A limited time privacy protection consistency method under an event triggering mechanism

Abstract

The application discloses a limited time privacy protection consistency method under an event triggering mechanism, based on the event triggering mechanism, effective event triggering conditions are derived, and limited time theory is introduced to guarantee the convergence performance of multi-agent consistency, meanwhile, an output mapping function is introduced to ensure that the state of each agent in the multi-agent system is unknown to the outside world, that is, the real state information of the agent cannot be acquired by adjacent agents and external intruders, and limited time privacy protection consistency convergence is realized. The method of the application combines the event triggering mechanism and the limited time theory, improves the convergence performance of multi-agent privacy protection consistency control, and reduces the resource consumption of algorithm calculation, comprehensively considers communication security, bandwidth constraints and performance indexes, further expands the application scene of the algorithm, and to some extent, completes the comprehensive consideration of privacy protection, system performance and execution efficiency and the like.

Description

Technical Field

[0001] This invention belongs to the field of privacy protection consistency control technology, specifically relating to a limited-time privacy protection consistency method under an event-triggered mechanism. Background Technology

[0002] With the rapid development of communication, information, and computer technologies, the application areas of the Internet of Things (IoT), cyber-physical systems (CPS), artificial intelligence (AI), and 5G technologies are constantly expanding, bringing with them significant concerns about network node security. From the 1991 "cyber Pearl Harbor" attack to the 2017 US wind farm safety experiment, these events demonstrate the deep coupling, interconnectedness, and mutual influence between information system security (including communication, network, data, and hardware / software security) and physical system security (including system operation, physical equipment, and product quality safety), seriously jeopardizing people's lives. Therefore, in the vast information exchange processes of cyber-physical systems, ensuring the privacy of information at each node is of paramount importance.

[0003] Multi-agent systems (MAS) integrate control, communication, and computation, forming a typical cyber-physical system model. However, they also face significant challenges, such as network and communication node security. Researching privacy protection in MAS can provide scientific guidance for cyber-physical system security modeling and offer a new perspective for collaborative control analysis and synthesis of MAS.

[0004] Current research largely focuses on the security of multi-agent systems (MAS), neglecting to comprehensively consider bandwidth constraints and convergence performance. In many practical applications, the extensive information interaction generated in MAS systems inevitably leads to communication bandwidth constraints, and event-triggered mechanisms are currently an effective method to reduce this. Furthermore, with the deepening understanding of consensus problems in MAS systems, convergence performance has become crucial, typically determining when and how quickly the system converges. Many studies have introduced finite-time or fixed-time theories to increase convergence speed. While some research has addressed performance constraints such as bandwidth limitations and innovatively proposed different event-triggered mechanisms to reduce energy consumption and controller update frequency, these studies have not comprehensively considered the communication security, bandwidth constraints, and performance metrics of MAS systems. Summary of the Invention

[0005] To address the aforementioned technical problems, this invention proposes a time-limited privacy protection consistency method under an event-triggered mechanism.

[0006] The technical solution adopted in this invention is: a finite-time privacy protection consistency method under an event-triggered mechanism, the specific steps of which are as follows:

[0007] S1. Establish the dynamic model of the agents in the multi-agent system and give the communication topology of the system.

[0008] S2. For the multi-agent model proposed in step S1, design a finite-time privacy-preserving consistency control framework. By introducing an output mapping function, the real state of each agent is unknown to the neighboring agents. The finite-time theory is introduced to enable the multi-agent model to converge in a finite time.

[0009] S3. Design a finite-time privacy-preserving consistency controller based on an event-triggered mechanism. Define the state measurement error, the consistency error of the real state, and the consistency error of the hidden state, and derive effective event-triggered conditions so that the agent can update the controller when the event-triggered conditions are met.

[0010] S4. Substitute the finite-time privacy-preserving consistency controller established in step S3 into the agent model to derive the closed-loop system equation, which ultimately enables the multi-agent system to achieve consistent convergence within a finite time and ensures that neighboring agents cannot obtain the true state information of the entity.

[0011] Furthermore, step S1 specifically includes the following:

[0012] S11. The multi-agent system has n agents, and its communication topology can be represented by a weighted undirected graph G = (V, E).

[0013] In this system, each agent represents a node, the set of nodes is denoted by V, and the set of edges is denoted by E. ij This indicates that agents i and j can interact with each other, and the adjacency matrix A = [a ij ] represents the connectivity relationship in a multi-agent system, a ij Let represent each element in the adjacency matrix. If (i,j)∈E, then a ij >0, otherwise a ij =0. The Laplace matrix L = [l ij The definition of ] is L = DA, D = diag[d1,...,d n ] represents a weight matrix and satisfies l ij This represents the individual elements in the Laplace matrix.

[0014] S12. The dynamic model of agents in a multi-agent system is as follows:

[0015]

[0016] in, Let i represent the state variable of the i-th agent. Let represent the integral over the state variable, and t represent the time variable. The control input representing the intelligent agent, i.e., the controller that needs to be designed. and They represent the set of positive integers and the set of n-dimensional real numbers, respectively.

[0017] S13. If the agent's true state cannot be reconstructed from its known output trajectory and dynamic model, then the agent's initial state x... i (0) is unknowable if there exists a finite time T that satisfies:

[0018]

[0019] Where, x j Let (t) represent the state variable of the j-th agent. If there exists an output mapping function h that satisfies... x i (t) represents the state variable of the i-th agent, h i (t,x i (t) represents the output mapping function of the i-th agent, and the function is different for each agent. i (t,x i (t) can ensure that the state of the agent is unknown, and the function h i (t,x i (t) is strictly increasing.

[0020] Furthermore, step S2 specifically includes the following:

[0021] S21. Introduce a continuously time-varying output mapping function in a multi-agent system. This function is used to achieve privacy masking of the initial state. The function expression is:

[0022]

[0023] in, Representation and agent state vector Masks of the same size output state vectors. Let T represent the general formula for a vector that can be divided into n subvectors, where the variable subscripts indicate the corresponding agent numbers, and T represents the transpose of the matrix. and Let represent the set of positive real numbers and the set of n-dimensional real vectors, respectively. h(t,x(t),π) is the mapping function, which is the state variable hidden by the mapping function. The output y(t) of the hidden state variable is transmitted to the neighboring agents through the communication topology network composed of the multi-agent system.

[0024] The expression for a multi-agent system with privacy protection features is:

[0025]

[0026] in, Let f(·) denote the integral of the state vector, and f(·) be the dynamic model of the agent. It is assumed that the dynamic model of the agent is known to the outside world, each agent can obtain the masked output state vector y(t) of all neighboring agents, and each agent cannot directly obtain the real state of the neighboring agents and the real expression of the mapping function.

[0027] S22. For the multi-agent model involved in step S12, this model is a continuous-time system. If there exists a continuous positive definite function V(x), and there exist constants c > 0 and 0 < τ < 1, satisfying the following expression:

[0028]

[0029] in, Let V(x) be the first derivative of the state vector x(t) in step S21. By solving the above inequality, we can obtain that when t > T(x0), the system converges to 0. Then, the finite time T(x0) satisfies:

[0030]

[0031] Where x0 represents the initial state of the system.

[0032] Furthermore, step S3 specifically includes the following:

[0033] S31. To facilitate the design of subsequent event triggering conditions, the state measurement error e of agent i is... i (t) is defined as follows:

[0034]

[0035] in, This indicates the current trigger moment of the multi-agent system controller. Indicates the next trigger time. This represents the state variable corresponding to the current triggering moment. A traditional finite-time event-triggered controller is designed as follows:

[0036]

[0037] Among them, u i (t) corresponds to the controller involved in step S12, which does not consider privacy protection. μ and α represent control gains, and satisfy μ∈(0,1), α>0, and time. definition Let b represent the set of non-negative integers, where b is an element of the set of non-negative integers. This indicates the current triggering time of agent j. Indicates the solution The auxiliary time variable, and sig(x) μ =sign(x)|x| μ The function sign(·) is a sign function, N i Represents all neighboring intelligent agents of agent i.

[0038] S32. As can be seen from the privacy protection method involved in step S21, the specific output mapping function expression for agent i is:

[0039]

[0040] Where, π i ={φ i ,σ i ,δ i ,γ i The four elements in this set represent the variable gain of the mapping function described above. The gain varies for different agents, and this continuous-time function gradually decreases. When applied to a multi-agent system, the corresponding vector form is:

[0041] y(t)=h(t,x(t),π)=(I n +φe -Σt (x(t)+e) -Δt γ), (10)

[0042] Among them, I n Let φ represent an n-dimensional identity matrix, φ = diag(φ1,...,φ). n ), Σ=diag(σ1,...,σ n ), Δ=diag(δ1,...,δ n ) and γ=[γ1,...,γ n The subscript of the element in the above variables represents the corresponding agent number.

[0043] S33. The finite-time privacy-preserving consistency controller based on an event-triggered mechanism is designed as follows:

[0044]

[0045] Where the control gain α > 0, 0 ≤ μ < 1, the state measurement error in step S31 is redefined as:

[0046]

[0047] in, This represents the output of the mapping function corresponding to the current triggering moment, i.e., the hidden state variable information obtained through privacy protection measures.

[0048] S34. To obtain the event triggering conditions for controller updates, define the following relationship:

[0049]

[0050] Among them, Z i (t) represents the consistency error corresponding to the output of the mapping function, y j (t) represents the masked output of agent j, M i (t) represents the consistency error of the system's true state variables, x j (t) represents the state variable of agent j, E i (t) represents the summation of state measurement errors. Therefore, the event triggering condition corresponding to the controller designed in step S33 is:

[0051] |E i (t)|≤ε i |Z i (t)|, (14)

[0052] Among them, the pre-set parameter ε i It is a positive vector, therefore, the next event trigger time is:

[0053]

[0054] In summary, the controller design is complete, and the corresponding event triggering conditions are obtained.

[0055] Furthermore, step S4 specifically includes the following:

[0056] S41. To obtain the closed-loop system equations, the state measurement errors involved in step S33 are incorporated into the controller:

[0057]

[0058] S42. Substituting the result obtained in step S41 into the dynamic model involved in step S12 yields:

[0059]

[0060] The corresponding vector form of the closed-loop system equations is:

[0061]

[0062] Where Z(t) and E(t) represent the values ​​corresponding to Z respectively. i(t) and E i The vector form of (t), It is the Kronecker product.

[0063] In summary, the above steps complete the design of a time-limited privacy protection consistency control based on an event-triggered mechanism.

[0064] The beneficial effects of this invention are as follows: The method of this invention is based on an event-triggered mechanism, deriving effective event-triggered conditions and introducing finite-time theory to ensure the convergence performance of multi-agent consistency. Simultaneously, an output mapping function is introduced to ensure that the state of each agent in the multi-agent system is unknown to the outside world; that is, neighboring agents and external intruders cannot obtain the true state information of a given agent, thus achieving finite-time privacy-preserving consistency convergence. This invention's method, combining event-triggered mechanism and finite-time theory, improves the convergence performance of multi-agent privacy-preserving consistency control and reduces the resource consumption of the algorithm. By comprehensively considering communication security, bandwidth constraints, and performance indicators, it further expands the application scenarios of the algorithm and, to a certain extent, addresses the integration of privacy protection, system performance, and execution efficiency. Attached Figure Description

[0065] Figure 1 This is a flowchart of a time-limited privacy protection consistency method under an event-triggered mechanism according to the present invention.

[0066] Figure 2 This is a communication topology diagram of multiple agents in an embodiment of the present invention.

[0067] Figure 3 This is a diagram showing the actual state trajectory of agent i in an embodiment of the present invention.

[0068] Figure 4 This is the output state trajectory diagram of the mapping function of agent i in this embodiment of the invention.

[0069] Figure 5 This is a diagram showing the event triggering times of the intelligent agent in an embodiment of the present invention.

[0070] Figure 6 This is a diagram showing the measurement error and boundary constraint threshold of the intelligent agent in an embodiment of the present invention. Detailed Implementation

[0071] The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0072] like Figure 1 The flowchart of a finite-time privacy protection consistency method under an event-triggered mechanism of the present invention is shown below, with the specific steps as follows:

[0073] S1. Establish the agent model in the multi-agent system and give the communication topology of the system;

[0074] S2. For the multi-agent model proposed in step S1, design a finite-time privacy-preserving consistency control framework. By introducing an output mapping function, the real state of each agent is unknown to the neighboring agents. The finite-time theory is introduced to enable the multi-agent model to converge in a finite time.

[0075] S3. Design a finite-time privacy-preserving consistency controller based on an event-triggered mechanism. Define the state measurement error, the consistency error of the real state, and the consistency error of the hidden state, and derive effective event-triggered conditions so that the agent can update the controller when the event-triggered conditions are met.

[0076] S4. Substitute the finite-time privacy-preserving consistency controller established in step S3 into the agent model to derive the closed-loop system equation, which ultimately enables the multi-agent system to achieve consistent convergence within a finite time and ensures that neighboring agents cannot obtain the true state information of the entity.

[0077] In this embodiment, step S1 specifically includes the following:

[0078] S11. The multi-agent system has n agents, and its communication topology can be represented by a weighted undirected graph G = (V, E).

[0079] In this system, each agent represents a node, the set of nodes is denoted by V, and the set of edges is denoted by E. ij This indicates that agents i and j can interact with each other, and the adjacency matrix A = [a ij ] represents the connectivity relationship in a multi-agent system, a ij Let represent each element in the adjacency matrix. If (i,j)∈E, then a ij >0, otherwise a ij =0. The Laplace matrix L = [l ij The definition of ] is L = DA, D = diag[d1,...,d n ] represents a weight matrix and satisfies l ij This represents the individual elements in the Laplace matrix.

[0080] S12. The dynamic model of agents in a multi-agent system is as follows:

[0081]

[0082] in, Let i represent the state variable of the i-th agent. Let represent the integral over the state variable, and t represent the time variable. The control input representing the intelligent agent, i.e., the controller that needs to be designed. and They represent the set of positive integers and the set of n-dimensional real numbers, respectively.

[0083] S13. To achieve finite-time privacy-preserving consistency control for multi-agent systems, in this embodiment, it is defined that if the true state of an agent cannot be reconstructed from its known output trajectory and dynamic model, then the initial state x of the agent is... i (0) is unknowable if there exists a finite time T that satisfies:

[0084]

[0085] Where, x j Let (t) represent the state variable of the j-th agent. If there exists an output mapping function h that satisfies... x i (t) represents the state variable of the i-th agent, h i (t,x i (t) represents the output mapping function of the i-th agent, and the function is different for each agent. i (t,x i (t) can ensure that the state of the agent is unknown, and the function h i (t,x i (t) is strictly monotonically increasing.

[0086] In summary, if the above conditions are met, the controller designed in this embodiment can achieve time-limited privacy-preserving consistency control of multi-agent systems.

[0087] In this embodiment, step S2 specifically includes the following:

[0088] S21. The premise of privacy protection consistency is that all intelligent agents eventually receive the same value, while avoiding changing their initial state x. i (0) Leakage to other intelligent agent nodes: In this embodiment, a continuously time-varying output mapping function is introduced into the multi-agent system. This function can be used to achieve privacy masking of the initial state. The function expression is:

[0089]

[0090] in, Representation and agent state vector Masks of the same size output state vectors. Let T represent the general formula for a vector that can be divided into n subvectors, where the variable subscripts indicate the corresponding agent numbers, and T represents the transpose of the matrix. and Let represent the set of positive real numbers and the set of n-dimensional real vectors, respectively. h(t,x(t),π) is the mapping function, which is the state variable hidden by the mapping function. The output y(t) of the hidden state variable is transmitted to the neighboring agents through the communication topology network composed of the multi-agent system.

[0091] Therefore, the expression for a multi-agent system with privacy protection is:

[0092]

[0093] in, Let f(·) represent the integral of the state vector, and f(·) be the dynamic model of the agent. In this embodiment, it is assumed that the dynamic model of the agent is known to the outside world, each agent can obtain the masked output state vector y(t) of all neighboring agents, and each agent cannot directly obtain the real state of the neighboring agents and the real expression of the mapping function.

[0094] S22. For the multi-agent model involved in step S12, this model is a continuous-time system. If there exists a continuous positive definite function V(x), and there exist constants c > 0 and 0 < τ < 1, satisfying the following expression:

[0095]

[0096] in, Let V(x) be the first derivative of the state vector x(t) in step S21. By solving the above inequality, we can obtain that when t > T(x0), the system converges to 0. Then, the finite time T(x0) satisfies:

[0097]

[0098] Here, x0 represents the initial state of the system. This step introduces the finite-time theory and derives the specific expression for finite time, laying the groundwork for the subsequent design of a finite-time privacy-preserving consistency controller.

[0099] As can be seen from steps S21 and S22, in this embodiment, the output mapping function is used as a means of multi-agent privacy protection, which can effectively hide and protect the state of the agent, ensure the privacy of information in the information interaction with neighboring agents, and introduce finite time theory for further application in the design of subsequent controllers.

[0100] In this embodiment, step S3 specifically includes the following:

[0101] S31. To facilitate the design of subsequent event triggering conditions, the state measurement error e of agent i is... i (t) is defined as follows:

[0102]

[0103] in, This indicates the current trigger moment of the multi-agent system controller. Indicates the next trigger time. This represents the state variable corresponding to the current triggering moment. A traditional finite-time event-triggered controller is designed as follows:

[0104]

[0105] Among them, u i (t) corresponds to the controller involved in step S12, which does not consider privacy protection. μ and α represent control gains, and satisfy μ∈(0,1), α>0, and time. definition Let b represent the set of non-negative integers, where b is an element of the set of non-negative integers. This indicates the current triggering time of agent j. Indicates the solution The auxiliary time variable, and sig(x) μ =sign(x)|x| μ The function sign(·) is a sign function, N i Represents all neighboring intelligent agents of agent i.

[0106] S32. As can be seen from the privacy protection method involved in step S21, the specific output mapping function expression for agent i is:

[0107]

[0108] Where, π i ={φ i ,σ i ,δ i ,γ i The four elements in this set represent the variable gain of the mapping function described above. The gain varies for different agents, and this continuous-time function gradually decreases. When applied to a multi-agent system, the corresponding vector form is:

[0109] y(t)=h(t,x(t),π)=(I n +φe -Σt (x(t)+e) -Δt γ), (28)

[0110] Among them, I n Let φ represent an n-dimensional identity matrix, φ = diag(φ1,...,φ). n), Σ=diag(σ1,...,σ n ), Δ=diag(δ1,...,δ n ) and γ=[γ1,…,γ n The subscript of the element in the above variables represents the corresponding agent number.

[0111] S33. The finite-time privacy-preserving consistency controller based on an event-triggered mechanism is designed as follows:

[0112]

[0113] Where the control gain α > 0, 0 ≤ μ < 1, the state measurement error in step S31 is redefined as:

[0114]

[0115] in, This represents the output of the mapping function corresponding to the current triggering moment, i.e., the hidden state variable information obtained through privacy protection measures.

[0116] S34. To obtain the event triggering conditions for controller updates, define the following relationship:

[0117]

[0118] Among them, Z i (t) represents the consistency error corresponding to the output of the mapping function, y j (t) represents the masked output of agent j, M i (t) represents the consistency error of the system's true state variables, x j (t) represents the state variable of agent j, E i (t) represents the summation of state measurement errors. Therefore, the event triggering condition corresponding to the controller designed in step S33 is:

[0119] |E i (t)|≤ε i |Z i (t)|, (32)

[0120] Among them, the pre-set parameter ε i It is a positive vector, therefore, the next event trigger time is:

[0121]

[0122] In summary, the controller design was completed, and the corresponding event triggering conditions were obtained.

[0123] In this embodiment, step S4 specifically includes the following:

[0124] S41. To obtain the closed-loop system equations, the state measurement errors involved in step S33 are incorporated into the controller:

[0125]

[0126] S42. Substituting the result obtained in step S41 into the dynamic model involved in step S12 yields:

[0127]

[0128] The corresponding vector form of the closed-loop system equations is:

[0129]

[0130] Where Z(t) and E(t) represent the values ​​corresponding to Z respectively. i (t) and E i The vector form of (t), It is the Kronecker product.

[0131] In summary, the above steps complete the design of a time-limited privacy protection consistency control based on an event-triggered mechanism.

[0132] The multi-agent communication topology diagram in this embodiment is as follows: Figure 2 As shown, there are 5 independent agents, each of which can be considered a communication node. The initial state of the system is x. i (0) = [-1.8, 12.4, -0.6, -6, 11] T The selected input mapping function is y i (t)=(1+0.8e -1.2t (x) i (t)-e -1.5t The control gain is set to α = 0.5, μ = 0.75, and the parameter ε is related to the event triggering condition. i =0.1.

[0133] Figure 3 This demonstrates the real state trajectory of agent i in a multi-agent system. Figure 4 To introduce a privacy-preserving algorithm, the mapping function of agent i outputs the state trajectory. Figure 5 This is a graph showing the triggering times of the agent after introducing an event-triggered mechanism. Figure 6The relationship between the measurement error of each agent and the boundary constraint threshold is represented. The simulation results show that the finite-time privacy-preserving consistency control based on the event triggering mechanism is finally achieved in this embodiment. The false states of the agents eventually converge within a finite time and the convergence value is consistent with the true convergence value of the agent state. The simulation results show that the proposed control scheme can achieve finite-time privacy-preserving consistency control of multi-agent systems.

[0134] Those skilled in the art will recognize that the embodiments described herein are intended to help the reader understand the principles of the invention, and should be understood that the scope of protection of the invention is not limited to such specific statements and embodiments. Those skilled in the art can make various other specific modifications and combinations based on the technical teachings disclosed in this invention without departing from the spirit of the invention, and these modifications and combinations are still within the scope of protection of this invention.

Claims

1. A time-limited privacy-preserving consistency method under an event-triggered mechanism, the specific steps of which are as follows: S1. Establish the dynamic model of the agents in the multi-agent system and give the communication topology of the system. S2. For the multi-agent model proposed in step S1, design a finite-time privacy-preserving consistency control framework. By introducing an output mapping function, the real state of each agent is unknown to the neighboring agents. The finite-time theory is introduced to enable the multi-agent model to converge in a finite time. S3. Design a finite-time privacy-preserving consistency controller based on an event-triggered mechanism. Define the state measurement error, the consistency error of the real state, and the consistency error of the hidden state, and derive effective event-triggered conditions so that the agent can update the controller when the event-triggered conditions are met. S4. Substitute the finite-time privacy-preserving consistency controller established in step S3 into the agent model to derive the closed-loop system equation, which ultimately enables the multi-agent system to achieve consistent convergence within a finite time and ensures that neighboring agents cannot obtain the true state information of the entity.

2. The finite-time privacy protection consistency method under an event-triggered mechanism according to claim 1, characterized in that, In step S1, the specific details are as follows: S11. The multi-agent system has n agents, and its communication topology can be represented by a weighted undirected graph. To indicate; In this system, each agent represents a node, the set of nodes is denoted by V, and the set of edges is denoted by E. This indicates that agents i and j can interact with each other, and the adjacency matrix represents this. This represents the connectivity relationships within a multi-agent system. Represents each element in the adjacency matrix, if Then there is ,otherwise Laplace matrix The definition of , Represent the weight matrix and satisfy , Represents the elements in the Laplace matrix; S12. The dynamic model of agents in a multi-agent system is as follows: （1）； in, Let i represent the state variable of the i-th agent. Let represent the integral over the state variable, and t represent the time variable. The control input representing the intelligent agent, i.e., the controller that needs to be designed. and Represent the set of positive integers and the set of n-dimensional real numbers, respectively; S13. If there exists a finite time T that satisfies: （2）； in, Let h represent the state variable of the j-th agent. If there exists an output mapping function h that satisfies... , Let i represent the state variable of the i-th agent. Let represent the output mapping function of the i-th agent, and the function is different for each agent. It can ensure that the state of the agent is unknown, and the function It is strictly incremental.

3. The finite-time privacy protection consistency method under an event-triggered mechanism according to claim 2, characterized in that, In step S2, the specific details are as follows: S21. Introduce a continuously time-varying output mapping function in a multi-agent system. This function is used to achieve privacy masking of the initial state. The function expression is: （3）； in, Representation and agent state vector Masks of the same size output state vectors. Let T represent the general formula for a vector that can be divided into n subvectors, where the variable subscripts indicate the corresponding agent numbers, and T represents the transpose of the matrix. and Let them represent the set of positive real numbers and the set of n-dimensional real vectors, respectively. It is a mapping function, that is, the state variables after being hidden by the mapping function, and the output of the hidden state variables. This information is transmitted to neighboring agents through a communication topology network composed of a multi-agent system. The expression for a multi-agent system with privacy protection features is: （4）； in, Represents the integral of the state vector. The dynamic model of the agent is assumed to be known to the outside world, and each agent can obtain the masked output state vectors of all its neighbors. Furthermore, each agent cannot directly obtain the true state of its neighboring agents or the true expression of the mapping function; S22. For the multi-agent model involved in step S12, if the model is a continuous-time system, then there exists a continuously positive definite function. And the existence of constants and It satisfies the following expression: （5）； in, express It concerns the state vector in step S21. The first derivative is obtained by solving the above inequality. Afterwards, the system converges to 0, which is a finite-time condition. satisfy: （6）； in, This represents the initial state of the system.

4. The finite-time privacy protection consistency method under an event-triggered mechanism according to claim 3, characterized in that, In step S3, the specific details are as follows: S31. Error in state measurement of agent i The definition is as follows: （7）； in, This indicates the current trigger moment of the multi-agent system controller. Indicates the next trigger time. This represents the state variable corresponding to the current triggering moment. A traditional finite-time event-triggered controller is designed as follows: （8）； in, The controller involved in step S12 does not consider privacy protection issues. , Represents the control gain, and satisfies , ,time ,definition , Represents the set of non-negative integers. An element belonging to the set of non-negative integers. This indicates the current triggering time of agent j. Indicates the solution The auxiliary time variable, and ,function It is a symbolic function. Represents all neighboring intelligent agents of agent i; S32. As can be seen from the privacy protection method involved in step S21, the specific output mapping function expression for agent i is: （9）； in, The four elements in this set represent the variable gain of the aforementioned mapping function. The gain varies for different agents, and this continuous-time function gradually decreases. Applying this function to a multi-agent system, the corresponding vector form is: ； in, Represents an n-dimensional identity matrix. , , and The subscript of the element in the above variables represents the corresponding agent number; S33. The finite-time privacy-preserving consistency controller based on an event-triggered mechanism is designed as follows: （11）； Among them, control gain , The state measurement error in step S31 is redefined as follows: （12）； in, This represents the output of the mapping function corresponding to the current triggering moment, i.e., the hidden state variable information obtained through privacy protection measures; S34. To obtain the event triggering conditions for controller updates, define the following relationship: （13）； in, This indicates the consistency error corresponding to the output of the mapping function. This represents the mask output of agent j. This represents the consistency error of the system's true state variables. Represents the state variable of agent j. The summation of state measurement errors indicates that the event triggering condition for the controller designed in step S33 is: （14）； Among them, the pre-set parameters It is a positive vector, therefore, the next event trigger time is: （15）。 5. The finite-time privacy protection consistency method under an event-triggered mechanism according to claim 4, characterized in that, In step S4, the specific details are as follows: S41. Incorporate the state measurement error involved in step S33 into the controller: （16）； S42. Substituting the result obtained in step S41 into the dynamic model involved in step S12 yields: （17）； The corresponding vector form of the closed-loop system equations is: （18）； in, and They represent the corresponding and vector form, It is the Kronecker product; In summary, the above steps complete the design of a time-limited privacy protection consistency control based on an event-triggered mechanism.

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