A multi-agent system security clustering consensus control method, system and device

Abstract

This invention discloses a secure clustering consensus control method, system, and device for multi-agent systems. The method includes: constructing a clustering network and dynamic model of the multi-agent system based on external disturbance factors; obtaining the communication topology between agents based on the clustering network; constructing an adaptive event-triggered strategy with memory characteristics on the clustering network to transform the system clustering consensus problem into a convergence analysis problem of the error system; then obtaining sufficient conditions for the distributed controller to satisfy anti-interference performance and mean square exponential stability through the Lyapunov-Krasovskii functional; finally decoupling nonlinear factors to obtain the LMI condition; and solving for the controller gain and specified relevant parameters to achieve secure clustering consensus control of the multi-agent system under conditions of limited communication resources and deception attacks. This invention can ensure the achievement of clustering consensus and safe and stable operation of the multi-agent system under deception attacks and perturbed network communication.

Description

Technical Field

[0001] This invention relates to the field of cooperative control technology for multi-agent systems, specifically to a method, system, and device for secure clustering and consistent control of multi-agent systems based on an adaptive memory event triggering strategy. Background Technology

[0002] With the large-scale application of complex multi-agent systems such as smart grids, drone swarms, multi-robot collaboration, and smart logistics, the consistency control problem, as a core issue in the field of multi-agent system collaborative control technology, has received widespread attention.

[0003] Traditional consistency control typically focuses on achieving global consistency, requiring all agents to converge to the same state. This approach is greatly limited in real-world collaborative scenarios that require partitioning clusters for parallel task operations, such as disaster search and rescue and intelligent logistics. In contrast, clustering consistency frameworks allow agent systems to dynamically partition or reorganize clusters according to task requirements. This enables agent systems to flexibly adapt to changing tasks and environments, greatly enhancing the scalability and task adaptability of agent systems.

[0004] Driven by the development of cyber-physical technologies, the network environment is increasingly characterized by openness, heterogeneity, and dynamism, while also facing more prominent network security threats. Common network intrusions, such as spoofing attacks, damage the accuracy and consistency of system states by altering transmitted data or injecting erroneous information into communication channels, leading to communication delays, data tampering, and even system crashes. These attacks are highly destructive and covert. When applied to agent systems within a clustering consensus framework, due to hardware limitations and limited network bandwidth, communication resources between agents are restricted. Existing traditional periodic control strategies may lead to wasted communication resources or insufficient control precision. Therefore, under spoofing attacks, how to combine communication resource efficiency with cluster coordinated control and maintain the stability of complex dynamic systems remains a crucial problem that urgently needs to be solved.

[0005] Therefore, this application proposes a clustering consensus control method for the security of multi-agent systems to solve the above-mentioned technical problems. Summary of the Invention

[0006] The main objective of this invention is to provide a secure clustering consensus control method for multi-agent systems. This method utilizes an adaptive dynamic event-triggered strategy with memory characteristics for communication between agents, and uses the historical state of the multi-agent system as the basis for determining whether to transmit data. It also incorporates a distributed system based on locally stored memory data. The controller ensures the achievement of clustering consensus and safe and stable operation of multi-agent systems under deception attacks and perturbed network communication. Its adaptive event triggering mechanism with memory function can reduce network communication load, improve system operating efficiency, and reduce communication resource consumption. At the same time, it can adaptively detect and suppress the impact of deception attacks on the system, ensuring the security and stability of the system when false data is injected by deception attacks, and ultimately solving the technical problems proposed in the background.

[0007] The present invention solves the above-mentioned technical problems by adopting the following technical solutions: A secure clustering consensus control method for multi-agent systems, comprising the following steps executed via computer equipment: Step S1. Based on external disturbance factors, construct a multi-agent system clustering network consisting of N follower agents and M cluster leader agents, and simultaneously construct a dynamic mathematical model of the multi-agent system; Step S2. Obtain the communication topology matrix between agents based on the multi-agent system clustering network to ensure that the graph topology of each cluster contains a directed spanning tree and satisfies the in-degree balance condition; Step S3. Considering the insecure network communication environment that may suffer from network communication latency and spoofing attacks, an adaptive event-triggered strategy with memory characteristics is constructed on the multi-agent system clustering network based on a dynamic mathematical model. A Bernoulli probability model is used to model randomly occurring spoofing attacks. The system clustering consistency problem is transformed into a convergence analysis problem of the error system by utilizing the state following error between the follower agent and the corresponding cluster leader agent. Then, through appropriate Lyapunov-Krasovskii functionals and by decoupling nonlinear factors using congruence transformation and mathematical scaling, the distributed controller satisfies... The sufficient conditions for LMI in terms of anti-interference performance and mean square exponential stability can be solved in computer software. Step S4. Based on the conditions in steps S1-S3, solve the LMI conditions to obtain the controller gain. And related parameters (based on the communication topology matrix between agents and LMI conditions, to solve for the controller gain) (and corresponding specified parameters), through the designed distributed controller, to achieve secure clustering consensus control of multi-agent systems in a specified environment with limited communication resources and spoofing attacks.

[0008] Preferably, the dynamic mathematical model of the multi-agent system in step S1 includes: The dynamics model of a linear system with N follower agents is defined as follows:

[0009] in, It is the state of follower agent i at time t. It is the state derivative of follower agent i at time t after the update, representing the dynamic state change of follower agent i. It is the output signal of the follower agent i at time t. It is the control input of the follower agent i at time t. It is the bounded disturbance input of the follower agent i at time t. It is a constant system matrix; A linear system dynamics model with M clusters corresponding to leader agents is defined as follows:

[0010] in They represent the first time at time t. The state and output signals of a leader agent It is the updated time t at the th moment. The state derivative of the leader agent represents the state derivative of the first leader agent. Dynamic changes in the state of the leader agent.

[0011] Preferably, step S1 further includes constructing a deception attack signal. Let represent the deceptive attack signal injected by attack follower agent i into the s-th historical time packet stored in its distributed controller at time t. Due to system hardware limitations and network security protocols, the deceptive attack signal generally has limited energy and the attack will not occur continuously. Assume the deceptive attack signal is:

[0012] Let this be an attack constant coefficient, at which point there exists Let be the following error between follower agent i and its leader agent at time t.

[0013] Preferably, the topological constraint verification and partitioning process in step S2 of obtaining the inter-agent communication topology matrix in the multi-agent system clustering network includes: Step S21. Define the clustering network topology and the cluster Laplacian matrix: Constructing a weighted directed graph of the network topology among agents in a multi-agent system clustering network. ,in It is a collection of multiple intelligent agents. It is an edge set. Represents the adjacency matrix associated with this directed graph, where the matrix elements are... The communication coupling weights between follower agent i and neighbor agent j are used to construct the graph. The relevant Laplacian matrix is , where matrix elements and ; Divide all agents into M clusters, forming M subgroups, and construct a set of diagonal matrices. This describes the communication between follower agents and leader agents. If follower agent i can receive information from the leader agent, then... ,otherwise The clustering Laplacian matrix for M clusters is defined as follows:

[0014] in, Is a sub-cluster Related subgraphs It represents a subgraph Sub-Laplacian matrix for intra-cluster communication; It is a descriptor graph arrive The sub-Laplacian matrix for inter-cluster communication; At this point, the communication topology matrix of the multi-agent system clustering network is obtained. ; Based on the clustering clusters and matrices defined by the intelligent agent system, Decomposition yields a diagonal matrix sum matrix , It is the Laplacian matrix within M clusters. It is the Laplacian matrix among M clusters; Finally, the communication topology matrix between agents within the same cluster is obtained. And the communication topology matrix between agents in different clusters ; Where the matrix Both are used to model the communication topology between agents in clustered networks, facilitating subsequent calculation of controller gain. And specify the relevant parameters; Step S22. Verify that the cluster graph topology contains a directed spanning tree condition: Verification image Does the pathway include at least one set of leader agents? A directed spanning tree is defined as a condition where the root node can reach all its follower nodes within the cluster. If this condition is not met, the cluster's communication topology is reconstructed. With the associated Laplacian matrix, a new ; Step S23. Verify that the cluster graph topology satisfies the in-degree balance condition: For a matrix whose row sum is zero Verification image Check if the graph topology satisfies the in-degree balance condition, such that the sum of the communication coupling weights between agents across the cluster is zero. If the verification fails, reconstruct the cluster's communication topology graph. With the associated Laplacian matrix, a new ; In step S2 above, the topology is not required to be strongly connected; it is only required that each cluster graph topology contains a spanning tree and satisfies the in-degree balance condition. Furthermore, it requires that the state information of neighboring agents be available, but does not require that the state information of the entire multi-agent system be available.

[0015] The verified topology described above is used for subsequent error system construction and controller design.

[0016] Preferably, the specific operation process of step S3 includes: Step S31. Construct an adaptive memory event triggering mechanism based on historical triggering information to store triggering data at historical moments, and introduce a memory weight coefficient to comprehensively measure whether the system sampling data packet is transmitted to the local distributed controller; Step S32. Construct a locally distributed system with memory characteristics based on a dynamic mathematical model. The deception attack model for the controller and Bernoulli model is as follows:

[0017] in, Represents the latest sampling time of the sensor. represent At any given moment, the follower agent i belongs to the leader agent of its cluster. The state; Represents the follower agent i and the set of neighbors. The communication coupling weights between agents j in the middle. Represents follower agent i and the leader agent of its cluster. Communication coupling weights between them; The sequence of historical trigger moments considered by the memory event triggering mechanism can be represented by a maximum number of historical trigger moments. indivual; It is the memory weight coefficient of the historical trigger time s, used to measure the proportion and weight of the memory data. It is the gain matrix of the memory controller to be designed; This represents the physical sampling time interval of the sensor. Let k represent the s-th historical trigger moment of follower agent i, and k be the trigger number of follower agent i. yes The current storage of the follower intelligent agent i The measurement error calculated from the current state data and the latest sampled state data from the sensor; It is the follower agent i that was deceived during transmission and injected into the storage. Constantly memorize attack data within the data set; Using Bernoulli's model Describe whether follower agent i is subjected to a deception attack at time t. When it indicates that the follower agent i has not been deceived, When the follower agent i is deceived, its expected value is: , Let be the probability of a deception attack occurring, with variance . , Represents the square root of the variance; Step S33. Define the state following error between follower agent i and its leader agent. And consider the maximum network communication latency for controller data transmission. Constructing a following error system ; Step S34. Based on Lyapunov-Krasovskii functionals It is broken down into various sub-functions. Defined as:

[0018]

[0019]

[0020] ; Define weak infinitesimal operators Combined with the following error system The output of the adaptive memory event triggering mechanism is used to obtain the distributed controller's desired response. A set of sufficient condition matrices for solving the anti-interference performance and mean square exponential stability are given, and the specified conditions are finally derived as follows: Based on the proposed control protocol and memory event triggering mechanism, for a given positive real number... and the probability of deception attack The square root of the variance Memory weight coefficient The obtained clustering topology matrix There exists a positive definite real matrix of weights for the event triggering mechanism that needs to be solved. real matrix Control gain matrix and the parameter diagonal matrix Therefore, a condition matrix is ​​set. and The following relationship must be satisfied for the system to achieve mean square exponential convergence and stability while also satisfying the performance metric: of Anti-interference performance:

[0021] Among the symbols Submatrix transpose; symbol Represents the symmetric element in a matrix; symbol Represents the Kronecker product operation; Representing zero matrices and identity matrices of appropriate dimensions; Represents an identity matrix of dimension N; Each submatrix The definition is as follows:

[0022]

[0023]

[0024] in:

[0025]

[0026]

[0027] in, This represents the maximum delay. Positive parameters related to the event triggering mechanism are set; For deception attacks, constant coefficients are used. To measure Performance indicators of anti-interference performance.

[0028] Step S35. Perform linear decoupling processing on the derived condition matrix to finally obtain the LMI conditions that can be solved in computer software. These conditions are used in step S4 to solve for the controller gain. The specific calculation process includes: Based on the proposed control protocol and memory event triggering mechanism, for a given positive real number... and the probability of deception attack The square root of the variance Memory weight coefficient The obtained clustering topology matrix There exists a positive definite real matrix of weights for the event triggering mechanism that needs to be solved. Lyapunov functional parameter positive definite real matrix real matrix Control gain matrix and the parameter diagonal matrix Therefore, a condition matrix that can be solved by a computer is set. and The following relationship must be satisfied to obtain a solution that enables the system to achieve mean square exponential convergence and stability while satisfying the performance index: of Relevant control parameters for anti-interference performance:

[0029] Among the symbols Submatrix transpose; symbol Represents the symmetric element in a matrix; symbol Represents the Kronecker product operation of matrices; Representing zero matrices and identity matrices of appropriate dimensions; Represents an identity matrix of dimension N; Each parameter submatrix The form is as follows:

[0030]

[0031]

[0032] in,

[0033]

[0034] The above parameter submatrix Matrix factors in and parameter submatrix Matrix factors in The condition is derived from the negative definite condition of the Lyapunov functional and satisfies The performance is a mean square exponentially convergent and stable parameter matrix. This represents the maximum delay. Positive parameters related to the event triggering mechanism are set; For deception attacks, constant coefficients are used. To measure Performance indicators of anti-interference performance.

[0035] Preferably, the adaptive memory event triggering mechanism in step S31 is defined as follows:

[0036] The output of this triggering mechanism is used for the stability derivation in step S34 and the parameter solution in step S4. Among them, symbols It is the next triggering moment when the follower agent i meets the triggering condition. It is the latest triggering time of follower agent i, and k is the triggering number of follower agent i. It is the event-triggered auxiliary function of the follower agent i at time t. and These are the event triggering condition function and adaptive triggering threshold of the follower agent i at time t, respectively:

[0037] in, It is the derivative of the adaptive trigger threshold of follower agent i at time t after the update, representing the dynamic change of the trigger threshold. The initial value of the trigger threshold is... ; It is a weighted real matrix. Given a positive real number, For a given follower agent i, trigger relevant positive parameters for the event. yes Measurement error of follower agent i at time step The transpose form, and They are At time i, the error function of the neighbor within the cluster of the follower agent i Inter-cluster neighbor error function The transpose of; Intra-cluster error function Inter-cluster error function The specific form is as follows:

[0038] Preferably, given the initial conditions in step S34, the final derivation process is as follows: When external disturbances When given a positive real number For Lyapunov functionals satisfy: ; Define symbols Let P and P represent the largest and smallest eigenvalues ​​of the parameter matrix P in the Lyapunov functional, respectively, with symbols... Let the largest eigenvalues ​​of the parameter matrices Q and R in the Lyapunov functional be represented, and the scaling condition be obtained:

[0039]

[0040] Constructing convergence rate parameters Norm parameter of error with respect to the initial time ,exist and The specific form is:

[0041] in, For functionals The mathematical expectation, For tracking error system The expected value of the error norm. For maximum delay, The initial value of the event triggering threshold for follower agent i; In conclusion, we finally arrive at: It satisfies the mean square exponent stability.

[0042] Preferably, in step S34, under zero initial conditions... The final derivation process is as follows: When external disturbances When, given Anti-interference performance indicators The following exists:

[0043] From 0 to By performing integration, we obtain:

[0044] because It is bounded, therefore we can obtain: The performance indicators are met. of Anti-interference performance; in for After weak infinitesimal operator The result after the calculation For output error The quadratic form, For external disturbances The quadratic form.

[0045] Preferably, the controller gain is solved in step S4. The specific solution process for specifying relevant parameters includes: Using the solver in computer software, the LMI condition in step S35 is solved to obtain a real matrix that satisfies the sufficient stability condition. and , and After congruent transformation, we obtain: the control gain matrix. Event triggering mechanism weighted positive definite real matrix , , Lyapunov functional parameter positive definite real matrix , , Real matrix .

[0046] In another aspect, the present invention also discloses a clustering consensus control system for a secure multi-agent system, which, based on networked multi-agent systems, executes the steps of any of the above-described clustering consensus control methods for a secure multi-agent system, including the following modules: The topology information acquisition and judgment unit is used to obtain the communication topology matrix between agents for the clustering network of multi-agent systems divided into multiple clusters, and to check and ensure that the communication graph topology structure of each cluster contains a directed spanning tree and satisfies the in-degree balance condition. The adaptive event triggering unit based on memory characteristics has the function of caching system status data, and combines system status data information for adaptive detection and adjustment of whether to transmit system data to the distributed controller. The control gain and parameter calculation unit is used to calculate and solve the LMI conditions to obtain the mean square exponential convergence stability of the system. The control gain for anti-interference performance and the parameters for the adaptive event triggering strategy based on memory characteristics are specified. The clustering consensus control unit is used to input the control gain and adaptive event triggering strategy specified parameters calculated by the above unit into the actuator so that the multi-agent system can achieve safe clustering consensus.

[0047] In another aspect, the present invention also discloses a computer device, including a memory and a processor, wherein the memory stores a computer program, and when the computer program is executed by the processor, the processor performs the steps of the method described above.

[0048] As can be seen from the above technical solution, the present invention provides a secure clustering consensus control method for multi-agent systems. Compared with the prior art, the present invention has the following advantages: 1. This invention introduces multiple historical state information and adaptively adjusts the trigger threshold to construct an adaptive event triggering mechanism with memory characteristics, which can effectively reduce unnecessary data transmission, thereby significantly reducing the communication burden and improving bandwidth utilization.

[0049] 2. This invention introduces a distributed control protocol based on memory characteristics into the controller and combines it with Bernoulli stochastic process modeling of deception attack behavior. By adaptively adjusting the triggering policy parameters and controller gain, it can ensure the mean square exponential stability convergence of the system state even in the presence of deception attacks, significantly improving the security and robustness of multi-agent systems in open network environments.

[0050] 3. By employing a clustering consensus control method based on memory characteristics, combined with topology decomposition and adaptive event triggering strategies, this invention enables follower agents within each cluster to quickly track the state of the corresponding leader agent, achieving consensus on multi-cluster partitioning that is consistent within the cluster but different between clusters. This supports more complex collaborative task architectures, thereby facilitating the expansion of the feasibility of multi-agent systems in complex fields such as intelligent transportation and aerospace formations.

[0051] 4. This invention employs an adaptive dynamic event-triggered strategy with memory characteristics for communication between agents, and uses the historical state of the multi-agent system as the basis for determining whether to transmit data. It also incorporates a distributed system based on locally stored memory data. The controller ensures the achievement of clustering consensus and safe and stable operation of multi-agent systems under deception attacks and perturbed network communications.

[0052] It should be understood that the descriptions in this section are not intended to identify key or essential features of embodiments of the invention, nor are they intended to limit the scope of the invention. Other features of the invention will become readily apparent from the following description. Of course, implementing any product of the invention does not necessarily require achieving all of the advantages described above simultaneously. Attached Figure Description

[0053] The accompanying drawings, which form part of this application, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an undue limitation of the invention. In the drawings: Figure 1 This is a schematic diagram of the overall process of the present invention; Figure 2 This is a schematic diagram of the system structure of a single intelligent agent according to an embodiment of the present invention; Figure 3 This is a schematic diagram of the communication topology of a three-cluster clustering intelligent agent formation system according to an embodiment of the present invention; Figure 4 This is a three-dimensional spatial position diagram of the intelligent agent formation system according to an embodiment of the present invention; Figure 5 This is a diagram showing the time trigger interval and attack time in an embodiment of the present invention. Detailed Implementation

[0054] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of them. Unless otherwise specified, the embodiments and features in the embodiments of this application can be combined with each other. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0055] For details in the embodiments, please refer to Figures 1 to 5 .

[0056] like Figure 1 As shown in the embodiments of the present invention, the secure clustering consensus control method for multi-agent systems includes the following steps: Step S1. Based on external disturbance factors, construct a multi-agent system clustering network consisting of N follower agents and M cluster leader agents, and a dynamic mathematical model of the multi-agent system's susceptibility to energy-limited deception attacks.

[0057] Specifically, it includes: Step S11. First, define the following linear system dynamics model with N follower agents:

[0058] in, It is the state of follower agent i at time t. It is the state derivative of follower agent i at time t after the update, representing the dynamic state change of follower agent i. It is the output signal of the follower agent i at time t. It is the control input of the follower agent i at time t. It is the bounded disturbance input of the follower agent i at time t. It is a constant system matrix; A linear system dynamics model with M leader agents is defined as follows:

[0059] in They represent the first time at time t. The state and output signals of a leader agent It is the updated time t at the th moment. The state derivative of the leader agent represents the state derivative of the first leader agent. Dynamic changes in the state of the leader agent.

[0060] Step S12. Establish a mathematical model of the possible deception attack signals with limited energy: See Figure 2 In this invention, attackers can launch a deception attack by injecting false data into the network channel from the event triggering unit to the distributed controller. This malicious behavior will eventually cause the agent's controller to receive and use the tampered data and give incorrect execution instructions, which will greatly impair the clustering consistency performance of the multi-agent system.

[0061] Therefore, the method in this application mathematically describes the deception attack signal as follows: , representing the deceptive attack signal injected into the data packet of the s-th historical moment stored in its distributed controller when attacking follower agent i. Due to system hardware limitations and network security protocols, deceptive attack signals generally have limited energy and the attack will not occur continuously. Assume the deceptive attack signal is:

[0062] This is an attack constant coefficient. The following error between follower agent i and its leader agent is defined in subsequent step S33.

[0063] Step S2. Obtain the communication topology between agents based on the multi-agent system clustering network to ensure that the graph topology of each cluster contains a directed spanning tree and satisfies the in-degree balance condition.

[0064] Specifically, it includes: Step S21. Define the clustering network topology and the cluster Laplacian matrix: Constructing a weighted directed graph of the network topology between intelligent agents in the embodiment ,in It is a collection of multiple intelligent agents. It is a set of edges Represents the adjacency matrix associated with this directed graph, where the matrix elements are... The communication coupling weights between follower agent i and neighbor agent j are used to construct the graph. The relevant Laplacian matrix is , where matrix elements and ; Divide all agents into M clusters, forming M subgroups, and construct a set of diagonal matrices. Used to describe follower agents and leader agents In communication between the leader and follower agents, if the follower agent i can receive information from the leader agent, then... ,otherwise The clustering Laplacian matrix for M clusters is defined as follows:

[0065] in, Is a sub-cluster Related subgraphs It represents a subgraph Sub-Laplacian matrix for intra-cluster communication; It is a descriptor graph arrive The sub-Laplacian matrix for inter-cluster communication; At this point, the communication topology matrix of the multi-agent system clustering network is obtained. ; Based on the clustering clusters and matrices defined by the intelligent agent system, Decomposition yields a diagonal matrix sum matrix , It is the Laplacian matrix within M clusters. It is the Laplacian matrix among M clusters; Finally, the communication topology matrix between agents within the same cluster is obtained. And the communication topology matrix between agents in different clusters ; Where the matrix Both are used to model the communication topology between agents in clustered networks, facilitating subsequent calculation of controller gain. And specify the relevant parameters; Step S22. Verify that the cluster graph topology contains a directed spanning tree condition: picture There exists a leader-type intelligent agent. For a directed path that can reach all follower nodes in the cluster from the root node, verify that it contains at least one directed spanning tree condition. Step S23. Verify that the cluster graph topology satisfies the in-degree balance condition: It is a matrix with a row sum of zero, verifying that the graph topology satisfies the in-degree balance condition, and the weights of communication coupling between cross-cluster agents add up to zero.

[0066] In step S2 above, the topology is not required to be strongly connected; it is only required that each cluster graph topology contains a spanning tree and satisfies the in-degree balance condition.

[0067] Furthermore, it requires that the state information of neighboring agents be available, but does not require that the state information of the entire multi-agent system be available.

[0068] Step S3. Considering the insecure network communication environment that may suffer from network communication latency and spoofing attacks, an adaptive event-triggered strategy with memory characteristics is constructed on the multi-agent system clustering network based on a dynamic mathematical model. A Bernoulli probability model is used to model randomly occurring spoofing attacks. The system clustering consistency problem is transformed into a convergence analysis problem of the error system by utilizing the state following error between the follower agent and the corresponding cluster leader agent. Then, through appropriate Lyapunov-Krasovskii functionals and by decoupling nonlinear factors using congruence transformation and mathematical scaling, the distributed controller satisfies... The sufficient conditions for LMI in terms of anti-interference performance and mean square exponential stability can be solved in computer software. Specifically, it includes: Step S31. Design an adaptive event triggering mechanism with memory characteristics: To reduce the harm caused by deception attacks to the system and alleviate communication load, this invention designs an adaptive memory event triggering mechanism based on historical triggering information. This mechanism can store triggering data at historical moments and introduces a memory weight coefficient to comprehensively evaluate whether the system's sampled data packets are transmitted to the local distributed controller. This mechanism can be described as follows:

[0069] Among them, symbols It is the next triggering moment when the follower agent i meets the triggering condition. It is the latest triggering time of follower agent i, and k is the triggering number of follower agent i. It is the event-triggered auxiliary function of the follower agent i at time t. and These are the event triggering condition function and the adaptive triggering threshold of the follower agent i at time t, respectively, and their specific forms are given below:

[0070] in, Represents the latest sampling time of the sensor. The sequence of historical trigger moments considered by the memory event triggering mechanism can be represented by a maximum number of historical trigger moments. indivual; It is the memory weight coefficient of the historical trigger time s, used to measure the proportion and weight of the memory data. It is the gain matrix of the memory controller to be designed; It is the derivative of the adaptive trigger threshold of follower agent i at time t after the update, representing the dynamic change of the trigger threshold. The initial value of the trigger threshold is... ; It is a weighted real matrix. Given a positive real number, For a given follower agent i, trigger relevant positive parameters for the event. yes The measurement error is calculated by comparing the state data of the historical time s stored by the follower agent i at the current time with the state data sampled by the sensor at the latest time. yes The transpose of; and They are At time i, the error function of the neighbor within the cluster of the follower agent i Inter-cluster neighbor error function The transpose of .

[0071] Intra-cluster error function Inter-cluster error function The specific form is as follows:

[0072] in, Represents the s-th historical trigger moment of follower agent i, and k is the trigger number of follower agent i; represent At any given moment, the follower agent i belongs to the leader agent of its cluster. The state; Represents the follower agent i and the set of neighbors. The communication coupling weights between agents j in the middle. Represents follower agent i and the leader agent of its cluster. Communication coupling weights between them; Step S32. Design a local distributed system with memory characteristics. Controller:

[0073] in, It is the follower agent i that was deceived during transmission and injected into the storage. Constantly memorize attack data within the data set; Using Bernoulli's model Describe whether follower agent i is subjected to a deception attack at time t. When it indicates that the follower agent i has not been deceived, When the follower agent i is deceived, its expected value is: , Let be the probability of a deception attack occurring, with variance . , Represents the square root of the variance; Here, a distributed control protocol based on memory characteristics is introduced into the controller, and deception attack behavior is modeled by Bernoulli stochastic process. By adaptively adjusting the trigger policy parameters and controller gain, the mean square exponential stability of the system state can be guaranteed even in the presence of deception attacks, which significantly improves the security and robustness of multi-agent systems in open network environments.

[0074] Furthermore, by introducing multiple historical state information and adaptively adjusting the trigger threshold, an adaptive event triggering mechanism with memory characteristics is constructed, which can effectively reduce unnecessary data transmission, thereby significantly reducing the communication burden and improving bandwidth utilization.

[0075] Step S33. Construct the following error system: First, define the state following error between the follower agent i and its leader agent:

[0076] in, represent At any given moment, the follower agent i belongs to the leader agent of its cluster. The state; Considering the network communication latency of controller data transmission: ,definition , ,in represents the lower and upper bounds of the time delay (minimum and maximum time delay), and h is the physical sampling time interval of the sensor.

[0077] The error system dynamics are as follows:

[0078] Written in compact form:

[0079] in,

[0080] Step S34. Given the Lyapunov-Krasovskii functional, for a given positive parameter, derive the system to achieve mean-square exponential convergence and stability while satisfying the following conditions: The sufficient conditions for performance are as follows: Based on the design of steps S31-S33: Based on the proposed control protocol and memory event triggering mechanism, for a given positive real number... and the probability of deception attack The square root of the variance Memory weight coefficient The obtained clustering topology matrix There exists a positive definite real matrix of weights for the event triggering mechanism that needs to be solved. real matrix Control gain matrix and the parameter diagonal matrix Therefore, a condition matrix is ​​set. and The following relationship must be satisfied for the system to achieve mean square exponential convergence and stability while also satisfying the performance metric: of Anti-interference performance:

[0081] Among the symbols Submatrix transpose; symbol Represents the symmetric element in a matrix; symbol Represents the Kronecker product operation; Representing zero matrices and identity matrices of appropriate dimensions; Represents an identity matrix of dimension N; Each submatrix The definition is as follows:

[0082]

[0083] in,

[0084]

[0085]

[0086] in, This represents the maximum delay. Positive parameters related to the event triggering mechanism are set; For deception attacks, constant coefficients are used. To measure Performance indicators of anti-interference performance.

[0087] Prove that the mean square exponential stability is satisfied and Performance strategy: There exists a Lyapunov-Krasovskii functional for It is broken down into various sub-functions. Defined as: , , , .

[0088] For the Lyapunov function given above The weak infinitesimal operator is defined by the following mathematical formula. Operation format:

[0089] in, For time-based and the current random state Lyapunov function, Representing Lyapunov functions Using weak infinitesimal operators The result of the operation.

[0090] Then, through mathematical scaling and other methods, it can be derived that...

[0091] That is

[0092] in, , for The matrix transpose form, For output error The quadratic form, For external disturbances The quadratic form.

[0093] (1) Given the initial conditions, when the external disturbance hour,

[0094] From Dynkin's formula, we get:

[0095] Right now:

[0096] Define symbols Let P and P represent the largest and smallest eigenvalues ​​of the parameter matrix P in the Lyapunov functional, respectively, with symbols... Let the largest eigenvalues ​​of the parameter matrices Q and R in the Lyapunov functional be represented, and the scaling condition be obtained:

[0097] , Constructing convergence rate parameters Norm parameter of error with respect to the initial time ,exist and The specific form is:

[0098] in, For functionals The mathematical expectation, For tracking error system The expected value of the error norm. For maximum delay, The initial value of the event triggering threshold for follower agent i; In conclusion, we finally arrive at: This satisfies the mean square exponent stability. (2) Under zero initial conditions When external disturbances When, given Anti-interference performance indicators The following exists: ; From 0 to By performing integration, we obtain: , because It is bounded, therefore we can obtain:

[0099] Right now The performance indicators are met. of Anti-interference performance; in for After weak infinitesimal operator The result after the calculation For output error The quadratic form, For external disturbances The quadratic form.

[0100] In summary, it has been proven that the system satisfies mean square exponential stability and Anti-interference performance.

[0101] Step S35. Linearize the condition matrix proposed in step S34 to obtain the LMI conditions that can be solved in computer software: Based on the proposed control protocol and memory event triggering mechanism, for a given positive real number... and the probability of deception attack The square root of the variance Memory weight coefficient The obtained clustering topology matrix There exists a positive definite real matrix of weights for the event triggering mechanism that needs to be solved. Lyapunov functional parameter positive definite real matrix real matrix Control gain matrix and the parameter diagonal matrix Therefore, a condition matrix that can be solved by a computer is set. and The following relationship must be satisfied to obtain a solution that enables the system to achieve mean square exponential stable convergence and satisfy the performance index: of Relevant control parameters for anti-interference performance:

[0102] Among the symbols Submatrix transpose; symbol Represents the symmetric element in a matrix; symbol Represents the Kronecker product operation; Representing zero matrices and identity matrices of appropriate dimensions; Represents an identity matrix of dimension N; Each submatrix The definition is as follows:

[0103]

[0104] in,

[0105]

[0106] in, This represents the maximum delay. Positive parameters related to the event triggering mechanism are set; For deception attacks, constant coefficients are used. To measure Performance indicators of anti-interference performance.

[0107] Step S4. Based on the conditions in steps S1-S3, solve the LMI conditions to obtain the controller gain. And related parameters (based on the communication topology matrix between agents and LMI conditions, to solve for the controller gain) (And corresponding specified parameters), through the designed distributed controller, to achieve secure clustering consensus control of a multi-agent system under specified environments with limited communication resources and spoofing attacks. The specific process includes: Using the solver in computer software, the LMI condition in step S35 is solved to obtain a real matrix that satisfies the sufficient stability condition. and , and After congruent transformation, we obtain: the control gain matrix. Event triggering mechanism weighted positive definite real matrix , , Lyapunov functional parameter positive definite real matrix , , Real matrix .

[0108] In summary, this method employs an adaptive dynamic event-triggered strategy with memory characteristics for communication between agents, and uses the historical state of the multi-agent system as the basis for determining whether to transmit data. It also incorporates a distributed system based on locally stored memory data. The controller ensures the achievement of clustering consensus and safe and stable operation of the multi-agent system under deception attacks and perturbed network communication. Its adaptive event triggering mechanism with memory function can reduce network communication load, improve system operating efficiency, and reduce communication resource consumption. At the same time, it can adaptively detect and suppress the impact of deception attacks on the system, ensuring the security and stability of the system when false data is injected by deception attacks.

[0109] Furthermore, this invention also discloses a clustering consensus control system for a secure multi-agent system, which, based on networked multi-agent systems, executes the steps of the clustering consensus control method for a secure multi-agent system described in the above embodiments, including the following modules: (1) Topology information acquisition and judgment unit, used to obtain the communication topology matrix between agents for the clustering network of multi-agent systems divided into multiple clusters, and to check and ensure that the communication graph topology structure of each cluster contains a directed spanning tree and satisfies the in-degree balance condition.

[0110] This module performs the following calculations: L1. Obtain the adjacency matrix of the clustered network topology. With clustered Laplacian matrix and matrix ,get , , ; L2. Verify that the graph topology of each cluster contains at least one directed spanning tree; L3. Verify the cluster graph topology matrix It is a matrix whose row sum is zero.

[0111] (2) An adaptive event triggering unit based on memory characteristics has the function of caching system status data, and combines system status data information for adaptive detection and adjustment of whether to transmit system data to the distributed controller.

[0112] This module performs the following calculations: Design an adaptive event triggering mechanism with memory characteristics:

[0113] in, , ,

[0114] (3) Control gain and parameter calculation unit, used to calculate and solve the LMI conditions to obtain the mean square exponential convergence stability of the system. The parameters are specified for the control gain of anti-interference performance and the adaptive event triggering strategy based on memory characteristics.

[0115] This module performs the following calculations: Solving the LMI conditions proposed in step S35 yields a real matrix that satisfies the sufficient stability condition. and , and : Based on the proposed control protocol and memory event triggering mechanism, for a given positive real number... and the probability of deception attack The square root of the variance Memory weight coefficient The obtained clustering topology matrix There exists a positive definite real matrix of weights for the event triggering mechanism that needs to be solved. Lyapunov functional parameter positive definite real matrix real matrix Control gain matrix and the parameter diagonal matrix Therefore, a condition matrix that can be solved by a computer is set. and The following relationship must be satisfied to obtain a solution that enables the system to achieve mean square exponential stable convergence and satisfy the performance index: of Relevant control parameters for anti-interference performance:

[0116] Each submatrix The definition is as follows:

[0117]

[0118] in,

[0119]

[0120] After congruent transformation, we obtain: the control gain matrix. Event triggering mechanism weighted positive definite real matrix , , Lyapunov functional parameter positive definite real matrix , , Real matrix .

[0121] (4) Clustering consensus control unit, used to input the controller and transmit the control gain and adaptive event triggering strategy specified parameters calculated by the above unit to the actuator so that the multi-agent system can achieve safe clustering consensus.

[0122] This module performs the following calculations: The control gain is obtained through step S4. Substituting this into the distributed clustering consensus controller designed in this invention, we obtain the control input:

[0123] In summary, by employing a clustering consensus control method based on memory characteristics, combined with topology decomposition and adaptive event triggering strategies, this system enables follower agents within each cluster to quickly track the state of their corresponding leader agents. This achieves consensus on multi-cluster partitioning that is consistent within the cluster but can differ between clusters, thereby supporting more complex collaborative task architectures. This facilitates the expansion of the feasibility of multi-agent systems in complex fields such as intelligent transportation and aerospace formations.

[0124] Furthermore, the method constructed in this invention is applicable to collaborative control scenarios with limited resources and significant security threats, especially to multi-agent systems with hierarchical topology, such as drone swarm operations, space exploration, and smart logistics, and has the advantages of efficient communication, security and reliability, and flexible collaboration.

[0125] In this embodiment of the invention, a three-cluster intelligent agent formation system consisting of 3 leader agents and 13 follower agents is considered as an example to verify the proposed design method. The system architecture of a single agent is as follows: Figure 2 As shown, the communication topology between agents is as follows: Figure 3 As shown, a dynamic model of the relative orbital motion of the intelligent agent is established using the CW equations, which describe the relative motion between two spacecraft orbiting in near-circular orbits:

[0126] definition It is the three-dimensional position vector of the agent, and the control component in the corresponding direction is defined as Taking perturbations into account, the physical model of the intelligent agent is given as follows:

[0127] in ,make , , The above system is then transformed into the system model in step S11, combined with the actual physical meaning, angular velocity attack probability The square root of the variance The system parameters are given below: By giving parameters:

[0128] consider Each historical moment, and the corresponding memory weight coefficient. Performance indicators The control gain and weight matrix are obtained by solving the LMI conditions in step S35 using a solver in computer software, as follows:

[0129] The above solution results were then used for experimental simulation in MATLAB. The simulation results are as follows: Figure 4 and Figure 5 As shown. Figure 4 The spatial positions of the 13 follower agents reached a consensus in three clusters: follower agents 1-6 reached consensus with leader agent 1*; follower agents 7-9 reached consensus with leader agent 2*; and follower agents 10-13 reached consensus with leader agent 3*. The event triggering diagram for selecting a follower agent is shown below. Figure 5 As shown in the simulation data, the event triggering interval is relatively sparse. When a spoofing attack occurs, the adaptive memory event triggering strategy designed in this invention can immediately detect the response trigger and update the data packets transmitted to the controller. This indicates that the strategy can effectively reduce communication consumption while also greatly suppressing the impact of spoofing attacks on the system.

[0130] In summary, this invention can achieve clustering consensus at an exponential rate, which facilitates further improvement of system security. Moreover, the designed algorithm is fast and easy to operate.

[0131] In another aspect, the present invention also discloses a computer device, including a memory and a processor, wherein the memory stores a computer program, and when the computer program is executed by the processor, the processor performs the steps of the method described above.

[0132] In another embodiment provided in this application, a computer program product containing instructions is also provided, which, when run on a computer, causes the computer to execute any of the multi-agent system secure clustering consensus control methods described in the above embodiments.

[0133] It is understood that the system provided in the embodiments of the present invention corresponds to the method provided in the embodiments of the present invention, and the explanation, examples and beneficial effects of the relevant content can be referred to the corresponding parts of the above methods.

[0134] This application also provides an electronic device, including a processor, a communication interface, a memory, and a communication bus, wherein the processor, communication interface, and memory communicate with each other via the communication bus. Memory, used to store computer programs; The processor, when executing the program stored in memory, implements the aforementioned safe clustering consensus control method for multi-agent systems.

[0135] The communication bus mentioned in the above-mentioned electronic devices can be a standard bus for interconnecting peripheral components or an extended industrial standard structure bus, etc. This communication bus can be divided into address bus, data bus, control bus, etc.

[0136] The communication interface is used for communication between the aforementioned electronic devices and other devices.

[0137] The memory may include random access memory or non-volatile memory, such as at least one disk storage device. Optionally, the memory may also be at least one storage device located remotely from the aforementioned processor.

[0138] The processors mentioned above can be general-purpose processors, including central processing units, network processors, etc.; they can also be digital signal processors, application-specific integrated circuits, field-programmable gate arrays or other programmable logic devices, discrete gate or transistor logic devices, or discrete hardware components.

[0139] In the above embodiments, implementation can be achieved entirely or partially through software, hardware, firmware, or any combination thereof. When implemented using software, it can be implemented entirely or partially in the form of a computer program product. The computer program product includes one or more computer instructions. When the computer program instructions are loaded and executed on a computer, all or part of the processes or functions described in the embodiments of this application are generated. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The computer instructions can be stored in a computer-readable storage medium or transmitted from one computer-readable storage medium to another. For example, the computer instructions can be transmitted from one website, computer, server, or data center to another website, computer, server, or data center via wired or wireless means. The computer-readable storage medium can be any available medium accessible to a computer or a data storage device such as a server or data center that integrates one or more available media. The available medium can be a magnetic medium, an optical medium, or a semiconductor medium, etc.

[0140] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

[0141] Furthermore, it should be noted that if any directional indication (such as up, down, left, right, front, back, etc.) is involved in the embodiments of the present invention, the directional indication is only used to explain the relative positional relationship and movement of each component in a specific posture. If the specific posture changes, the directional indication will also change accordingly.

[0142] Furthermore, if the embodiments of this invention involve descriptions such as "first" or "second," these descriptions are for descriptive purposes only and should not be construed as indicating or implying their relative importance or implicitly specifying the number of technical features indicated. Therefore, a feature defined with "first" or "second" may explicitly or implicitly include at least one of those features. Additionally, the meaning of "and / or" throughout the text includes three parallel solutions; for example, "A and / or B" includes solution A, solution B, or a solution where both A and B are satisfied simultaneously. Furthermore, in the embodiments of this invention, "multiple" refers to two or more. Moreover, the technical solutions of the various embodiments can be combined with each other, but this must be based on the ability of those skilled in the art to implement them. When the combination of technical solutions is contradictory or cannot be implemented, it should be considered that such a combination of technical solutions does not exist and is not within the scope of protection claimed by this invention.

Claims

1. A method for cluster consensus control of multi-agent system security, characterized in that, include: Step S1. Based on external disturbance factors, construct a multi-agent system clustering network consisting of N follower agents and M cluster leader agents, and simultaneously construct a dynamic mathematical model of the multi-agent system; Step S2. Obtain the communication topology matrix between agents based on the multi-agent system clustering network to ensure that the graph topology of each cluster contains a directed spanning tree and satisfies the in-degree balance condition; Step S3. Based on the dynamic mathematical model, construct an adaptive event-triggered strategy with memory characteristics on the multi-agent system clustering network, transforming the system clustering consistency problem into a convergence analysis problem of the error system. Use a Bernoulli probability model to model randomly occurring deception attacks, and then obtain the distributed controller satisfying the Lyapunov-Krasovskii functional and decouple nonlinear factors. Sufficient conditions for LMI in terms of anti-interference performance and mean square exponential stability; Step S4. Solving the controller gain based on the communication topology matrix between agents and LMI condition and the specified relevant parameters, through the designed distributed controller, the safety clustering consistency control of multi-agent system in the specified environment is realized. In step S2, the process of obtaining the inter-agent communication topology matrix in the multi-agent system clustering network includes the following topology constraint verification and partitioning procedures: Weighted directed graphs for constructing inter-agent network topologies in multi-agent system clustering networks. ,in It is a collection of multiple intelligent agents. It is an edge set. Represents the adjacency matrix associated with this directed graph, where the matrix elements are... The communication coupling weights between follower agent i and neighbor agent j are used to construct the graph. The relevant Laplacian matrix is , where matrix elements and ; Divide all agents into M clusters, forming M subgroups, and construct a set of diagonal matrices. This describes the communication between follower agents and leader agents. If follower agent i can receive information from the leader agent, then... ,otherwise The clustering Laplacian matrix for M clusters is defined as follows: in, Is a sub-cluster Related subgraphs It represents a subgraph The sub-Laplacian matrix for intra-cluster communication. It is a descriptor graph arrive The sub-Laplacian matrix for inter-cluster communication; At this point, the communication topology matrix of the multi-agent system clustering network is obtained. ; Based on the clustering clusters and matrices defined by the intelligent agent system, Decomposition yields a diagonal matrix sum matrix , It is the Laplacian matrix within M clusters. It is the Laplacian matrix among M clusters; a final inter-agent communication topology matrix within the same cluster and an inter-agent communication topology matrix between different clusters ; wherein the matrix are used to model the communication topology relationship between agents in the clustered network, facilitating subsequent solving of controller gains and designated relevant parameters; Verification image Does the pathway include at least one set of leader agents? A directed spanning tree is defined as a condition where the root node can reach all its follower nodes within the cluster. If this condition is not met, the cluster's communication topology is reconstructed. With the associated Laplacian matrix, a new ; For a matrix whose row sum is zero Verification image Check if the graph topology satisfies the in-degree balance condition, such that the sum of the communication coupling weights between agents across the cluster is zero. If the verification fails, reconstruct the cluster's communication topology graph. With the associated Laplacian matrix, a new ; The specific operation process of step S3 includes: Step S31. Construct an adaptive memory event triggering mechanism based on historical triggering information to store triggering data at historical moments, and introduce a memory weight coefficient to comprehensively measure whether the system sampled data packet is transmitted to the local distributed controller; Step S32. Construct a locally distributed system with memory characteristics based on a dynamic mathematical model. The deception attack model for the controller and Bernoulli model is as follows: in, Represents the latest sampling time of the sensor. represent At any given moment, the follower agent i belongs to the leader agent of its cluster. The state; Represents the follower agent i and the set of neighbors. The communication coupling weights between agents j in the middle. Represents follower agent i and the leader agent of its cluster. Communication coupling weights between them; The sequence of historical trigger moments considered by the memory event triggering mechanism can be represented by a maximum number of historical trigger moments. indivual; It is the memory weight coefficient of the historical trigger time s, used to measure the proportion and weight of the memory data. It is the gain matrix of the memory controller to be designed; This represents the physical sampling time interval of the sensor. Let k represent the s-th historical trigger moment of follower agent i, and k be the trigger number of follower agent i. yes The current storage of the follower intelligent agent i The measurement error calculated from the current state data and the latest sampled state data from the sensor; It is the follower agent i that was deceived during transmission and injected into the storage. Constantly memorize attack data within the data set; Using Bernoulli's model Describe whether follower agent i is subjected to a deception attack at time t. When it indicates that the follower agent i has not been deceived, When the follower agent i is deceived, its expected value is: , Let be the probability of a deception attack occurring, with variance . , Represents the square root of the variance; Step S33. Define the state following error between follower agent i and its leader agent. And consider the maximum network communication latency for controller data transmission. Constructing a following error system ; Step S34. Based on Lyapunov-Krasovskii functionals For a given positive parameter, combined with the following error system The output of the adaptive memory event triggering mechanism is used to obtain the distributed controller's desired response. A set of sufficient condition matrices to be solved for anti-interference performance and mean square exponential stability; Step S35. Perform linear decoupling processing on the derived condition matrix to finally obtain the LMI conditions that can be solved in computer software, which are used to solve the controller gain in step S4.

2. The method of claim 1, wherein The dynamic mathematical model of the multi-agent system in step S1 includes: A linear system dynamics model with N follower agents, where the dynamics of follower agent i are defined as follows: in, It is the state of follower agent i at time t. It is the state derivative of follower agent i at time t after the update, representing the dynamic state change of follower agent i. It is the output signal of the follower agent i at time t. It is the control input of the follower agent i at time t. It is the bounded disturbance input of the follower agent i at time t. It is a constant system matrix; M clusters correspond to the linear system dynamics model of the leader agent, where the dynamics of the mth leader agent is defined as: ​ in They represent the first time at time t. The state and output signals of a leader agent It is the updated time t at the th moment. The state derivative of the leader agent represents the state of the first leader agent. Dynamic changes in the state of the leader agent.

3. The method of claim 1, wherein The adaptive memory event triggering mechanism in step S31 is defined as follows: The output of this triggering mechanism is used for the stability derivation in step S34 and the parameter solution in step S4. Among them, symbols It is the next triggering moment when the follower agent i meets the triggering condition. It is the latest triggering time of follower agent i, and k is the triggering number of follower agent i. It is the event-triggered auxiliary function of the follower agent i at time t. and These are the event triggering condition function and adaptive triggering threshold of the follower agent i at time t, respectively. This is the preset positive parameter for the follower agent i under the event triggering mechanism.

4. The method of claim 3, wherein In step S34, given the initial conditions, when an external disturbance occurs... When given a positive real number For Lyapunov functionals Meets stability requirements: To satisfy the convergence rate as The mean square exponential convergence; norm parameter of initial time error with convergence rate is of the form in, For tracking error system The error norm and mathematical expectation; symbol Let P and P represent the largest and smallest eigenvalues ​​of the parameter matrix P in the Lyapunov functional, respectively, with symbols... Let Q represent the largest eigenvalue of the parameter matrices Q and R in the Lyapunov functional. For maximum delay, The initial value of the event triggering threshold for follower agent i.

5. The method of claim 3, wherein The step S34 has zero initial condition When external disturbance , given Anti-jamming performance index , the final result is: To meet the performance index is Anti-jamming performance ; where is the output error error norm mathematical expectation, is the external disturbance disturbance norm mathematical expectation.

6. The method of claim 3, wherein, The specific process of linearizing the condition matrix in step S35 to obtain the LMI conditions includes: Based on the adaptive memory event triggering mechanism proposed in step S31 and the control protocol proposed in step S32, the clustering topology matrix obtained in step S2... With specified parameters, set the LMI condition matrix that can be solved by a computer. and The following relationship must be satisfied, and the solution must be obtained to ensure that the system achieves mean square exponential convergence and stability while satisfying the performance index as follows: of Control gain matrix for anti-interference performance Parameters related to the event triggering mechanism: in and This is derived from Lyapunov's stability theorem and satisfies... The parameter condition matrix for performance with mean square exponential convergence stability. It is the positive definite real matrix of the Lyapunov functional parameters to be solved. It is the real matrix to be solved; symbol Represents the symmetric element in a matrix; symbol Represents the Kronecker product operation of matrices; Representing zero matrices and identity matrices of appropriate dimensions; Represents an identity matrix of dimension N; This represents the maximum delay. To measure Performance indicators of anti-interference performance.

7. A multi-agent system security clustering consensus control system, characterized in that, Based on networked multi-agent systems, the steps of performing the method as described in any one of claims 1 to 6 include the following modules: The topology information acquisition and judgment unit is used to obtain the communication topology matrix between agents for the clustering network of multi-agent systems divided into multiple clusters, and to check and ensure that the communication graph topology structure of each cluster contains a directed spanning tree and satisfies the in-degree balance condition. The adaptive event triggering unit based on memory characteristics has the function of caching system status data, and combines system status data information for adaptive detection and adjustment of whether to transmit system data to the distributed controller. a control gain and parameter calculation unit for calculating a solution to the LMI condition to obtain a control gain and adaptive event-triggered strategy designation parameters based on memory characteristics that allow the system to achieve mean square exponential convergence stability and anti-interference performance The clustering consensus control unit is used to input the control gain and adaptive event triggering strategy specified parameters calculated by the above unit into the actuator so that the multi-agent system can achieve safe clustering consensus.

8. A computer device, comprising: It includes a memory and a processor, the memory storing a computer program that, when executed by the processor, causes the processor to perform the steps of the method as described in any one of claims 1 to 6.

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