Multi-agent privacy protection method under universal interactive topological structure

Abstract

The invention belongs to the field of computer science and control, and particularly relates to a multi-agent privacy protection method under universal interactive topology, which comprises the following steps of: 1, determining a communication topology network of a multi-agent system, and selecting a Laplacian matrix to represent an information interaction relationship among agents; 2, on the basis of the step 1, establishing a dynamical model of the intelligent agent; step 3, designing a state decomposition model under the dynamic model and the communication topology network, so that the state decomposition model has a certain privacy protection capability while realizing average consistency; and step 4, introducing a disturbance mechanism into the state decomposition model to realize that the initial privacy of the intelligent agent is not snooped by internal honest but curious nodes and external eavesdroppers in any connection mode. According to the method, the privacy of the agents can be protected from being peeped by internal honest but curious nodes and external eavesdroppers while average consistency of the agents is achieved.

Description

Technical Field

[0001] The present invention belongs to the field of computer science and control, and specifically relates to a multi-agent privacy protection method under a universal interactive topological structure. Background Art

[0002] Achieving state consistency in multi-agent collaborative control is an important research issue and has been widely used in the fields of multi-robots, wireless sensor communications, and distributed target optimization. In a multi-agent system, the initial states of each agent are generally different, so it is necessary to reach a consensus on the states of each agent through local dynamic interactions. The traditional distributed consensus algorithm is that each agent communicates locally with its neighbors, transmits its own state information and receives state information from its neighbors, and dynamically updates its own state through the collected information until the states of all agents in the system are consistent. If the consistency state finally reached by all agents is the average of their initial states, it is called average consistency. The traditional algorithm effectively solves the problem of multi-agent average consistency by having each agent transmit its true state information directly on the channel. However, the internal state of the agent is private or contains sensitive information. If it interacts directly with other agents and is open, it will be obtained by external attackers, resulting in privacy information leakage, which may have an immeasurable impact on the entire system. Therefore, it is necessary to set up a protection mechanism for the information transmitted by the agent communication link to ensure the security and confidentiality of system information and achieve the expected collaborative goals.

[0003] Existing privacy protection methods, such as those based on adding noise, cryptography, perturbation injection, and state decomposition, are limited by the communication topology when facing privacy snooping from internal honest but curious nodes and external eavesdroppers. Privacy protection is only effective when there are neutral neighbor nodes of the spied-on node or the input and output information is not completely leaked. When the internal honest but curious agent happens to be the only neighbor of an agent to transmit information, the privacy protection methods proposed in the existing literature fail. In actual application scenarios, the communication topology of multi-agent systems often has a local structure with unique neighbors. If there happens to be a curious eavesdropper among these agents, then the existing methods will not be able to achieve privacy protection for the entire system. Summary of the invention

[0004] In view of the above problems existing in the prior art, the present invention proposes a multi-agent privacy protection method under a universal interactive topology, which can protect the privacy of the agents from being spied on by internal honest but curious nodes and external eavesdroppers while achieving average consensus among the agents.

[0005] In order to achieve the above object, the technical solution specifically adopted by the present invention is as follows:

[0006] A multi-agent privacy protection method under a universal interactive topology includes the following steps:

[0007] Step 1: Determine the communication topology network of the multi-agent system and use the Laplace matrix to represent the information interaction relationship between agents;

[0008] Step 2: Based on step 1, a dynamic model of the intelligent agent is established so that all intelligent agents can eventually achieve average consistency;

[0009] Step 3: Based on the dynamic model established in step 2 and the communication topology network in step 1, a state decomposition model is designed to achieve average consistency while having a certain privacy protection capability;

[0010] Step 4. Based on step 3, a perturbation mechanism is introduced into the state decomposition model to ensure that the initial privacy of the agent cannot be spied on by internal honest but curious nodes and external eavesdroppers under any connection mode.

[0011] Furthermore, in step S2, the dynamics model of the intelligent agent is a first-order discrete dynamics model, and the first-order discrete dynamics model is as follows:

[0012]

[0013] Among them, x i [k] represents the state of agent i at time k, x j [k] represents the state of the neighbors of agent i at time k, x i [k+1] represents the state of agent i at time k+1, where k starts from zero; V j represents the neighbors of agent i, ò represents the control gain, max{d i} represents the maximum degree of all agents in the multi-agent system, requiring Under this first-order discrete dynamics model, the state information of each agent will converge to the average of the initial values.

[0014] Furthermore, step S3 includes the following steps:

[0015] Step 3.1: For the actual control variable x i [k] performs state decomposition and decomposes its state into as well as And satisfy the initial conditions

[0016] Step 3.2: Construct an average consistency model based on state decomposition. The average consistency model provides a consistency control protocol based on state decomposition as follows:

[0017]

[0018] in, a iβ =a βi =1, under this control protocol, all states will converge to the average of the initial values.

[0019] Furthermore, step 4 comprises the following steps:

[0020] Step 4.1, each agent selects a perturbation parameter and interacts with its neighbors. Specifically: each agent needs to pass an arbitrary value to its external neighbors in the network at the beginning;

[0021] Step 4.2, introducing a disturbance mechanism into the state decomposition model to construct a state decomposition privacy protection model with disturbance;

[0022] Step 4.3: interact with neighbors based on the state decomposition privacy protection model, wherein visible nodes interact with external neighbors, and invisible nodes only interact with visible nodes, and calculate the disturbance function at the update time;

[0023] Step 4.4: Decompose the privacy protection model based on the state with disturbance and update the disturbance function at the next moment to obtain the state at the next moment.

[0024] Furthermore, in step 4.2, after the state decomposition model introduces a disturbance mechanism, the state decomposition privacy protection model of each agent is as follows:

[0025]

[0026] in, Respectively represent the states of the visible and invisible child nodes of agent i at time k; θ i [k] represents the perturbation value applied by agent i at time k.

[0027] Furthermore, the perturbation function in step 4.3 is:

[0028]

[0029] in, represents the initial perturbation parameter of agent i, represents the initial perturbation parameters of agent i’s neighbors.

[0030] The present invention has the following characteristics and beneficial effects:

[0031] 1) The present invention adopts a state decomposition mechanism with disturbance, which can protect the privacy of the intelligent agent from being spied on by internal honest but curious nodes and external eavesdroppers while achieving average consensus among the intelligent agents.

[0032] 2) The present invention ensures the effectiveness of privacy protection capabilities under universal interactive topological structures. In actual scenarios, the privacy security of intelligent agents will not be restricted by topological connections. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] Other features, objects and advantages of the present invention will become more apparent from the detailed description of non-limiting embodiments made with reference to the following drawings:

[0034] Figure 1 This is a flowchart of a multi-agent privacy protection method under a universal interactive topology according to an embodiment of the present invention.

[0035] Figure 2 This is a communication topology diagram of a multi-agent system in an embodiment of the present invention.

[0036] Figure 3 This is a state trajectory diagram of all intelligent agents in the first implementation of the embodiment of the present invention.

[0037] Figure 4 This is a state trajectory diagram of all intelligent agents in the second implementation of the embodiment of the present invention.

[0038] Figure 5 1 is a comparison diagram of the state trajectories of a single-link node in an embodiment of the present invention. DETAILED DESCRIPTION

[0039] The present invention is described in detail below in conjunction with specific embodiments. The following embodiments will help those skilled in the art to further understand the present invention, but are not intended to limit the present invention in any form. It should be noted that, in the absence of conflict, the embodiments of the present invention and the features in the embodiments can be combined with each other.

[0040] Although the current multi-agent privacy protection methods can protect the privacy of the agent to a certain extent, when the number of neighbors of the agent is only one, its privacy will be spied on by internal honest but curious nodes or external eavesdroppers, resulting in privacy leakage. In view of the limitation of topological connections in privacy protection methods, this paper proposes a multi-agent privacy protection method under a universal interactive topological structure, such as Figure 1 As shown, the specific steps are as follows:

[0041] Step 1: Construct the communication network topology of the multi-agent system and use the Laplace matrix to represent the information interaction relationship between agents. Specifically: consider a multi-agent system consisting of N agents. In this system, the communication network of the agents is a strongly connected and balanced graph, which is mainly composed of a set of nodes. and edge sets Among them, the node set represents the set of all agents in the system; ε∈(i, j) means that agent i can send information to agent j. Agent j is called the external neighbor of agent i, and agent i is the internal neighbor of agent j. Correspondingly, and denotes the sum of the internal and external neighbor sets of agent i, respectively. If for any agent i in the node set, Then the graph is called a balanced graph. This means that for any agent in a balanced graph, the amount of information it sends is the same as the amount of information it receives. The degree of a node can be defined as In this equilibrium diagram, the weight matrix Defined as: If (i, j) ∈ ε, then the weight component a of edge (i, j) is ij =1, otherwise a ij = 0, and define a ii = 0. The Laplace matrix is ​​defined as The Laplacian matrix components of (i, j)

[0042] Step 2: Establish a first-order discrete dynamics model of each agent on the multi-agent system communication network constructed in step 1, so that all agents can eventually achieve average consistency; the first-order discrete dynamics model is as follows:

[0043]

[0044] Among them, x i [k] represents the state of agent i at time k, x j [k] represents the state of the neighbors of agent i at time k, x i [k+1] represents the state of agent i at time k+1, where k starts from zero; V j represents the neighbor node of agent i, ò represents the control gain, max{d i} represents the maximum degree of all agents in the multi-agent system, requiring Under this first-order discrete dynamics model, the state information of each agent will converge to the average of the initial values.

[0045] Step 3: Based on the dynamic model of step 2 and the topological network of step 1, a state decomposition model is designed to realize the state decomposition of the intelligent agent. Specifically:

[0046] Step 3-1: For the actual control variable x i [k] performs state decomposition and decomposes its state into as well as And satisfy the initial conditions After the actual control variable state is decomposed, As a visible node, it inherits the topological connection relationship of the original node and directly interacts with its neighbors. As a hidden node, only Bidirectional information exchange is carried out. Under this state decomposition relationship, the properties of the strongly connected equilibrium graph defined in step 1 will not be destroyed.

[0047] Step 3-2: Construct an average consistency model based on state decomposition. The consistency control protocol based on state decomposition given by the average consistency model is as follows:

[0048]

[0049] in, a iβ =a βi = 1. Under this control protocol, all states will converge to the average of the initial values, and the results are consistent with the dynamic model established in step 2, as shown below:

[0050]

[0051] Step 4: Introduce a perturbation mechanism into the state decomposition model to ensure that the initial privacy of the agent cannot be spied on by internal honest but curious nodes and external eavesdroppers in any connection mode. Specifically:

[0052] Step 4-1: In the state decomposition average consensus algorithm proposed in step 3, when the node whose privacy is stolen has only one neighbor, the attacker can successfully deduce its initial privacy through the information he has, as shown below:

[0053]

[0054]

[0055] Among them, Γ i is the set of information that the attacker can obtain, and z[k+1] is the state estimate constructed by the attacker. In the above case, this value will eventually approach the initial privacy of the spied node.

[0056] To address this problem, a perturbation design is introduced into the state decomposition consensus algorithm proposed in step 3 to ensure that the initial privacy of the agent cannot be spied on by internal honest but curious nodes and external eavesdroppers under any connection mode, thereby improving the shortcomings of the multi-agent privacy protection algorithm in topological connection.

[0057] Step 4-2: First, each agent selects a perturbation parameter and interacts with its neighbors. Specifically, each agent needs to pass an arbitrary value to its external neighbors in the network at the beginning, denoted as On this basis, each agent still performs state decomposition as in step 3.

[0058] Step 4-3: Construct a state decomposition privacy protection model with disturbances. Specifically, after introducing the disturbance mechanism, the state decomposition privacy protection model of each agent is as follows:

[0059]

[0060] Based on the state decomposition privacy protection model, the nodes interact with neighbors, where visible nodes interact with external neighbors, and invisible nodes only interact with visible nodes, and the perturbation function at the update time is calculated:

[0061]

[0062] By mathematical induction, we can prove that Under this model, it is only guaranteed that the states of visible nodes will eventually converge to an average consistency after state decomposition, while the final convergence value of hidden nodes is a hidden.

[0063] Step 4-4: Decompose the privacy protection model based on the state with disturbance and update the disturbance function at the moment to obtain the state at the next moment.

[0064] Example:

[0065] Consider a multi-agent network consisting of 4 agents with a communication topology such as Figure 2 As shown, it meets the requirements of a directed connected balanced graph. Next, two sets of system implementations are defined, and their initial state values ​​are as follows:

[0066]

[0067] The two sets of implementations are consistent in the initial values ​​of the visible nodes, but the initial values ​​of two nodes are different before decomposition. Then, the perturbation parameters of the two sets of implementations are consistent, that is,

[0068] Under the above definition, the running trajectories of the visible nodes and invisible nodes of the two systems are as follows: Figure 3 and Figure 4 As shown in the figure, we can see that the state trajectory of the visible child nodes of each agent in both implementations eventually converges to the average value of the initial value, which is 2.5. For the value of the invisible child node, its convergence value is different from that of the visible child node, but is a hidden value related to itself.

[0069] In the multi-agent network considered in this example, agent 4 has only one neighbor. Its initial privacy cannot be guaranteed to be leaked under the existing multi-agent privacy protection algorithm. However, the two sets of implementations considered in this example have different initial values ​​for agent 4, but the information they output to the outside world is as follows: Figure 5 The results are completely consistent, and the convergence values ​​of the invisible nodes themselves are different. At the same time, there are endless examples of building the same visible output for different initial values. Then the attacker cannot perceive the change of such an initial value through the information he can obtain, and thus cannot deduce the initial privacy of the spied node. Finally, we can see the advantage of the present invention, that is, the initial privacy of the intelligent agent can be protected even when there is only one neighbor.

[0070] The above shows and describes the basic principles, main features and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited by the above embodiments. The above embodiments and descriptions are only preferred examples of the present invention and are not intended to limit the present invention. Without departing from the spirit and scope of the present invention, the present invention may have various changes and improvements, which fall within the scope of the present invention. The scope of protection of the present invention is defined by the attached claims and their equivalents.

Claims

1. A multi-agent privacy protection method under a universal interactive topology, characterized by: The steps include: Step 1: Determine the communication topology network of the multi-agent system and use the Laplace matrix to represent the information interaction relationship between agents; Step 2: Based on step 1, establish a dynamic model of the intelligent agent; Step 3: Under the dynamic model and the communication topology network, a state decomposition model is designed to achieve average consistency while having a certain privacy protection capability; Step 4: Introduce a perturbation mechanism into the state decomposition model to ensure that the initial privacy of the agent cannot be spied on by internal honest but curious nodes and external eavesdroppers under any connection mode.

2. The multi-agent privacy protection method under a universal interactive topology as claimed in claim 1, characterized in that: In the step S2, the dynamics model of the intelligent agent is a first-order discrete dynamics model.

3. The multi-agent privacy protection method under a universal interactive topology as claimed in claim 2, characterized in that: The first-order discrete dynamics model is as follows: Among them, x i [k] represents the state of agent i at time k, x j [k] represents the state of the neighbors of agent i at time k, x i [k+1] represents the state of agent i at time k+1, where k starts from zero; V j represents the neighbor node of agent i, ò represents the control gain, max{d i } represents the maximum degree of all agents in the multi-agent system, requiring Under this first-order discrete dynamics model, the state information of each agent will converge to the average of the initial values.

4. The multi-agent privacy protection method under a universal interactive topology as claimed in claim 1, characterized in that: The step S3 comprises the following steps: Step 3.1: For the actual control variable x i [k] performs state decomposition and decomposes its state into as well as And satisfy the initial conditions Step 3.2: Construct an average consistency model based on state decomposition.

5. The multi-agent privacy protection method under a universal interactive topology as claimed in claim 4, characterized in that: The average consistency model provides a consistency control protocol based on state decomposition as follows: in, a iβ =a βi =1, under this control protocol, all states will converge to the average of the initial values.

6. The multi-agent privacy protection method under a universal interactive topology as claimed in claim 1, characterized in that: The step 4 comprises the following steps: Step 4.1, each agent selects a perturbation parameter and interacts with its neighbors. Specifically: each agent needs to pass an arbitrary value to its external neighbors in the network at the beginning; Step 4.2, introducing a disturbance mechanism into the state decomposition model to construct a state decomposition privacy protection model with disturbance; Step 4.3: interact with neighbors based on the state decomposition privacy protection model, wherein visible nodes interact with external neighbors, and invisible nodes only interact with visible nodes, and calculate the disturbance function at the update time; Step 4.4: Decompose the privacy protection model based on the state with disturbance and update the disturbance function at the next moment to obtain the state at the next moment.

7. The multi-agent privacy protection method under a universal interactive topology as claimed in claim 6, characterized in that: In step 4.2, after the state decomposition model introduces the disturbance mechanism, the state decomposition privacy protection model of each agent is as follows: in, Respectively represent the states of the visible and invisible child nodes of agent i at time k; θ i [k] represents the perturbation value applied by agent i at time k.

8. The multi-agent privacy protection method under a universal interactive topology as claimed in claim 6, characterized in that: The perturbation function in step 4.3 is: in, represents the initial perturbation parameter of agent i, represents the initial perturbation parameters of agent i’s neighbors.

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