Privacy and control performance collaborative design method in multi-agent system

Abstract

The invention discloses a privacy and control performance collaborative design method in a multi-agent system, and the method comprises the steps: S1, dividing the multi-agent system into a plurality of independent agents, and constructing a communication topological graph of the communication between the agents; s2, constructing a second-order continuous multi-agent system cooperation control protocol containing Gaussian mechanism differential privacy; s3, based on the communication topological graph and a second-order continuous multi-agent system cooperation control protocol, a collaborative design optimization model is constructed, and the optimization objective of the collaborative design optimization model is to minimize the weighted sum of the network communication load and the privacy leakage degree of all agents. Constraint conditions of the collaborative design optimization model comprise a system steady-state performance error upper bound, a network algebraic connectivity lower bound and a minimum privacy protection level of each agent; and S4, solving the collaborative design optimization model to obtain an optimal weight of each communication link in the communication topology network and an optimal privacy protection parameter of the position and the speed of each agent.

Description

Technical Field

[0001] This application relates to the field of control and privacy protection technology for multi-agent systems. Specifically, it relates to a collaborative design method for privacy and control performance in multi-agent systems. Background Technology

[0002] Multi-agent systems, through information sharing and collaboration among their agents, can accomplish complex cooperative tasks, such as drone swarming, intelligent vehicle cooperative driving, and distributed robotics. In these applications, agents typically need to share their state information (such as position and speed) in real time to achieve cooperative control. However, this information sharing also brings serious privacy risks. For example, in vehicle-to-everything (V2X) systems, malicious attackers can analyze vehicle broadcasts of position and speed information to infer sensitive information such as the driver's travel trajectory and lifestyle. Differential privacy, a rigorous and quantifiable privacy protection framework, has been introduced into the field of dynamic systems in recent years due to its excellent properties, such as immunity to post-processing. However, existing research mostly focuses on protecting the position privacy of first-order multi-agent systems. For second-order systems involving both position and speed, privacy protection schemes are more complex and research is still insufficient. Simply overlaying privacy protection mechanisms onto existing control systems often significantly reduces the cooperative control performance of the system. Currently, there is a lack of a cooperative design framework that can uniformly consider the dual privacy (position and speed) requirements of second-order systems, system control performance, and the underlying communication network topology. Existing solutions typically separate privacy, control, and topology design, making it difficult to achieve an optimal balance between the strength of privacy protection and system performance. Summary of the Invention

[0003] The purpose of this application is to provide a collaborative design method for privacy and control performance in a multi-agent system, and the specific technical solution is as follows:

[0004] A collaborative design method for privacy and control performance in a multi-agent system includes: S1, dividing the multi-agent system into multiple independent agents and constructing a communication topology graph for communication between each agent; S2, based on the communication topology graph constructed in S1, constructing a second-order continuous multi-agent system cooperative control protocol incorporating Gaussian differential privacy; S3, based on the communication topology graph constructed in S1 and the second-order continuous multi-agent system cooperative control protocol constructed in S2, constructing a collaborative design optimization model. The optimization objective of this collaborative design optimization model is to minimize the weighted sum of network communication load and the degree of privacy leakage of all agents. The constraints of this collaborative design optimization model include an upper bound on the steady-state performance error of the system, a lower bound on the algebraic connectivity of the network, and a minimum privacy protection level for each agent; S4, solving the collaborative design optimization model constructed in S3 to obtain the optimal weights of each communication link in the communication topology network and the optimal privacy protection parameters for the position and velocity of each agent.

[0005] When constructing the communication topology diagram between each agent in S1, the following are included:

[0006] S1.1 The multi-agent system is defined as consisting of N independent agents, each agent's state including its position vector. velocity vector and the dimensions of the agent ;

[0007] S1.2 Define an initial undirected, weighted, and connected communication topology graph. ,in For a set of nodes, For the system edge set, Let represent the weighted adjacency matrix of an undirected graph, and for In other words, ,otherwise ;

[0008] S1.3, Define the neighbor set as ;

[0009] S1.4, Intelligent Agent The weighted degree is expressed as Maximum degree is The degree matrix is ​​defined as follows: ;

[0010] S1.5 Determine the communication topology diagram The weighted Laplace matrix, which describes the connectivity and coupling strength between agents. The Laplace matrix is ​​expressed as: ;

[0011] S1.6, Set position control gain and speed control gain To ensure system stability, the gain must meet the following constraints: , , and ,in Communication topology diagram The algebraic connectivity of the Laplace matrix.

[0012] When constructing a cooperative control protocol for a second-order continuous multi-agent system that incorporates Gaussian differential privacy in S2, the following are included:

[0013] S2.1, The second-order continuous multi-agent cooperative control protocol is represented as:

[0014] ,

[0015] in, , , Let be the dimension of the state vector of a single agent at a given moment.

[0016] S2.2. In S2.1, the second-order continuous multi-agent cooperative control protocol introduces process noise, and the network dynamics are then expressed as:

[0017] ,

[0018] in, , These are zero-mean Gaussian process noises corresponding to position and velocity, respectively.

[0019] S2.3, Settings The variance of the Gaussian noise is determined by the privacy budget parameter set for each agent. Privacy failure probability and adjacency parameters Dynamically determined;

[0020] S2.4, Take , Given , , ;

[0021] S2.5, When:

[0022] ,

[0023] The Gaussian mechanism is then represented as: , satisfy Differential privacy, in which, To complement the Gaussian distribution, and ;

[0024] S2.6, Definition: Therefore, the noise standard deviation must meet the following requirements. ;

[0025] S2.7 Before sharing its own state with its neighbors, it injects independent and identically distributed Gaussian noise into its own state. The privacy protection state is as follows: , When all agents adopt this strategy, the agents Only its neighbor set can be retrieved. Neighbors Disturbance state and Substituting these perturbation states into the dynamic equations yields a multi-agent cooperative control protocol that includes privacy protection:

[0026] ,

[0027] This protocol corresponds to four noise terms, and the covariance matrices of all noise terms are as follows: , , and .

[0028] The objective function of the collaborative design optimization model in S3 is:

[0029] ,

[0030] in, For the weighted Laplace matrix space, given the initial topology Laplace matrix constraint; The sum of the degrees of all nodes; minimizing this term yields a solution with smaller edge weights and sparser connections. This term represents the overall privacy level of all agents; minimizing this term enhances privacy protection because... and The smaller the value, the stronger the corresponding privacy protection; Weighting factors This determines the relative priority among these objectives, with larger ones... More emphasis is placed on enhanced privacy, while smaller They tend to prefer sparse network topologies.

[0031] The constraints of the collaborative design optimization model in S3 are expressed as follows:

[0032] S3.1 Performance Constraints:

[0033] ,

[0034] in:

[0035] The steady-state mean square error of the system ,in, Let be the state dimension. This is a value set by the user.

[0036] S3.2, System stability constraints:

[0037] , , ,

[0038] When control gain and If the constraints are met, the system is stable.

[0039] S3.3 Privacy Constraints:

[0040] For any ,have , ,

[0041] That is, the privacy parameters of each intelligent agent should not be lower than the preset minimum privacy level;

[0042] S3.4 Connectivity Constraints:

[0043] ,

[0044] Algebraic connectivity of network topology Not lower than the preset value .

[0045] Solving the collaborative design optimization model in S4 includes:

[0046] The solution employs sequential convex programming or nonlinear optimization techniques. In each iteration of the solution process, the nonconvex constraints are approximated by convex approximation functions. At the same time, the Laplacian matrix is ​​updated while maintaining graph connectivity. Through explicit mathematical relationships, a standardized framework is provided for the systematic balance between the two competing goals of privacy protection and collaborative performance.

[0047] S5. Based on the multi-agent system configured in S1-S4, test and analyze the privacy protection effectiveness and control performance of the multi-agent system.

[0048] In S5, the verification of privacy protection effectiveness includes: when each agent... Location trajectory and velocity trajectory Each satisfies and - In differential privacy, is it difficult for an attacker to infer the true trajectory of a single agent given that all shared perturbation information is available?

[0049] In S5, the control performance verification includes: under continuous privacy noise and process noise interference, the system's position state can converge, while the velocity state reaches a consistent value near the expected value and maintains dynamic equilibrium. The actual measured steady-state mean square error of the system satisfies... Requirements.

[0050] The advantages of this application lie in its simultaneous consideration of the position and velocity privacy of agents within the cooperative control framework, making it applicable to a wider range of second-order dynamic system applications. A performance error upper bound is established through rigorous mathematical derivation and used as an optimization constraint, ensuring that the cooperative control performance of the system still meets the preset requirements even after the injection of privacy noise. By jointly optimizing privacy, performance, and topology, the optimal operating point of the system under given constraints is found, achieving an optimal trade-off between privacy protection and system performance, rather than a simple compromise. The control protocol is fully distributed, requiring no central coordinator, thus enhancing the system's reliability and scalability. Furthermore, by adjusting the weight coefficients and constraints in the optimization objective, it can flexibly adapt to the different application scenarios' emphasis on privacy and performance. Attached Figure Description

[0051] Figure 1 This is the initial communication topology diagram used in this application;

[0052] Figure 2 This application provides a second-order differential privacy mechanism for a single agent.

[0053] Figure 3 In Simulation 1, different performance error thresholds were used. Convergence curves of the system's position and velocity states;

[0054] Figure 4 In Simulation 1, a bubble chart is used to illustrate the trade-off between performance and privacy.

[0055] Figure 5 To maximize the privacy of different agents in Simulation 2 Convergence curves of the system's position and velocity states;

[0056] Figure 6 In Simulation 2, a bubble chart is used to illustrate the impact of different maximum privacy levels on network topology.

[0057] Figure 7 In Simulation 3, different minimum connectivity Convergence curves of the system's position and velocity states;

[0058] Figure 8 In Simulation 3, a bubble diagram is used to illustrate the impact of different minimum connectivity levels on the network topology.

[0059] Figure 9 In Simulation 4, different weighting factors Convergence curves of the system's position and velocity states;

[0060] Figure 10 In Simulation 4, a bubble chart is used to illustrate the impact of different weighting factors on the network topology. Detailed Implementation

[0061] To make the objectives, technical solutions, and advantages of this application clearer, the application will be further described in detail below with reference to specific embodiments and accompanying drawings. It should be understood that these descriptions are merely exemplary and not intended to limit the scope of this application. Furthermore, descriptions of well-known structures and technologies are omitted in the following description to avoid unnecessarily obscuring the concepts of this application.

[0062] like Figure 1 and Figure 2 As shown, a collaborative design method for privacy and control performance in a multi-agent system includes:

[0063] S1. Divide the multi-agent system into multiple independent agents and construct a communication topology diagram for communication between each agent. Specifically, constructing the communication topology diagram for communication between each agent includes:

[0064] S1.1 The multi-agent system is defined as consisting of N independent agents, each agent's state including its position vector. velocity vector and the dimensions of the agent ;

[0065] S1.2 Define an initial undirected, weighted, and connected communication topology graph. ,in For a set of nodes, For the system edge set, Let represent the weighted adjacency matrix of an undirected graph, and for In other words, ,otherwise ;

[0066] S1.3, Define the neighbor set as ;

[0067] S1.4, Intelligent Agent The weighted degree is expressed as Maximum degree is The degree matrix is ​​defined as follows: ;

[0068] S1.5 Determine the communication topology diagram The weighted Laplace matrix, which describes the connectivity and coupling strength between agents. The Laplace matrix is ​​expressed as: ;

[0069] S1.6, Set position control gain and speed control gain To ensure system stability, the gain must meet the following constraints: , , and ,in Communication topology diagram The algebraic connectivity of the Laplace matrix.

[0070] S2. Based on the communication topology constructed in S1, construct a cooperative control protocol for a second-order continuous multi-agent system that incorporates Gaussian differential privacy. Specifically, constructing the cooperative control protocol for a second-order continuous multi-agent system that incorporates Gaussian differential privacy includes:

[0071] S2.1, The second-order continuous multi-agent cooperative control protocol is represented as:

[0072] ,

[0073] in, , , Let be the dimension of the state vector of a single agent at a given moment.

[0074] S2.2. In S2.1, the second-order continuous multi-agent cooperative control protocol introduces process noise, and the network dynamics are then expressed as:

[0075] ,

[0076] in, , These are zero-mean Gaussian process noises corresponding to position and velocity, respectively.

[0077] S2.3, Settings The variance of the Gaussian noise is determined by the privacy budget parameter set for each agent. Privacy failure probability and adjacency parameters Dynamically determined;

[0078] S2.4, Take , Given , , ;

[0079] S2.5, When:

[0080] ,

[0081] The Gaussian mechanism is then represented as: , satisfy Differential privacy, in which, To complement the Gaussian distribution, and ;

[0082] S2.6, Definition: Therefore, the noise standard deviation must meet the following requirements. ;

[0083] S2.7 Before sharing its own state with its neighbors, it injects independent and identically distributed Gaussian noise into its own state. The privacy protection state is as follows: , When all agents adopt this strategy, the agents Only its neighbor set can be retrieved. Neighbors Disturbance state and Substituting these perturbation states into the dynamic equations yields a multi-agent cooperative control protocol that includes privacy protection:

[0084] ,

[0085] This protocol corresponds to four noise terms, and the covariance matrices of all noise terms are as follows: , , and .

[0086] S3. Based on the communication topology constructed in S1 and the second-order continuous multi-agent system cooperative control protocol constructed in S2, a cooperative design optimization model is constructed. The optimization objective of this model is to minimize the weighted sum of network communication load and the degree of privacy leakage of all agents. The constraints of this model include an upper bound on the steady-state performance error, a lower bound on the network algebraic connectivity, and a minimum privacy protection level for each agent. Specifically, the objective function of the cooperative design optimization model is:

[0087] ,

[0088] in, For the weighted Laplace matrix space, given the initial topology Laplace matrix constraint; The sum of the degrees of all nodes; minimizing this term yields a solution with smaller edge weights and sparser connections. This term represents the overall privacy level of all agents; minimizing this term enhances privacy protection because... and The smaller the value, the stronger the corresponding privacy protection; Weighting factors This determines the relative priority among these objectives, with larger ones... More emphasis is placed on enhanced privacy, while smaller They tend to prefer sparse network topologies.

[0089] The constraints of the collaborative design optimization model are expressed as follows:

[0090] S3.1 Performance Constraints:

[0091] ,

[0092] in:

[0093] The steady-state mean square error of the system ,in, Let be the state dimension. This is a value set by the user.

[0094] S3.2, System stability constraints:

[0095] , , ,

[0096] When control gain and If the constraints are met, the system is stable.

[0097] S3.3 Privacy Constraints:

[0098] For any ,have , ,

[0099] That is, the privacy parameters of each intelligent agent should not be lower than the preset minimum privacy level;

[0100] S3.4 Connectivity Constraints:

[0101] ,

[0102] Algebraic connectivity of network topology Not lower than the preset value .

[0103] S4. Solve the cooperative design optimization model constructed in S3 to obtain the optimal weights of each communication link in the communication topology network, as well as the optimal privacy-preserving parameters for the position and velocity of each agent. Specifically, solving the cooperative design optimization model involves: using sequential convex programming or nonlinear optimization techniques. In each iteration of the solution process, non-convex constraints are approximated by convex approximation functions, and the Laplace matrix is ​​updated while maintaining graph connectivity. Through explicit mathematical relationships, a standardized framework is provided for systematically balancing the two competing objectives of privacy protection and cooperative performance.

[0104] S5. Based on the multi-agent system configured in S1-S4, test and analyze the privacy protection effectiveness and control performance of the multi-agent system. Specifically, the privacy protection effectiveness verification includes: when each agent... Location trajectory and velocity trajectory Each satisfies and - In differential privacy scenarios, given that an attacker has access to all shared perturbation information, is it difficult to infer the true trajectory of a single agent? Control performance verification includes: under continuous privacy noise and process noise interference, the system's position state converges, while the velocity state reaches a consistent value near the expected value and maintains dynamic equilibrium. The actual measured steady-state mean square error of the system satisfies... This approach meets the requirements of traditional methods that "design the network first and then add privacy features." Compared to this approach, this embodiment, through collaborative design, can achieve the same performance metrics. This allows for stronger overall privacy protection; or, at the same level of privacy, better control performance and lower communication costs.

[0105] When configuring and running a second-order continuous-time multi-agent cooperative control system designed according to this application, which has dual privacy protection for position and velocity, the following are included:

[0106] A. System parameter configuration and initialization

[0107] The settings system includes There are 1 intelligent agents, and the state of each agent is: and ,in For position vectors, For velocity vectors, For agents, define an initial undirected, weighted, connected communication topology graph. The weighted Laplacian matrix of the graph is determined, which describes the connectivity and coupling strength between agents. Set position to control gain. and speed control gain To ensure system stability, the gain must meet the following constraints: , , and ,in Let be the algebraic connectivity of the graph Laplace matrix.

[0108] For each intelligent agent Configure privacy parameters for its position and velocity trajectory: privacy budget Privacy failure probability is Adjacency parameters are Based on the Gaussian mechanism, the required noise standard deviation is calculated as follows: .in, , , This is a Gaussian complement function.

[0109] Set an upper bound for the global steady-state mean square error of the system. As a performance constraint, and the minimum algebraic connectivity of the network As a connectivity constraint.

[0110] B. Operation of the Privacy Protection Collaborative Control System

[0111] After the system is configured, each intelligent agent Perform the following operations in parallel over a continuous timeframe: obtain its own real-time location. and real speed Generate location privacy noise , And calculate the state after the perturbation, i.e. , .

[0112] The disturbed state is transmitted through a communication network. Broadcast to all its neighboring intelligent agents Intelligent agents It also receives the states from all neighboring agents after adding noise, and calculates the control input according to the following second-order continuous-time cooperative control protocol:

[0113]

[0114] in, and It is the inherent zero-mean Gaussian process noise of the system. Based on the calculated derivative, the system updates its position and velocity state through integration, thus achieving continuous motion.

[0115] C. Collaborative Design Optimization

[0116] To achieve the optimal balance between privacy, performance, and communication cost, this embodiment provides a collaborative design optimization method. The decision variable for the optimization problem is the communication link weight. Location privacy parameters of all agents Speed ​​privacy parameters Our optimization goal is:

[0117]

[0118] The objective function aims to minimize the weighted sum of total communication load and total privacy leakage, where These are adjustable weighting coefficients.

[0119] The constraints are:

[0120] (1) ;

[0121] in,

[0122] .

[0123] (2) , , and ;

[0124] (3) For any ,have , ;

[0125] (4) .

[0126] Performance constraint (1) and stability constraint (2) are optimization variables. and The non-convex nature of the objective function makes this problem computationally challenging. The objective function essentially represents a multi-objective optimization problem, where the weighting factors... Enables designers to work with network sparsity With privacy protection Prioritize them accordingly. There are tight couplings between the constraints: changes in privacy parameters will affect noise variance. and Modifications to the topology affect performance boundaries, while changes to the topology will affect algebraic connectivity. and error boundary molecule All of these have an impact.

[0127] Based on the objective function and constraints described above, the nonlinear programming problem is solved using numerical optimization tools. The optimal weights obtained from the solution are then... and optimal privacy parameters This is deployed into the communication and privacy processing modules of each agent. Specifically, the problem can be solved using sequential convex programming or other nonlinear optimization techniques. In each iteration of the solution process, the nonconvex constraints are approximated by a convex approximation function, while the Laplacian matrix is ​​updated while maintaining graph connectivity. Despite the computational complexity, this problem-solving approach provides a standardized framework for systematically balancing the competing goals of privacy protection and cooperative performance through explicit mathematical relationships.

[0128] D. System Performance Examples

[0129] To illustrate the technical effects of the present invention, the system configured as described above was tested and analyzed:

[0130] (1) Verification of privacy protection effectiveness: Through theoretical analysis, it can be seen that each intelligent agent Location trajectory and velocity trajectory Each satisfies and - Differential privacy. This means that even if an attacker obtains all the shared perturbation information, it is difficult to infer the true trajectory of a single agent.

[0131] (2) Verification of control performance: Under the interference of continuous privacy noise and process noise, the position state of the system can converge, while the velocity state reaches a consistent value near the expected value and maintains dynamic equilibrium. The actual measured steady-state mean square error of the system meets the requirements. The requirements will be explained in detail in the subsequent numerical simulations.

[0132] (3) Advantages of collaborative design: Compared with the traditional method of "designing the network first and then adding privacy", this embodiment can achieve the same performance indicators through collaborative design. This allows for stronger overall privacy protection; or, at the same level of privacy, better control performance and lower communication costs.

[0133] To make this application easier to understand, specific numerical simulation examples are used below to explain the rationality and scalability of the above embodiments.

[0134] The initial topology graph is as follows Figure 1 As shown, there are 10 nodes and 14 connections. A single intelligent agent... First, differential privacy Gaussian noise is added, and then information is shared with neighboring intelligent agents to achieve privacy protection. A schematic diagram of this mechanism is shown below. Figure 2 As shown in the figure. Next, the correctness of the collaborative design is verified through simulation analysis with four different parameters.

[0135] Simulation 1

[0136] like Figure 3 and Figure 4 As shown, this simulation demonstrates how system performance requirements affect the final level of privacy protection.

[0137] Set up a system with 10 agents, with the initial communication topology as follows: Figure 1 As shown. Fixed control gain. , , , , , , .make The result is as follows Figure 4 As shown. With The increase, The value will decrease, meaning that if performance is relaxed, the AI ​​will be more inclined to protect privacy.

[0138] Simulation 2

[0139] like Figure 5 and Figure 6 As shown in the figure, this simulation demonstrates the impact of the agent's maximum privacy requirements on the network structure.

[0140] Basic parameters are the same as in Simulation 1, with fixed parameters. ,make The result is as follows Figure 6 As shown, when each agent is allowed weaker privacy, collaborative design uses as few edge weights as possible to satisfy constraints. That is, when the privacy level of agents is reduced, they require less communication to achieve the same performance level.

[0141] Simulation 3

[0142] like Figure 7 and Figure 8 As shown in the figure, this simulation demonstrates the impact of network connectivity requirements on system design.

[0143] Basic parameters are the same as in Simulation 1, with fixed parameters. ,make The result is as follows Figure 8 As shown. With Increased connectivity requires stronger network connectivity, leading to a general increase in edge weights in the bubble graph, while also increasing the privacy parameters of each agent. Increased connectivity means reduced privacy protection. This indicates that higher connectivity requirements necessitate stronger information exchange, thereby weakening privacy protection capabilities.

[0144] Simulation 4

[0145] like Figure 9 and Figure 10As shown in the figure, this simulation demonstrates the moderating effect of the weighting factor in the optimization objective.

[0146] Basic parameters are the same as in Simulation 1, with fixed parameters. ,make The result is as follows Figure 10 As shown, with the weighting factor As the value increases, the objective function will tend to minimize it. Instead As the weighting factor increases, each AI entity experiences greater privacy. Figure 10 (d) shows that further increasing the weighting factor will not have a greater effect on protecting the privacy of the agent. At this point, the privacy of the intelligent agent is already quite strong. This indicates that there is a saturation point: beyond this point, further prioritizing privacy will yield very limited benefits.

[0147] The positional trajectories shown in the upper subplot exhibit a consistent pattern: initially dispersed, they converge to a common value, after which all agents move at a uniform speed. Variations in the range and slope of the ordinate arise from random initial conditions and do not affect the basic convergence behavior.

[0148] The velocity trajectories shown in the lower subplot exhibit continuous oscillations around the ensemble average velocity. This reflects the dynamic balance between the continuous injection of Gaussian noise (which would disrupt consistency) and the cooperative control law. The bounded amplitude of the oscillations confirms that the system achieves practical consistency despite the privacy-preserving perturbations.

[0149] These results collectively demonstrate that the multi-agent system maintains effective convergence within the proposed privacy-topology cooperative design framework. The differential privacy mechanism successfully protects sensitive state information, while the optimized network topology compensates for performance degradation caused by privacy noise, thus achieving a balance between privacy protection and cooperative control performance.

Claims

1. A method for collaborative design of privacy and control performance in a multi-agent system, characterized in that, include: S1. Divide the multi-agent system into multiple independent agents and construct a communication topology diagram for communication between each agent; S2. Based on the communication topology diagram constructed in S1, construct a cooperative control protocol for a second-order continuous multi-agent system that includes Gaussian differential privacy mechanism. S3. Based on the communication topology constructed in S1 and the second-order continuous multi-agent system cooperative control protocol constructed in S2, a cooperative design optimization model is constructed. The optimization objective of the cooperative design optimization model is to minimize the weighted sum of network communication load and the degree of privacy leakage of all agents. The constraints of the cooperative design optimization model include the upper bound of the steady-state performance error of the system, the lower bound of the network algebraic connectivity, and the minimum privacy protection level of each agent. S4. Solve the collaborative design optimization model constructed in S3 to obtain the optimal weights of each communication link in the communication topology network, as well as the optimal privacy protection parameters for the position and velocity of each agent.

2. The privacy and control performance collaborative design method in a multi-agent system as described in claim 1, characterized in that, The construction of the communication topology diagram between each agent in S1 includes: S1.1 The multi-agent system is defined as consisting of N independent agents, each agent's state including its position vector. velocity vector and the dimensions of the agent ; S1.2 Define an initial undirected, weighted, and connected communication topology graph. ,in For a set of nodes, For the system edge set, Let represent the weighted adjacency matrix of an undirected graph, and for In other words, ,otherwise ; S1.3, Define the neighbor set as ; S1.4, Intelligent Agent The weighted degree is expressed as Maximum degree is The degree matrix is ​​defined as follows: ; S1.5 Determine the communication topology diagram The weighted Laplace matrix, which describes the connectivity and coupling strength between agents. The Laplace matrix is ​​expressed as: ; S1.6, Set position control gain and speed control gain To ensure system stability, the gain must meet the following constraints: , , and ,in Communication topology diagram The algebraic connectivity of the Laplace matrix.

3. The privacy and control performance collaborative design method in a multi-agent system as described in claim 2, characterized in that, The S2 section describes the construction of a cooperative control protocol for a second-order continuous multi-agent system that incorporates Gaussian differential privacy. S2.1, The second-order continuous multi-agent cooperative control protocol is represented as: ， in, , , Let be the dimension of the state vector of a single agent at a given moment. S2.2, In S2.1, the second-order continuous multi-agent cooperative control protocol introduces process noise, then the network dynamics are represented as follows: ， in, , These are zero-mean Gaussian process noises corresponding to position and velocity, respectively. S2.3, Settings The variance of the Gaussian noise is determined by the privacy budget parameter set for each agent. Privacy failure probability and adjacency parameters Dynamically determined; S2.4, Take , Given , , ; S2.5, when: ， The Gaussian mechanism is then represented as: , satisfy Differential privacy, in which, To complement the Gaussian distribution, and ; S2.6, Definition: Therefore, the noise standard deviation must meet the following requirements. ; S2.7 Before sharing its own state with its neighbors, it injects independent and identically distributed Gaussian noise into its own state. The privacy protection state is as follows: , When all agents adopt this strategy, the agents Only its neighbor set can be retrieved. Neighbors Disturbance state and Substituting these perturbation states into the dynamic equations yields a multi-agent cooperative control protocol that includes privacy protection: ， This protocol corresponds to four noise terms, and the covariance matrices of all noise terms are as follows: , , and .

4. The privacy and control performance collaborative design method in a multi-agent system as described in claim 3, characterized in that, The objective function of the collaborative design optimization model in S3 is: ， in, For the weighted Laplace matrix space, given the initial topology Laplace matrix constraint; The sum of the degrees of all nodes; minimizing this term yields a solution with smaller edge weights and sparser connections. This term represents the overall privacy level of all agents; minimizing this term enhances privacy protection because... and The smaller the value, the stronger the corresponding privacy protection; Weighting factors This determines the relative priority among these objectives, with larger ones... More emphasis is placed on enhanced privacy, while smaller They tend to prefer sparse network topologies.

5. The privacy and control performance collaborative design method in a multi-agent system as described in claim 4, characterized in that, The constraints of the collaborative design optimization model in S3 are expressed as follows: S3.1 Performance Constraints: ， in: The steady-state mean square error of the system ,in, Let be the state dimension. This is a value set by the user. S3.2, System stability constraints: 、 ， ， When control gain and If the constraints are met, the system is stable. S3.3 Privacy Constraints: For any ,have , , That is, the privacy parameters of each intelligent agent should not be lower than the preset minimum privacy level; S3.4 Connectivity Constraints: ， Algebraic connectivity of network topology Not lower than the preset value .

6. The privacy and control performance collaborative design method in a multi-agent system as described in claim 5, characterized in that, Solving the collaborative design optimization model in S4 includes: The solution employs sequential convex programming or nonlinear optimization techniques. In each iteration of the solution process, the nonconvex constraints are approximated by convex approximation functions. At the same time, the Laplacian matrix is ​​updated while maintaining graph connectivity. Through explicit mathematical relationships, a standardized framework is provided for the systematic balance between the two competing goals of privacy protection and collaborative performance.

7. The privacy and control performance collaborative design method in a multi-agent system as described in claim 6, characterized in that, Also includes: S5. Based on the multi-agent system configured in S1-S4, test and analyze the privacy protection effectiveness and control performance of the multi-agent system.

8. The privacy and control performance collaborative design method in a multi-agent system as described in claim 7, characterized in that, The S5 step of verifying the effectiveness of privacy protection includes: when each intelligent agent... Location trajectory and velocity trajectory Each satisfies and - In differential privacy, is it difficult for an attacker to infer the true trajectory of a single agent given that all shared perturbation information is available? 9. The privacy and control performance collaborative design method in a multi-agent system as described in claim 7, characterized in that, The control performance verification in S5 includes: under continuous privacy noise and process noise interference, the system's position state can converge, while the velocity state reaches a consistent value near the expected value and maintains dynamic equilibrium. The actual measured steady-state mean square error of the system satisfies... Requirements.

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