agents at the k moment, represents the speed state of the M measurable agents at the k moment, represents the displacement state of the N-M unmeasurable agents at the k moment, represents the speed state of the N-M unmeasurable agents at the k moment, respectively represent the sub-block composed of the first row and the first column in the unit matrix, and the sub-block composed of the first row and the to the column, and respectively represent the sub-block composed of the first row and the first column in the Laplacian matrix, and the sub-block composed of the first row and the to the column; Step 2.2: sub-sampling the state of the measurable agent, and solving the equation group (2) obtained in step 2.1 based on the least square method to obtain the estimated value of the position and speed of the unmeasurable agent Q and .

[0016] Further, the step 3 comprises: Step 3.1: obtaining the dynamic matrix representation of the unmeasurable agent from step 1, and replacing the real value with the state estimation value of the unmeasurable agent obtained in step 2 to obtain formula (3): (3) ​wherein, and denote the sub-blocks of the identity matrix consisting of the first to the first row and the first column, and the sub-blocks consisting of the first to the first row and the first to the first column, respectively, and denote the sub-blocks of the Laplacian matrix consisting of the first to the first row and the first column, and the sub-blocks consisting of the first to the first row and the first to the first column, respectively; Step 3.2: Transforming the formula (3) obtained in step 1 to obtain formula (4): (4) so as to convert the topology identification of the unobservable agent into solving wherein, , denotes the first row vector of the matrix ,

[0017] Step 3.3: Based on the formula (4) obtained in step 3.2, according to the state estimation of the unobservable agent obtained by Q times sampling and solving in step 2, the measurement matrix and the measurement signal are constructed:

[0018]

[0019] wherein, is the state estimation of the unobservable agent obtained by each sampling, is the signal obtained by each sampling; Step 3.4: Compressive sensing is used to obtain the estimated value of the signal .

[0020] Further, the step 3.4 comprises: (1) Calculating the unitization matrix :

[0021] wherein, denotes The p-th column vector, The measurement matrix is ​​normalized to obtain... ; (2) Estimating the signal sparsity; (a) Given a matrix for:

[0022] calculate All Sort in descending order, and arrange the corresponding indexes in the corresponding order. ; (b) Index in order Add to the set one by one ; (c) Inspection conditions Whether it is satisfied, among which Representation matrix The column index belongs to the current set The submatrix formed by the column vectors in the matrix, i.e. If satisfied, the set Number of elements in This is the estimated value of sparsity, and proceeds to (3); otherwise, continue with (b). (3) Recovery signal ; (a) Given a matrix for:

[0023] calculate All Sort in descending order, and then arrange the corresponding indexes in the corresponding order. Select the first from the index sequence Add an index to the collection ; (b) Initialize the residual signal as follows Solve the following equation using batch least squares:

[0024] in, Representation matrix The column index belongs to the set The submatrix formed by the column vectors in the matrix, i.e. , Indicates that closest The coefficient vector; Solving for the results an estimate of the signal ; then calculate if is less than a preset value, go to (d); otherwise, execute (c); (c) for the set , keep the indices corresponding to the largest values in , remove other indices; update the residual signal as ; then calculate

[0025] rank all in descending order, and rearrange the corresponding indices in the same order ; select the first indices from the index sequence, and add them to the set ; (d) obtain an estimate of the signal , denoted as , which is defined as follows: if , the component at the corresponding position in is 0; otherwise, the component at the corresponding position is equal to the component of at the corresponding index.

[0026] Further, the second-order multi-agent system satisfies the following conditions: Condition 1: the consensus control protocol of the second-order multi-agent system satisfies

[0027] where denote the position, velocity and control input of the i-th agent at time , respectively, denote the gain parameters of the position and velocity, respectively, and N is the total number of agents, , denote the connection relationship between node i and node j, if there is a connection , otherwise ; Condition 2: the number of unobservable agents M cannot be more than the number of observable agents, i.e. ; Condition 3: let agent be an unobservable agent, and let denote the interaction weight of agent to each observable agent; if agent If there is no interaction between an observable agent and a certain agent, the corresponding weight is recorded as 0; the considered interaction is directed or undirected, if directed, the direction should be from the unobservable agent to the observable agent; the weights are constructed into a vector:

[0028] The vector corresponding to all unobservable agents The matrix is column full rank.

[0029] According to another aspect of the present application, a computer system is provided, comprising a memory, a processor and a computer program stored on the memory, characterized in that the processor executes the computer program to implement the steps of the method for identifying the topology of a second-order multi-agent system according to any one of the preceding aspects.

[0030] According to another aspect of the present application, a computer readable storage medium is provided, having a computer program stored thereon, characterized in that the computer program, when executed by a processor, implements the steps of the method for identifying the topology of a second-order multi-agent system according to any one of the preceding aspects.

[0031] According to another aspect of the present application, a computer program product is provided, comprising a computer program, characterized in that the computer program, when executed by a processor, implements the steps of the method for identifying the topology of a second-order multi-agent system according to any one of the preceding aspects.

[0032] Overall, the above technical solutions conceived by the present application can achieve the following beneficial effects compared with the prior art: Firstly, compared with the prior art which mainly relies on graph theory and system theory, the present method effectively avoids strong dependence on prior conditions such as system controllability and observability, significantly reducing the demand for known information of system structure and parameters. Even in the case of long-term absence of part of the state of the agent in a complex environment, the present method can still accurately identify the unknown topology structure of the system, demonstrating good applicability and robustness.

[0033] Secondly, in view of the problem of limited sensor resources and limited communication bandwidth in actual scenarios, the present method introduces the theory of compressed sensing, which can still effectively reconstruct the topology relationship of unobservable agents under the condition of limited state sampling. This not only significantly reduces the cost of data acquisition and transmission, but also reduces the dependence on high-precision sensors, so that efficient and reliable topology identification can still be achieved under the condition of limited resources or incomplete information. BRIEF DESCRIPTION OF DRAWINGS

[0034] Figure 1 is the topology identification flowchart of unobservable agents in a second-order multi-agent system based on compressed sensing according to the preferred embodiment of the present application.

[0035] Figure 2 is the flow chart of the agent renumbering and model conversion algorithm proposed by the preferred embodiment of the present application.

[0036] Figure 3 is the flow chart of the state estimation of the unobservable agent proposed by the preferred embodiment of the present application.

[0037] Figure 4 is the flow chart of the topology identification of the unobservable agent proposed by the preferred embodiment of the present application.

[0038] Figure 5 is the structure diagram of the 10-agent system in the preferred embodiment of the present application, wherein 3, 5, 7, and 14 are unobservable agents, and the numbering here is the original numbering before the renumbering algorithm is executed. The state estimation and topology identification results shown later also use the original numbering.

[0039] Figure 6 is the evolution of the state of the observable agent over time in the preferred embodiment of the present application, wherein (a) is the evolution of the position of the observable agent over time, and (b) is the evolution of the speed of the observable agent over time.

[0040] Figure 7 is the state estimation result of the unobservable agent in the preferred embodiment of the present application, wherein (a) is the true value (blue) and the estimated value (red) of the position of the unobservable agent, and (b) is the true value (blue) and the estimated value (red) of the speed of the unobservable agent.

[0041] Figure 8 is the local topology identification result of the unobservable agent in the preferred embodiment of the present application, wherein only the unobservable nodes are shown. DETAILED DESCRIPTION

[0042] In order to make the purpose, technical scheme and advantages of the present application clearer, the present application will be further described in detail below in combination with the drawings and examples. It should be understood that the specific examples described herein are only used to explain the present application and do not limit the present application. In addition, the technical features involved in each embodiment of the present application described below can be combined with each other as long as they do not conflict with each other.

[0043] Among the many data-driven identification methods, the topology identification method based on compressed sensing can reconstruct the sparse topology structure with high precision under less sampling data, and its dependence on system prior knowledge is also lower than that of the graph-based method, so it is more advantageous in the case of limited information, and is particularly suitable for scenarios where the state of some agents is unobservable.

[0044] Figure terminology and symbol introduction: first introduce some basic terminology about network graph, the topology relationship between agents can be represented by a graph This indicates that the vertex set Represents each agent in a multi-agent system. And edge set Representing the topological relationships between agents If it is an undirected graph, then there are undirected edges. Information can be transferred between nodes at two vertices; these two nodes are called neighboring nodes. If it is a directed graph, edges... Indicates a line by point to A one-way edge, where i, j = 1 to n and i ≠ j. In the network, nodes... and Only one-way information transmission can occur, i.e., node Information can be transmitted to nodes Up, but node Information cannot be transmitted to the node . They represent Time of the first The position, velocity, and control input of each agent. Represents the identity matrix. The Laplacian matrix represents the topology of a multi-agent system.

[0045] To characterize the dynamic behavior of swarm intelligence in unmanned systems, this paper abstracts autonomous agent swarms such as unmanned surface vessels (USVs) into second-order multi-agent systems. Each agent possesses not only a position state but also a velocity state, both of which jointly determine its temporal evolution. Specifically, this invention targets systems containing n= In a second-order multi-agent system with *n* agents, let *n* agents be defined. The state of an agent is measurable, and its dynamic equations are described as follows:

[0046] in Indicates the first An intelligent agent in The position (displacement) state at any given moment. Indicates its speed state. This indicates its control input, reflecting the acceleration or manipulation commands of the intelligent agent under local interaction. represents the sampling period. This model can be used to describe the motion of an unmanned surface vehicle on a plane, and is also applicable to the motion process of other autonomous systems such as unmanned ground vehicles. The agents in the system usually do not rely on a central controller, but obtain neighbor information and adjust their own state through distributed local interaction, thereby emerging cluster intelligent behaviors such as formation keeping, formation transformation, and cooperative search at the global level. The dynamics of the second-order multi-agent system is not only a mathematical abstract model, but also an important characterization framework for the cluster intelligence of unmanned systems.

[0047] The use of the present application needs to meet the following conditions: 1. The consistency control protocol of the system satisfies:

[0048] wherein respectively represent the gain parameters of the position and the velocity, represents the connection weight between node i and node j.

[0049] 2. The number M of unobservable agents cannot be more than the number of observable agents, that is, ; 3. In the multi-agent system, let agent be an unobservable agent, which can have interaction relationship with several observable agents. The weight is used to represent the interaction weight of agent to each observable agent. If there is no interaction between agent and a certain observable agent, the corresponding weight is 0. The considered interaction can be directed or undirected, and if it is directed, the direction should be from the unobservable agent to the observable agent. These weights are constructed into a vector:

[0050] The vectors corresponding to all unobservable agents constitute a matrix, and the matrix is column full rank.

[0051] The research scheme of the unobservable agent topology identification method in the second-order multi-agent system based on compressed sensing proposed by the present application is as follows: Figure 1As shown, the algorithm comprises three sub-algorithms. First, Algorithm 1 renumbers the states of each agent in the multi-agent system based on their measurability, facilitating subsequent algorithm execution. Simultaneously, it transforms the system model, decoupling the known and unknown topologies through matrix partitioning. Then, in Algorithm 2, using the numbering and model transformation results obtained from Algorithm 1, the state of the unmeasurable agents is estimated based on the sampled signals of the measurable agent states. Finally, Algorithm 3 constructs a measurement matrix and sampled signals based on the state estimation results of the unmeasurable agents from Algorithm 2, thereby solving for the topological structure of the unmeasurable agents. The main innovative aspects of this invention will be described in detail below: Step 1: Agent Numbering and Model Conversion A by In a multi-agent system consisting of several agents, it is assumed that there exists The state of each agent can be measured. The state of each agent is unmeasurable. To facilitate subsequent topological identification of these unmeasurable agents, it is necessary to... Each agent is renumbered. Specifically, the measurable agents are renumbered. The agent numbers are as follows: Let the numbers of the unmeasurable intelligent agents be respectively .

[0052] Define the system position vector:

[0053] Velocity vector:

[0054] The transformed model expression is obtained as follows: (1) in It is the identity matrix. Let be the Laplacian matrix of the topology of the intelligent agent system. Equation (1) can decouple the known topology from the unknown topology by dividing the matrix into blocks.

[0055] Step 2: State estimation of unmeasurable agents For the model obtained in step 1, consider the state-measurable frontier. An intelligent agent can obtain:

[0056] After deformation, we get: (2) in,

[0057]

[0058] Here, and denote the sub-blocks of the identity matrix consisting of the first columns and the first rows, respectively, and the sub-blocks consisting of the first columns and the th to th rows, respectively. Similarly, and denote the sub-blocks of the Laplacian matrix consisting of the first columns and the first rows, respectively, and the sub-blocks consisting of the first columns and the th to th rows, respectively.

[0059] Since the topology of the first agents and the connection pattern from the unobservable agent to the observable agents are known, the state estimation of the unobservable agent is obtained by solving (2) based on the least square method.

[0060] Step 3: Topology identification of the unobservable agent (3) where and denote the estimation of the position and velocity of the unobservable agent, respectively. and denote the sub-blocks of the identity matrix consisting of the first columns and the first rows, respectively, and the sub-blocks consisting of the first columns and the th to th rows, respectively. Similarly, and denote the sub-blocks of the Laplacian matrix consisting of the first columns and the first rows, respectively, and the sub-blocks consisting of the first columns and the th to th rows, respectively. Further transformation yields (4) where

[0061] ​​​​Therefore, topology recognition of unmeasurable intelligent agents is transformed into the following problem:

[0062] (5) in Representation matrix The row vectors. Equation (5) can be decomposed into: There are several subproblems, each of which can be represented as: (6) in , is the sparse signal to be solved, which contains topological information of the unmeasurable part of the network. , Representing vectors The Each component. The topology of the unmeasurable agent can be obtained by solving the problem shown in equation (6). In practice, the state of the measurable agent is... Q After sampling and executing Algorithm 2, the matrix can be obtained. Called a measurement matrix, vector This is called a measurement signal.

[0063] Furthermore, the proposed topology identification method for unmeasurable agents in a second-order multi-agent system based on compressed sensing first renumbers the multi-agent system and transforms the model to decouple known and unknown topologies. Then, based on the decoupled measurable agent state information, the state information of unmeasurable agents is estimated. Finally, based on the state estimation results of unmeasurable agents, a measurement matrix and measurement signals are constructed to identify the unknown topology of the unmeasurable agents. The specific implementation steps of these three algorithms are as follows: Step 1: Agent renumbering and model transformation Step 1.1: Traverse all agents and renumber the agents whose states are measurable. The agent whose state is unpredictable is numbered as .

[0064] Step 1.2: Construct the position vector and velocity vector of the intelligent agent system to obtain the matrix representation of the dynamics of the entire system, as shown in Equation (1).

[0065] Step 1.3: Decouple the known topology from the unknown topology to obtain the dynamic matrix representations of the measurable and unmeasurable intelligent agents, respectively.

[0066] Step 2: State estimation of unmeasurable agents Step 2.1: Transform the dynamic matrix representation of the measurable intelligent agent to obtain the expression shown in equation (2).

[0067] Step 2.2: Sample the state of the measurable agent Q times, and solve the system of equations (2) obtained in Step 1 using the least squares method to obtain the state estimate of the unmeasurable agent. and .

[0068] Step 3: Topology recognition of unmeasurable intelligent agents Step 3.1: Obtain the dynamic matrix representation of the unmeasurable agent from Algorithm 1, and replace the true value with the state estimate of the unmeasurable agent obtained from Algorithm 2 to obtain Equation (3).

[0069] Step 3.2: Transform equation (3) obtained in step 1 to obtain equation (4).

[0070] Step 3.3: Based on the result equation (4) obtained in Step 2, construct the measurement matrix according to the state estimate of the unmeasurable agent obtained by Q sampling and solving in Algorithm 2. and measurement signals .

[0071] Step 3.4: Compressed Sensing Solution (1) Calculate the normalized matrix: in Representation matrix The p Column vectors. The measurement matrix is ​​normalized to obtain... ; (2) Estimating the signal Sparsity.

[0072] (a) Given a matrix for:

[0073] calculate All Sort in descending order, and arrange the corresponding indexes in the corresponding order. . (b) Index in order Add to the set one by one . (c) Inspection conditions Does it satisfy the condition? If it does, the set... The number of elements in (denoted as) () is the estimated value of sparsity, and proceed to (3); otherwise, continue to (b).

[0074] (3): Recovery signal . (a) Given matrix is:

[0075] Compute Sort all in descending order and rearrange the corresponding indices in the same order . Select the first indices from the index sequence and add them to the set . (b) Initialize the residual signal as . Solve for

[0076] Get the estimate of , denoted as . Then compute If is small enough, go to (d); otherwise, perform (c).

[0077] (c) For the set , keep the indices corresponding to the largest values in and remove the other indices. Update the residual signal as . Then compute

[0078] Sort all in descending order and rearrange the corresponding indices in the same order . Select the first indices from the index sequence and add them to the set .

[0079] (d) Get the estimate of the signal , denoted as , which is defined as follows: if , the component at the corresponding position in is 0; otherwise, the component at the corresponding position is equal to the component of at the corresponding index.

[0080] It is readily understood by those skilled in the art that the above description is only preferred embodiments of the present application, and is not intended to limit the present application, and any modification, equivalent replacement and improvement made within the spirit and principle of the present application shall be included in the protection scope of the present application.

Claims

1. A second-order multi-agent system topology identification method for partially intelligent agent unobservable conditions, characterized by, The method comprises the following steps: Step 1: intelligent agent renumbering and model conversion According to whether the state of each intelligent agent in the multi-intelligent agent system is measurable, each intelligent agent is renumbered, and the system model is converted, and the decoupling of the known topology and the unknown topology is realized through matrix block; Step 2: state estimation of unmeasurable intelligent agents Using the numbering and model conversion results obtained in step 1, the state of the unmeasurable intelligent agents is estimated according to the sampling signals of the measurable intelligent agent states; Step 3: topology identification of unmeasurable intelligent agents Based on the state estimation results of the unmeasurable intelligent agents in step 2, the measurement matrix and the sampling signal are constructed, so as to solve the topology structure of the unmeasurable intelligent agents.

2. The method of claim 1, wherein, The step 1 comprises: Step 1.1: Traverse all agents, renumber the agents with state measurable to , and the agents with state unmeasurable to ; Step 1.2: constructing the position vector and the velocity vector of the intelligent agent system, and obtaining the matrix representation of the dynamics of the entire system, as shown in formula (1): （1） wherein, is the position vector of the system at time k, is the velocity vector of the system at time k, k+1 denotes the next time of k, denotes the sampling period, denote the gain parameters for position and velocity, respectively, is the identity matrix, is the Laplacian matrix of the agent system topology graph, which can be decoupled from the known topology and the unknown topology by matrix block in equation (1); Step 1.3: decoupling the known topology and the unknown topology, and obtaining the dynamic matrix representation of the measurable intelligent agents and the unmeasurable intelligent agents respectively.

3. The method of claim 2, wherein, The step 2 comprises: Step 2.1: deforming the dynamic matrix representation of the measurable intelligent agents, and obtaining the expression as shown in formula (2): （2） Wherein, Let k represent the displacement state of M measurable agents at time k. This represents the velocity state of M measurable agents at time k. Let k represent the displacement state of NM unmeasurable agents at time k. This represents the velocity state of NM unmeasurable agents at time k. They respectively represent the units in the identity matrix that are formed by the previous... Go forward Sub-blocks composed of columns, and sub-blocks composed of the previous columns. Line and number To the Sub-blocks composed of columns and These represent the components of the Laplacian matrix, from the previous... Go forward Sub-blocks composed of columns, and sub-blocks composed of the previous columns. Line and number To the Sub-blocks composed of columns; Step 2.2: Subsample the states of the observable agents and solve the system of equations (2) obtained in step 2.1 based on least squares to obtain estimates of the position and velocity of the unobservable agent Q and .​ 4. The method of claim 3, wherein, The step 3 comprises: Step 3.1: obtaining the dynamic matrix representation of the unmeasurable intelligent agents from step 1, and replacing the real value with the state estimation value of the unmeasurable intelligent agents obtained in step 2, to obtain formula (3): （3） wherein, and denote sub-blocks of the identity matrix consisting of rows to and preceding columns and to and columns to respectively, and denote sub-blocks of the Laplacian matrix consisting of rows to and preceding columns and to and columns to respectively; Step 3.2: converting formula (3) obtained in step 1 to obtain formula (4): （4） This transforms topology recognition of unmeasurable intelligent agents into solving... ,in, , Representation matrix The row vectors. Step 3.3: Based on the obtained formula (4) in step 3.2, the measurement matrix H is constructed according to the Q times sampling and the state estimation of the unobservable agent obtained in step 2 and the measurement signal : wherein is the state estimate of the unobservable agent obtained at each sample, is the signal obtained at each sample; Step 3.4: Compressive sensing to solve for the estimate of the signal .​ 5. The method of claim 4, wherein, The step 3.4 comprises: (1) Computing the unitization matrix : wherein denotes the p-th column vector of ; unitizing the measurement matrix to obtain ; (2) estimating sparsity of the signal ​ (a) Given matrix For: Computing All In descending order, and in the corresponding order of the corresponding index ; (b) sequentially indexing adding to the set one at a time ; (c) Check condition is satisfied, where denotes the matrix whose column indices belong to the current set , i.e. ; if it is satisfied, the number of elements in the set is the estimate of the sparsity and go to (3); otherwise continue with (b);​ (3) Restoring signal ; (a) a given matrix is: Computing , all are arranged in descending order, and the corresponding indexes are arranged in the corresponding order ; select the first indexes from the index sequence and add them to the set ; (b) initializing the residual signal as ; solving the following equation using batch least squares method: where denotes the matrix whose column indices belong to the set consists of the column vectors of , denotes the coefficient vector that minimizes the distance to Solving for the estimate of , denoted by ; then compute If is less than a preset value, go to (d); otherwise, perform (c); (c) For the set , keep the indices corresponding to the largest values of , remove the other indices; update the residual signal to ; then compute Sort all Sort in descending order and rearrange the corresponding indices in the same order Select the first indices from the sequence of indices and add them to the set ; (d) obtaining an estimate of the signal defined as: the component at the corresponding position in is 0; otherwise, the component at the corresponding position is equal to the component at the corresponding index.​​ 6. The method of claim 1, wherein, The second-order multi-intelligent agent system satisfies the following conditions: Condition 1: the consensus control protocol of the second-order multi-intelligent agent system satisfies: wherein, respectively represent the position, velocity and control input of the i-th agent at time t, respectively represent the position and velocity gain parameters, and N is the total number of agents, , represents the connection relationship between node i and node j, if there is a connection , otherwise ;​ Condition 2, the number of unobservable agents M cannot be more than the number of observable agents, i.e. ; Condition 3, let the agent be intelligent For an unobservable agent, let the weights represent the agent For each observable agent, the interaction weight; if there is no interaction between the agent and the observable agent, the corresponding weight is 0; the interaction considered is directed or undirected, if directed, the direction should be from the unobservable agent to the observable agent; these weights are constructed into a vector: all the unobservable agents correspond to vectors constitute a matrix which is full rank in columns.

7. A computer system comprising a memory, a processor and a computer program stored on the memory, characterized in that The processor executes the computer program to realize the steps of the topology identification method of the second-order multi-intelligent agent system according to any one of claims 1-6.

8. A computer-readable storage medium having stored thereon a computer program, characterized in that, The computer program is executed by the processor to realize the steps of the topology identification method of the second-order multi-intelligent agent system according to any one of claims 1-6.

9. A computer program product comprising a computer program, characterized in that, The computer program is executed by the processor to realize the steps of the topology identification method of the second-order multi-intelligent agent system according to any one of claims 1-6.

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