A multi-agent fault-tolerant formation control method fusing graph attention network and safety constraints

Abstract

This invention proposes a multi-agent fault-tolerant formation control method integrating graph attention networks and safety constraints. The method includes: establishing a multi-agent nonlinear dynamic model and a directed communication topology; acquiring the neighbor states, relative formation errors, and fault residual information of each agent; using a graph attention network to weighted aggregate neighbor information and dynamically allocate neighbor influence weights to reduce the impact of abnormal or faulty nodes on formation control; constructing a distributed formation tracking error and establishing a fault-tolerant control model based on actuator faults, external disturbances, and model uncertainties; designing safety constraint functions to constrain the safe distance between agents, control input amplitude, and formation error boundaries; estimating unknown nonlinear terms and fault effects based on a neural network adaptive compensation mechanism, and generating a distributed fault-tolerant formation controller by combining safety constraint correction terms. This invention can improve the formation safety, robustness, and fault-tolerant control performance of multi-agent systems under conditions of topology changes, neighbor anomalies, and actuator faults.

Description

Technical Field

[0001] This invention belongs to the field of multi-agent cooperative control, specifically relating to a multi-agent fault-tolerant formation control method that integrates graph attention networks and safety constraints. Background Technology

[0002] With the rapid development of intelligent equipment such as drones, mobile robots, unmanned vehicles, and unmanned surface vessels, multi-agent systems have been widely used in scenarios such as collaborative inspection, area search, target tracking, disaster relief, and military reconnaissance. Formation control, as an important issue in multi-agent cooperative control, requires multiple agents to maintain a preset formation during movement and to achieve stable tracking based on the lead agent or mission trajectory.

[0003] Existing multi-agent formation control methods typically rely on fixed communication topologies or preset neighbor weights to construct formation errors. When the system scales up, communication links change, or some neighbor agents exhibit abnormal states, fixed weights struggle to accurately reflect the influence of different neighbors on the current agent. This can easily lead to abnormal node information being continuously introduced into the controller, thereby reducing the stability and robustness of the formation system.

[0004] Furthermore, in practical applications, agents may be affected by external disturbances, model uncertainties, actuator efficiency losses, and bias faults. While traditional fault-tolerant formation control methods can compensate for faults and disturbances to some extent, their ability to identify anomalous neighbor information and handle safety constraints remains insufficient, making it difficult to simultaneously guarantee formation tracking accuracy, collision avoidance safety, and control input enforceability. Therefore, it is necessary to propose a multi-agent fault-tolerant formation control method that can dynamically assess the impact of neighbor information, compensate for fault disturbances, and satisfy safety constraints. Summary of the Invention

[0005] To address the problems existing in the prior art, this invention proposes a multi-agent fault-tolerant formation control method that integrates graph attention networks and safety constraints. The method includes: establishing a multi-agent nonlinear dynamic model comprising a lead agent and multiple follower agents, and constructing a corresponding directed communication topology graph; constructing neighbor interaction features based on the state information, communication state information, and fault residual information of the follower agents and their neighbor agents; inputting the neighbor interaction features into a graph attention network to obtain neighbor attention weights, and constructing a distributed formation tracking error based on these weights; constructing error filtering variables based on the distributed formation tracking error, and estimating unknown nonlinear terms, actuator fault effects, and external disturbances using a neural network adaptive compensation mechanism; generating a nominal fault-tolerant formation control input based on the error filtering variables and the neural network adaptive compensation result; correcting the nominal fault-tolerant formation control input using a safety constraint function to obtain the final distributed fault-tolerant formation control input; and applying the final distributed fault-tolerant formation control input to the corresponding follower agents to achieve safe fault-tolerant formation control of the multi-agent system.

[0006] The beneficial effects of this invention are: This invention proposes a multi-agent fault-tolerant formation control method that integrates graph attention networks and safety constraints. By introducing a graph attention network to dynamically weight neighbor information, it achieves effective utilization of critical neighbor information and suppresses the impact of abnormal neighbor information. Through constructing a distributed formation error based on neighbor attention weights, it achieves coordinated formation control using only local neighbor information, improving the method's adaptability to communication topology changes and missing local information. By designing a neural network adaptive compensation mechanism, it achieves online estimation and compensation for unknown nonlinear dynamics, actuator failures, and external disturbances. By constructing a safety constraint correction mechanism, it integrates inter-agent safety distance constraints, formation error boundary constraints, and control input constraints into the control input generation process, ensuring that the system meets safety requirements during operation. This invention can maintain formation stability and tracking performance under conditions of neighbor anomalies, actuator failures, external disturbances, and communication topology changes, improving the fault tolerance, safety, and coordinated control capabilities of multi-agent systems. Attached Figure Description

[0007] Figure 1 This is a flowchart of the multi-agent fault-tolerant formation control method in an embodiment of the present invention; Figure 2 This is a schematic diagram of the navigator-follower directed communication topology in an embodiment of the present invention; Figure 3 This is a fault perception graph attention neighbor aggregation structure diagram in an embodiment of the present invention; Figure 4 This is a flowchart of the neural network fault-tolerant formation control method in an embodiment of the present invention; Detailed Implementation

[0008] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. 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.

[0009] A multi-agent fault-tolerant formation control method integrating graph attention networks and safety constraints includes: establishing a multi-agent nonlinear dynamic model comprising a leader agent and multiple follower agents, and constructing a corresponding directed communication topology graph; constructing neighbor interaction features based on the state information, communication state information, and fault residual information of the follower agents and their neighbor agents; inputting the neighbor interaction features into a graph attention network to obtain neighbor attention weights, and constructing a distributed formation tracking error based on the neighbor attention weights; constructing error filtering variables based on the distributed formation tracking error, and estimating unknown nonlinear terms, actuator fault effects, and external disturbances using a neural network adaptive compensation mechanism; generating a nominal fault-tolerant formation control input based on the error filtering variables and the neural network adaptive compensation result; correcting the nominal fault-tolerant formation control input using a safety constraint function to obtain a final distributed fault-tolerant formation control input; and applying the final distributed fault-tolerant formation control input to the corresponding follower agents to achieve safe fault-tolerant formation control of the multi-agent system.

[0010] A specific implementation of a multi-agent fault-tolerant formation control that integrates graph attention networks and security constraints, wherein the control architecture is as follows: Figure 1 As shown, the method includes: S1. Establish a multi-agent nonlinear dynamics model that includes a leader agent and multiple follower agents, and construct a leader-follower directed communication topology.

[0011] The multi-agent nonlinear dynamics model and directed communication topology graph construction aim to provide a foundation for system dynamic description and information interaction for subsequent neighbor information weighting, distributed formation tracking error construction, neural network adaptive compensation, and safety constraint correction. By establishing a leader-follower formation structure, the position, velocity, control input, unknown nonlinear dynamics, actuator faults, and external disturbances of each following agent are clearly defined. Simultaneously, the directed communication topology graph describes the information transmission relationships between agents, enabling each following agent to complete distributed control computations relying solely on its own and neighbor information.

[0012] In this embodiment, the specific implementation process of the multi-agent nonlinear dynamics model and the directed communication topology graph is as follows: Step 1: Set up a multi-agent formation system. Select one lead agent and N follower agents to form a lead-follow multi-agent system, where the lead agent is numbered 0, and the follower agents are numbered 1, 2, ..., N. The lead agent provides a reference trajectory, and the follower agents perform formation tracking control based on their own state, neighbor states, and desired formation offset.

[0013] For the i There are a following agent, whose position vector is denoted as . The velocity vector is The state vector is:

[0014] in, n This represents the spatial dimension of the agent's movement.

[0015] The state of the leading intelligent agent is recorded as p 0 v 0 Its trajectory can be given by a preset path planning module, a manual instruction module, or a higher-level task planning module. The control objective of the following agent is: under the conditions of unknown nonlinearity, actuator failure, and external disturbances, to ensure that each following agent satisfies: in, d i0 For the first i The expected relative displacement of the following agent relative to the leading agent.

[0016] Step two: Establish a nonlinear dynamic model for the following agent. For the first... i A following agent is described by a second-order nonlinear dynamics model: , in, f i (x i ) For unknown nonlinear dynamic terms; B i To control the input matrix; u i For the first i A follower agent's control input; This is the actuator efficiency factor; ϕ i For actuator bias fault items; d i This represents the external disturbance term.

[0017] During the actual calculation process of the controller, the first i Each following agent collects its own position in each control cycle. p i ,speed v i Control input u i The system also collects neighbor broadcast status information, which is then used as input data for subsequent neighbor attention weight calculation and neural network adaptive compensation.

[0018] Step 3: Establish an actuator failure model. Actuator efficiency factor. The expression used to characterize the decrease in actuator output capability is: in, m The number of actuator channels, 0 < l ik ≤1. When l ik When =1, it means the first... k Each actuator is in normal working condition; when 0 < l ik When <1, it means the first k One actuator has an efficiency loss fault.

[0019] Actuator bias fault items ϕ i This term represents the additional deviation present in the actuator output. This deviation can be a constant deviation, a slowly varying deviation, or a bounded time-varying deviation. External disturbance term. d i This term is used to represent the uncertain impacts caused by environmental factors. For unmanned aerial vehicle (UAV) systems, the external disturbance term can represent wind field disturbances; for mobile robot systems, the external disturbance term can represent changes in ground friction or load.

[0020] Step 4: Construct the directed communication topology graph. The directed communication topology graph of the multi-agent system is defined as follows: G=(V, E, A) in, V ={0, 1, 2, ⋯ , N} represents a set of nodes, where node 0 represents the leading agent, and nodes 1 through 2 represent the following nodes. N Indicates following the intelligent agent; E It is a set of directed edges; A =[ a ij [] is the adjacency matrix. If the... i The following agent can receive the first j The state information of each agent, then aij >0; otherwise a ij =0.

[0021] No. i The set of neighbors of a following agent is represented as: If the first i If a following agent can directly receive the state information of the leading agent, then the leading agent access coefficient is... b i >0; otherwise b i =0. In actual communication, each following agent only stores the most recent broadcast state, communication delay, communication quality, and fault residual of the agents in its own neighbor set, and does not need to obtain the global topology matrix. As shown in Figure 2, the leading agent and multiple following agents form a leading-following directed communication topology. The following agents exchange local state information through directed communication edges and form a preset formation structure according to the desired relative displacement.

[0022] S2. Based on the state information, communication state information and fault residual information of the following agent and its neighboring agents, construct the neighbor interaction features and use a graph attention network to calculate the neighbor attention weights.

[0023] The purpose of constructing neighbor interaction features and calculating neighbor attention weights is to dynamically evaluate the importance of different neighbor agents to the formation control of the currently following agent. Traditional multi-agent formation control methods typically use fixed adjacency weights. When a neighbor agent experiences state anomalies, communication anomalies, or actuator failures, abnormal neighbor information may still be continuously introduced into the controller, thereby reducing the stability and robustness of the formation system. Figure 3 As shown, this embodiment introduces a graph attention network to dynamically adjust the neighbor attention weights based on the relative state error of neighbors, communication state information, and fault residual information, thereby enhancing the utilization of key neighbor information and suppressing the impact of abnormal or faulty neighbors on formation control.

[0024] In this embodiment, the specific implementation process of constructing neighbor interaction features and calculating neighbor attention weights is as follows: Step 1: Obtain raw data on neighbor interactions. For the first... i A following agent acquires its own state in each control cycle. and receive neighboring intelligent agents j Status of the most recent broadcast ,in At the same time, records are kept of neighboring intelligent agents. j Corresponding communication latency t ijCommunication link quality q ij The most recent communication time and the expected relative displacement d ij .

[0025] Communication link quality q ij It can be obtained by normalizing the data packet reception rate, signal strength, or communication success rate, satisfying: 0≤ q ij ≤1 in, q ij =1 indicates that the communication link quality is good. q ij =0 indicates that the communication link is unavailable. Communication latency. t ij This indicates the current time and the time of the most recent reception from a neighboring agent. j The time difference between moments in the status information.

[0026] Step two, calculate the relative state error and fault residual. According to the... i A following agent and neighboring agents j Expected relative displacement between d ij Calculate the relative position error and relative velocity error: , In order to determine neighboring intelligent agents j Is there an abnormal state? i A following agent utilizes neighboring agents j Historical broadcast states and prediction models yield neighbor prediction states And calculate the fault residual: in, To be based on neighbor intelligent agents j The previously broadcast state, the predicted state obtained from the motion model, or the state predictor. If r ij If it is smaller, it indicates that the neighboring intelligent agent j The current broadcast state is highly consistent with the predicted state; if r ij A significant increase indicates that the neighboring intelligent agent... j There may be actuator failure, sensor malfunction, communication failure, or sudden motion.

[0027] Step 3: Form the neighbor interaction feature vector. Concatenate the relative position error, relative velocity error, expected relative displacement, communication delay, communication link quality, and fault residual to obtain the neighbor interaction features: in, g ij It includes both formation geometry and communication and abnormal state information. This neighbor interaction feature serves as the edge feature input to the graph attention network, used to describe the... i A following agent and neighboring agents j The degree of credibility of the information and the degree of control between them.

[0028] At the same time, construct the first i Node characteristics of a following agent z i : in, e i For distributed formation tracking error, s i This is the error filtering variable. For the initial time, e i and s i It can be calculated based on the initial neighbor state and the initial expected formation offset.

[0029] Step 4: Calculate the basic neighbor attention weights. This involves incorporating the features of the currently following agent node. z i Neighboring intelligent agent node characteristics z j and neighbor interaction features g ij Input a graph attention network and calculate the unnormalized attention score: in, W The node feature mapping matrix, W ζ The neighbor interaction feature mapping matrix, a For attention parameter vectors, This indicates a vector concatenation operation.

[0030] For the i The attention scores of all neighbors of each following agent are normalized to obtain the basic neighbor attention weights:

[0031] The basic neighbor attention weight reflects the neighbor agent's attention weight. jThe relative importance of a neighbor in the current local topology. If the relative error between a neighbor and the current agent is large, or if the neighbor has a stronger information association with the leading agent, then the attention weight of its basic neighbors will be increased accordingly.

[0032] Step 5: Generate fault-aware neighbor attention weights. To further suppress anomalous neighbor information, a neighbor credibility factor is constructed based on fault residuals and communication states: in, β 1. β 2 and β All three are positive parameters, used to adjust the impact of fault residual, communication delay, and communication link quality on neighbor trustworthiness, respectively.

[0033] Based on the neighbor credibility factor, the basic neighbor attention weights are adjusted to obtain the fault-aware neighbor attention weights: When the neighboring intelligent agent j Fault residual r ij Increased communication latency t ij Increase or improve communication link quality q ij When it decreases, the neighbor credibility factor m ij Decrease This leads to a reduction. As a result, the current following agent can automatically reduce the impact of abnormal neighbors, faulty neighbors, or unreliable neighbors during formation control.

[0034] S3. Construct a distributed formation tracking error based on neighbor attention weights, and use a neural network adaptive compensation mechanism to generate a nominal fault-tolerant formation control input.

[0035] The purpose of constructing distributed formation tracking errors and adaptive compensation using neural networks is to achieve online estimation and compensation for unknown nonlinear dynamics, actuator failures, and external disturbances, relying only on local neighbor information. For example, by introducing fault-aware neighbor attention weights into the distributed formation tracking error construction process, the current following agent can pay more attention to key neighbor information and reduce the impact of abnormal neighbor information on error calculation. By approximating the integrated unknowns using neural networks, the controller's adaptability to model uncertainties, actuator failures, and external disturbances can be improved. The overall process of the neural network fault-tolerant formation control method is as follows: Figure 4 As shown.

[0036] In this embodiment, the specific implementation process of constructing the distributed formation tracking error and generating the nominal fault-tolerant formation control input is as follows: Step 1: Construct distributed formation tracking error. i Each following agent constructs a distributed formation tracking error based on the fault-aware neighbor attention weights, neighbor states, and the leader agent's state: in, For fault-aware neighbor attention weights, p 0 represents the position of the leading intelligent agent. d i0 Let be the expected relative displacement of the i-th following agent relative to the leading agent. b i This is the navigation information access coefficient.

[0037] When the i When a following agent cannot directly receive the status information of the leading agent... b i =0, at this time the following agent indirectly obtains navigation information through neighboring agents; when the first =0, the following agent obtains navigation information indirectly ... i When a following agent can directly receive the status information of the leading agent. b i >0, the navigation tracking error term is introduced into the distributed formation tracking error.

[0038] Step 2: Construct error filtering variables. Based on the neighbor velocity information and the leader agent's velocity information, construct a distributed velocity error: in, v 0 represents the speed of the leading agent. Further construct the error filter variables: in, c i Positive design parameters. Error filtering variables. s i It is used to simultaneously reflect position formation deviation and speed synchronization deviation. When s i As it gradually decreases, it indicates the first... i The formation error and velocity error of each following agent tend to decrease.

[0039] Step 3: Establish a neural network approximation model for the comprehensive unknowns. Due to the presence of unknown nonlinear dynamics, actuator efficiency loss faults, actuator bias faults, and external disturbances in the following agent, the comprehensive unknowns are defined as follows: in, X i This is the input vector for the neural network. In actual implementation, Xi Options include: in, g i The neighbor aggregation information is obtained by weighting the neighbor states with fault-aware neighbor attention weights: A radial basis function neural network is used to approximate the comprehensive unknown term: , in, For the ideal weight matrix, W i This is the weight estimation matrix. H i (X i ) This represents the output vector of the hidden layer in a radial basis function neural network. e i This is the bounded approximation error.

[0040] Step four, update the neural network weights. The output vector of the hidden layer of the radial basis function neural network is represented as: Where L is the number of hidden layer nodes. l The output of each hidden layer node is: in, c l Center of radial basis functions b l denoted as the width of the radial basis functions.

[0041] Based on error filtering variables s i Design an adaptive update law for neural network weights: Among them, Γ i It is a positive definite adaptive gain matrix. s i This is a positive leakage factor. The first term is used to adjust the neural network weights based on real-time formation errors, and the second term is used to suppress the drift of neural network weights during long-term operation, thereby improving system robustness.

[0042] Step 5: Generate the nominal fault-tolerant formation control input. Based on the error filtering variables, neural network estimation results, and reference compensation term, generate the... i Nominal fault-tolerant grouping control input for each following agent:

[0043] in, for B i The generalized inverse matrix, k i Positive control gain, This is an estimate of the comprehensive unknowns. a ri This is a reference compensation term. The reference compensation term can be constructed based on the navigator's acceleration, the expected rate of change of formation offset, and neighbor reference motion information.

[0044] Nominal fault-tolerant formation control input u i0 It consists of an error feedback term, a neural network compensation term, and a reference compensation term. The error feedback term is used to suppress formation errors, the neural network compensation term is used to compensate for unknown nonlinear dynamics, actuator failures, and external disturbances, and the reference compensation term is used to improve the tracking capability of the navigator's reference trajectory.

[0045] S4. Construct a safety constraint function to correct the nominal fault-tolerant formation control input, and obtain the final distributed fault-tolerant formation control input.

[0046] The purpose of safety constraint functions and control input correction is to ensure that the multi-agent system meets the constraints of safe distance between agents, formation error boundary constraints, and control input amplitude constraints while guaranteeing formation tracking performance and fault tolerance compensation capabilities. The nominal fault-tolerant formation control input is mainly used to improve error convergence performance and fault compensation capabilities; however, when the distance between agents is too close, the formation error is close to the boundary, or the control input is close to saturation, it may still lead to collision risks, error exceeding limits, or actuator overruns. Therefore, this embodiment introduces a safety constraint correction mechanism to make minimal corrections to the nominal fault-tolerant formation control input while keeping it as unchanged as possible, so that the final distributed fault-tolerant formation control input meets the requirements for safe operation.

[0047] In this embodiment, the specific implementation process for generating the security constraint function and the final distributed fault-tolerant formation control input is as follows: Step 1: Establish safe distance constraints between agents. For the first... i A following agent and its neighboring agents j Define the safe distance function between agents:

[0048] in, d safed This is a preset minimum safe distance. When h ij When ≥0, it means the first... iA following agent and neighboring agents j The distance between them shall not be less than the minimum safe distance; when h ij A value less than 0 indicates a risk of collision.

[0049] To ensure that the safety distance constraint is continuously satisfied during system operation, the following constraints are set: in, c ij This is a positive parameter. This constraint is used to limit the relative motion tendency of two agents when approaching the safety boundary, preventing them from continuing towards a collision.

[0050] Step 2: Establish formation error boundary constraints and control input amplitude constraints. Define the formation error boundary function: in, r i For the first i The maximum allowed formation error boundary for a following agent. When h ei A value ≥ 0 indicates that the distributed formation tracking error is within the allowable range. To prevent formation errors from exceeding the limit, the following constraints are set:

[0051] in, c ei It is a positive parameter.

[0052] Simultaneously, control input amplitude constraints are set based on the physical capabilities of the agent's actuators: in, u min To control the lower limit of input, u max This constraint controls the upper limit of the input. It is used to prevent the control input from exceeding the actuator's executable range.

[0053] Step 3: Construct a safety-constrained optimization problem. The nominal fault-tolerant group control input... u i0 Using the desired control input as the constraints, the safety distance constraints between agents, the formation error boundary constraints, and the control input amplitude constraints, a safety-constrained optimization problem is established: , , , in, u i The final distributed fault-tolerant formation control input is defined as the optimization problem that minimizes the deviation between the final control input and the nominal fault-tolerant formation control input while satisfying safety constraints, thereby preserving the original formation tracking performance as much as possible.

[0054] Step four: Solve online and apply the final distributed fault-tolerant array control input. i Each following agent, within each control cycle, solves a safety-constrained optimization problem online based on its current state, neighbor states, distributed formation tracking error, fault-aware neighbor attention weights, and nominal fault-tolerant formation control input, to obtain the final distributed fault-tolerant formation control input. u i and will u i It acts on the corresponding actuator.

[0055] When the distance between agents is far from the safety boundary, the formation error is not close to the allowable boundary, and the control input is not close to saturation, the solution to the safety-constrained optimization problem satisfies: When the distance between intelligent agents approaches the minimum safe distance, the formation error approaches the allowable boundary, or the control input approaches the amplitude limit, the safety constraint correction mechanism automatically adjusts the control input so that the final control input meets the requirements for safe operation.

[0056] Step 5: Verify the boundedness and safety of the closed-loop system. To demonstrate the stability of the closed-loop system, construct the following Lyapunov function: in, The error is the estimation error of the neural network weights. Substituting the adaptive update law of the neural network weights and the nominal fault-tolerant formation control input into the error system, we get: in, This is a bounded term caused by neural network approximation error, upper bound of external disturbances, and safety constraint correction terms. By selecting an appropriate control gain... k i Adaptive gain matrix Γi and leakage factor you This can guarantee the error filtering variables s i Distributed formation tracking error e i and neural network weight estimation error Consistency is ultimately bounded.

[0057] Meanwhile, as can be seen from the safety constraint optimization problem, the final distributed fault-tolerant array control input is... u i This invention satisfies the constraints of safe distance between agents, formation error boundary constraints, and control input amplitude constraints. Therefore, it can achieve safe and fault-tolerant formation control of multi-agent systems under conditions of neighbor anomalies, actuator efficiency loss faults, actuator bias faults, unknown nonlinear dynamics, and external disturbances.

[0058] Those skilled in the art will understand that all or part of the steps in the various methods of the above embodiments can be implemented by a program instructing related hardware. The program can be stored in a computer-readable storage medium, which may include ROM, RAM, disk, or optical disk, etc.

[0059] The above-described embodiments further illustrate the purpose, technical solution, and advantages of the present invention. It should be understood that the above-described embodiments are merely preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made to the present invention within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A multi-agent fault-tolerant grouping control method integrating graph attention networks and safety constraints, characterized in that, include: Establish a multi-agent nonlinear dynamics model that includes a lead agent and multiple follower agents, and construct the corresponding directed communication topology graph; Based on the state information, communication state information, and fault residual information of the following agent and its neighboring agents, a neighbor interaction feature is constructed; the neighbor interaction feature is input into a graph attention network to obtain the neighbor attention weights, and a distributed formation tracking error is constructed based on the neighbor attention weights; an error filtering variable is constructed based on the distributed formation tracking error, and an adaptive compensation mechanism of a neural network is used to estimate unknown nonlinear terms, actuator fault effects, and external disturbances. A nominal fault-tolerant formation control input is generated based on the error filtering variables and the adaptive compensation results of the neural network; the nominal fault-tolerant formation control input is corrected using a safety constraint function to obtain the final distributed fault-tolerant formation control input; the final distributed fault-tolerant formation control input is applied to the corresponding following agent to realize the safe fault-tolerant formation control of the multi-agent system.

2. The multi-agent fault-tolerant formation control method according to claim 1, characterized in that, The multi-agent nonlinear dynamics model includes the agent's position state, velocity state, unknown nonlinear dynamic term, actuator efficiency loss fault term, actuator bias fault term, and external disturbance term; wherein, the actuator efficiency loss fault term is used to characterize the decrease in actuator output capability, and the actuator bias fault term is used to characterize the additional deviation in the actuator output.

3. The multi-agent fault-tolerant formation control method according to claim 2, characterized in that, The multi-agent nonlinear dynamics model is expressed as follows: ； ； in, p i For the first i The location of each agent. v i For speed, For state vectors, For unknown nonlinear dynamic terms, B i To control the input matrix, u i To control the input, For actuator efficiency factor, For actuator bias fault items, d i This represents the external disturbance term.

4. The multi-agent fault-tolerant formation control method according to claim 1, characterized in that, The neighbor interaction features include the relative position error, relative velocity error, expected formation spacing, communication status information, and fault residual information between the current following agent and the neighboring agents. The fault residual information is obtained from the deviation between the broadcast state and the predicted state of the neighboring agent, and is used to characterize the degree of abnormality of the neighboring agent.

5. The multi-agent fault-tolerant formation control method according to claim 4, characterized in that, The graph attention network calculates neighbor attention weights based on the neighbor interaction features. When the fault residual information of a neighbor agent increases, the degree of communication abnormality increases, or the relative state deviation increases abnormally, the neighbor attention weight corresponding to that neighbor agent is reduced to reduce the impact of abnormal or faulty neighbors on the formation tracking error.

6. The multi-agent fault-tolerant formation control method according to claim 5, characterized in that, The distributed formation tracking error is constructed from the neighbor attention weights, the neighbor relative position errors, and the tracking error of the leading agent, and is expressed as follows: ； in, e i For the first i Distributed formation tracking error of individual following agents N i Gather for his neighbors, α ij Neighbor attention weight, p 0 Position of the leading intelligent agent, d ij To follow the desired relative displacement between agents, d i0 To determine the expected relative displacement of the following agent relative to the lead agent. b i This is the navigation information access coefficient.

7. The multi-agent fault-tolerant formation control method according to claim 6, characterized in that, The neural network adaptive compensation mechanism uses a radial basis function neural network to estimate unknown nonlinear terms, actuator fault effects, and external disturbances online, and updates the neural network weights based on the error filtering variables constructed from the distributed formation tracking error. The nominal fault-tolerant formation control inputs include an error feedback term, a neural network compensation term, and a reference acceleration term.

8. The multi-agent fault-tolerant formation control method according to claim 7, characterized in that, The security constraint function includes inter-agent safety distance constraints, formation error boundary constraints, and control input amplitude constraints; the nominal fault-tolerant formation control input is corrected using the security constraint function to obtain the final distributed fault-tolerant formation control input. in, u i0 Input for nominally fault-tolerant formation control. u i This serves as the final distributed fault-tolerant formation control input. The final distributed fault-tolerant formation control input satisfies the safety distance between agents, formation error boundaries, and control input amplitude limits, enabling the multi-agent system to achieve safe fault-tolerant formation control under conditions of neighbor anomalies, actuator efficiency losses, actuator bias faults, and external disturbances.

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