A Resilient Consistency Control Method for Multi-Agent Systems Under Network Attacks

Abstract

This invention is applicable to the field of cooperative control of multi-agent systems. It achieves autonomous repair of damaged networks through network state verification and network topology reconstruction, and establishes an autonomous interaction model of agents based on a dynamic restraint strategy. It provides a resilient consistency control method for multi-agent systems under network attacks. The method includes: determining the multi-agent system model; constructing state estimation vectors for agents, confirming relationships between nodes using the maximum consensus method, and verifying the connectivity state of the communication network; determining the characteristics of connected components based on the identifiers of information agents, and randomly connecting connected components with and without information agents to achieve topology reconstruction; the convergence of the constructed observer and controller is fixed-time convergence. This invention theoretically extends existing cooperative control methods, reducing their dependence on network connectivity and enabling them to handle more complex interactions between agents in dynamic networks.

Description

Technical Field

[0001] This invention relates to the field of cooperative control of multi-agent systems, and more particularly to a method for resilient consistency control of multi-agent systems under network attacks. Background Technology

[0002] Multi-agent system cooperative control designs distributed control methods through cooperation and coordination among agents to achieve the overall system goal and respond to tasks and the environment. Network topology and control algorithms jointly determine the evolutionary outcome of the multi-agent system. The former represents the interaction relationships between agents, i.e., which nodes influence the movement of a node; the latter represents the specific rules for adjusting the movement of a node based on its state information. Significant progress has been made in designing control algorithms to achieve collaborative behavior in complex scenarios when the network topology is predetermined and connectivity conditions are met. Existing research focuses on the construction of control algorithms, using network connectivity as a priori conditions, and the effectiveness of control implementation highly depends on idealized communication assumptions. For undirected and directed network structures, existing control methods heavily rely on corresponding network connectivity properties, such as fully connected, jointly connected, and strongly connected. Furthermore, when the network is attacked, the above connectivity conditions cannot be met. Existing cooperative control methods design control strategies through time-dwelling methods, assuming that the network can recover to its original good state within a certain time. On the one hand, this imposes strict limitations on the attack frequency and duration; on the other hand, when the system faces multiple and complex attacks, the control methods may fail. Summary of the Invention

[0003] To address the shortcomings of existing technologies, the present invention aims to propose a resilient consistency control method for multi-agent systems under network attacks. This method aims to enhance the resilience of the control method in the face of network attacks by incorporating topology reconstruction, establishing a new interaction model to promote deep coupling between network topology and control algorithms in complex scenarios, and advancing the theoretical development and engineering applications of collaborative control for multi-agent systems.

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

[0005] Determine the model of the multi-agent system;

[0006] Constructing intelligent agents The state estimation vector is combined with the maximum consensus method to confirm the relationship between nodes and verify the connectivity state of the communication network.

[0007] Based on the characteristics of identifying connected components using information agents, connected components with information agents can autonomously interact with connected components without information agents, that is, the agents in the two connected components can be randomly connected, thereby achieving topology reconstruction.

[0008] By combining a dynamic restraint strategy, an observer is constructed to estimate the desired state, and this estimated state can achieve consistency over a fixed time.

[0009] Establish a tracking controller so that the actual state of the agent converges to the designed estimated state within a fixed time.

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

[0011] Multi-agent systems include There are one agent and one leader, where the agent model is as follows:

[0012] Formula 1: , ;

[0013] The leader model is:

[0014] Formula 2: , ;

[0015] in and These represent the agent's position state, velocity state, and control input, respectively. and This represents the changes in the agent's position and velocity; The identifier of the intelligent agent, i.e., which intelligent agent it is; and This indicates the leader's position and speed status; and This indicates changes in the leader's position and speed; and This represents mismatched and matched interference in the dynamics of an agent. and Mismatch and matching interferences in leader dynamics, satisfying:

[0016] Assumption 1: For any ;and For known positive constants;

[0017] The network topology of a multi-agent system is an undirected graph. It means that among them For a set of nodes, Let the set of edges be the adjacency matrix of the undirected graph. If the element of a node is equal to 1, then the node's element is equal to 1. and nodes If an edge exists, the value is 0; define the Laplace 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 consensus method. The content of verifying the connectivity state of the communication network includes:

[0019] Constructing intelligent agents The state estimation vector of the road ,in For intelligent agents The state estimation vector of the road exist The first moment Each element is updated using a maximum consistency method:

[0020] Formula 3: ;

[0021] in, Represents intelligent agents The neighborhood, Indicates time, For the update time step, Representing intelligent agents The state estimation vector of the road exist The first moment One element; Representing intelligent agents The state estimation vector of the road exist The first moment Given n elements, the initial conditions for estimating the state are:

[0022] Formula 4: ;

[0023] in, Representing intelligent agents The state estimation vector of the road exist The first moment One element, The vector after the second iteration It consists only of 0s and 1s, and its value determines the actions of the agent. To intelligent agents Is there a road between them?

[0024] make For intelligent agents The state estimation vector of the road exist The sum of all elements at time t is used to construct a new connected state estimation vector. ,in For intelligent agents Connectivity state estimation vector exist The first moment The update rules for each element are as follows:

[0025] Formula 5: ;

[0026] Formula 6: ;

[0027] Representing intelligent agents Connectivity state estimation vector exist The first moment One element; Representing intelligent agents Connectivity state estimation vector exist The first moment One element; Representing intelligent agents Connectivity state estimation vector exist The first moment One element; at this time, if The connectivity state vector after the next iteration All components are When the system is connected, then the system is connected; when the system is disconnected, if and Then the intelligent agent and intelligent agents The connected components of the system are determined by being in the same connected component.

[0028] As a further technical solution of the present invention, based on the characteristic of identifying connected components using information intelligent agents, connected components with information intelligent agents are enabled to autonomously interact with connected components without information intelligent agents to achieve topology reconstruction. This includes:

[0029] Based on the characteristics of identifying connected components using information agents, connected components with information agents can achieve convergence under the influence of leader information, while connected components without information agents exhibit unexpected behavior. Random connections are made between any node in such connected components and any node in connected components with information agents to achieve topology reconstruction and restore network connectivity.

[0030] As a further technical solution of the present invention, the content of constructing the desired state in which the observer can achieve fixed-time consistent convergence under a dynamic network, combined with a dynamic restraint strategy, includes:

[0031] make and For intelligent agents The position estimation state and velocity estimation state are used to establish the following distributed error with an autonomous interaction model based on the dynamic restraint method:

[0032] Formula 7: ;

[0033] in, The agent is able to obtain information about the leader, otherwise In a system where only some agents can obtain information about the leader, these agents are called information agents. Representing intelligent agents For an intelligent agent to engage in autonomous interaction, otherwise ; and An agent that establishes new connections with autonomous interactive agents. Position estimation state and velocity estimation state, and Representative by The determined intelligent agent Position estimation state and velocity estimation state; Representing intelligent agents Distributed location error, Representing intelligent agents For the distributed velocity error, the following theorem is given:

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

[0035] Formula 8: ;

[0036] in Representing intelligent agents Changes in position estimation state and changes in velocity estimation state; and The parameters are designed for the observer and satisfy: ; For standard symbolic functions, ,in Represents a positive constant greater than 0.

[0037] As a further technical solution of the present invention, the content of establishing a tracking controller to make the actual state of the 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. Error between actual speed state and estimated speed state And introduce a virtual speed term and virtual control items ,in For the control of intelligent agents, For changes in virtual control items;

[0039] make As the transformed velocity error, the system transformation is:

[0040] Formula 24: ;

[0041] in, This represents the change in error between the actual position state and the estimated position state. To estimate the velocity residual term, Estimate the location residual term; at this point, design the virtual velocity as follows:

[0042] Formula 25: ;

[0043] in This is an auxiliary term used to suppress mismatch interference. For the change of this auxiliary item, and These are the control parameters corresponding to the virtual speed;

[0044] The virtual control design is as follows:

[0045] Formula 26: ;

[0046] in and These are the control parameters corresponding to virtual control;

[0047] The following theorem is given:

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

[0049] Formula 27: ;

[0050] A multi-agent system achieves consistency within a fixed time period, and the controller parameters are designed as follows: .

[0051] The beneficial effects achieved by this invention are as follows:

[0052] The control method of this invention takes into account changes in network topology. It uses an autonomous interaction model to represent the new connection relationships generated by the system restoring network connectivity through topology reconstruction when facing network attacks. This theoretically extends existing cooperative control methods, reducing their dependence on network connectivity and enabling them to handle more complex interaction relationships between agents in dynamic networks. Attached Figure Description

[0053] Figure 1 The flowchart of a resilient consistency control method for a multi-agent system under network attacks provided by the present invention is shown. Detailed Implementation

[0054] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention are described clearly and completely below. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of them. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0055] In the description of this invention, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of indicated technical features. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of this invention, "a plurality of" means two or more, unless otherwise explicitly specified.

[0056] Please see Figure 1 This invention provides a method for resilient consistency control of a multi-agent system under network attacks, the method comprising the following steps:

[0057] Determine the model of the multi-agent system;

[0058] Constructing intelligent agents The state estimation vector is combined with the maximum consensus method to confirm the relationship between nodes and verify the connectivity state of the communication network.

[0059] Based on the characteristics of identifying connected components using information agents, connected components with information agents can autonomously interact with connected components without information agents, that is, the agents in the two connected components can be randomly connected, thereby achieving topology reconstruction.

[0060] By combining a dynamic restraint strategy, an observer is constructed to estimate the desired state, and this estimated state can achieve consistency over a fixed time.

[0061] Establish a tracking controller so that the actual state of the agent converges to the designed estimated state within a fixed time.

[0062] By adjusting the parameters in the observer and controller, and regulating each agent through the established elastic consistency control method, fixed-time consistency of the multi-agent system can be achieved.

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

[0064] Multi-agent systems include There are one agent and one leader, where the agent model is as follows:

[0065] Formula 1: , ;

[0066] The leader model is:

[0067] Formula 2: , ;

[0068] in and These represent the agent's position state, velocity state, and control input, respectively. and This represents the changes in the agent's position and velocity; The identifier of the intelligent agent, i.e., which intelligent agent it is; and This indicates the leader's position and speed status; and This indicates changes in the leader's position and speed; and This represents mismatched and matched interference in the dynamics of an agent. and Mismatch and matching interferences in leader dynamics, satisfying:

[0069] Assumption 1: For any ;and For known positive constants;

[0070] The network topology of a multi-agent system is an undirected graph. It means that among them For a set of nodes, Let the set of edges be the adjacency matrix of the undirected graph. If the element of a node is equal to 1, then the node's element is equal to 1. and nodes If an edge exists, the value is 0; define the Laplace 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 agent is constructed, and the relationship between nodes is confirmed by combining the maximum consensus method. The content of verifying the connectivity state of the communication network includes:

[0072] Constructing intelligent agents The state estimation vector of the road ,in For intelligent agents The state estimation vector of the road exist The first moment Each element is updated using a maximum consistency method:

[0073] Formula 3: ;

[0074] in, Represents intelligent agents The neighborhood, Indicates time, For the update time step, Representing intelligent agents The state estimation vector of the road exist The first moment One element; Representing intelligent agents The state estimation vector of the road exist The first moment Given n elements, the initial conditions for estimating the state are:

[0075] Formula 4: ;

[0076] in, Representing intelligent agents The state estimation vector of the road exist The first moment One element, The vector after the second iteration It consists only of 0s and 1s, and its value determines the actions of the agent. To intelligent agents Is there a road between them?

[0077] make For intelligent agents The state estimation vector of the road exist The sum of all elements at time t is used to construct a new connected state estimation vector. ,in For intelligent agents Connectivity state estimation vector exist The first moment The update rules for each element are as follows:

[0078] Formula 5: ;

[0079] Formula 6: ;

[0080] Representing intelligent agents Connectivity state estimation vector exist The first moment One element; Representing intelligent agents Connectivity state estimation vector exist The first moment One element; Representing intelligent agents Connectivity state estimation vector exist The first moment One element; at this time, if The connectivity state vector after the next iteration All components are When the system is connected, then the system is connected; when the system is disconnected, if and Then the intelligent agent and intelligent agents The connected components of the system are determined by being in the same connected component.

[0081] In this embodiment, based on the characteristic of identifying connected components using information agents, connected components with information agents autonomously interact with connected components without information agents to achieve topology reconstruction. This includes:

[0082] Based on the characteristics of identifying connected components using information agents, connected components with information agents can achieve convergence under the influence of leader information, while connected components without information agents exhibit unexpected behavior. Random connections are made between any node in such connected components and any node in connected components with information agents to achieve topology reconstruction and restore network connectivity.

[0083] Networks undergoing topology reconstruction are dynamic and satisfy certain connectivity requirements. However, since the reconstruction process is essentially an autonomous evolutionary process, the final network structure varies depending on the scenario and is difficult to describe using a specific connectivity property. To achieve consistency in multi-agent systems under such dynamic networks, we establish an autonomous interaction model of the system based on a dynamic restraint strategy to characterize the new connections generated by topology reconstruction. We propose a resilient consistency control method for multi-agent systems consisting of an observer and a tracking controller, with the convergence of the observer and controller occurring in a fixed time.

[0084] In this embodiment, a dynamic restraint strategy is combined to construct an observer that estimates the desired state. This estimated state can achieve consistency over a fixed time. Specifically, the following is included:

[0085] make and For intelligent agents The position estimation state and velocity estimation state are used to establish the following distributed error with an autonomous interaction model based on the dynamic restraint method:

[0086] Formula 7: ;

[0087] in, The agent is able to obtain information about the leader, otherwise In a system where only some agents can obtain information about the leader, these agents are called information agents. Representing intelligent agents For an intelligent agent to engage in autonomous interaction, otherwise ; and An agent that establishes new connections with autonomous interactive agents. Position estimation state and velocity estimation state, and Representative by The determined intelligent agent Position estimation state and velocity estimation state; Representing intelligent agents Distributed location error, Representing intelligent agents For the distributed velocity error, the following theorem is given:

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

[0089] Formula 8: ;

[0090] in Representing intelligent agents Changes in position estimation state and changes in velocity estimation state; and The parameters are designed for the observer and satisfy: ; For standard symbolic functions, ,in Represents a positive constant greater than 0.

[0091] prove:

[0092] (1) Assume the system has For an agent whose state cannot be accessed, first establish a velocity-related Lyapunov function. :

[0093] Formula 9: ;

[0094] Further split into ,in and Let's define the velocity-dependent Lyapunov functions for subsystems that can obtain the state of the information agent and for subsystems that cannot obtain the state of the information agent:

[0095] Formula 10: ;

[0096] in Representing intelligent agents Speed ​​estimation state and the speed difference of the leader, , representing intelligent agents Velocity estimation state and its autonomous interaction with the intelligent agent Speed ​​difference, and The Laplace matrix represents the subsystems that can obtain the state of the information agent and the subsystems that cannot obtain the state of the information agent. The diagonal matrix formed; , This is the vector representation of the corresponding velocity difference.

[0097] First of all, Differentiation yields:

[0098] Formula 11: ;

[0099] in Let represent the smallest eigenvalue of the matrix. According to the result of Formula 11:

[0100] Formula 12: , ;

[0101] Secondly, for Differentiation yields:

[0102] Formula 13: ;

[0103] Therefore when hour, Formula 13 becomes:

[0104] Formula 14: ;

[0105] According to the result of Formula 14,

[0106] Formula 15: , ;

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

[0108] Formula 16: ;

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

[0110] ;

[0111] Further split into , in and For the position-dependent Lyapunov functions of subsystems that can obtain the state of the information agent and for subsystems that cannot obtain the state of the information agent:

[0112] Formula 17: ;

[0113] in Representing intelligent agents Position estimation state and the difference between the leader's position, Representing intelligent agents Position estimation state and its autonomous interaction agent The positional difference. This is the vector representation of the corresponding positional difference.

[0114] right Differentiation yields:

[0115] Formula 18: ;

[0116] From the result of Formula 16, we can see that when hour, At this point, formula 18 becomes:

[0117] Formula 19: ;

[0118] According to the result of Formula 14:

[0119] Formula 20: , ;

[0120] Furthermore, regarding Differentiation yields:

[0121] Formula 21: ;

[0122] From the results of formulas 16 and 20, it can be seen 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 formulas 16 and 23, it can be seen that for , .

[0127] In this embodiment, the establishment of a tracking controller, which enables the agent's actual state to converge to the designed estimated state within a fixed time, includes:

[0128] Define the error between the actual position state and the estimated position state. Error between actual speed state and estimated speed state And introduce a virtual speed term and virtual control items ,in For the control of intelligent agents, For changes in virtual control items;

[0129] make As the transformed velocity error, the system transformation is:

[0130] Formula 24: ;

[0131] in, This represents the change in error between the actual position state and the estimated position state. To estimate the velocity residual term, Estimate the location residual term; at this point, design the virtual velocity as follows:

[0132] Formula 25: ;

[0133] in This is an auxiliary term used to suppress mismatch interference. For the change of this auxiliary item, and These are the control parameters corresponding to the virtual speed;

[0134] The virtual control design is as follows:

[0135] Formula 26: ;

[0136] in and These are the control parameters corresponding to virtual control;

[0137] The following theorem is given:

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

[0139] Formula 27: ;

[0140] A multi-agent system achieves consistency within a fixed time period, and the controller parameters are designed as follows: .

[0141] Define the error between the actual position state and the estimated position state. Error between actual speed state and estimated speed state And introduce a virtual speed term and virtual control items ,in For the control of intelligent agents, For changes in virtual control items;

[0142] make As the transformed velocity error, the system transformation is:

[0143] Formula 24: ;

[0144] in, This represents the change in error between the actual position state and the estimated position state. To estimate the velocity residual term, Estimate the location residual term; at this point, design the virtual velocity as follows:

[0145] Formula 25: ;

[0146] in This is an auxiliary term used to suppress mismatch interference. For the change of this auxiliary item, and These are the control parameters corresponding to the virtual speed;

[0147] The virtual control design is as follows:

[0148] Formula 26: ;

[0149] in and These are the control parameters corresponding to virtual control;

[0150] The following theorem is given:

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

[0152] Formula 27: ;

[0153] A multi-agent system achieves consistency within a fixed time period, and the controller parameters are designed as follows: .

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

[0155] Formula 28: ;

[0156] when hour, Then formula 28 becomes

[0157] Formula 29: ;

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

[0159] Further consideration Changes:

[0160] Formula 30: ;

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

[0162] Formula 31: ;

[0163] The results of Formula 31 show that It will be at a fixed time Convergence, i.e. , , that is to say The system achieves consistency within a fixed time period.

[0164] It should be noted that, in this document, the term "comprising" or any other variation thereof is intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes that element.

[0165] The above are merely preferred embodiments of the present invention and do not limit the patent scope of the present invention. Any equivalent structural or procedural transformations made using the present invention specification, or direct or indirect applications in other related technical fields, are similarly included within the patent protection scope of the present invention.

Claims

1. A method for resilient consistency control of a multi-agent system under network attacks, characterized in that, The method comprises the following steps: Determine the model of the multi-agent system; Construct the state estimation vector of the agent, combine the maximum consensus method to confirm the relationship between nodes, and verify the connectivity state of the communication network. Based on the characteristics of identifying connected components using information agents, connected components with information agents can autonomously interact with connected components without information agents to achieve topology reconstruction. By combining a dynamic restraint strategy, an observer is constructed to estimate the desired state, thereby achieving fixed-time consistency. Establish a tracking controller so that the actual state of the agent converges to the designed estimated state within a fixed time. Determining the content of a multi-agent system model includes: Multi-agent systems include There are one agent and one leader, where the agent model is as follows: Formula 1: , ; The leader model is: Formula 2: , ; in and These represent the agent's position state, velocity state, and control input, respectively. and This represents the changes in the agent's position and velocity; The identifier of the intelligent agent, i.e., which intelligent agent it is; and This indicates the leader's position and speed status; and This indicates changes in the leader's position and speed; and This represents mismatched and matched interference in the dynamics of an agent. and Mismatch and matching interferences in leader dynamics, satisfying: Assumption 1: For any ;and For known positive constants; The network topology of a multi-agent system is an undirected graph. It means that, among them For a set of nodes, Let be the set of edges, and define the adjacency matrix of the undirected graph as follows: Its elements If the node is equal to 1 and nodes If an edge exists, the value is 0; define the Laplace matrix. ,when When, its elements are ,otherwise An undirected graph is said to be connected if there is a path between any two nodes. Constructing the state estimation vector of the agent, combining the maximum consensus method to confirm the relationships between nodes, and verifying the connectivity state of the communication network include: Constructing intelligent agents The state estimation vector of the road ,in For intelligent agents The state estimation vector of the road exist The first moment Each element is updated using a maximum consistency method: Formula 3: ; in, Represents intelligent agents The neighborhood, Indicates time, For the update time step, Representing intelligent agents The state estimation vector of the road exist The first moment One element; Representing intelligent agents The state estimation vector of the road exist The first moment Given elements, the initial conditions for estimating the state are: Formula 4: ; in, Representing intelligent agents The state estimation vector of the road exist The first moment One element, The vector after the second iteration It consists only of 0s and 1s, and its value determines the actions of the agent. To intelligent agents Is there a road between them? make For intelligent agents The state estimation vector of the road exist The sum of all elements at time t is used to construct a new connected state estimation vector. ,in For intelligent agents Connectivity state estimation vector exist The first moment The update rules for each element are as follows: Formula 5: ; Formula 6: ; Representing intelligent agents Connectivity state estimation vector exist The first moment One element; Representing intelligent agents Connectivity state estimation vector exist The first moment One element; Representing intelligent agents Connectivity state estimation vector exist The first moment One element; at this time, if The connectivity state vector after the next iteration All components are When the system is connected, then the system is connected; when the system is disconnected, if and Then the intelligent agent and intelligent agents The connected components of the system are determined by being in the same connected component.

2. The method for resilient consistency control of a multi-agent system under network attacks according to claim 1, characterized in that, Based on the characteristic of identifying connected components using information agents, the topology reconstruction is achieved by enabling connected components with information agents to autonomously interact with connected components without information agents. This includes: Based on the characteristics of identifying connected components using information agents, connected components with information agents achieve convergence under the influence of leader information, while connected components without information agents exhibit unexpected behavior. Random connections are made between any nodes in such connected components, enabling topology reconstruction and restoring network connectivity.

3. The method for resilient consistency control of a multi-agent system under network attacks according to claim 1, characterized in that, Combining a dynamic restraint strategy, the process of 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 are used to establish the following distributed error with an autonomous interaction model based on the dynamic restraint method: Formula 7: ; in, The agent is able to obtain information about the leader, otherwise In a system where only some agents can obtain information about the leader, these agents are called information agents. Representing intelligent agents For an intelligent agent to engage in autonomous interaction, otherwise ; and An agent that establishes new connections with autonomous interactive agents. Position estimation state and velocity estimation state, and Representative by The determined intelligent agent Position estimation state and velocity estimation state; Representing intelligent agents Distributed location error, Representing intelligent agents For the distributed velocity error, the following theorem is given: Theorem 1: When Assumption 1 is satisfied, if the estimated state Dynamic satisfaction: Formula 8: ; in Representing intelligent agents Changes in position estimation state and changes in velocity estimation state; and The parameters are designed for the observer and satisfy: ; For standard symbolic functions, ,in Represents a positive constant greater than 0.

4. The method for resilient consistency control of a multi-agent system under network attacks according to claim 1, characterized in that, The process of establishing a tracking controller to ensure that the agent's actual state converges to the designed estimated state within a fixed time includes: Define the error between the actual position state and the estimated position state. Error between actual speed state and estimated speed state And introduce a virtual speed term and virtual control items ,in For the control of intelligent agents, For changes in virtual control items; make As the transformed velocity error, the system transformation is: Formula 24: ; in, This represents the change in error between the actual position state and the estimated position state. To estimate the velocity residual term, Estimate the location residual term; at this point, design the virtual velocity as follows: Formula 25: ; in This is an auxiliary term used to suppress mismatch interference. For the change of this auxiliary item, and These are the control parameters corresponding to the virtual speed; The virtual control design is as follows: Formula 26: ; in and These are the control parameters corresponding to virtual control; The following theorem is given: Theorem 2: When Assumption 1 is satisfied, when the control design of the agent is as follows: Formula 27: ; A multi-agent system achieves consistency within a fixed time period, and the controller parameters are designed as follows: 。

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