Second-order system privacy protection average consistency method based on edge disturbance

Abstract

The invention discloses a second-order system privacy protection average consistency method based on edge disturbance, and the method comprises the following steps: determining a communication topological graph and a Laplacian matrix of a multi-agent system, and representing the information interaction relation between agents through the Laplacian matrix; establishing a dynamic model of the multi-agent system; during initial iteration, each agent generates a disturbance signal for each edge connected with the agent, and the type of an attacker is determined; after the attack type is confirmed, respectively adding a disturbance signal in the position information and the speed information transmitted to the neighbor by the intelligent agent and transmitting the information after interference generation to the neighbor; after the disturbance signal stage is finished, the intelligent agent is switched to a standard second-order dynamic average consistency algorithm, and the state of the intelligent agent is updated according to information fed back by neighbors. According to the method, the convergence precision of a consistency algorithm is not sacrificed while privacy protection is guaranteed, the method is suitable for a resource-limited environment, and privacy stealing of internal and external attackers can be effectively resisted.

Description

Technical Field

[0001] The present invention belongs to the field of computer science and control, and specifically relates to a privacy protection average consistency method for a second-order system based on edge perturbation. Background Art

[0002] In recent years, with the advancement of science and technology and the evolution of the times, control tasks have become more complex. For example, drone systems, intelligent transportation systems, smart grid systems, and sensor networks all rely on large-scale data computing and analysis, while single agents or traditional centralized processing systems have gradually exposed their limitations and are unable to meet existing needs. Therefore, cluster systems (also known as multi-agent systems) have emerged.

[0003] A multi-agent system consists of multiple agents with autonomy and independent decision-making capabilities. Each agent executes a distributed control protocol and completes the specified task through interaction, communication and collaboration. With the widespread use of multi-agent systems in practical applications, distributed control protocols have gradually attracted the attention and in-depth research of researchers at home and abroad. Consistency control, as one of the key issues in distributed control, has been widely used and studied.

[0004] The core goal of consistency control is to achieve consistency of state, information or behavior among multiple agents within a limited time through information exchange between agents. In traditional consistency algorithms, in order to achieve consistency, multiple agents usually need to pass their true state values ​​to neighboring agents for distributed computing. However, this mechanism leads to a serious problem, that is, the initial state messages of the agents, which often contain sensitive or private data, are easily stolen by malicious attackers, resulting in information leakage and serious consequences. For example, in some military missions, when drone clusters use traditional consistency algorithms to complete specific tasks, their location information will not be kept private. This information leakage brings two potential security risks. On the one hand, there may be some malicious agents in the network, which can easily obtain the initial state of their neighboring agents and then launch attacks. On the other hand, there may also be attackers outside the network. If these attackers obtain information in transmission by invading the communication link, the initial state of the agent will be leaked, which may be used to attack the entire network. However, existing privacy protection methods have problems such as high computational and communication costs, limited application to first-order systems, trade-offs between privacy and accuracy, and insufficient protection against external attackers. Therefore, it has become a necessary and urgent technical need to develop a privacy-preserving average consistency algorithm with high convergence accuracy, low computational cost, and applicable to second-order systems. Summary of the invention

[0005] In view of the above-mentioned problems existing in the prior art, the present invention proposes a second-order system privacy protection average consistency method based on edge perturbation, which has low communication overhead and is suitable for resource-constrained environments. While ensuring privacy protection, it does not sacrifice the convergence accuracy of the consistency algorithm. It is suitable for strongly connected directed balanced graphs and can effectively resist privacy theft by internal and external attackers.

[0006] In order to achieve the above object, the technical solution specifically adopted by the present invention is as follows:

[0007] A privacy-preserving average consistency method for a second-order system based on edge perturbation includes the following steps:

[0008] Step 1: Determine the communication topology and Laplace matrix of the multi-agent system, and use the Laplace matrix to represent the information interaction relationship between agents;

[0009] Step 2: Establish a dynamic model of the multi-agent system;

[0010] Step 3: At the initial iteration, each agent generates a disturbance signal for each edge connected to it to determine the attacker type; the disturbance information follows specific constraints;

[0011] Step 4: After confirming the attack type, the agent adds a disturbance signal to the position information and speed information transmitted to its neighbors and transmits the generated disturbed information to its neighbors;

[0012] Step 5: After the disturbance signal phase ends, the agent switches to the standard second-order dynamic average consensus algorithm and updates its own state based on the information fed back by its neighbors.

[0013] Furthermore, in step 1, the communication topology between agents is a directed graph Represents a node set containing and directed edge sets Laplace matrix L = [l ij ]∈R N×N The definition is as follows: When i≠j, l ij =-a ij ; When i = j, Re(μ) and Im(μ) represent the real part and imaginary part of the eigenvalue μ of the Laplace matrix L, respectively.

[0014] Furthermore, in step 2, a discrete-time second-order agent system consisting of N agents is modeled, and the dynamic model of each agent is expressed in the following form:

[0015] x i [k+1]=x i [k]+v i [k]

[0016] v i [k+1]=v i [k]+u i [k],i=1,2,…,N

[0017] Where k = 1, 2, ... are positive integers, x i [k]∈R N and v i [k]∈R N represent the position state and velocity state of the ith agent at iteration k, respectively, and u i [k]∈R N is the control input of the ith agent.

[0018] Furthermore, in step 3, for the internal curious attacker, its ability to determine the initial state of the agent is limited to the information set it obtains. Information Set The definition is as follows:

[0019]

[0020] Among them, ∈1,∈2,∈3,∈4 are coupling coefficients, and are the initial position and velocity states of the injected disturbance information, and is the disturbance information, and are the incoming neighbor set and outgoing neighbor set of agent i respectively.

[0021] Randomly select an agent in the topology graph and name it agent 1, and randomly select it from the neighbor set Select an agent and name it Agent 2, and the remaining agents in the topology map are named Consider two implementation methods. First, confirm the initial state of the two implementation methods. In the first implementation method, define Agent 1, Agent 2, and The initial positions and velocities of the agents in the set are x1[0], x2[0], x3[0], v1[0], v2[0], v3[0] respectively; in the second implementation: define agent 1, agent 2 and V 3 The initial position and velocity states of the agents in the set are in,

[0022] Then, according to the relationship of the initial state, the disturbance information and disturbance coefficient are designed as follows:

[0023]

[0024]

[0025] in, i,j∈1,2,3 is the disturbance information injected into the position information transmitted by agent i to agent j, is the corresponding perturbation information matrix; i,j∈1,2,3 is the disturbance information injected into the velocity information transmitted by agent i to agent j, is the corresponding perturbation information matrix; is the coupling coefficient in the second implementation mode; d i ,i∈1,2,3 is the degree of the node, a ij ,i,j∈1,2,3 are elements in the adjacency matrix, A ij is the corresponding matrix.

[0026] Furthermore, in step 3, when targeting an external eavesdropper, the information set of the external eavesdropper is The definition is as follows:

[0027]

[0028] Among them, ∈1,∈3,∈4 are coupling coefficients, and are the initial position and velocity states of the injected disturbance information respectively;

[0029] Define v[k] = [v1[k], v2[k], v3[k]] T ,x[k]=[x1[k],x2[k],x3[k]] T ,The relationship between the coupling coefficient and the initial state under the two implementation methods is as follows:

[0030]

[0031] Among them, δ∈2∈(-∞,0)∪(0,∞);

[0032] According to the relationship of the initial state, the relationship of the disturbance information is designed:

[0033]

[0034] Furthermore, after confirming the attack type, when agent i transmits position information and speed information to its neighbors, specific disturbance information is added to the position information and speed information respectively. and( or ) to generate the transmission information after interference.

[0035] Furthermore, in step 5, when the disturbance signal phase ends, that is, k>0, all agents will switch to the standard second-order dynamic average consensus algorithm for state update. In this phase, each agent updates its own state according to the following formula based on the information fed back by its neighbors:

[0036] x i [k+1]=x i [k]+v i [k]

[0037]

[0038] Among them, ∈3 and ∈4 are coupling coefficients, satisfying ∈4>∈3>0 and

[0039] The present invention has the following characteristics and beneficial effects:

[0040] The present invention proposes a privacy-preserving average consensus algorithm for a second-order discrete multi-agent system based on edge perturbation, which mainly targets the privacy leakage problem existing in the second-order system and has the following advantages: 1) By injecting perturbation signals at the edge, the initial position information and speed information of the agent are effectively protected from being obtained by internal honest but curious agents and external eavesdroppers, while accurately converging to the average consistent state; 2) The algorithm is applicable to strongly connected balanced graphs, overcoming the limitation of existing methods that are limited to bidirectional transmission topologies and expanding the scope of application; 3) The algorithm of the present invention is lightweight and easy to implement, reducing computational and communication overheads. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] 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:

[0042] Figure 1 The communication topology diagrams of the first and second embodiments of the present invention are shown;

[0043] Figure 2 It is a position state update diagram of the five intelligent agents of the internal curiosity in the first and second implementation modes in the first embodiment of the present invention;

[0044] Figure 3 It is a speed state update diagram of the five intelligent agents of the internal curiosity in the first and second implementation modes in the first embodiment of the present invention;

[0045] Figure 4 Schematic diagram of transmission information including location status for internal curiosity in the first and second implementation modes in the first embodiment of the present invention

[0046] Figure 5 Schematic diagram of transmission information including speed status for internal curiosity in the first and second implementation modes in the first embodiment of the present invention

[0047] Figure 6 It is a position state update diagram of five intelligent agents against external attackers in the first and second implementation modes in the second embodiment of the present invention;

[0048] Figure 7 It is a speed state update diagram of five intelligent agents against external attackers in the first and second implementation modes in the second embodiment of the present invention;

[0049] Figure 8 A schematic diagram of transmission information including position status in the first and second implementation modes for an external attacker in the second embodiment of the present invention;

[0050] Fig. 9 A schematic diagram of transmission information including speed status in the first and second implementation modes for an external attacker in the second embodiment of the present invention;

[0051] Fig.10 This is a flow chart of the invention of Embodiment 1 and Embodiment 2 of the present invention. DETAILED DESCRIPTION

[0052] 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.

[0053] In order to solve the problems of existing privacy protection methods, such as high computational and communication costs, limited application to first-order systems, trade-off between privacy and accuracy, and insufficient protection against external attackers, this embodiment of the present invention provides a privacy protection average consistency method for a second-order multi-agent system based on edge perturbation, and the specific steps are as follows:

[0054] Step 1: Determine the communication topology of the multi-agent system and the Laplace matrix L; Specifically: In a network consisting of N agents, the communication topology between agents is a directed graph Indicates that it contains N nodes. The communication topology contains the node set and directed edge sets There are directed edges ε in the network ij Represented as a node pair (v i ,v j ), which means that node v i You can send a jTransmit information, the incoming neighbor set and outgoing neighbor set of node i and Represent the in-neighbors and out-neighbors of node i respectively. The in-degree and out-degree of node i are defined as and If the in-degree and out-degree of all nodes in the graph are equal, then the graph is called a balanced graph. In a balanced graph, we define For a simple graph consisting of N agents Its adjacency matrix A=[a ij ]∈R N×N The definition is as follows: ii =0; if and only if ε ij ∈ε, a ij =1, otherwise a ij = 0, where i, j = 1, 2, ..., N and i ≠ j. Laplace matrix L = [l ij ]∈R N×N The definition is as follows: When i≠j, l ij =-a ij ; When i = j, Re(μ) and Im(μ) represent the real part and imaginary part of the eigenvalue μ of the Laplace matrix L, respectively.

[0055] Step 2: Model the discrete-time second-order agent system consisting of N agents. The dynamic model of each agent can be expressed as follows:

[0056] x i [k+1]=x i [k]+v i [k]

[0057] v i [k+1]=v i [k]+u i [k],i=1,2,…,N

[0058] Where k = 1, 2, ... are positive integers, x i [k]∈R N and v i [k]∈R N represent the position state and velocity state of the ith agent at iteration k, respectively, and u i [k]∈R N is the control input of the ith agent.

[0059] Step 3: When k = 0, each agent generates disturbance information to determine the attacker type; specifically, for agent i, if there is a directed edge ε ij∈ε, then agent i can generate two perturbation information for each edge connected to agent j, which are and These perturbation signals are added to the information transmitted between agents to ensure privacy protection. and satisfy:

[0060] 1) If and 2) and in,

[0061] Step 3-1: For an internal curious attacker, his ability to determine the initial state of the agent is limited to the information set he obtains. If the attacker receives exactly the same information when facing two agents with different initial positions and speeds, he will not be able to distinguish the different initial positions and speeds based on the collected information sets. The definition is as follows:

[0062]

[0063] Among them, ∈1,∈2,∈3,∈4 are coupling coefficients, and are the initial position and velocity states of the injected disturbance information, and For disturbance information.

[0064] Without loss of generality, we randomly select an agent in the topological graph and name it agent 1, because the topological graph is a strongly connected balanced graph, and the neighbor set of agent 1 is It must not be empty, we randomly enter the neighbor set Select an agent and name it Agent 2, and the remaining agents in the topology map are named We define Agent 1, Agent 2, and The position and velocity information of the agents in the set are: x1[k],x2[k],x3[k]=[x4[k],…,x N [k]] T ,v1[k],v2[k],v3[k]=[v4[k],…,v N [k]] T .

[0065] Further, we define the Laplace matrix L, the adjacency matrix A, and the perturbation information matrices P and Q as block matrices, as follows:

[0066]

[0067] Step 3-2: Consider two implementation methods. First, confirm the initial state of the two implementation methods. In the first implementation method, we define Agent 1, Agent 2, and The initial position and velocity states of the agents in the set are x1[0], x2[0], x3[0], v1[0], v2[0], v3[0], and the disturbance information is further defined. And coupling coefficients ∈1,∈2,∈3,∈4. In the second implementation: we define the initial states as The specific relationship is as follows:

[0068] Step 3-3: Based on the relationship of the initial state, we further design the disturbance information and coupling coefficient in the second implementation method, as follows:

[0069]

[0070] in i,j∈1,2,3 is the disturbance information injected into the position information transmitted by agent i to agent j, is the corresponding perturbation information matrix; i,j∈1,2,3 is the disturbance information injected into the velocity information transmitted by agent i to agent j, is the corresponding perturbation information matrix; is the coupling coefficient in the second implementation.

[0071] Step 3-4: For external eavesdroppers, we also use the idea of ​​step 3-1. The information set of the external eavesdropper is defined as follows:

[0072]

[0073] Among them, ∈1,∈3,∈4 are coupling coefficients, and are the initial position and velocity states of the injected disturbance information respectively.

[0074] Step 3-5: Define v[k] = [v1[k], v2[k], v3[k]] T ,x[k]=[x1[k],x2[k],x3[k]] T ,The relationship between the coupling coefficient and the initial state under the two implementation methods is as follows:

[0075]

[0076] Among them, δ∈2∈(-∞,0)∪(0,∞).

[0077] Step 3-6: Based on the relationship of the initial state, we further design the relationship of the disturbance information:

[0078]

[0079] Step 4: After confirming the attack type, when agent i transmits position information and speed information to its neighbors, it adds specific disturbance information to the position information and speed information respectively. and( or ) to generate the transmission information after interference. For example, other implementations of perturbations follow the same idea. The position information transmitted by agent i to its neighbor agent j and speed information Defined as:

[0080]

[0081] The initial state after these disturbances and is passed to agent j to ensure that the initial state privacy of the agent is protected from internal or external attackers during the information transmission process. The rules for each agent to update are as follows:

[0082] x i [1] = x i [0]+v i [0]

[0083]

[0084] Among them, ∈1∈(-∞,0)∪(0,∞) and ∈2∈(-∞,0)∪(0,∞) are both constants.

[0085] Step 5: When the disturbance signal phase ends, that is, k>0, all agents will switch to the standard second-order dynamic average consensus algorithm for state update. In this phase, each agent updates its own state according to the following formula based on the information fed back by its neighbors:

[0086] x i [k+1]=x i [k]+v i [k]

[0087]

[0088] Among them, ∈3 and ∈4 are coupling coefficients, satisfying ∈4>∈3>0 and

[0089] Example 1: Take five multi-agents as an example, where agent 2 is an internally honest but curious agent. The topology diagram is shown below:

[0090] In the first implementation, the specific parameters are as follows:

[0091] x1[0]=8,x2[0]=2,x3[0]=-1,x4[0]=-4,x5[0]=-10

[0092] v1[0]=4, v2[0]=-1, v3[0]=-3, v4[0]=2, v5[0]=3

[0093] ∈1=0.2,∈2=0.4,∈3=0.9,∈4=1

[0094]

[0095] In the second implementation, the corresponding initial state, coupling coefficient and disturbance information are as follows:

[0096]

[0097]

[0098] The states of the five agents and the position and speed information transmitted at the initial moment are as follows: Figure 2-Figure 5 shown. Figure 2 and Figure 3 It shows that the second-order dynamic average consistency can be accurately achieved in both implementation methods. Figure 4 It shows that the position information transmitted between all agents is exactly the same. Figure 5 This shows that except for Agent 3 and Agent 4, the speed information transmitted by other agents is the same. Therefore, the information received by the internal curious agent 2 is completely consistent, and it is impossible to distinguish the initial states of other agents.

[0099] Embodiment 2: The present invention provides another example, in which agent 2 acts as an external eavesdropper to ensure that the initial state is not affected by its attack.

[0100] In the second implementation, the information corresponding to the first implementation in Example 1 is as follows:

[0101]

[0102] The states of the five agents and the position and speed information transmitted at the initial moment are as follows: Figure 6-Figure 9 shown. Figure 6 and Figure 7 It shows that all agents can accurately achieve second-order dynamic average consistency in both implementations. Figure 8 and Fig. 9 It shows that in both implementations, the position and velocity information transmitted by all agents in the first iteration are the same. Therefore, the external eavesdropper 2 receives exactly the same information and cannot determine the initial states of other agents.

[0103] 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 privacy-preserving average consistency method for second-order systems based on edge perturbations, characterized by: The steps include: Step 1: Determine the communication topology and Laplace matrix of the multi-agent system, and use the Laplace matrix to represent the information interaction relationship between agents; Step 2: Establish a dynamic model of the multi-agent system; Step 3: At the initial iteration, each agent generates a perturbation signal for each edge connected to it to determine the attacker type; Step 4: After confirming the attack type, the agent adds a disturbance signal to the position information and speed information transmitted to its neighbors and transmits the generated disturbed information to its neighbors; Step 5: After the disturbance signal phase ends, the agent switches to the standard second-order dynamic average consensus algorithm and updates its own state based on the information fed back by its neighbors.

2. The second-order system privacy protection average consistency method based on edge perturbation as claimed in claim 1, characterized in that: In step 1, the communication topology between agents is a directed graph Represents a node set containing and directed edge sets 3. The second-order system privacy protection average consistency method based on edge perturbation as claimed in claim 1, characterized in that: In step 1, the Laplace matrix L=[l ij ]∈R N×N The definition is as follows: When i≠j, l ij =-a ij ; When i = j, Re(μ) and Im(μ) represent the real part and imaginary part of the eigenvalue μ of the Laplace matrix L, respectively.

4. The second-order system privacy protection average consistency method based on edge perturbation as claimed in claim 1, characterized in that: In step 2, a discrete-time second-order agent system consisting of N agents is modeled, and the dynamic model of each agent is expressed as follows: x i [k+1]=x i [k]+v i [k] v i [k+1]=v i [k]+u i [k],i=1,2,…,N Where k = 1, 2, ... are positive integers, x i [k]∈R N and v i [k]∈R N represent the position state and velocity state of the ith agent at iteration k, respectively, and u i (k)∈R N is the control input of the ith agent.

5. The second-order system privacy protection average consistency method based on edge perturbation as claimed in claim 1, characterized in that: In step 3, the ability of the internal curious attacker to determine the initial state of the agent is limited to the information set it obtains. Information Set The definition is as follows: Among them, ∈1,∈2,∈3,∈4 are coupling coefficients, and are the initial position and velocity states of the injected disturbance information, and is the disturbance information, and are the incoming neighbor set and outgoing neighbor set of agent i respectively; Randomly select an agent in the topology graph and name it agent 1, and randomly select it from the neighbor set Select an agent and name it Agent 2, and the remaining agents in the topology map are named Consider two implementation methods. First, confirm the initial state of the two implementation methods. In the first implementation method, define Agent 1, Agent 2, and The initial position and velocity states of the agents in the set are x1[0], x2[0], x3[0], v1[0], v2[0], v3[0], and the disturbance information is further defined. and coupling coefficients ∈1,∈2,∈3,∈4; In the second implementation: define agent 1, agent 2, and The initial position and velocity states of the agents in the set are in, Then, according to the relationship of the initial state, the disturbance information and disturbance coefficient are designed as follows: in, is the disturbance information injected into the position information transmitted by agent i to agent j, is the corresponding perturbation information matrix; is the disturbance information injected into the velocity information transmitted by agent i to agent j, is the corresponding perturbation information matrix; is the coupling coefficient in the second implementation mode; d i ,i∈1,2,3 is the degree of the node, a ij ,i,j∈1,2,3 are elements in the adjacency matrix, A ij is the corresponding matrix.

6. The second-order system privacy protection average consistency method based on edge perturbation as claimed in claim 1, characterized in that: In step 3, when targeting an external eavesdropper, the information set of the external eavesdropper is The definition is as follows: Among them, ∈1,∈3,∈4 are coupling coefficients, and are the initial position and velocity states of the injected disturbance information respectively; Define v[k] = [v1[k], v2[k], v3[k]] T ,x[k]=[x1[k],x2[k],x3[k]] T ,The relationship between the coupling coefficient and the initial state under the two implementation methods is as follows: Among them, δ∈2∈(-∞,0)∪(0,∞); According to the relationship of the initial state, the relationship of the disturbance information is designed:

7. The second-order system privacy protection average consistency method based on edge perturbation as claimed in claim 1, characterized in that: After confirming the attack type, when agent i transmits position information and speed information to its neighbors, specific disturbance information is added to the position information and speed information respectively. and( or ) to generate the transmission information after interference.

8. The second-order system privacy protection average consistency method based on edge perturbation as claimed in claim 1, characterized in that: In step 5, when the disturbance signal phase ends, that is, k>0, all agents will switch to the standard second-order dynamic average consensus algorithm for state update.

9. The second-order system privacy protection average consistency method based on edge perturbation as claimed in claim 1, characterized in that: In step 5, each agent updates its own state according to the following formula based on the information fed back by its neighbors: x i [k+1]=x i [k]+v i [k] Among them, ∈3 and ∈4 are coupling coefficients, satisfying ∈4>∈3>0 and

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