A multi-agent system quantization consistency privacy protection method based on general state decomposition

Abstract

The application discloses a kind of general state decomposition-based multi-agent system quantization consistency privacy protection method, comprising the following steps: design general state decomposition-based privacy protection mechanism, each node is according to the demand and ability of itself and the setting of the weight of state decomposition, reconstitutes the false initial state for transmission communication;Establish multi-agent system quantization consistency control model: consider the system formed by N nodes, based on graph theory knowledge, the relationship between the dynamic behavior of each node is expressed by difference equation, under the assumption of quantization transmission, introduce coding decoding quantization mechanism, give the specific setting of encoder and decoder;Introduce eavesdropping attack model: consider the eavesdropping of internal curious node and external eavesdropper to the state in network;The result of system consistency convergence is analyzed correctly: based on graph theory, matrix theory and stability theory knowledge, the dynamic behavior of agent is analyzed, and the final convergence consistency result is obtained;The privacy of multi-agent system is analyzed, the nondistinguishability of initial state change is used, the privacy analysis under different eavesdropping attacks is given by designing privacy protection quantization index.The application makes the control protocol designed simple and easy to operate, can save communication resources at the same time, and guarantee correct convergence and provide more comprehensive privacy protection.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of multi-agent system control and information security technology, and particularly relates to a multi-agent system quantitative consensus privacy protection method based on general state decomposition. BACKGROUND

[0002] Due to the rapid development of distributed sensor, communication, computing and microprocessor technology, the coordinated control of multi-agent systems has become one of the main concerns in the field of system and control science. The consensus problem has attracted the research interest of social networks, algorithms, control, estimation and many other disciplines.

[0003] However, with the increasing complexity of the task and the expansion of application scenarios, many existing consensus algorithms cannot achieve some higher requirements. For example, in a digital interactive network, due to the limited communication bandwidth and computing capacity, the information exchanged by the agents needs to be quantized before transmission, so the consensus problem in quantized communication is a subject worthy of study. Due to the influence of quantization, nonlinearity is introduced into the evolution law, making the generated dynamic system more difficult to study and more difficult to achieve correct consensus convergence. Many existing algorithms cannot effectively ensure that the system reaches consensus, or may converge to a random value instead of the target average value, or there is an error related to the quantization level of the accurate value.

[0004] In addition, many existing quantized consensus results ignore the privacy protection problem. During the operation of the consensus algorithm, there may be some curious nodes (or eavesdroppers) inside or outside the network who try to infer the initial state of some benign agents. The initial state, as an important information fusion source in the consensus problem, usually contains some sensitive information or personal privacy. For example, the initial opinion on a certain topic or theme in a social network; the initial position of the agent (which can be a home address or organization headquarters) in a set problem; the parameters of the cost function in an economic scheduling problem, etc. Therefore, it is of great significance to consider privacy protection in the quantized consensus algorithm.

[0005] Currently, there are few documents that consider both privacy protection and quantized communication. In the quantized communication environment, the differential privacy method is used to protect the initial state, but the results show that the consensus value converged to is a random variable in the neighborhood of the average value of the initial state, and cannot guarantee accurate convergence. Although some researchers have designed a dynamic quantization scheme to ensure that the system can reach consensus in the presence of an adversary, it only considers external eavesdroppers, and internal curious nodes will directly obtain the true initial state of the nodes. In addition, some documents use encryption methods to solve the privacy protection quantized consensus problem, but it usually causes more computing and communication pressure.

[0006] In summary, it is not trivial to directly consider privacy protection in quantized communication research, and the main challenges and difficulties are: (i) the simultaneous existence of quantization and privacy protection mechanisms makes it more difficult to achieve the correctness of the final convergence result; (ii) the initial state of the node needs to satisfy that it can be any real number; (iii) it is necessary to ensure more comprehensive privacy protection (internal curious nodes and external eavesdroppers). In addition, the designed mechanism should be simple to implement, low in calculation and communication cost. SUMMARY

[0007] The purpose of the application is to provide a multi-agent system quantized consensus privacy protection method based on general state decomposition, which makes the designed control protocol simple and easy to implement, saves communication resources, and ensures correct consensus convergence and provides more comprehensive privacy protection.

[0008] Technical scheme: The multi-agent system quantized consensus privacy protection method based on general state decomposition provided by the application comprises the following steps:

[0009] Step 1, design a privacy protection mechanism based on general state decomposition, each node decomposes the state and sets the weight according to its own needs and capabilities, and reconstructs a false initial state for transmission and communication;

[0010] Step 2, establish a multi-agent system quantized consensus control model; consider a system composed of N nodes, based on graph theory knowledge, use a difference equation to represent the relationship between the dynamic behaviors of each node, under the assumption of quantized transmission, introduce an encoding and decoding quantization mechanism, and give the specific settings of the encoder and decoder;

[0011] Step 3, introduce a eavesdropping attack model; consider the eavesdropping of the state in the network by internal curious nodes and external eavesdroppers;

[0012] Step 4, based on the privacy protection mechanism and the quantized consensus control model, give the final privacy protection quantized protocol, and analyze the correctness of the consensus convergence result of the multi-agent system;

[0013] Step 5, analyze the privacy of the multi-agent system, use the indistinguishability of the initial state change, design a quantized index for privacy protection, and give the privacy analysis under different eavesdropping attacks.

[0014] Further, in step 1, the state decomposition is as follows: node i (i = 1, 2,..., N) generates n i ≥0 virtual nodes according to its own needs (which may be resource or communication capability constraints), and the communication and weight design between node i and the virtual nodes generated by it is completely unknown to other nodes in the network, since virtual nodes are added to the network, a new network graph G ′Then node i (i = 1, 2, ..., N) no longer uses the original initial state value, and its generation n i +1 random number, For these values, It is used to replace the actual initial state x i (0) is a spurious initial value. Indicates that in n i The initial state applied to each virtual node generates random initial values ​​that are arbitrarily chosen from the set of real numbers.

[0015] Furthermore, the generated random initial values ​​can be arbitrarily chosen from the set of real numbers. To ensure the achievement of the correct average consistency objective, the following constraints are imposed:

[0016]

[0017] in This represents the total number of all virtual nodes.

[0018] Furthermore, in step 2, encoder E i Designed as follows:

[0019]

[0020] Where ξ i (k) is E i The internal state of Δ i (k) is E i The output of will be sent to the neighbors of agent i, s(k)>0, k≥0 represents the scaling function, x i (k) represents the agent's state at time k, and q(·) is a quantizer that quantizes the real-valued state into an integer-valued state. Specifically, q(·) is described as: R→Q={0,±i,i=1,2,…,K}

[0021]

[0022] Where R represents the real number field, Q represents the quantization level set, and the total number of quantization levels is 2K+1.

[0023] Furthermore, in step 2, decoder D ji Designed as follows:

[0024]

[0025] in D represents ji The output of represents the action of agent i on state x. j Estimate of (k).

[0026] Furthermore, in step 3, an internal curious node refers to an agent that correctly follows all protocol steps but attempts to obtain information about other agents based on the collected data; an external eavesdropper refers to an eavesdropper who accesses information by intruding into the communication channel. The eavesdropper knows the network topology and all shared data in the network, but cannot obtain states that are not shared in the network.

[0027] Furthermore, in step 4, the final privacy protection quantification consistency control protocol is as follows:

[0028]

[0029] Where u i (k) represents the control input of agent i at time k; This represents the true neighbors of node i before state decomposition. This represents all virtual nodes added to node i; a ij [k],i,j∈G′ represents the weights of the edges connecting nodes i and j in the network topology G′ at time k.

[0030] Furthermore, in step 5, the privacy protection quantification index is represented by the information collected by the adversary (curious node or eavesdropper) at time k. As time evolves, given any time κ, all the collected information is: gather This indicates that agent i is capable of generating the same information. The set of all initial states, Privacy is defined as

[0031]

[0032] According to d YNiOZ[\ The expression yields d. YNiOZ[\ The larger the value, the greater the uncertainty in the opponent's acquisition of the initial state, and the greater the maximum impossibility d. YNiOZ[\ =∞ means that the opponent cannot find a unique x. i (0), and x cannot even be found. i The meaningful range of (0).

[0033] Beneficial effects: Compared with the prior art, the present application has the following remarkable advantages: the present application aims at the problems of eavesdropping attacks and limited communication resources that may be encountered in the implementation of average consensus process for multi-agent systems, uses a dynamic encoding and decoding scheme, integrates a general state decomposition method with greater design freedom into the quantization communication environment, and ensures the implementation of accurate average consensus; in addition, the initial state in the algorithm can be any real number, rather than an integer, a more general state decomposition method is first proposed, the number of virtual nodes generated is no longer fixed and determined by the network topology, but can be decomposed according to the resource or capacity requirements of each agent, so that the new state decomposition mechanism is more universal and has greater design freedom, and can better meet the needs of different nodes; finally, the proposed method can effectively resist internal and external adversaries, achieve the maximum privacy protection effect in the quantization environment, and thus ensure a safer communication environment with lower computational cost. BRIEF DESCRIPTION OF DRAWINGS

[0034] Figure 1 The present application is a method flowchart.

[0035] Figure 2(a) is a network topology example of the present application.

[0036] Figure 2(b) is a decomposed topology diagram of the present application.

[0037] Figure 3 The present application is an agent state trajectory diagram after using the differential privacy method.

[0038] Figure 4 The present application is an agent state trajectory diagram after using the general state decomposition method.

[0039] Figure 5 The present application is an agent state estimation diagram under two different initial states. DETAILED DESCRIPTION

[0040] As shown in Figure 1 A multi-agent system quantization consensus privacy protection method based on general state decomposition includes the following steps:

[0041] Step 1: design a privacy protection mechanism based on general state decomposition, each node decomposes the state and sets the weight according to its own demand and capacity, and reconstructs the false initial state for transmission and communication.

[0042] Each node i (i = 1, 2, …, N) generates n iThere are ≥0 virtual nodes. For other nodes in the network, the communication and weight design between node i and its generated virtual nodes are completely unknown. Due to the addition of virtual nodes to the network, a new network graph G is reconstructed. ′ Then node i (i = 1, 2, ..., N) no longer uses the original initial state value, and its generation n i +1 random number, For these values, It is used to replace the actual initial state x i (0) is a spurious initial value. Indicates that in n i The initial state applied to each virtual node. The generated random initial values ​​can be arbitrarily chosen from the set of real numbers, but to ensure the achievement of the correct average consistency objective, the following constraints need to be imposed on them:

[0043]

[0044] In an embodiment of the present invention, a network topology with 6 nodes as shown in Figure 2(a) is selected. The initial state of each node is x(0) = (7.0573, -3.4323, -2.7413, 4.1917, 6.1636, -4.8213). k ∈R l The weighted adjacency matrix is ​​represented as

[0045]

[0046] Under the general state decomposition mechanism, the reconstructed network topology is shown in Figure 2(b). It can be seen that different nodes generate different numbers of virtual nodes, which can be used to express their privacy requirements. Specifically, nodes 3 and 6 do not generate any virtual nodes, indicating that they are not concerned about privacy leaks. Then, based on the knowledge of (N,n) = (6,6), each node can set new initial values ​​for itself and its virtual nodes under constraints, resulting in topology G. ′ All nodes in the sequence will generate a new initial state sequence, which can be designed as follows:

[0047]

[0048] It is noted that both the original initial state sequence and the newly formed initial state sequence are sequences of real numbers, which expands the scope of existing privacy protection methods.

[0049] Step 2: Establish a quantization consistency control model for a multi-agent system: Consider a system consisting of N nodes. Based on graph theory, use difference equations to represent the relationship between the dynamic behaviors of each node. Under the assumption of quantization transmission, introduce an encoding and decoding quantization mechanism and give the specific settings of the encoder and decoder.

[0050] A multi-agent network consisting of N agents can be modeled as an undirected graph G = (V, E, A).x i (k)∈R represents the state of agent i at time k, and its dynamic update formula is:

[0051] x i (k+1)=x i (k)+gu i (k),

[0052] Where g>0 represents the gain parameter, u i (k)∈R represents the control input of agent i.

[0053] Furthermore, a distributed encoding / decoding scheme is introduced, which ensures that all agents achieve average consistency exponentially. First, for each node i (i = 1, 2, ..., N), the data is transmitted to its neighboring nodes j, j ∈ N. i The information is provided by encoder E i The coding is designed as follows:

[0054]

[0055] Where ξ i (k) is E i The internal state of Δ i (k) is E i The output of s(k) > 0, k ≥ 0 represents the scaling function, and q(·) is the quantizer, which can quantize real-valued states into integer-valued states. Specifically, q(·): R → Q = {0, ±i, i = 1, 2, ..., K}

[0056]

[0057] Where Q represents the quantization level set, and the total number of quantization levels is 2K+1.

[0058] Next, for each transmission channel (i,j)∈E, when node i obtains information Δ from its neighbor j j When (k), it uses the following decoder D ji To estimate the state x before quantization j (k):

[0059]

[0060] in D represents ji The output of represents the action of agent i on state x. j Estimate of (k).

[0061] Finally, according to the encoding / decoding scheme, the control protocol u i (k) is designed as:

[0062]

[0063] But in this embodiment, we consider the privacy protection problem of the initial state of the agent, so the final controller design needs to consider the possible eavesdropping attacks in the network and combine the proposed general state decomposition method.

[0064] Step 3: Introduce the eavesdropping attack model: consider the eavesdropping of the internal curious node and the external eavesdropper on the state in the network.

[0065] Here, the internal curious node refers to an agent that correctly follows all protocol steps, but tries to obtain information about other agents based on the collected data. The external eavesdropper refers to an eavesdropper who can access information by hacking into the communication channel. The eavesdropper can know the network topology and all shared data in the network, but cannot obtain the state that is not shared in the network.

[0066] Step 4: Based on the privacy protection mechanism and the quantized consensus control model, the final privacy protection quantized consensus protocol is given, and the correctness of the consensus convergence result of the multi-agent system is analyzed.

[0067] Assume that the communication network G is connected, where c1, c8 are known non-negative constants, is the initial consensus error. The above two assumptions, one is the restriction on the network topology, which requires that the network topology is connected, which is a necessary and sufficient condition to ensure the realization of the system consensus. One is that the upper bound of the initial state of the agent and the initial state consensus error is known. When the initial state of all agents is known, the upper bound c1, c8 can be calculated naturally.

[0068] If the above two assumptions are true, then for any given

[0069]

[0070] where Under the scaling function s(t) = s U γ – and the 2K+1-level consensus quantizer, the quantized consensus protocol:

[0071]

[0072] can guarantee the correct average consensus asymptotic realization, i.e.

[0073]

[0074] Then, the general state decomposition method proposed in this paper is compared with the differential privacy method to illustrate its advantage in precise convergence. By Figure 3 It can be observed that the state trajectory of the node cannot converge to the accurate average value. It can only fall in a neighborhood of the average value of the initial state. Further, the convergence performance of the system based on the general state decomposition method is verified. Let g = 0.46, K = 6, γ = 0.95, s U = 3.5836, it can be found that the accurate average consensus of all agents can be achieved, as Figure 4 shown.

[0075] Step 5: The privacy of the multi-agent system is analyzed. By using the unidentifiability of the change of the initial state, a privacy protection quantitative index is designed, and the privacy analysis under different eavesdropping attacks is given.

[0076] Suppose the information collected by the adversary (curious node or eavesdropper) at time k is represented as With the evolution of time, given any time κ, all collected information is The set represents all initial state sets that can generate the same information for agent i, and the privacy of is defined as

[0077]

[0078] According to the expression of d YNiOZ[\ , it can be concluded that the larger d YNiOZ[\ is, the greater the uncertainty of the adversary to obtain the initial state is. The maximum uncertainty d YNiOZ[\ = ∞ means that the adversary cannot find a unique x i (0) or even a meaningful range of x i (0).

[0079] Based on the given privacy protection index, it can be concluded that under the general state decomposition mechanism, if node i has at least one non-curious neighbor, its initial state (without limit to value) cannot be obtained by the curious node within the network and the eavesdropper outside the network.

[0080] In this embodiment, it is assumed that the curious node 6 plans to obtain the initial state of its neighbor agent 1, and another execution of the initial state sequence can be constructed as x'(0) = (7.3273, -3.7023, -2.7413, 4.1917,

[0081] 6.1636, -4.8213) k , ensuring that the average value is still 1.0696. Accordingly, a set of false initial state sequences can be generated as

[0082]

[0083] Compared with the original sequence The state for communicating with other real nodes remains unchanged, that is, Only the state of the virtual node is adjusted to handle the change of the original state, but this is completely unknown to the curious node. Finally, based on the redesigned coupling weight Figure 5 It is described that the estimate of the agent 6 to the state x1(0) under two different initial state sequences is consistent. That is, it cannot distinguish between the two observation sequences, and therefore cannot infer the initial state of node 1, and the analysis of the external eavesdropper is consistent with the curious node.

[0084] In summary, the present application can provide a privacy protection method based on general state decomposition in the case of multi-agent system existing eavesdropping attack and limited communication resources, and integrate the general state decomposition method with greater design freedom into the quantization communication environment by using dynamic encoding and decoding scheme.

Claims

1. A method for quantified consistency privacy protection in multi-agent systems based on general state decomposition, characterized in that, Includes the following steps: Step 1: Design a privacy protection mechanism based on general state decomposition. Each node decomposes its state and sets weights according to its own needs and capabilities, reconstructing a false initial state for transmission and communication. The state decomposition is as follows: Node i (i = 1, 2, ..., N) generates n according to its own needs. i If there are ≥0 virtual nodes, a new network graph G' is reconstructed. Then, node i (i = 1, 2, ..., N) no longer uses the original initial state value, and its generation n i +1 random number, For these values, It is used to replace the actual initial state x i (0) is a spurious initial value. Indicates that in n i The initial state applied to each virtual node generates random initial values ​​that are arbitrarily chosen from the set of real numbers; Step 2: Establish a quantization consensus control model for a multi-agent system. Consider a system consisting of N nodes. Based on graph theory, use difference equations to represent the relationships between the dynamic behaviors of each node. Under the assumption of quantization transmission, introduce an encoding-decoding quantization mechanism and provide the specific settings for the encoder and decoder. The generated random initial values ​​are arbitrarily selected from the set of real numbers. To ensure the achievement of the correct average consensus objective, the following constraints are imposed: in This represents the total number of all virtual nodes; Step 3: Introduce an eavesdropping attack model; consider the eavesdropping of network states by internal curious nodes and external eavesdroppers; Step 4: Based on the privacy protection mechanism and the quantitative consistency control model, the final privacy protection quantitative consistency protocol is given, and the correctness of the consistency convergence result of the multi-agent system is analyzed. Step 5: Analyze the privacy of the multi-agent system. By utilizing the indistinguishability of initial state changes, design quantitative indicators for privacy protection and provide privacy analysis under different eavesdropping attacks.

2. The method for quantified consistency privacy protection of multi-agent systems based on general state decomposition as described in claim 1, characterized in that, In step 2, encoder E i Designed as follows: Where ξ i (k) is E i The internal state of Δ i (k) is E i The output of will be sent to the neighbors of agent i, s(k)>0, k≥0 represents the scaling function, x i (k) represents the agent's state at time k, and q(·) is a quantizer that quantizes the real-valued state into an integer-valued state. Specifically, q(·) is described as: R→Q={0,±i,i=1,2,…,K} Where R represents the real number field, Q represents the quantization level set, and the total number of quantization levels is 2K+1.

3. The method for quantified consistency privacy protection of multi-agent systems based on general state decomposition as described in claim 1, characterized in that, In step 2, decoder D ji Designed as follows: in D represents ji The output of represents the action of agent i on state x. j Estimate of (k).

4. The method for quantified consistency privacy protection in multi-agent systems based on general state decomposition as described in claim 1, characterized in that, In step 3, an internal curious node refers to an agent that correctly follows all protocol steps but attempts to obtain information about other agents based on the collected data. An external eavesdropper refers to an eavesdropper who accesses information by intruding into the communication channel. The eavesdropper knows the network topology and all the shared data in the network, but cannot obtain the state that is not shared in the network.

5. The method for quantized consistency privacy protection in multi-agent systems based on general state decomposition as described in claim 1, characterized in that, In step 4, the final privacy protection quantification consistency control protocol is as follows: Where u i (k) represents the control input of agent i at time k; This represents the true neighbors of node i before state decomposition. This represents all virtual nodes added to node i; a ij [k],i,j∈G' represents the weights of the edges connecting nodes i and j in the network topology G' at time k.

6. The method for quantized consistency privacy protection in multi-agent systems based on general state decomposition as described in claim 1, characterized in that, In step 5, the privacy protection quantification index is represented by the information collected by the adversary at time k. As time evolves, given any time κ, all the collected information is: gather This indicates that agent i is capable of generating the same information. The set of all initial states, Privacy is defined as According to d privacy The expression yields d. privacy The larger the value, the greater the uncertainty of the opponent acquiring the initial state, and the greater the maximum impossibility d. privacy =∞ means that the opponent cannot find a unique x. i (0), and x cannot even be found. i The meaningful range of (0).

Images