CN117675416B - Privacy protection average consensus method for multi-agent networking system and multi-agent networking system - Google Patents
Privacy protection average consensus method for multi-agent networking system and multi-agent networking system Download PDFInfo
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Abstract
The invention discloses a privacy protection average consensus method of a multi-agent networking system and the multi-agent networking system. The first type of agent determines an updated implicit auxiliary sub-state according to the pre-update explicit auxiliary sub-state and the pre-update implicit auxiliary sub-state, determines an updated explicit auxiliary sub-state according to the pre-update explicit auxiliary sub-state, the pre-update implicit auxiliary sub-state, the control inputs or auxiliary states sent by each neighbor node or the explicit auxiliary sub-state, determines an updated explicit sub-state according to the updated scale factors and the updated explicit auxiliary sub-state, determines an updated implicit sub-state according to the updated scale factors and the updated implicit auxiliary sub-state, and determines an updated auxiliary state according to the pre-update auxiliary state, the control inputs or auxiliary states sent by each neighbor node or the explicit auxiliary sub-state. The privacy protection is realized in the average consensus process, the operand is reduced, and the convergence is rapid.
Description
Technical Field
The invention relates to a privacy protection average consensus method of a multi-agent networking system and the multi-agent networking system.
Background
The multi-agent networking system is a network system composed of a large number of independent autonomous, mutually cooperative agent nodes with communication capability. The average consensus of the multi-agent networking system refers to that all nodes in the multi-agent networking system converge the state of the nodes to the average value of the state initial values of all nodes in the system through distributed information interaction and state updating. In recent years, with the rapid development of multi-agent networking systems, average consensus is widely applied in various fields such as information fusion, distributed optimization and decision making, load balancing, and the like.
In the existing research about the average consensus of the multi-agent networking system, the interactive information among agent nodes is explicitly transmitted in a channel, and sensitive data and private information therein are easily stolen and inferred by an attacker, thus destroying the security of the system. Therefore, it is important to introduce privacy preserving mechanisms in the consensus process.
The chinese patent application CN110213279a discloses a privacy protection method based on state decomposition, in which the real state of each node is divided into an explicit state and an implicit state, the explicit state is used for communication between nodes, the implicit state is used for privacy protection, and a bidirectional communication link exists between the explicit state and the implicit state. The initial values of the explicit and implicit states and the constraint are twice the initial value of the real state, under which constraint the values of both can be randomly chosen in the real domain. In the method, the explicit and implicit states can be converged asymptotically and accurately to a desired average value, and the real state is not revealed to the neighbor nodes or external attackers. However, introducing a state decomposition method to perform privacy protection will lead to network topology complexity, so that the convergence speed of the average consensus algorithm is reduced, and the calculation overhead of the network is increased.
Disclosure of Invention
The invention provides a privacy protection average consensus method of a multi-agent networking system and the multi-agent networking system, wherein a state hiding method is utilized to replace a state decomposition method to provide privacy protection for key nodes, so that the average consensus is achieved, meanwhile, network topology required by the privacy protection is simplified, the convergence speed of an average consensus algorithm is improved, the overall operation amount is reduced, and the algorithm structure is simpler.
The invention provides the following technical scheme: a multi-agent networked system privacy preserving average consensus method, the communication structure of the multi-agent networked system being represented as a connected undirected graph, for the multi-agent networked system being divided into a first type of agent and a second type of agent, the method comprising:
introducing information interaction with hidden states, wherein a first type of intelligent agent sends an explicit auxiliary sub-state of the intelligent agent to all neighbor nodes of the intelligent agent, an end node in a second type of intelligent agent sends an auxiliary state of the intelligent agent to all neighbor nodes of the intelligent agent, and a non-end node in the intelligent agent sends a first control input of the intelligent agent to all neighbor nodes of the intelligent agent, wherein if two second type of intelligent agents establish communication connection, one of the intelligent agents is necessarily the end node, and the other intelligent agent is the non-end node;
multiple rounds of iterative updating, wherein a first class of agents determines an updated implicit auxiliary sub-state according to an pre-update explicit auxiliary sub-state and an pre-update implicit auxiliary sub-state, determines an updated explicit auxiliary sub-state according to the pre-update explicit auxiliary sub-state, the pre-update implicit auxiliary sub-state, a first control input or auxiliary state or the explicit auxiliary sub-state to which each neighbor node sends, determines an updated explicit sub-state according to an updated scale factor and the updated explicit auxiliary sub-state, determines an updated implicit sub-state according to an updated scale factor and the updated implicit auxiliary sub-state, determines an updated auxiliary state according to the pre-update auxiliary state, a first control input or auxiliary state or the explicit auxiliary sub-state to which each neighbor node sends, and determines an updated state according to the updated auxiliary state and the updated scale factor, wherein the updated scale factor of any one agent is determined according to the pre-update scale factor and the pre-update scale factor of each neighbor node;
wherein the control input sent by the second type of agent to the first type of agent for updating the explicit auxiliary sub-state is denoted as a first control input, and the control input received by the second type of agent for updating the auxiliary state is denoted as a fourth control input.
The invention provides the following technical scheme: a multi-agent networked system whose communication structure is represented as a connected undirected graph, the multi-agent networked system being divided into a first type of agent and a second type of agent, any one of the multi-agent networked systems including a memory and a processor and a program stored on the processor, the processor running the program to cause the multi-agent networked system to perform the aforementioned multi-agent networked system privacy preserving average consensus method.
Compared with the prior art, the technical scheme of the invention has the following advantages. Compared with a single state decomposition method, the state hiding method has the advantages that the number of additional states required for realizing privacy protection in a network is reduced, and the consumption of computing resources and the complexity of network topology are reduced. The method expands the optional range of step sizes in the iterative updating method, reduces the number of additional states required for realizing privacy protection, and ensures faster consensus reaching speed.
Drawings
Fig. 1 is a schematic diagram of a privacy preserving average consensus method of a multi-agent networked system according to an embodiment of the present invention.
Fig. 2 is a schematic diagram of a network topology and an information interaction process according to an embodiment of the present invention.
Fig. 3 is a graph showing a state value changing with iteration times in the privacy preserving average consensus method of the multi-agent networked system according to the embodiment of the present invention.
Fig. 4 is a plot of state value versus iteration number for the comparative example.
Fig. 5 is a plot of eavesdropper state estimate versus iteration number.
Fig. 6 is a schematic structural diagram of a controller in an agent according to an embodiment of the present invention.
Detailed Description
The present invention will be further described with reference to specific examples, but the scope of the present invention is not limited thereto.
For any one of the groupsNThe multi-agent networking system composed of the agents can be used as a graphG={V,SAnd } to describe. Any intelligent agent individualiCan be used for drawingGSingle node in (a)v i Describing, define a set of all node componentsV={v 1 , v 2 ,...,v N }. Intelligent individualiAnd (3) withjCan be mappedGThe edge of (B)v i ,v j ) Describing, define the set of all edge compositions asS={v i ∈V,v j ∈V|(v i ,v j ) }. Definition of arbitrary agentiIs a set of neighbor nodes of (a)N i ={v j ∈V|(v i ,v j) ∈S}；|N i I represents an agentiIs a neighbor number of the neighbor. The application scene of the invention is limited to be an undirected edge, and the communication between two intelligent agents is bidirectional. The meaning of nodes and agents in the present invention is equivalent. The communication structure of the multi-agent networked system is represented as a connected undirected graph.
Intelligent bodyiState variable of (2)y i To indicate that the status of the agent may characterize the location, speed, etc. information of the agent. After introducing the state decomposition mechanism, the state of the intelligent agenty i Is decomposed into explicit substatesAnd implicit sub-state->Implicit sub-states may be selected to characterize the actual state of the agent in the consensus process.
The specific steps of the present invention are as follows, in conjunction with fig. 1.
Step one: and starting the multi-agent networking system, and acquiring the neighbor number information of the intelligent agent individual. If the communication topology of the multi-agent networking system is preset, that is, the agent individuals have previously solved the identities of the surrounding neighbors, the agent individuals can directly acquire the number information of the neighbors. If the multi-agent networking system establishes a communication topology through several rounds of data transmission, the agent individual can determine the number of neighbors of the agent individual by using the transmitted data.
Step two: and (3) state decomposition selection, wherein the self defaults to be the first type of intelligent agent, if the self neighbor number is 1, the self is set to be the second type of intelligent agent, the self neighbor number is sent to all the self neighbor nodes, then the self is set to be the second type of intelligent agent if the self neighbor number is larger than the neighbor number of all the self neighbor nodes, and then the self classification result is sent to all the self neighbor nodes.
The first type of agent is an agent that performs state decomposition, and the second type of agent is an agent that does not perform state decomposition.
Introducing state decomposition characterization variablessTo identify whether a node is selected for state decomposition, if sov i Selected to perform state decompositions i =2, which can be understood as a nodev i Is broken down into two parts. If nodev i Not selected for state decompositions i =1, characterize nodev i Is not decomposed.
Networking any node (e.g., node) in a system with multiple agentsv i ) For example, the process of state decomposition includes the following steps.
1) Initializing nodesv i State decomposition characterization variables of (2)s i =2. If the number of neighbors is |N i Let I=1, lets i =1 and sends own neighbor number information to all surrounding neighborsN i |。
2) The neighbor number information of the neighbor node and all neighbor nodes are combinedj∈N i And comparing the sent neighbor number information. If it isThens i =1. To all neighbor nodesj∈N i Transmitting state decomposition characterizing variables of selfs i 。
And step two, excluding nodes with only one neighbor in the network and nodes with the maximum neighbor number locally, and selecting other nodes to perform state decomposition. If the nodes with the largest neighbor number in the network are not adjacent to each other, the method can make the step range from the state decomposition methodEnlarge to +.>The increase of the maximum selectable step size together with the additional state reduction required to achieve privacy protection ensures a faster convergence speed of the method. The relevant symbol definition is referred to below.
The auxiliary state is introduced to assist the agent state to achieve an average consensus, and is only used as an intermediate variable of the state update process, and has no specific physical significance. The auxiliary state is denoted by x and the real state of the agent itself is denoted by y.
3) If it iss i =2, node pairv i Auxiliary state of (2)x i The state decomposition is carried out and the state is decomposed,x i the initial value satisfies the constraint，/>For initial value of explicit auxiliary sub-state, < ->For the initial value of the implicit auxiliary sub-state, < ->Is the actual state initial value of the intelligent agent; if it iss i =1, then nodev i The initial value of the auxiliary state of (a) isx i [0]=y i [0]。
In other embodiments, the communication topology of the multi-agent networked system is known, and the state-resolution characterization variables of each agent and the state-resolution characterization variables of its neighbor agents are set in advance.
Step three: and introducing information interaction with hidden states, wherein a first type of intelligent agent sends an explicit auxiliary sub-state of the intelligent agent to all neighbor nodes of the intelligent agent, an end node in a second type of intelligent agent sends an auxiliary state of the intelligent agent to all neighbor nodes of the intelligent agent, and a non-end node in the second type of intelligent agent sends a first control input of the intelligent agent to all neighbor nodes of the intelligent agent, wherein if communication connection is established between two second type of intelligent agents, one of the intelligent agents is necessarily the end node, and the other intelligent agent is the non-end node.
The implicit sub-state and the implicit state are stored locally and are not disclosed externally.
Referring to fig. 2, an agentv 4 (using its auxiliary state in FIG. 2)x 4 Representation) and agentsv 5 (using its auxiliary state in FIG. 2)x 5 Representation), agentv 4 Is an end node (i.e. it has only one neighbor), an agentv 5 Is a non-end node (i.e., it has only a plurality of neighbors).
A common form of average consistency algorithm is:
wherein the method comprises the steps ofx i [k]Is the firstkAgent during secondary iterationiIs used for the control of the state of (a),x j [k]is the firstkAgent during secondary iterationjIs used for the control of the state of (a),εto step size, the value needs to satisfy,w ij [k]Is the firstkAgent during secondary iterationiAnd (3) withjThe coupling weight between them. Control of the orderInput->The form of the coherency algorithm can be rewritten as:
。
in the present invention, a collection is definedFor the set of nodes selected for state decomposition +.>The set of nodes that are not selected for state decomposition is characterized. Simultaneous definition ofIs a set of nodes with only one neighbor node, i.e., an end node set. Considering the application scope of the state decomposition method, set +.>The node in (a) cannot achieve privacy protection through a state decomposition method. Therefore, the set +.>The nodes in the network are subjected to state decomposition, so that the network topology is further simplified, and network resources and cost are saved.
1) For nodesIt will send self explicit auxiliary sub-state directly to all neighbor nodes of itself +.>Simultaneously with all neighbor nodes->(first type of agent in neighbor node and second type of agent at end) cross-coupling weights/>And->Then, one of the two is selected as a common value of the two by adopting a corresponding rule. For example, the maximum principle can be used if +.>Then set->So that the two are kept the same,krepresenting the iteration round. The node performing state decomposition externally transmits its own explicit auxiliary sub-state, which is not revealed to the external nodes.
The reason why it is notj∈N i And performing interaction of the coupling weights. Because ifjBelongs to a collectionWhen the nodeiDoes not know the neighborsjIs only composed of nodesiSave that there is no interactive choice of coupling weights between them, "\" represents set subtraction.
Hereinafter three coupling weightsw ij 、、/>When (when)kTheir values can be arbitrarily chosen in the real domain when =0, for any number of iterationskCoupling weight +.0>、/>And->Can be within%ηAny choice within the scope of 1) (e.g. random choice),ηis a constant greater than zero. Because of the undirected graph, the neighbor coupling weights are required to be the same all the time, but the coupling weights selected by themselves at each moment in the communication process cannot be equal, and a common weight is determined through information interaction.
The design manner of the coupling weight, such as giving the coupling weight time-varying property, can enable the method to adapt to more application scenes.
In other embodiments, the coupling weights may also be preset and fixed.
2) If nodeThat is, as an end node in the second class of nodes, the description nodev i Only one neighbor does not need to perform state decomposition, and the existing privacy protection method and the technical scheme of the invention cannot provide privacy protection effectiveness for the neighbor, so that the neighbor does not perform state decomposition and can send own auxiliary statex i [k]To the neighbor node.
3) If nodeI.e. as non-end node in the second class of nodes, its neighborsv j Can only belong to the collection->Or phi. In this case, the nodev i Not interactively coupling weights with any neighbor nodew ji It will directly select the coupling weights locallyw ji And is used directly to calculate control inputs. Nodev i Upon receiving a neighbor nodev j After the transmitted auxiliary state or explicit auxiliary sub-state information, according to the coupling weight of the auxiliary state or explicit auxiliary sub-state informationw ji [k]Calculate the fourth control inputu ji [k]Finally, the fourth control inputu ji [k]To a neighbouring node which is also a second class nodev j . To distinguish between different types of control inputs, the present invention distinguishes control inputsu ji [k]Referred to as the fourth control input.
Step four: and a plurality of iterative updates, wherein the first type of agent determines an updated implicit auxiliary sub-state according to the pre-update explicit auxiliary sub-state and the pre-update implicit auxiliary sub-state, determines an updated explicit auxiliary sub-state according to the pre-update explicit auxiliary sub-state, the pre-update implicit auxiliary sub-state, the first control input or auxiliary state or the explicit auxiliary sub-state sent by each neighbor node to the first type of agent, determines an updated explicit sub-state according to the updated scale factor and the updated explicit auxiliary sub-state, determines an updated implicit sub-state according to the updated scale factor and the updated implicit auxiliary sub-state, determines an updated auxiliary state according to the pre-update auxiliary state, the fourth control input or auxiliary state or the explicit auxiliary sub-state sent by each neighbor node, and determines an updated state according to the updated auxiliary state and the updated scale factor, wherein the updated scale factor of any agent is determined according to the pre-update scale factor and the pre-update scale factor of each neighbor node.
The iteratively updated formula is as follows:
where k and k +1 represent the iteration number of the update,p i is an intelligent bodyiIs used for the control of the ratio of (a) to (b),p j is an intelligent bodyjIs used for the control of the ratio of (a) to (b),N i is an intelligent bodyiIs used to determine the neighbor set of a neighbor,v j representing an agentj，v i Representing an agenti，Is an intelligent bodyjFor intelligent bodyiIs,/-a second control input of->Is an intelligent bodyiExplicit auxiliary sub-state of->Is an intelligent bodyjFor intelligent bodyiIs provided with a first control input for the control signal,is an intelligent bodyiImplicit auxiliary sub-state,/->Is an intelligent bodyiFor intelligent bodyiIs provided with a third control input for the control signal,x i is an intelligent bodyiIs used for the auxiliary state of the (a),u ij is an intelligent bodyjFor intelligent bodyiFourth control input of->Is an intelligent bodyiExplicit sub-state of->Is an intelligent bodyiIs used to determine the hidden sub-state of (c),y i is an intelligent bodyiIs used for the control of the state of (a),Vis a collection of agents, Φ is a collection of agents of a first type, +>Is a set of second type agents, epsilon is the step size,w ij 、/>、/>representing nodes in turnv i And nodev j Coupled weights, nodes of (a)v i Coupling weights of explicit auxiliary sub-states to implicit auxiliary sub-states and nodesv i Coupling weights of implicit auxiliary sub-state to explicit auxiliary sub-state, +.>Is an intelligent bodyjIs provided with an explicit auxiliary sub-state,x j is an intelligent bodyjIs a secondary state of (a).
For three coupling weightsw ij 、、/>When (when)kTheir values can be arbitrarily chosen in the real domain when =0, for any number of iterationskCoupling weight +.0>、/>And->Can be within%ηAny choice within the scope of 1) (e.g. random choice, but also a fixed value),ηis a constant greater than zero.
Definition of the scaling factor aspNodev i Corresponding scale factorp i Is the iteration initial value of (a). Nodev i Auxiliary state initial value +.>In step two, setting.
Representing nodesv i Iterative rule of scale factor->Representing nodesv i Scale factor of (2) at the firstkJoint nodes at multiple iterationsv j And a second control input for information calculation. Second control input +.>May be a nodev i Calculated, or may be a nodev j Calculated and sent to the nodev i Depending on the particular design of the program flow.
Representing nodes for state decompositionv i Iterative rules for explicit auxiliary sub-states, +.>Representing nodesv i Explicit auxiliary sub-state at the firstkJoint nodes at multiple iterationsv j The control input of the information calculation (called first control input for distinction) is due to the nodev j The types are different, so classification definition is required, and the specific form is as above. It should be noted that in particular,v j= v i definition in the case indicates a nodev i Control inputs for self explicit auxiliary sub-state in combination with implicit auxiliary sub-state calculation.
Representing nodes for state decompositionv i Iterative rules of implicit auxiliary sub-states, +.>Representing nodesv i Implicit auxiliary State in the firstkMultiple iterationsThe control input that is needed (called the third control input for distinction).
Representing nodes without state decompositionv i Iterative rules of state->Representing nodesv i The auxiliary state is at the firstkJoint nodes at multiple iterationsv j Control input of information calculation (fourth control input).
、/>And +.>Respectively representv i For different types of nodes, the node is provided with explicit sub-states, implicit sub-states and iterative rules of states.
The invention can realize accurate average consensus and simultaneously complete privacy protection. The state of the agent can asymptotically converge exactly to the average value of the initial state of the whole network, i.e. for anyAnd +.>All haveThe method comprises the steps of carrying out a first treatment on the surface of the For any eavesdropping node and external eavesdroppers with all interaction information of the network reserved, the method can realize protection of any precision of the initial state of the intelligent body.
The details of the present invention will be described below with reference to the related examples and the accompanying drawings.
Setting a slaveAs a sample of the invention, a network of 5 agents has a topology as shown in FIG. 2, which is an undirected connectivity graph. Corresponding neighbor matrix (each term represents a coupling weightw ij ) The method comprises the following steps:
。
in the case of the figure of the drawings in which,represents node->First, thekExplicit auxiliary sub-state values at the time of the iteration; />Represents node->First, thekImplicit auxiliary sub-state values at the time of the iteration; />Represents node->First, thekAuxiliary state values at the time of the iteration; />Representing nodesv i Explicit auxiliary sub-state at the firstkJoint nodes at multiple iterationsv j A control input (first control input) for information calculation; />Representing nodesv i The auxiliary state is at the firstkJoint nodes at multiple iterationsv j Control input of information calculation (fourth control input).
Step one: and acquiring neighbor number information of each node through information interaction.
Step two: and executing a state decomposition selection step, wherein the nodes selectively perform state decomposition according to the values of the state characterization vector.
To highlight the advantages of the present invention, the method of the present invention is compared with the method in CN110213279a in this example, and initial values are set as follows:
。
the initial values can be set arbitrarily as long as the corresponding state constraints are satisfied, and the setting in the sample serves only an exemplary role and does not limit the application scope of the present invention.
Step three: state hiding is started, and state hiding is carried out on the node selected for state decomposition.
Step four: the step sizes are respectively set to be the maximum value which can be taken in each method, and all coupling weights in the iteration process are set to be a fixed value of 0.99. By calculating according to the respective state iteration update method, we can obtain a state convergence curve, as shown in fig. 3 and 4. It can be seen that the method of the present invention has a significantly faster state convergence speed and can achieve accurate average consensus. Ave in fig. 3 and 4 represents a desired average consensus value.
To further illustrate the privacy preserving effectiveness of the method of the present invention, without loss of generality, it is assumed that an eavesdropper aims at acquiring the nodev 1 The state estimator that an eavesdropper can use is in the form of:
the initial state of the estimator should be designed as. Assuming that the eavesdropper can obtain the removalu 12 [0]All butu j1 [k]And it is assumed that, for an eavesdropper,u j1 [k]=0. The results in fig. 5 indicate that an eavesdropper cannot recover from the stolen informationv 1 State information of (2).
Based on the same inventive concept, referring to fig. 6, an embodiment of the present invention also provides a multi-agent networked system, wherein each agent includes a memory in which a program is stored and a processor that runs the program to cause the multi-agent networked system to perform the aforementioned method. Fig. 6 shows a block diagram of a controller in an agent.
The embodiments of the present invention are described in a progressive manner, and the same and similar parts of the embodiments are all referred to each other, and each embodiment is mainly described in the differences from the other embodiments.
The scope of the present invention is not limited to the above-described embodiments, and it is apparent that various modifications and variations can be made to the present invention by those skilled in the art without departing from the scope and spirit of the invention. It is intended that the present invention also include such modifications and alterations insofar as they come within the scope of the appended claims or the equivalents thereof.
Claims (7)
1. The utility model provides a multi-agent networking system privacy protection average consensus method which is characterized in that a communication structure of the multi-agent networking system is expressed as a connected undirected graph, the multi-agent networking system is divided into a first type agent and a second type agent, and the method comprises the following steps:
introducing information interaction with hidden states, wherein a first type of intelligent agent sends an explicit auxiliary sub-state of the intelligent agent to all neighbor nodes of the intelligent agent, an end node in a second type of intelligent agent sends an auxiliary state of the intelligent agent to all neighbor nodes of the intelligent agent, and a non-end node in the intelligent agent sends control input of the intelligent agent to all neighbor nodes of the intelligent agent, wherein if two second type of intelligent agents are in communication connection, one of the intelligent agents is necessarily the end node, and the other intelligent agent is the non-end node;
multiple rounds of iterative updating, wherein a first class of agents determines an updated implicit auxiliary sub-state according to an pre-update explicit auxiliary sub-state and an pre-update implicit auxiliary sub-state, determines an updated explicit auxiliary sub-state according to the pre-update explicit auxiliary sub-state, the pre-update implicit auxiliary sub-state, the control input or auxiliary state sent by each neighbor node to the pre-update implicit auxiliary sub-state, or the explicit auxiliary sub-state, determines an updated explicit sub-state according to an updated scale factor and the updated explicit auxiliary sub-state, determines an updated implicit sub-state according to an updated scale factor and the updated implicit auxiliary sub-state, determines an updated auxiliary state according to the pre-update auxiliary state, the control input or auxiliary state sent by each neighbor node to the pre-update implicit auxiliary sub-state, or the explicit auxiliary sub-state, and determines an updated state according to the updated auxiliary state and the updated scale factor, wherein the updated scale factor of any agent is determined according to the pre-update scale factor and the pre-update scale factor of each neighbor node;
wherein the control input sent by the second type of agent to the first type of agent for updating the explicit auxiliary sub-state is denoted as a first control input, and the control input received by the second type of agent for updating the auxiliary state is denoted as a fourth control input.
2. The method as recited in claim 1, further comprising:
and (3) state decomposition selection, wherein the self defaults to be the first type of intelligent agent, if the self neighbor number is 1, the self is set to be the second type of intelligent agent, the self neighbor number is sent to all the self neighbor nodes, then the self is set to be the second type of intelligent agent if the self neighbor number is larger than the neighbor number of all the self neighbor nodes, and then the self classification result is sent to all the self neighbor nodes.
3. The method of claim 1, wherein the initial value of the explicit auxiliary sub-state of the first type of agentInitial value of implicit auxiliary sub-state +.>Initial value +.>The method meets the following conditions:；
initial value of auxiliary state of second-class agentx i [0]The method comprises the following steps:x i [0]=y i [0]subscript ofiIs the number of the agent.
4. The method of claim 1, wherein the step of iteratively updating the plurality of rounds satisfies the formula:
where k and k +1 represent the iteration number of the update,p i is an intelligent bodyiIs used for the control of the ratio of (a) to (b),p j is an intelligent bodyjIs used for the control of the ratio of (a) to (b),N i is an intelligent bodyiIs used to determine the neighbor set of a neighbor,v j representing an agentj，v i Representing an agenti，Is an intelligent bodyjFor intelligent bodyiIs,/-a second control input of->Is an intelligent bodyiExplicit auxiliary sub-state of->Is an intelligent bodyjFor intelligent bodyiIs->Is an intelligent bodyiImplicit auxiliary sub-state,/->Is an intelligent bodyiFor intelligent bodyiIs provided with a third control input for the control signal,x i is an intelligent bodyiIs used for the auxiliary state of the (a),u ij is an intelligent bodyjFor intelligent bodyiFourth control input of->Is an intelligent bodyiExplicit sub-state of->Is an intelligent bodyiIs used to determine the hidden sub-state of (c),y i is an intelligent bodyiIs used for the control of the state of (a),Vis a collection of agents, Φ is a collection of agents of a first type, +>Is a set of second type agents, epsilon is the step size,w ij 、/>、/>representing nodes in turnv i And nodev j Coupled weights, nodes of (a)v i Coupling weights of explicit auxiliary sub-states to implicit auxiliary sub-states and nodesv i Coupling weights of implicit auxiliary sub-state to explicit auxiliary sub-state, +.>Is an intelligent bodyjIs provided with an explicit auxiliary sub-state,x j is an intelligent bodyjIs a secondary state of (a).
5. The method of claim 4, wherein the first type of agent has an initial value of 2 and the second type of agent has an initial value of 1.
6. The method of claim 4, wherein the weights are coupledw ij [k]The setting mode of (2) is as follows:
when k= at the time of 0, the temperature of the liquid,w ij arbitrarily chosen in the real number domain, when k > 0,w ij to achieve the aim ofηThe range of 1) is arbitrarily selected from the range,ηis a constant greater than zero, wherein the first type of intelligent agent performs information interaction with the first type of intelligent agent in the neighbor node and the second type of intelligent agent at the end part to achieve the coupling weightw ij [k]And (3) withw ji [k]Equal, non-end nodes in second-class agentiSelecting locally generated coupling weightsw ji [k]Coupling weightsw ij Representing nodesv j Opposite nodev i Is coupled with the weightw ji Representing nodesv i Opposite nodev j Is a function of (a) and (b).
7. A multi-agent networked system whose communication structure is represented as a connected undirected graph, the multi-agent networked system being divided into a first type of agent and a second type of agent, characterized in that any one of the multi-agent networked system includes a memory and a processor and a program stored on the processor, the processor running the program to cause the multi-agent networked system to execute the multi-agent networked system privacy protection average consensus method according to any one of claims 1 to 6.
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