Multi-agent system elasticity consistency control method under network attack

Abstract

The invention is applicable to the field of cooperative control of a multi-agent system, realizes self-repairing of a damaged network through network state verification and network topology reconstruction, establishes an autonomous interaction model of an agent based on a dynamic containment strategy, and provides an elastic consistency control method for the multi-agent system under network attack. The method comprises the following steps: determining a multi-agent system model; constructing a state estimation vector of the intelligent agent, determining a relationship between nodes in combination with a maximum consistency method, and verifying a communication network connectivity state; determining the characteristics of the connected components based on the identifiers of the information agents, and enabling the connected components with the information agents to be randomly connected with the connected components without the information agents to realize topology reconstruction; convergence of the constructed observer and the controller is fixed time convergence. According to the method, the conventional cooperative control method is theoretically expanded, so that the dependence on the network connectivity is reduced, and a more complex interaction relationship between the intelligent agents in the dynamic network can be processed.

Description

Technical Field

[0001] The present invention relates to the field of collaborative control of multi-agent systems, and in particular to a method for elastic consistency control of multi-agent systems under network attacks. Background Art

[0002] Collaborative control of multi-agent systems involves designing distributed control methods through cooperation and coordination between agents to achieve the overall system objectives and complete responses to tasks and environments. The network topology and control algorithm jointly determine the evolution of the multi-agent system. The former represents the interactions between agents, i.e., which nodes influence the movement of a node; the latter defines the specific rules by which a node's movement is adjusted based on its state information. When the network topology is predetermined and connectivity requirements are met, significant progress has been made in designing control algorithms to achieve group collaborative behavior in complex scenarios. Existing research focuses on the construction of control algorithms, using the connectivity of the network topology as a priori conditions. The effectiveness of control implementation relies heavily on idealized communication assumptions. For both undirected and directed network structures, existing control methods rely heavily on corresponding network connectivity properties, such as full connectivity, joint connectivity, and strong connectivity. Furthermore, when the network is attacked, these connectivity requirements cannot be met. Existing collaborative control methods use time-retention methods to design control strategies, assuming that the network can recover to its original healthy state within a certain period of time. On the one hand, this imposes strict limits on the frequency and duration of attacks. On the other hand, when the system faces multiple and complex attacks, the control methods may fail. Summary of the Invention

[0003] In response to the shortcomings of the existing technology, the purpose of the present invention is to propose a resilient consistency control method for multi-agent systems under network attacks, aiming to make the control method have a certain degree of resilience when facing network attacks by combining topology reconstruction, establish a new interaction model to promote the deep coupling of the network topology and control algorithm of the multi-agent system in complex scenarios, and promote the theoretical development of collaborative control of multi-agent systems and its engineering application.

[0004] A method for controlling the resilience and consistency of a multi-agent system under network attacks, the method comprising the following steps:

[0005] Determine the multi-agent system model;

[0006] Constructing an agent The state estimation vector is combined with the maximum consistency method to confirm the relationship between nodes and verify the connectivity status of the communication network;

[0007] Based on the identification of information agents, the characteristics of connected components are determined, and connected components with information agents are allowed to interact autonomously with connected components without information agents. In other words, the agents in the two connected components are randomly connected, thereby achieving topological reconstruction;

[0008] Combined with the dynamic pinning strategy, an observer is constructed to estimate the desired state, which can achieve fixed-time consistency;

[0009] A tracking controller is established to make the actual state of the agent converge to the designed estimated state within a fixed time.

[0010] As a further technical solution of the present invention, determining the content of the multi-agent system model includes:

[0011] Multi-agent systems include agents and 1 leader, where the agent model is:

[0012] Formula 1: , ;

[0013] The leader's model is:

[0014] Formula 2: , ;

[0015] in and Represent the position state, velocity state and control input of the agent respectively; and Represents the position change and speed change of the agent; Indicates the identity of the agent, that is, the agent number; and Indicates the position and speed status of the leader; and Indicates the leader's position change and speed change; and represents mismatched interference and matched interference in the agent dynamics, and Mismatch and match interference in leader dynamics, and satisfying:

[0016] Assumption 1: For any ;and is a known positive constant;

[0017] The network topology of a multi-agent system is composed of an undirected graph Indicates that is a node set, As the edge set, the adjacency matrix of the undirected graph is defined as , whose elements are equal to 1 if the node and nodes There is an edge, otherwise it is equal to 0; define the Laplacian matrix ,when When , its elements are ,otherwise , an undirected graph is said to be connected if there is a path between any two nodes.

[0018] As a further technical solution of the present invention, the state estimation vector of the intelligent agent is constructed, and the relationship between nodes is confirmed by combining the maximum consistency method. The contents of verifying the connectivity status of the communication network include:

[0019] Constructing an agent The road state estimation vector ,in For intelligent agents The road state estimation vector exist The moment elements and establish a maximum consistency method for updating:

[0020] Formula 3: ;

[0021] in, Representing an agent Neighborhood, Indicates time, is the update time step, Representative Agent The road state estimation vector exist The moment elements; Representative Agent The road state estimation vector exist The moment elements, the initial conditions of the estimated state are:

[0022] Formula 4: ;

[0023] in, Representative Agent The road state estimation vector exist The moment elements, The vector after iterations It consists only of 0 and 1, and its value determines the To the agent Is there a path between them?

[0024] make For intelligent agents The road state estimation vector exist The sum of all elements at the moment constructs a new connectivity state estimation vector ,in For intelligent agents The connectivity state estimation vector exist The moment The update rules are as follows:

[0025] Formula 5: ;

[0026] Formula 6: ;

[0027] Representative Agent The connectivity state estimation vector exist The moment elements; Representative Agent The connectivity state estimation vector exist The moment elements; Representative Agent The connectivity state estimation vector exist The moment elements; at this time, if The connectivity state vector after iterations All components of When , the system is connected; when the system is not connected, if and , then the agent and agents In the same connected component, the connected components of the system are determined.

[0028] As a further technical solution of the present invention, the characteristics of connected components are determined based on the identification of information agents, and connected components with information agents are allowed to interact autonomously with connected components without information agents to achieve topology reconstruction, including:

[0029] The characteristics of the connected components are determined based on the identification of the information agent. The connected components with information agents can converge under the influence of leader information, while the connected components without information agents produce unexpected behaviors. Any node in such connected components is randomly connected, and a random connection is established with any node in the connected components with information agents to achieve topology reconstruction and restore the connectivity of the network.

[0030] As a further technical solution of the present invention, in combination with the dynamic pinning strategy, the contents of constructing the desired state of the observer capable of achieving fixed-time consistency convergence in a dynamic network include:

[0031] make and For intelligent agents The position estimation state and velocity estimation state of are given by the dynamic pinning method, and the following distributed error with autonomous interaction model is established:

[0032] Formula 7: ;

[0033] in, The agent can obtain the leader's information, otherwise ,Only some agents in the system can obtain the leader’s information, which are called information agents; Representative Agent For autonomously interacting agents, otherwise ; and Represents an agent that establishes a new connection relationship with an autonomous interactive agent The position estimation state and velocity estimation state, and Representatives The determined agent The position estimation state and velocity estimation state of ; Representative Agent The distributed position error, Representative Agent The distributed velocity error is given as follows:

[0034] Theorem 1: When Assumption 1 is satisfied, if the estimated state Dynamic satisfaction:

[0035] Formula 8: ;

[0036] in Representative Agent Changes in the position estimate state and changes in the velocity estimate state; and are the parameters designed in the observer and satisfy: ; is the standard symbolic function, ,in Represents a positive constant greater than 0.

[0037] As a further technical solution of the present invention, establishing a tracking controller to make the actual state of the intelligent agent converge to the designed estimated state within a fixed time includes:

[0038] Define the error between the actual position state and the estimated position state , the error between the actual speed state and the estimated speed state , and introduce a virtual velocity term and virtual controls ,in For the control of the intelligent agent, For changes in virtual control items;

[0039] make As the converted speed error, the system transformation is:

[0040] Formula 24: ;

[0041] in, is the change in error between the actual position state and the estimated position state; is the estimated velocity residual term, Estimate the position residual term. At this time, the virtual speed is designed as:

[0042] Formula 25: ;

[0043] in is an auxiliary term used to suppress mismatch interference, For the changes of this auxiliary item, and is the control parameter corresponding to the virtual speed;

[0044] The virtual control is designed as:

[0045] Formula 26: ;

[0046] in and is the control parameter corresponding to the virtual control;

[0047] The following theorem is given:

[0048] Theorem 2: When Assumption 1 is satisfied, when the control design of the agent is:

[0049] Formula 27: ;

[0050] The multi-agent system achieves consensus within a fixed time, and the controller parameters are designed to be .

[0051] Beneficial effects achieved by the present invention:

[0052] The design of the control method of the present invention takes into account the changes in network topology. The autonomous interaction model represents the new connection relationship generated by the system restoring network connectivity through topology reconstruction when facing a network attack. It theoretically expands the existing collaborative control method, reduces its dependence on network connectivity, and can handle more complex interaction relationships between intelligent agents in dynamic networks. BRIEF DESCRIPTION OF THE DRAWINGS

[0053] Figure 1 This is a flowchart of a method for controlling the elastic consistency of a multi-agent system under network attacks provided by the present invention. DETAILED DESCRIPTION

[0054] To make the purpose, technical solutions, and advantages of the embodiments of the present invention more clear, the technical solutions in the embodiments of the present invention are clearly and completely described below. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0055] In the description of the present invention, the terms "first" and "second" are used for descriptive purposes only and should not be understood to indicate or imply relative importance or implicitly specify the number of the technical features indicated. Therefore, a feature specified as "first" or "second" may explicitly or implicitly include one or more of the features. In the description of the present invention, "plurality" means two or more, unless otherwise specifically defined.

[0056] See also Figure 1 The embodiment of the present invention provides a method for controlling the resilience and consistency of a multi-agent system under a network attack, the method comprising the following steps:

[0057] Determine the multi-agent system model;

[0058] Constructing an agent The state estimation vector is combined with the maximum consistency method to confirm the relationship between nodes and verify the connectivity status of the communication network;

[0059] Based on the identification of information agents, the characteristics of connected components are determined, and connected components with information agents are allowed to interact autonomously with connected components without information agents. In other words, the agents in the two connected components are randomly connected, thereby achieving topological reconstruction;

[0060] Combined with the dynamic pinning strategy, an observer is constructed to estimate the desired state, which can achieve fixed-time consistency;

[0061] Establish a tracking controller to make the actual state of the intelligent agent converge to the designed estimated state within a fixed time;

[0062] By adjusting the parameters in the observer and controller, each agent is regulated through the established elastic consistency control method to achieve fixed-time consistency of the multi-agent system.

[0063] In this embodiment, determining the content of the multi-agent system model includes:

[0064] Multi-agent systems include agents and 1 leader, where the agent model is:

[0065] Formula 1: , ;

[0066] The leader's model is:

[0067] Formula 2: , ;

[0068] in and Represent the position state, velocity state and control input of the agent respectively; and Represents the position change and speed change of the agent; Indicates the identity of the agent, that is, the agent number; and Indicates the position and speed status of the leader; and Indicates the leader's position change and speed change; and represents mismatched interference and matched interference in the agent dynamics, and Mismatch and match interference in leader dynamics, and satisfying:

[0069] Assumption 1: For any ;and is a known positive constant;

[0070] The network topology of a multi-agent system is composed of an undirected graph Indicates that is a node set, As the edge set, the adjacency matrix of the undirected graph is defined as , whose elements are equal to 1 if the node and nodes There is an edge, otherwise it is equal to 0; define the Laplacian matrix ,when When , its elements are ,otherwise , an undirected graph is said to be connected if there is a path between any two nodes.

[0071] In this embodiment, the state estimation vector of the intelligent agent is constructed, and the relationship between nodes is confirmed by combining the maximum consistency method. The contents of verifying the connectivity status of the communication network include:

[0072] Constructing an agent The road state estimation vector ,in For intelligent agents The road state estimation vector exist The moment elements and establish a maximum consistency method for updating:

[0073] Formula 3: ;

[0074] in, Representing an agent Neighborhood, Indicates time, is the update time step, Representative Agent The road state estimation vector exist The moment elements; Representative Agent The road state estimation vector exist The moment elements, the initial conditions of the estimated state are:

[0075] Formula 4: ;

[0076] in, Representative Agent The road state estimation vector exist The moment elements, The vector after iterations It consists only of 0 and 1, and its value determines the To the agent Is there a path between them?

[0077] make For intelligent agents The road state estimation vector exist The sum of all elements at the moment constructs a new connectivity state estimation vector ,in For intelligent agents The connectivity state estimation vector exist The moment The update rules are as follows:

[0078] Formula 5: ;

[0079] Formula 6: ;

[0080] Representative Agent The connectivity state estimation vector exist The moment elements; Representative Agent The connectivity state estimation vector exist The moment elements; Representative Agent The connectivity state estimation vector exist The moment elements; at this time, if The connectivity state vector after iterations All components of When , the system is connected; when the system is not connected, if and , then the agent and agents In the same connected component, the connected components of the system are determined.

[0081] In this embodiment, the characteristics of connected components are determined based on the identification of information agents, and connected components with information agents are allowed to autonomously interact with connected components without information agents. The contents of topology reconstruction include:

[0082] The characteristics of the connected components are determined based on the identification of the information agent. The connected components with information agents can converge under the influence of leader information, while the connected components without information agents produce unexpected behaviors. Any node in such connected components is randomly connected, and a random connection is established with any node in the connected components with information agents to achieve topology reconstruction and restore the connectivity of the network.

[0083] Networks that undergo topological reconstruction are dynamic and meet certain connectivity requirements. However, because the reconstruction process is inherently an autonomous evolution, the resulting network structure varies from scenario to scenario, making it difficult to describe using a specific connectivity specification. To achieve consistency in multi-agent systems under these dynamic networks, we establish an autonomous interaction model based on a dynamic containment strategy to characterize the new connectivity relationships generated by topological reconstruction. We propose a two-step, observer-based tracking controller approach for resilient consistency control of multi-agent systems, with fixed-time convergence of the observer and controller.

[0084] In this embodiment, a dynamic pinning strategy is combined to construct an observer to estimate the desired state. This estimated state can achieve fixed-time consistency. Specifically, the following contents are included:

[0085] make and For intelligent agents The position estimation state and velocity estimation state of are given by the dynamic pinning method, and the following distributed error with autonomous interaction model is established:

[0086] Formula 7: ;

[0087] in, The agent can obtain the leader's information, otherwise ,Only some agents in the system can obtain the leader’s information, which are called information agents; Representative Agent For autonomously interacting agents, otherwise ; and Represents an agent that establishes a new connection relationship with an autonomous interactive agent The position estimation state and velocity estimation state, and Representatives The determined agent The position estimation state and velocity estimation state of ; Representative Agent The distributed position error, Representative Agent The distributed velocity error is given as follows:

[0088] Theorem 1: When Assumption 1 is satisfied, if the estimated state Dynamic satisfaction:

[0089] Formula 8: ;

[0090] in Representative Agent Changes in the position estimate state and changes in the velocity estimate state; and are the parameters designed in the observer and satisfy: ; is the standard symbolic function, ,in Represents a positive constant greater than 0.

[0091] prove:

[0092] (1) Assume that the system has The state of the agent that cannot obtain information, first establish the speed-related Lyapunov function :

[0093] Formula 9: ;

[0094] Further split into ,in and is the speed-related Lyapunov function corresponding to the subsystem that can obtain the state of the information agent and the speed-related Lyapunov function corresponding to the subsystem that cannot obtain the state of the information agent:

[0095] Formula 10: ;

[0096] in Representative Agent The speed difference between the estimated state and the leader, , representing the intelligent agent Velocity estimation state and its autonomous interaction agent The speed difference, and is the Laplace matrix corresponding to the subsystem that can obtain the state of the information agent and the subsystem that cannot obtain the state of the information agent, The diagonal matrix formed; , is the vector expression of the corresponding speed difference.

[0097] First, yes Taking the derivative we get:

[0098] Formula 11: ;

[0099] in Represents the minimum eigenvalue of the matrix. According to the result of formula 11, we can know that:

[0100] Formula 12: , ;

[0101] Secondly, Taking the derivative we get:

[0102] Formula 13: ;

[0103] , so when hour, , Formula 13 becomes:

[0104] Formula 14: ;

[0105] According to the result of formula 14,

[0106] Formula 15: , ;

[0107] Integrating the results of formulas 12 and 15, we can see that when hour:

[0108] Formula 16: ;

[0109] (2) Establishing position-dependent Lyapunov functions :

[0110] ;

[0111] Further split into , in and The position-dependent Lyapunov function corresponding to the subsystem that can obtain the state of the information agent and the position-dependent Lyapunov function corresponding to the subsystem that cannot obtain the state of the information agent are:

[0112] Formula 17: ;

[0113] in Representative Agent The difference between the estimated position state and the leader's position, Representative Agent Position estimation state and autonomous interaction with the agent The location is poor. is the vector expression of the corresponding position difference.

[0114] right Taking the derivative we get:

[0115] Formula 18: ;

[0116] From the result of formula 16, we can see that when hour, , at this time Formula 18 is transformed into:

[0117] Formula 19: ;

[0118] According to the result of formula 14:

[0119] Formula 20: , ;

[0120] Further, Taking the derivative we get:

[0121] Formula 21: ;

[0122] From the results of formula 16 and formula 20, we can see that when , , Formula 21 is transformed into:

[0123] Formula 22: ;

[0124] According to the result of formula 22:

[0125] Formula 23: , ;

[0126] Combining the results of formula 16 and formula 23, we can know that for , .

[0127] In this embodiment, the contents of establishing a tracking controller so that the actual state of the agent converges to the designed estimated state within a fixed time include:

[0128] Define the error between the actual position state and the estimated position state , the error between the actual speed state and the estimated speed state , and introduce a virtual velocity term and virtual controls ,in For the control of the intelligent agent, For changes in virtual control items;

[0129] make As the converted speed error, the system transformation is:

[0130] Formula 24: ;

[0131] in, is the change in error between the actual position state and the estimated position state; is the estimated velocity residual term, Estimate the position residual term. At this time, the virtual speed is designed as:

[0132] Formula 25: ;

[0133] in is an auxiliary term used to suppress mismatch interference, For the changes of this auxiliary item, and is the control parameter corresponding to the virtual speed;

[0134] The virtual control is designed as:

[0135] Formula 26: ;

[0136] in and is the control parameter corresponding to the virtual control;

[0137] The following theorem is given:

[0138] Theorem 2: When Assumption 1 is satisfied, when the control design of the agent is:

[0139] Formula 27: ;

[0140] The multi-agent system achieves consensus within a fixed time, and the controller parameters are designed to be .

[0141] Define the error between the actual position state and the estimated position state , the error between the actual speed state and the estimated speed state , and introduce a virtual velocity term and virtual controls ,in For the control of the intelligent agent, For changes in virtual control items;

[0142] make As the converted speed error, the system transformation is:

[0143] Formula 24: ;

[0144] in, is the change in error between the actual position state and the estimated position state; is the estimated velocity residual term, Estimate the position residual term. At this time, the virtual speed is designed as:

[0145] Formula 25: ;

[0146] in is an auxiliary term used to suppress mismatch interference, For the changes of this auxiliary item, and is the control parameter corresponding to the virtual speed;

[0147] The virtual control is designed as:

[0148] Formula 26: ;

[0149] in and is the control parameter corresponding to the virtual control;

[0150] The following theorem is given:

[0151] Theorem 2: When Assumption 1 is satisfied, when the control design of the agent is:

[0152] Formula 27: ;

[0153] The multi-agent system achieves consensus within a fixed time, and the controller parameters are designed to be .

[0154] Proof: First establish the Lyapunov function , whose derivative satisfies:

[0155] Formula 28: ;

[0156] when hour, , then Formula 28 becomes

[0157] Formula 29: ;

[0158] Formula 29 shows that At a fixed time Internal convergence, that is, when hour ;

[0159] Further considerations Changes:

[0160] Formula 30: ;

[0161] Depend on and It can be seen that when , Formula 30 becomes

[0162] Formula 31: ;

[0163] The result of formula 31 shows that Will be at a fixed time Inner convergence, that is , , that is to say , the system achieves consistency in constant time.

[0164] It should be noted that, in this document, the term "comprises" or any other variant thereof is intended to cover non-exclusive inclusion, so that a process, method, article, or apparatus that includes a series of elements includes not only those elements, but also includes other elements not explicitly listed, or also includes elements inherent to such process, method, article, or apparatus. In the absence of further limitations, an element defined by the phrase "comprises a ..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes the element.

[0165] The above are only preferred embodiments of the present invention and are not intended to limit the patent scope of the present invention. Any equivalent structure or equivalent process transformation made using the description of the present invention, or directly or indirectly applied in other related technical fields, are also included in the patent protection scope of the present invention.

Claims

1. A method for controlling the resilience and consistency of a multi-agent system under network attacks, characterized by: The method comprises the following steps: Determine the multi-agent system model; Construct the state estimation vector of the intelligent agent, combine the maximum consistency method to confirm the relationship between nodes, and verify the connectivity status of the communication network; Based on the identification of information agents, the characteristics of connected components are determined, and connected components with information agents are allowed to interact autonomously with connected components without information agents to achieve topology reconstruction; Combined with the dynamic pinning strategy, an observer is constructed to estimate the desired state and achieve fixed-time consistency; A tracking controller is established to make the actual state of the agent converge to the designed estimated state within a fixed time.

2. The method for controlling the resilience and consistency of a multi-agent system under network attacks according to claim 1, characterized in that: The contents of the multi-agent system model include: Multi-agent systems include agents and 1 leader, where the agent model is: Formula 1: , ; The leader's model is: Formula 2: , ; in and Represent the position state, velocity state and control input of the agent respectively; and Represents the position change and speed change of the agent; Indicates the identity of the agent, that is, the agent number; and Indicates the position and speed status of the leader; and Indicates the leader's position change and speed change; and represents mismatched interference and matched interference in the agent dynamics, and Mismatch and match interference in leader dynamics, and satisfying: Assumption 1: For any ;and is a known positive constant; The network topology of a multi-agent system is composed of an undirected graph Indicates that is a node set, As the edge set, the adjacency matrix of the undirected graph is defined as , whose elements Equal to 1 if the node and nodes There is an edge, otherwise it is equal to 0; define the Laplacian matrix ,when When , its elements are ,otherwise , an undirected graph is said to be connected if there is a path between any two nodes.

3. The method for controlling the resilience and consistency of a multi-agent system under network attacks according to claim 2, characterized in that: Constructing the state estimation vector of the intelligent agent, combining the maximum consistency method to confirm the relationship between nodes, and verifying the connectivity status of the communication network include: Constructing an agent The road state estimation vector ,in For intelligent agents The road state estimation vector exist The moment elements and establish a maximum consistency method for updating: Formula 3: ; in, Representing an agent Neighborhood, Indicates time, is the update time step, Representative Agent The road state estimation vector exist The moment elements; Representative Agent The road state estimation vector exist The moment elements, the initial conditions of the estimated state are: Formula 4: ; in, Representative Agent The road state estimation vector exist The moment elements, The vector after iterations It consists only of 0 and 1, and its value determines the To the agent Is there a path between them? make For intelligent agents The road state estimation vector exist The sum of all elements at the moment constructs a new connectivity state estimation vector ,in For intelligent agents The connectivity state estimation vector exist The moment The update rules are as follows: Formula 5: ; Formula 6: ; Representative Agent The connectivity state estimation vector exist The moment elements; Representative Agent The connectivity state estimation vector exist The moment elements; Representative Agent The connectivity state estimation vector exist The moment elements; at this time, if The connectivity state vector after iterations All components of When , the system is connected; when the system is not connected, if and , then the agent and agents In the same connected component, the connected components of the system are determined.

4. The method for controlling the resilience and consistency of a multi-agent system under network attacks according to claim 1, characterized in that: Based on the identification of information agents, the characteristics of connected components are determined, and connected components with information agents are allowed to interact autonomously with connected components without information agents. The contents of topology reconstruction include: The characteristics of the connected components are determined based on the identification of the information agent. The connected components with information agents converge under the influence of the leader information, while the connected components without information agents produce unexpected behaviors. Any node in such connected components is randomly connected, and then a random connection is established with any node in the connected components with information agents to achieve topology reconstruction and restore the connectivity of the network.

5. The method for controlling the resilience and consistency of a multi-agent system under network attacks according to claim 2, characterized in that: Combining a dynamic containment strategy, constructing an observer to estimate the desired state and achieving fixed-time consistency includes: make and For intelligent agents The position estimation state and velocity estimation state of are given by the dynamic pinning method, and the following distributed error with autonomous interaction model is established: Formula 7: ; in, The agent can obtain the leader's information, otherwise ,Only some agents in the system can obtain the leader’s information, which are called information agents; Representative Agent For autonomously interacting agents, otherwise ; and Represents an agent that establishes a new connection relationship with an autonomous interactive agent The position estimation state and velocity estimation state, and Representatives The determined agent The position estimation state and velocity estimation state of ; Representative Agent The distributed position error, Representative Agent The distributed velocity error is given as follows: Theorem 1: When Assumption 1 is satisfied, if the estimated state Dynamic satisfaction: Formula 8: ; in Representative Agent Changes in the position estimate state and changes in the velocity estimate state; and are the parameters designed in the observer and satisfy: ; is the standard symbolic function, ,in Represents a positive constant greater than 0.

6. The method for controlling the resilience and consistency of a multi-agent system under network attacks according to claim 1, characterized in that: The contents of establishing a tracking controller so that the actual state of the intelligent agent converges to the designed estimated state within a fixed time include: Define the error between the actual position state and the estimated position state , the error between the actual speed state and the estimated speed state , and introduce a virtual velocity term and virtual controls ,in For the control of the intelligent agent, For changes in virtual control items; make As the converted speed error, the system transformation is: Formula 24: ; in, is the change in error between the actual position state and the estimated position state; is the estimated velocity residual term, Estimate the position residual term. At this time, the virtual speed is designed as: Formula 25: ; in is an auxiliary term used to suppress mismatch interference, For the changes of this auxiliary item, and is the control parameter corresponding to the virtual speed; The virtual control is designed as: Formula 26: ; in and is the control parameter corresponding to the virtual control; The following theorem is given: Theorem 2: When Assumption 1 is satisfied, when the control design of the agent is: Formula 27: ; The multi-agent system achieves consensus within a fixed time, and the controller parameters are designed to be .

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