Multi-agent system elastic consensus method and system with privacy protection capability

Abstract

The invention discloses a multi-agent system elastic consensus method and system with privacy protection capability, and relates to the technical field of computers. The method comprises the steps that in an initial security window period, privacy protection of an initial state of an intelligent agent is achieved through state decomposition, sub-state mixed updating and merging operation, in an environment with spoofing attack, a conventional intelligent agent filters malicious information in a mode of sorting and removing suspicious extreme values based on a weighted mean value sub-sequence reduction algorithm, and the privacy protection of the initial state of the intelligent agent is achieved. And updating the state based on the trusted neighbor set until a consensus is reached. According to the method, the privacy of the initial state of the intelligent agent can be protected while the unconstrained spoofing attack is resisted, the communication overhead is not increased, the calculation complexity is low, the convergence speed is high, and the method is suitable for resource-limited collaborative scenes such as an unmanned aerial vehicle cluster and a wireless sensor network.

Description

Technical Field

[0001] This application relates to the field of computer technology, specifically to a method and system for resilient consensus in a multi-agent system with privacy protection capabilities. Background Technology

[0002] Multi-Agent Systems (MAS), with their distributed architecture, autonomous operation, and collaborative capabilities, are widely used in mobile robots, drone swarms, smart grids, and other fields. MAS collaborative control primarily relies on various consensus algorithms, whose role is to ensure that all agents reach a consensus on a shared value of interest. Resilient consensus algorithms, as the core foundation of MAS collaboration, can guarantee correct consensus among other agents even when some agents fail or suffer malicious attacks. In achieving resilient consensus, agents need to exchange state information. Traditional resilient consensus algorithms, such as the Weighted Mean Subsequence Reduction (W-MSR) algorithm, resist interference from adversarial agents by having regular agents remove suspicious extreme values ​​during iterations, thus ensuring that the system can still achieve effective consensus even in the presence of malicious nodes. However, in a cyberattack environment, multi-agent systems struggle to simultaneously achieve resilient consensus and privacy protection. Summary of the Invention

[0003] The purpose of this invention is to provide a method and system for elastic consensus in multi-agent systems with privacy protection capabilities, which can solve the technical problem that multi-agent systems are unable to simultaneously achieve elastic consensus and privacy protection when facing the dual threats of deception attacks and eavesdropping attacks.

[0004] To achieve the above objectives, this application provides the following technical solution: In a first aspect, the present invention provides a resilient consensus method for multi-agent systems with privacy protection capabilities, comprising the following: S1, the state of each agent at the initial time k=0. Decomposed into the first substate With the second substate The first sub-state Used for interacting with neighboring intelligent agents, the second sub-state With the corresponding first sub-state Local interaction; S2, the first sub-state of each agent in the first state update iteration. Based on the first sub-state of the neighboring agent and its corresponding second sub-state Perform an update to obtain the first merged sub-state. The second sub-state Based on the corresponding first substate updating to obtain a second merged sub-state ; S3, merging the first merged sub-state and the second merged sub-state to obtain a merged state ; S4, starting from k = 1, for each iteration, each agent sends its current complete state at time k to neighbor agents and receives state information from neighbor agents; S5, each agent sorts the received neighbor states, and based on a preset maximum number of adversarial agents F, removes at most F neighbor state values higher than its complete state and at most F neighbor state values lower than its complete state to form a trusted neighbor set ; S6, each agent calculates and updates its complete state at the next time based on its complete state , the states of neighbors in the trusted neighbor set , and a preset weight, until the elastic consensus is reached.

[0005] Further, when the first sub-state and the second sub-state are decomposed in step S1, the following conditions are met: .

[0006] Further, in step S2, the update rules of the first sub-state and the second sub-state are as follows:

[0007] wherein, is a neighbor set of the agent , is an interaction weight of the agent and the neighbor at an initial time, is an interaction weight between the first sub-state and the second sub-state .

[0008] Further, in step S3, the calculation method of the merged state is as follows: .

[0009] Further, in step S5, at most F neighbor state values higher than its complete state The specific operation for the neighbor status value is as follows: If higher The number of neighbor states is greater than Then remove the one with the largest value. 1; otherwise, remove all those higher than 1. The neighbor status value.

[0010] Furthermore, in step S5, remove states that are less complete than themselves. The specific operation for the neighbor status value is as follows: If lower The number of neighbor states is greater than Then remove the one with the smallest value. 1; otherwise, remove all those below 10; The neighbor status value.

[0011] Furthermore, in step S6, the complete state for the next time step is updated. The rules are:

[0012] in, For a set of trusted neighbors, For intelligent agents Trusted Neighbors At any moment Interaction weights.

[0013] Secondly, the present invention also provides a multi-agent resilient consensus system with privacy protection capabilities, comprising: State decomposition module: used to decompose the states of each agent at the initial time k=0. Decomposed into the first substate With the second substate The first sub-state Used for interacting with neighboring intelligent agents, the second sub-state With the corresponding first sub-state Local interaction; Update module: Used to determine the first sub-state of each agent during the initial state update iteration. Based on the first sub-state of the neighboring agent and its corresponding second sub-state Perform an update to obtain the first merged sub-state. The second sub-state Based on the corresponding first substate Update to obtain the second merged sub-state ; State merging module: used to merge the first sub-state With the second merged sub-state Merge; obtain merged state ; Communication module: Used to, starting from time k=1, for each iteration, each agent reports its complete state at the current time k. Send to neighboring intelligent agents and receive status information from neighboring intelligent agents; Suspicious Value Filtering Module: This module sorts the received neighbor states for each agent and removes states with higher integrity than its own, based on a preset maximum number of adversarial agents F. The maximum number of neighboring state values ​​and the number of complete states below its own. The most F neighbor state values ​​are used to form a trusted neighbor set. ; Consensus update module: used by each agent based on its own complete state Trusted Neighbor Set The system calculates and updates the complete state for the next time step based on the states of the neighbors and their preset weights until a flexible consensus is reached.

[0014] Thirdly, the present invention also provides a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the steps of the privacy-preserving resilient consensus method for a multi-agent system.

[0015] Fourthly, the present invention also provides a computer-readable storage medium storing a computer program, characterized in that, when the computer program is executed by a processor, it implements the steps of the privacy-preserving resilient consensus method for a multi-agent system.

[0016] Compared with the prior art, the present invention has the following beneficial technical effects: This invention provides a resilient consensus method for multi-agent systems with privacy protection capabilities. It performs a single state decomposition and merging operation in the initial stage, and maintains and updates only a single complete state in subsequent consensus stages. Compared to the traditional SD-MSR algorithm, which requires maintaining two sub-states throughout the entire lifecycle, this invention significantly reduces computational complexity, adds no additional communication overhead, and achieves faster convergence, making it particularly suitable for resource-constrained multi-agent systems. This invention employs a W-MSR mechanism, where regular agents effectively filter out false information injected by adversarial agents by sorting and removing extreme suspicious values. As long as the number of adversarial agents does not exceed a preset limit, all regular agents can converge to the convex hull of the initial state, maintaining attack resistance and consensus accuracy comparable to the classic W-MSR algorithm. This invention, through state decomposition and reconstruction, splits the initial state of each agent into a first sub-state and a second sub-state, which are then merged into a new state after a mixed update. This process ensures that eavesdroppers can only observe the obfuscated information and cannot deduce the original initial state, achieving strong privacy protection independent of network topology. Attached Figure Description

[0017] Figure 1 This is a schematic diagram of a resilient consensus method for a multi-agent system with privacy protection capabilities, as described in an embodiment of the present invention.

[0018] Figure 2 This is a schematic diagram of state decomposition in an embodiment of the present invention.

[0019] Figure 3 This is a schematic diagram of state merging in an embodiment of the present invention.

[0020] Figure 4 This is a network topology diagram of five intelligent agents in an embodiment of the present invention.

[0021] Figure 5 This is a schematic diagram illustrating the process of removing the W-MSR algorithm consensus in an embodiment of the present invention.

[0022] Figure 6 This is a schematic diagram of the consensus process for removing the state decomposition mechanism in an embodiment of the present invention.

[0023] Figure 7 This is a schematic diagram of the consensus process of the algorithm of the present invention in an embodiment of the present invention.

[0024] Figure 8 This is a schematic diagram of the consensus process of the SD-MSR algorithm in an embodiment of the present invention. Detailed Implementation

[0025] In the following description, only certain exemplary embodiments are briefly described. As those skilled in the art will recognize, the described embodiments can be modified in various ways without departing from the spirit or scope of the invention. Therefore, the drawings and description are considered to be exemplary in nature and not restrictive.

[0026] See Figure 1 This invention provides a resilient consensus method for multi-agent systems with privacy protection capabilities, first considering the following: An undirected graph consisting of nodes The set of nodes is edge set The weight matrix is ,if This indicates a node. and nodes There exists an edge between them, and at this time there is... ,on the contrary . Node The set of neighbor nodes is represented as .

[0027] Considering the dual threats of deception attacks and eavesdropping attacks, by How can a MAS (Multi-Agent System) composed of multiple agents effectively protect the privacy of sensitive state information carried during interactions between agents while achieving resilient consensus? In a scenario without deception attacks, the expression for MAS achieving average consensus is: [The system includes agents, including adversarial agents and regular agents, and the method includes the following steps:]

[0028] in, It is an intelligent agent exist The state value at time 10:00 Represents intelligent agents A collection of neighboring intelligent agents It is an intelligent agent and intelligent agents At any moment Interaction weights.

[0029] The topology of a network is a crucial property determining its security. This invention introduces the concept of network robustness. Given an undirected graph... If for any two non-empty disjoint subsets and ( An undirected graph is said to be a graph that satisfies at least one of the following conditions. - Robust: , in Representing a subset a subset of nodes All nodes in this subset satisfy the condition that... Besides, there are at least Each neighboring node. Represents a set The number of elements in the text.

[0030] Consider two types of agents: 1) Adversarial agents, denoted as a set. 2) Conventional intelligent agents, denoted as a set In each iteration, adversarial agents arbitrarily update their own state and send the same value to their neighbors. Considering resource constraints in real-world scenarios, if most agents are attacked by the network, the multi-agent system will completely spiral out of control. Therefore, there is an upper limit to the number of adversarial agents; that is, at most a maximum of [number missing] agents can exist in the network. An adversarial agent.

[0031] The attack model is a coupled scenario of deception attack and eavesdropping attack, and the adversarial agent update rule is:

[0032] in, This invention allows for the creation of malicious manipulation functions of any form, without energy constraints, enabling continuous attacks of arbitrary strength. Regarding privacy breaches, this invention distinguishes between two types of eavesdroppers: Insider eavesdroppers: refers to one or more regular agents within a multi-agent system who, while following the algorithm steps, harbor malicious intent and attempt to use all the network data they legally receive to deduce sensitive information about other agents. External eavesdropper: refers to an attacker outside the multi-agent system who may obtain all plaintext data transmitted on the network by means of listening to communication links. It does not know the privacy protection methods used by the multi-agent system, but it knows the network topology.

[0033] In real-world scenarios, attackers need time to prepare and deploy their attacks; therefore, it is reasonable to assume that the system is initially in a secure state. Thus, it is assumed that the system is initially secure. It provides a secure environment for state decomposition operations, free from deception attacks. Based on the above, please refer to Figure 1 This invention provides a resilient consensus method for multi-agent systems with privacy protection capabilities, the specific steps of which are as follows: S1, the state of each agent at the initial time k=0. Decomposed into the first substate With the second substate The first sub-state Used for interacting with neighboring intelligent agents, the second sub-state With the corresponding first sub-state Local interaction; In a more specific embodiment provided by the present invention, see [reference needed]. Figure 2 First substate This is called the common substate, which will replace the original state in subsequent initial communications. It is sent to neighboring intelligent agents, meaning it is visible to the network. Second sub-state. This is called a private substate; it never leaves the local domain of agent i and is never sent to any other agent. Any eavesdropper (internal or external) can only observe the first substate. However, the second substate cannot be known. Therefore, it is impossible to directly restore This achieves privacy protection for the initial state. Among them, Figure 2 (a) shows the network topology before state decomposition. Figure 2 (b) is the network topology after state decomposition.

[0034] In step S1, the first sub-state is decomposed. With the second substate At that time, the following conditions are met: ; S2, the first sub-state of each agent in the first state update iteration. Based on the first sub-state of the neighboring agent and its corresponding second sub-state Perform an update to obtain the first merged sub-state. The second sub-state Based on the corresponding first substate Update to obtain the second merged sub-state ; In a more specific embodiment provided by the present invention, in step S2, the first sub-state Second substate The update rules are as follows:

[0035] in, For intelligent agents The neighborhood group, For intelligent agents with neighbors The interaction weights at the initial moment, The first substate Second substate Interaction weights between them.

[0036] In this step, the first sub-state Second substate Furthermore, a mixture is performed between the common sub-states of each agent. This further enhances privacy because even if an eavesdropper knows the update rules, they cannot deduce the initial state in reverse due to the lack of information about the private sub-states. At the same time, this update design guarantees a certain invariance of the global state of the multi-agent system.

[0037] S3, merge the first sub-state With the second merged sub-state Merge; obtain merged state ; In a more specific embodiment provided by the present invention, see [reference needed]. Figure 3 , Figure 3 (a) shows the network topology before state merging. Figure 3 (b) is the network topology after state merging. In step S3, the states are merged. The calculation method is as follows: .

[0038] After merging, each agent regains a complete merged state that can be used in subsequent consensus processes. Based on the state decomposition / merging rules and sub-state update rules, the overall average value of the multi-agent system remains unchanged before and after state decomposition. This ensures that the overall state of the multi-agent system does not shift significantly, maintaining the stability of the agent state information. That is:

[0039] The biggest difference between the proposed state decomposition mechanism and traditional state decomposition methods lies in the fact that traditional methods involve sub-state updates throughout the entire consensus process, while the realization of privacy protection for the agent's initial state does not require state decomposition to run through the entire consensus process. Specifically, in traditional methods, the state of each node is decomposed into two sub-states, both of which require iterative updates, which undoubtedly increases computational complexity and consumes more computational resources. In contrast, this invention only uses the state decomposition mechanism to reconstruct the node's initial state information in the first iteration. Subsequent proofs show that this method can not only effectively protect the privacy of the node's initial value but also reduce computational complexity during the consensus process.

[0040] In conclusion, arrive The state reconstruction phase can be regarded as a key preprocessing method. This phase mainly maps the initial values ​​of each agent to another domain, so that the privacy of the initial values ​​of the agents can be established in the privacy protection phase. The subsequent resilient consensus algorithm can realize the cooperation between agents while preventing privacy leakage, ensuring that the multi-agent system can still operate normally when facing various interferences and challenges, and improving the overall performance and reliability of the multi-agent system while protecting privacy.

[0041] The elastic consensus phase is mainly aimed at At this stage, the system faces a combined threat of deception and eavesdropping attacks. In MAS (Multi-Agent System), the presence of deception attacks prevents attacked agents from updating their states according to the pre-defined mechanism, thus affecting the overall performance of the system. To address this issue, this invention employs the classic resilient consensus algorithm W-MSR to ensure that MAS can still achieve resilient consensus even in the presence of deception attacks. Its core idea is that unattacked regular agents identify and eliminate potentially tampered data based on specific screening criteria, thereby ensuring that MAS can maintain resilient consensus even when facing deception attacks.

[0042] S4, starting from time k=1, for each iteration, each regular agent will record its complete state at time k. Send to neighboring intelligent agents and receive state information from neighboring intelligent agents; the adversarial intelligent agent updates its own state according to arbitrary malicious update rules and sends state information to its neighbors; S5, each regular agent sorts the received neighbor states and, based on the preset maximum number of adversarial agents F, removes those with higher complete states than its own. The maximum number of neighboring state values ​​and the number of complete states below its own. The most F neighbor state values ​​are used to form a trusted neighbor set. ; In a more specific embodiment provided by the present invention, a conventional intelligent agent After receiving the status values ​​of all neighbors, i performs the following sub-steps: The regular agent sorts all the received neighbor state values ​​(which may come from honest regular neighbors or malicious adversarial neighbors) in ascending order, resulting in an ordered list. ; intelligent agent i With ordered lists For each value in the comparison, in step S5, remove the values ​​that are higher than the current complete state. The specific operation for the neighbor status value is as follows: If higher The number of neighbor states is greater than Then remove the one with the largest value. 1; otherwise, remove all those higher than 1. Neighbor status values: In step S5, remove states that are less complete than themselves. The specific operation for the neighbor status value is as follows: If lower The number of neighbor states is greater than Then remove the one with the smallest value. 1; otherwise, remove all those below 10; The neighbor status value.

[0043] S6, each regular agent is based on its own complete state. Trusted Neighbor Set The complete state for the next time step is calculated and updated using the states of the middle neighbors and their preset weights. ; make Indicates at time step At that time, conventional intelligent agents The set of remaining neighboring nodes after removing suspicious values. (Regular agent) according to The state values ​​of the middle neighbor node set are updated according to the following update rules to obtain the complete state at the next time step. :

[0044] in, For a set of trusted neighbors, For intelligent agents Trusted Neighbors At any moment Interaction weights.

[0045] Theoretical analysis reveals that the proposed privacy-preserving W-MSR algorithm achieves synergistic optimization of privacy protection and resilient consensus through a phased design: At the privacy level, the algorithm performs state decomposition only in the initial stage of the system, splitting the agent's initial state into a public sub-state (participating in network interaction) and a private sub-state (only for local interaction). This state reconstruction mechanism blocks the derivation path of the original initial state by internal and external eavesdroppers, effectively resisting eavesdropping attacks from both, while avoiding excessive consumption of computational and communication resources caused by full-cycle state decomposition. At the resilient consensus level, the algorithm relies on the core logic of the W-MSR algorithm, ensuring that the number of adversarial agents in a multi-agent system does not exceed the upper limit. And the network topology satisfies - Under robust graph conditions, a conventional agent can sort and remove neighbor states. By performing operations on extreme values, the system filters out false information injected by deception attacks and ultimately converges precisely to the convex hull of the initial state, achieving elastic consensus. In the resource-constrained MAS scenario, it achieves privacy protection, resistance to deception attacks, and efficient resource utilization.

[0046] Example Based on the above methods, this embodiment provides the following solution: Consider a multi-agent system with five agents. The communication network topology of this multi-agent system is as follows: Figure 4 As shown, this is an undirected connected graph where each agent can communicate directly with a specific neighbor. For ease of explanation, the initial state value of each agent i is set to its number, i.e.: Consider the privacy protection performance of the algorithm in the presence of external eavesdroppers.

[0047] Consider an external eavesdropper capable of monitoring plaintext data transmitted across all communication links in the network and aware of the network topology, but unaware of the privacy protection mechanism employed in this invention. The eavesdropper's goal is to infer the initial state information of Agent 2. In simulation, variables are used. This indicates that the external eavesdropper is at time k. The estimated value.

[0048] Agent 5 is designated as an adversarial agent; therefore, the maximum number of adversarial agents is set to F=1. This adversarial agent does not follow the normal consensus update rules but instead updates its own state according to a time-varying malicious function and sends it to its neighbors. In this embodiment, its state update rule is set as follows: (k)=sin(k),k≥1, which means that agent 5 will continuously inject false information with high-frequency oscillations into the network in an attempt to disrupt the consensus process.

[0049] In the initial stage, since there are no network attacks, the W-MSR algorithm is not used to remove suspicious values. Therefore, the interaction weights between each agent and other agents can be used. Set as ,in After the privacy protection phase ends, the regular agent, due to the W-MSR algorithm removing suspicious values, can have its interaction weights with other agents adjusted. Set as ,in .

[0050] When the elastic consensus phase of the proposed algorithm is removed, the state trajectories of each agent are as follows:Figure 5 As shown in the figure, when the proposed algorithm does not employ the W-MSR algorithm, the state trajectories of each conventional agent are significantly affected by the adversarial agent 5, making it impossible to reach a consensus. Furthermore, when the state decomposition privacy protection mechanism in the proposed algorithm is removed, the state trajectories of each agent are as follows: Figure 6 As shown in the figure. The figure shows the eavesdropper's estimate. Initial values ​​of agent 2 The consistency proves that when the privacy protection mechanism is missing, the node's initial privacy information is stolen.

[0051] The experimental results of the proposed algorithm are as follows: Figure 7 As shown, the eavesdropper's estimated value differs significantly from the initial value of Agent 2, thus effectively protecting the privacy of Agent 2's initial state. Furthermore, even in the presence of adversarial agents, regular agents can reach consensus through the algorithm. Subsequently, a comparison with the SD-MSR algorithm proposed in existing literature yields the following results: Figure 8 As shown. Comparison Figure 7 and Figure 8 It can be observed that the SD-MSR algorithm, due to the need to update two sub-states in each iteration, increases the number of network nodes, resulting in a significantly slower convergence speed compared to the proposed algorithm. The proposed algorithm, however, only employs a state decomposition method in the initial stage, thus avoiding the problem of reduced convergence speed.

[0052] Example 2 In practical applications, this algorithm can be widely used in scenarios such as smart grid energy dispatching and drone swarm collaborative search and rescue. It can protect the sensitive state information of each agent from leakage and ensure stable consensus-building in the presence of attack nodes, guaranteeing efficient task completion. This embodiment presents a privacy-preserving multi-agent resilient consensus method under network attacks, implemented through the following steps: Step 1: Initialize parameters, input the maximum number of adversarial agents. Initial state information of the agent ; Step 2: Privacy Protection Phase Decompose the initial state information of the agent The sub-state is obtained based on equation (3). and substate and Information is exchanged and updated according to equation (4), and finally the sub-states are merged based on equation (5) to obtain the result. ; Step 3: Flexible Consensus Phase Conventional intelligent agents Send its own status information to its neighboring nodes It collects the state values ​​of neighboring nodes and then sorts the received state values ​​in ascending order to obtain an ordered set. ; Step 4: Conventional Intelligent Agent Set its own state value With ordered sets The values ​​in the set are compared one by one to obtain the set of values ​​that are larger than their own state values. and the set of values ​​smaller than its own state value ; Step 5: Remove extreme values, if Remove After If there are no elements, otherwise remove them. All elements in, if Then remove The front of the middle If there are no elements, otherwise remove them. All elements in; Step 6: Obtain the set of trusted neighbor values ​​after removing suspicious values. ; Step 7: According to the formula Update status.

[0053] This invention first constructs a network attack model encompassing deception and eavesdropping attacks. To address privacy concerns, a state decomposition method is employed, splitting the agent's initial state into public and private sub-states. Initial state privacy is protected through a single iterative reconstruction, avoiding the high computational overhead of traditional cryptographic methods. For resilient consensus requirements, a weighted mean subsequence reduction (W-MSR) algorithm is introduced, allowing regular agents to remove suspicious extreme values ​​during iterations, resisting interference from adversarial agents. Finally, by integrating these two approaches, a privacy-preserving MAS resilient consensus algorithm is designed, ensuring both initial state privacy and efficient secure consensus by regular agents.

[0054] In another embodiment of the present invention, a multi-agent resilient consensus system with privacy protection capabilities is also provided, comprising: State decomposition module: used to decompose the states of each agent at the initial time k=0. Decomposed into the first substate With the second substate The first sub-state Used for interacting with neighboring intelligent agents, the second sub-state With the corresponding first sub-state Local interaction; Update module: Used to determine the first sub-state of each agent during the initial state update iteration. Based on the first sub-state of the neighboring agent and its corresponding second sub-state Perform an update to obtain the first merged sub-state. The second sub-state Based on the corresponding first substate Update to obtain the second merged sub-state ; State merging module: used to merge the first sub-state With the second merged sub-state Merge; obtain merged state ; Communication module: Used to, starting from time k=1, for each iteration, each agent reports its complete state at the current time k. Send to neighboring intelligent agents and receive status information from neighboring intelligent agents; Suspicious Value Filtering Module: This module sorts the received neighbor states for each agent and removes states with higher integrity than its own, based on a preset maximum number of adversarial agents F. The maximum number of neighboring state values ​​and the number of complete states below its own. The most F neighbor state values ​​are used to form a trusted neighbor set. ; Consensus update module: used by each agent based on its own complete state Trusted Neighbor Set The system calculates and updates the complete state for the next time step based on the states of the neighbors and their preset weights until a flexible consensus is reached.

[0055] In another embodiment of the present invention, a computer device is provided, comprising a processor and a memory. The memory stores a computer program, which includes program instructions. The processor executes the program instructions stored in the computer storage medium. The processor may be a Central Processing Unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. It is the computing and control core of the terminal, suitable for implementing one or more instructions, specifically suitable for loading and executing one or more instructions from the computer storage medium to achieve a corresponding method flow or corresponding function. The processor described in this embodiment of the present invention can be used to operate a resilient consensus method for a multi-agent system with privacy protection capabilities.

[0056] In another embodiment of the present invention, a storage medium is provided, specifically a computer-readable storage medium (Memory), which is a memory device in a computer device used to store programs and data. It is understood that the computer-readable storage medium here can include both the built-in storage medium in the computer device and extended storage media supported by the computer device. The computer-readable storage medium provides storage space that stores the terminal's operating system. Furthermore, the storage space also stores one or more instructions suitable for loading and execution by a processor. These instructions can be one or more computer programs (including program code). It should be noted that the computer-readable storage medium here can be high-speed RAM or non-volatile memory, such as at least one disk storage device. The processor can load and execute one or more instructions stored in the computer-readable storage medium to implement the corresponding steps of the above-described method for a privacy-preserving multi-agent system resilient consensus mechanism.

[0057] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0058] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0059] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0060] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0061] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features therein; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A resilient consensus method for multi-agent systems with privacy protection capabilities, characterized in that, The method includes intelligent agents, including adversarial intelligent agents and conventional intelligent agents, and comprises the following steps: S1, the state of each agent at the initial time k=0. Decomposed into the first substate With the second substate The first sub-state Used for interacting with neighboring intelligent agents, the second sub-state With the corresponding first sub-state Local interaction; S2, the first sub-state of each agent in the first state update iteration. Based on the first sub-state of the neighboring agent and its corresponding second sub-state Perform an update to obtain the first merged sub-state. The second sub-state Based on the corresponding first substate Update to obtain the second merged sub-state ; S3, merge the first sub-state With the second merged sub-state Merge; obtain merged state ; S4, starting from time k=1, for each iteration, each regular agent will record its complete state at time k. Send to neighboring intelligent agents and receive state information from neighboring intelligent agents; the adversarial intelligent agent updates its own state according to arbitrary malicious update rules and sends state information to its neighbors; S5, each regular agent sorts the received neighbor states and, based on the preset maximum number of adversarial agents F, removes those with higher complete states than its own. The maximum number of neighboring state values ​​and the number of complete states below its own. The most F neighbor state values ​​are used to form a trusted neighbor set. ; S6, each regular agent is based on its own complete state. Trusted Neighbor Set The complete state for the next time step is calculated and updated using the states of the middle neighbors and their preset weights. ; S7. Repeat steps S4 to S6 until all the regular agents reach a resilient consensus.

2. The method for resilient consensus in a multi-agent system with privacy protection capabilities according to claim 1, characterized in that, In step S1, the first sub-state is decomposed. With the second substate At that time, the following conditions are met: 。 3. The method for resilient consensus in a multi-agent system with privacy protection capabilities according to claim 1, characterized in that, In step S2, the first sub-state Second substate The update rules are as follows: in, For intelligent agents The neighborhood group, For intelligent agents with neighbors Interaction weights at the initial moment The first substate Second substate Interaction weights between them.

4. The method for resilient consensus in a multi-agent system with privacy protection capabilities according to claim 1, characterized in that, In step S3, the merging state The calculation method is as follows: 。 5. A method for resilient consensus in a multi-agent system with privacy protection capabilities according to claim 1, characterized in that, In step S5, remove the complete state that is higher than itself. The specific operation for the neighbor status value is as follows: If higher The number of neighbor states is greater than Then remove the one with the largest value. 1; otherwise, remove all those higher than 1. The neighbor status value.

6. A method for resilient consensus in a multi-agent system with privacy protection capabilities according to claim 5, characterized in that, In step S5, remove states that are less complete than themselves. The specific operation for the neighbor status value is as follows: If lower The number of neighbor states is greater than Then remove the one with the smallest value. 1; otherwise, remove all those below 10; The neighbor status value.

7. A method for resilient consensus in a multi-agent system with privacy protection capabilities according to claim 1, characterized in that, In step S6, the complete state for the next time step is updated. The rules are: in, For a set of trusted neighbors, For intelligent agents Trusted Neighbors At any moment Interaction weights.

8. A multi-agent resilient consensus system with privacy protection capabilities, characterized in that, include: State decomposition module: used to decompose the states of each agent at the initial time k=0. Decomposed into the first substate With the second substate The first sub-state Used for interacting with neighboring intelligent agents, the second sub-state With the corresponding first sub-state Local interaction; Update module: Used to determine the first sub-state of each agent during the initial state update iteration. Based on the first sub-state of the neighboring agent and its corresponding second sub-state Perform an update to obtain the first merged sub-state. The second sub-state Based on the corresponding first substate Update to obtain the second merged sub-state ; State merging module: used to merge the first sub-state With the second merged sub-state Merge; obtain merged state ; Communication module: Used to, starting from time k=1, for each iteration, each agent transmits its complete state at the current time k. Send to neighboring intelligent agents and receive status information from neighboring intelligent agents; Suspicious Value Filtering Module: This module sorts the received neighbor states for each agent and removes states with higher integrity than its own, based on a preset maximum number of adversarial agents F. The maximum number of neighboring state values ​​and the number of complete states below its own. The most F neighbor state values ​​are used to form a trusted neighbor set. ; Consensus update module: used by each agent based on its own complete state Trusted Neighbor Set The system calculates and updates the complete state for the next time step based on the states of the neighbors and their preset weights until a flexible consensus is reached.

9. A computer device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements the steps of a resilient consensus method for a multi-agent system with privacy protection capabilities as described in any one of claims 1-7.

10. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by the processor, it implements the steps of a resilient consensus method for a multi-agent system with privacy protection capabilities as described in any one of claims 1-7.

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