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

Abstract

The invention discloses a multi-agent system quantization consistency privacy protection method based on general state decomposition, which comprises the following steps of: designing a privacy protection mechanism based on general state decomposition, and performing state decomposition and weight setting on each node according to own demand and capability, reconstructing a false initial state for transmission communication; establishing a quantization consistency control model of the multi-agent system: considering a system formed by N nodes, representing a relationship among dynamic behaviors of each node by using a difference equation based on graph theory knowledge, introducing an encoding and decoding quantization mechanism under the assumption of quantization transmission, and giving specific settings of an encoder and a decoder; an eavesdropping attack model is introduced, wherein eavesdropping of internal curious nodes and external eavesdroppers on states in the network is considered; performing correctness analysis on a system consistency convergence result: based on knowledge of a graph theory, a matrix theory and a stability theory, analyzing a dynamic behavior of an intelligent agent to obtain a final convergence consistency result; according to the method, the privacy of a multi-agent system is analyzed, and privacy analysis under different eavesdropping attacks is given by designing a quantitative index of privacy protection based on the non-distinguishability of initial state change. According to the invention, the designed control protocol is simple and easy to implement, communication resources can be saved, correct consistent convergence is ensured, and more comprehensive privacy protection is provided.

Description

Technical Field

[0001] The present invention relates to the field of multi-agent system control and information security technology, and in particular to a multi-agent system quantitative consistency privacy protection method based on general state decomposition. Background Art

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

[0003] However, with the increasing complexity of tasks and the continuous expansion of application scenarios, many existing consensus algorithms are unable to achieve some goals with higher requirements. For example, in digital interactive networks, due to limited communication bandwidth and computing power, the information exchanged by agents needs to be quantized before transmission. Therefore, the consistency problem in quantized communication is a topic worth studying. Due to the influence of quantization, nonlinearity is introduced into the evolution law, resulting in the generated dynamic system being more difficult to study than the original linear system, and it is also more difficult to achieve correct consistent convergence. Many existing algorithms cannot effectively ensure that the system reaches consistency, or may converge to random values ​​instead of the target average, or there are errors related to the quantization level of the exact value.

[0004] In addition, many existing quantitative consensus results ignore the issue of privacy protection. 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. As an important source of information fusion in the consensus problem, the initial state usually contains some sensitive information or personal privacy. For example, the initial opinion on a topic or theme in a social network; the initial location of an agent in a collection problem (which can be a home address or an organization's headquarters); the parameters of the cost function in an economic scheduling problem, etc. Therefore, it is of great significance to consider privacy protection in the quantitative consensus algorithm.

[0005] Currently, there are few papers that consider both privacy protection and quantitative communication. In a quantitative communication environment, differential privacy methods are used to protect the initial state, but the results show that the converged consensus value is a random variable in the neighborhood of the average value of the initial state, and accurate convergence cannot be guaranteed. Although researchers have designed a dynamic quantization scheme to ensure that the system can reach a 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 node. In addition, some papers have used encryption methods to solve the privacy protection quantitative consensus problem, but it usually leads to more computational and communication pressure.

[0006] In summary, it is non-trivial to directly consider privacy protection in quantized communication research. The main challenges and difficulties involved are: (i) the coexistence 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) more comprehensive privacy protection (internal curious nodes and external eavesdroppers) needs to be guaranteed. In addition, the designed mechanism should be simple to implement and have low computational and communication costs. Summary of the invention

[0007] Purpose of the invention: The present invention provides a quantitative consistency privacy protection method for multi-agent systems based on general state decomposition, which makes the designed control protocol simple and easy to implement, while saving communication resources, ensuring correct consistent convergence and providing more comprehensive privacy protection.

[0008] Technical solution: The invention discloses a method for protecting privacy in a multi-agent system based on general state decomposition and quantitative consistency, comprising 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 the false initial state used for transmission and communication;

[0010] Step 2: Establish a quantitative consistency control model for multi-agent systems; consider a system consisting of N nodes, and based on graph theory knowledge, use differential equations to express the relationship between the dynamic behaviors of each node. Under the assumption of quantitative transmission, introduce the encoding and decoding quantization mechanism, and give the specific settings of the encoder and decoder;

[0011] Step 3: Introduce the eavesdropping attack model; consider the eavesdropping of the network status by internal curious nodes and external eavesdroppers;

[0012] Step 4: Based on the privacy protection mechanism and the quantitative consistency control model, the final privacy protection quantitative consensus protocol is given, and the correctness of the results of the multi-agent system consistency convergence is analyzed;

[0013] Step 5: Analyze the privacy of the multi-agent system, take advantage of the indistinguishability of the initial state changes, design quantitative indicators of privacy protection, and provide privacy analysis under different eavesdropping attacks.

[0014] Furthermore, in step 1, the state decomposition is as follows: Node i, (i = 1, 2, ..., N) generates n nodes according to its own needs (which may be limited by resources or communication capabilities). i ≥0 virtual nodes. For other nodes in the network, the communication and weight design between node i and the virtual nodes it generates are completely unknown. Since virtual nodes are added 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 generated n i +1 random number, For these values, is used to replace the actual initial state x i (0) is a false initial value, Indicates that n i The initial state imposed on the virtual nodes is generated by randomly selecting the initial value from the set of real numbers.

[0015] Furthermore, the generated random initial value can be arbitrarily selected from the set of real numbers. In order to ensure the realization of the correct average consistency goal, the following constraints are imposed:

[0016]

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

[0018] Furthermore, in step 2, the encoder E i Designed for:

[0019]

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

[0021]

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

[0023] Furthermore, in step 2, the decoder D ji Designed for:

[0024]

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

[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 that accesses information by invading 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-preserving quantitative consistency control protocol is:

[0028]

[0029] where u i (k) represents the control input of agent i at time k; represents the real neighbors of node i before state decomposition, Represents all virtual nodes added by node i; a ij [k],i,j∈G′ represents the weight of the edge connecting nodes i and j in the network topology G′ at time k.

[0030] Furthermore, in step 5, the privacy protection quantitative index is assumed to be the information collected by the adversary (curious node or eavesdropper) at time k, expressed as As time evolves, given any time κ, all collected information is gather Indicates that agent i can generate the same information The set of all initial states of Privacy is defined as

[0031]

[0032] According to d YNiOZ[\ The expression of d YNiOZ[\ The larger the value, the greater the uncertainty of the opponent obtaining the initial state, and the maximum impossibility d YNiOZ[\ =∞ means the opponent cannot find a unique x i (0), can't even find x i (0) has a meaningful scope.

[0033] Beneficial effects: Compared with the prior art, the present invention has the following significant advantages: In view of the problems that may be encountered in the process of achieving average consensus in a multi-agent system, such as eavesdropping attacks and limited communication resources, the present invention uses a dynamic encoding and decoding scheme to integrate a general state decomposition method with greater design freedom into a quantitative communication environment, thereby ensuring the realization of precise average consistency; in addition, the initial state in the algorithm can be any real number, without having to be assumed to be an integer. For the first time, a more general state decomposition method is proposed. The number of generated virtual nodes is no longer fixed, nor is it determined by the network topology, but can be decomposed according to the resources or capability requirements of each agent. Therefore, the new state decomposition mechanism is more universal, and at the same time brings greater design freedom, which can better meet the needs of different nodes; finally, the proposed method can effectively resist internal and external adversaries and achieve maximum privacy protection in a quantitative environment, thereby ensuring a safer communication environment with lower computational costs. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Figure 1 It is a schematic diagram of the method flow of the present invention.

[0035] FIG. 2( a ) is a diagram showing an example of a network topology of the present invention.

[0036] FIG. 2( b ) is a topological diagram after decomposition of the present invention.

[0037] Figure 3 The state trajectory diagram of the agent after using the differential privacy method for the present invention.

[0038] Figure 4 The state trajectory diagram of the agent after using the general state decomposition method in the present invention.

[0039] Figure 5 It is a diagram of the estimated state of the intelligent agent of the present invention under two different initial states. DETAILED DESCRIPTION

[0040] like Figure 1 As shown in FIG. 1 , a quantitative consistency privacy protection method for a multi-agent system 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 needs and capabilities, and reconstructs the false initial state used for transmission and communication.

[0042] Each node i, (i = 1, 2, ..., N) generates n according to its own needs (which may be limited by resources or communication capabilities). i≥ 0 virtual nodes. For other nodes in the network, the communication and weight design between node i and the virtual nodes it generates are completely unknown. Since virtual nodes are added 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 generated n i +1 random number, For these values, is used to replace the actual initial state x i (0) is a false initial value, Indicates that n i The generated random initial values ​​can be selected arbitrarily from the set of real numbers, but in order to ensure the correct average consistency goal, the following constraints need to be imposed on them:

[0043]

[0044] In the embodiment of the present invention, a network topology with 6 nodes as shown in FIG2(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 ​​expressed 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. In particular, it can be found that nodes 3 and 6 do not generate any virtual nodes, which indicates that they do not care about privacy leakage. Then, based on the knowledge that (N,n)=(6,6), each node can set new initial values ​​for itself and its virtual nodes under the constraints. The topology G ′ All nodes in will generate a new initial state sequence, which can be designed as:

[0047]

[0048] Note that both the original initial state sequence and the newly formed initial state sequence are real number sequences, which expands the scope of application of existing privacy protection methods.

[0049] Step 2: Establish a quantitative consistency control model for multi-agent systems: Consider a system composed of N nodes. Based on graph theory knowledge, use differential equations to express the relationship between the dynamic behaviors of each node. Under the assumption of quantitative transmission, introduce the 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 can ensure that all agents achieve average consistency in an exponential manner. First, for each node i (i = 1, 2, ..., N), transmit to neighbor nodes j, j∈N i The information is provided by the encoder E i Encoding is designed as:

[0054]

[0055] where ξ i (k) is E i The internal state of 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, and q(·) is the quantizer, which can quantize the real-valued state to an integer-valued state. The specific description is q(·): R→Q={0,±i,i=1,2,…,K}

[0056]

[0057] Wherein Q represents the set quantization level, 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 (k), it uses the following decoder D ji To estimate the state x before quantization j (k):

[0059]

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

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

[0062]

[0063] However, in this embodiment, we consider the privacy protection 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 network state by internal curious nodes and external eavesdroppers.

[0065] Here, an internal curious node refers to an agent that follows all protocol steps correctly but tries to obtain information about other agents based on the collected data. An external eavesdropper refers to an eavesdropper that can access information by invading the communication channel. The eavesdropper can know the network topology and all the 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 quantitative consistency control model, the final privacy protection quantitative consensus protocol is given, and the correctness of the results of the consistency convergence of the multi-agent system is analyzed.

[0067] Assume that the communication network G is connected. where c 1 ,c 8 is a known non-negative constant, is the initial consistency error. The above two assumptions, one is the restriction on network topology, requiring network topology connectivity is a necessary and sufficient condition to ensure the consistency of the system. The other is that the initial state of the agent and the upper bound of the initial state consistency error are known. When the initial states of all agents are known, the upper bound c 1 ,c 8 Naturally it can be calculated.

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

[0069]

[0070] in In the scaling function s(t) = s U γ – And 2K+1-level consistent quantizer, quantization consensus protocol:

[0071]

[0072] The correct average uniform asymptotic realization is guaranteed, that is,

[0073]

[0074] Then, the general state decomposition method proposed in this paper is compared with the differential privacy method to illustrate its advantages in terms of accurate convergence. Figure 3 It can be observed that the state trajectory of the node cannot converge to the exact average value. It can only fall in a neighborhood of the initial state average value. 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, we can find that the exact average consistency of all agents can be achieved, such as Figure 4 shown.

[0075] Step 5: Analyze the privacy of the multi-agent system, take advantage of the indistinguishability of the initial state changes, design quantitative indicators of privacy protection, and provide privacy analysis under different eavesdropping attacks.

[0076] Assume that the information collected by the adversary (curious node or eavesdropper) at time k is expressed as As time evolves, given any time κ, all collected information is gather Indicates that agent i can generate the same information The set of all initial states of Privacy is defined as

[0077]

[0078] According to d YNiOZ[\ The expression of d YNiOZ[\ The larger it is, the greater the uncertainty of the opponent obtaining the initial state. The maximum impossibility d YNiOZ[\ =∞ means the opponent cannot find a unique x i (0), can't even find x i (0) has a meaningful scope.

[0079] Based on the given privacy protection indicators, 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 restrictions on the value) will not be obtained by curious nodes within the network and eavesdroppers outside the network.

[0080] In this embodiment, assuming that curious node 6 plans to obtain the initial state of its neighbor agent 1, 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] With the original sequence In contrast, the state used to communicate with other real nodes remains unchanged, i.e., Only the states of the virtual nodes are adjusted to handle the changes in the original states, which is completely unknown to the curious nodes. Finally, based on the redesigned coupling weights Figure 5 Describes the behavior of agent 6 in two different initial state sequences. 1 (0) is consistent. That is, it cannot distinguish between the two observation sequences and therefore cannot infer the initial state of node 1. The analysis of the external eavesdropper is consistent with that of the curious node.

[0084] In summary, the present invention can provide a privacy protection method based on general state decomposition when a multi-agent system is subject to eavesdropping attacks and communication resources are limited. By utilizing a dynamic encoding and decoding scheme, the general state decomposition method with greater design freedom is integrated into a quantitative communication environment.

Claims

1. A quantitative consistency privacy protection method for multi-agent systems based on general state decomposition, characterized by: The steps include: 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 the false initial state used for transmission and communication; Step 2: Establish a quantitative consistency control model for multi-agent systems; consider a system consisting of N nodes, and based on graph theory knowledge, use differential equations to express the relationship between the dynamic behaviors of each node. Under the assumption of quantitative transmission, introduce the encoding and decoding quantization mechanism, and give the specific settings of the encoder and decoder; Step 3: Introduce the eavesdropping attack model; consider the eavesdropping of the network status 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 consensus protocol is given, and the correctness of the results of the multi-agent system consistency convergence is analyzed; Step 5: Analyze the privacy of the multi-agent system, take advantage of the indistinguishability of the initial state changes, design quantitative indicators of privacy protection, and provide privacy analysis under different eavesdropping attacks.

2. The method for protecting privacy in a multi-agent system based on general state decomposition according to claim 1, characterized in that: In step 1, the state decomposition is as follows: node i, (i = 1, 2, ..., N) generates n according to its own needs. i ≥0 virtual nodes, reconstruct a new network graph G ′ , then node i, (i=1,2,…,N) no longer uses the original initial state value, and its generated n i +1 random number, For these values, is used to replace the actual initial state x i (0) is a false initial value, j=1,2,…,n i Indicates that n i The initial state imposed on the virtual nodes is generated by randomly selecting the initial value from the set of real numbers.

3. The method for protecting privacy in a multi-agent system based on general state decomposition according to claim 2, characterized in that: The generated random initial value can be arbitrarily selected from the set of real numbers. In order to ensure the realization of the correct average consistency goal, the following constraints are imposed: in Represents the total number of all virtual nodes.

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

5. The method for protecting privacy in a multi-agent system based on general state decomposition according to claim 1, characterized in that: In step 2, decoder D ji Designed for: in Indicates D ji The output of agent i represents the state x j (k) Estimate.

6. The method for protecting privacy in a multi-agent system based on general state decomposition according to claim 1, characterized in that: In step 3, the 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. The external eavesdropper refers to an eavesdropper that accesses information by invading 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.

7. The method for protecting privacy in a multi-agent system based on general state decomposition according to claim 1, characterized in that: In step 4, the final privacy-preserving quantitative consistency control protocol is: where u i (k) represents the control input of agent i at time k; represents the real neighbors of node i before state decomposition, Represents all virtual nodes added by node i; a ij [k],i,j∈G′ represents the weight of the edge connecting nodes i and j in the network topology G′ at time k.

8. The method for protecting privacy in a multi-agent system based on general state decomposition according to claim 1, characterized in that: In step 5, the privacy protection quantitative index is assumed to be the information collected by the adversary at time k, expressed as As time evolves, given any time κ, all collected information is gather Indicates that agent i can generate the same information The set of all initial states of Privacy is defined as According to d YNiOZ[\ The expression of d YNiOZ[\ The larger the value, the greater the uncertainty of the opponent obtaining the initial state, and the maximum impossibility d YNiOZ[\ =∞ means the opponent cannot find a unique x i (0), can't even find x i (0) has a meaningful scope.

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