Distributed average tracking control method and system based on adaptive neural network

Abstract

The application discloses a kind of distributed average tracking control method and system based on adaptive neural network, comprising: first, the network structure topological graph of heterogeneous nonlinear multi-agent system is constructed, wherein each node represents an agent, and the point set, edge set and neighbor information of each node of the graph are obtained;Second, based on the state equation of the system, a reference signal is set for each node;Then, a distributed average tracking method based on adaptive neural network is designed;Finally, adaptive parameters are designed to achieve distributed average tracking of multiple time-varying signals.By combining the radial basis function neural network with the internal model driven external disturbance observer, the application successfully achieves the average tracking of multiple time-varying reference signals under system uncertainty and external disturbance.Therefore, the application has important theoretical and practical value in the field of multi-robot cooperation.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of control and information technology, and particularly relates to a distributed average tracking control method and system based on an adaptive neural network. BACKGROUND

[0002] In recent years, multi-agent systems have attracted extensive attention in practical applications such as autonomous driving, sensor networks, unmanned aerial vehicle formation, and multi-robot cooperation. The core advantage of multi-agent systems lies in achieving global cooperative task objectives such as distributed estimation, cooperative tracking, and consensus control through local information interaction. However, due to the fact that each agent in a multi-agent system can only obtain local information, and the input signals of the system are usually time-varying and uncertain, it is challenging to achieve tracking of the global target. To address this issue, distributed average tracking control methods have gradually become a research hotspot, aiming to enable the state of an agent to track the average value of a set of time-varying input signals through local interaction, thereby achieving overall coordination of the system. In terms of applications, distributed average tracking can be used to coordinate flight paths and ensure the stability of the formation in unmanned aerial vehicle formation control; it can achieve dynamic balancing of power at each node in smart grids; and it can effectively achieve information sharing and task allocation, improving overall work efficiency in multi-robot cooperation tasks. These applications demonstrate the importance and wide applicability of distributed average tracking control in practical systems.

[0003] Traditional distributed average tracking methods are mostly based on linear control algorithms, requiring input signals to meet certain constraints such as slow changes or common characteristics. However, these methods show limitations when faced with the complexity and uncertainty of input signals. In addition, in actual multi-agent systems, the physical dynamics of agents often have nonlinear and uncertain characteristics, further increasing the difficulty of distributed average tracking. Therefore, in recent years, adaptive neural network-based control methods have been introduced into multi-agent systems, which can accurately track time-varying signals by online approximation of unknown system dynamics and external disturbances. Compared with traditional linear control methods, adaptive neural network-based control strategies can adapt to a wider range of nonlinear dynamic environments and improve tracking accuracy while ensuring system stability. This method can solve the state tracking problem in dynamic environments for multi-robot collaborative tasks and effectively alleviate the low collaboration efficiency caused by insufficient information sharing among robots. Through the introduction of adaptive neural networks, each robot can adjust its behavior in real time in complex environments to achieve accurate tracking of dynamic targets, significantly improving the collaboration ability and overall performance of the multi-robot system. In addition, this control strategy can significantly improve overall efficiency and response speed in task allocation and collaborative execution of multi-robot systems. Therefore, it is of great application value and practical significance to study a distributed average tracking control method based on adaptive neural networks. SUMMARY

[0004] The present application is directed to the defects of the prior art, and provides a distributed average tracking control method and system based on adaptive neural networks.

[0005] In order to achieve the above invention purposes, the technical solutions adopted by the present application are as follows:

[0006] A distributed average tracking control method based on adaptive neural networks, comprising the following steps:

[0007] S101, constructing a network structure topology of a heterogeneous nonlinear multi-agent system, wherein each node represents an agent, and obtaining the point set, edge set and adjacency information of each node of the graph to facilitate information interaction in the network;

[0008] S102, setting a reference signal for each node based on the state equation of the multi-agent system, the state equation including dynamic description of the position and velocity of each agent;

[0009] S103, designing a distributed average tracking control strategy based on adaptive neural networks for each agent, using the strategy to process the control input of the agent and track time-varying signals;

[0010] S104, design an adaptive parameter to obtain an adaptive control strategy, and perform distributed average tracking on multiple time-varying signals through the adaptive control strategy to ensure that the tracking errors of all intelligent agents converge to a predetermined range.

[0011] Further, the step S101 specifically comprises:

[0012] Using an undirected connected graph A multi-agent system composed of n intelligent agents is described. denotes a set of N nodes, denotes a set of edges, where denotes a graph, which is used to describe the communication topology of the multi-agent system. denotes a set of nodes, each of which represents an intelligent agent. ε denotes a set of edges, which defines the connection relationship between nodes. N denotes the total number of nodes. i and j denote the index or identifier of the node.

[0013] Further, the step S102 specifically comprises:

[0014] The motion of the intelligent agent is described by the following double-integrator dynamics state equation:

[0015]

[0016]

[0017] where x i (t) denotes the position (state) vector of the i-th intelligent agent at time t.

[0018] denotes the time derivative of the position of the i-th intelligent agent, i.e. its velocity.

[0019] v i (t) denotes the velocity vector of the i-th intelligent agent at time t.

[0020] denotes the time derivative of the velocity of the i-th intelligent agent, i.e. its acceleration.

[0021] f i (x i (t),v i (t)) denotes an unknown nonlinear vector-valued function that describes the dynamics of the i-th intelligent agent.

[0022] d i (t) denotes external disturbance or disturbance.

[0023] u i (t) denotes the control input of the i-th intelligent agent at time t.

[0024] represents i is an element of the set of nodes .

[0025] The dynamics of the reference signal are represented by:

[0026]

[0027] where represent the reference position, velocity and acceleration, respectively. represents the time derivative of the reference position of the i-th agent. represents the time derivative of the reference velocity of the i-th agent.

[0028] Further, the step S103 specifically comprises the following steps:

[0029] The average reference estimator is designed to obtain the average reference signal, specifically including designing an estimation filter, which is designed as follows:

[0030]

[0031] where, ξ i represents the state estimate of the i-th agent, which is considered as the estimated position of the agent reference signal, used to track the position of the reference signal, and is constantly updated by the filter.

[0032] represents the time derivative of ζ i , i.e. the rate of change of the estimated position, which is understood as the estimated velocity.

[0033] ζ i represents the rate of change of the state estimate of the i-th agent, which is used to estimate the reference velocity, reflecting the rate of change of the agent position estimate, and is constantly updated by the filter.

[0034] represents the time derivative of ζ i , i.e. the rate of change of the estimated velocity, which is understood as the estimated acceleration.

[0035] k is a gain parameter used to adjust the response speed and stability of the system.

[0036] represents the reference position of the i-th agent at time t.

[0037] represents the reference velocity of the i-th agent at time t.

[0038] β is another gain parameter used to adjust the strength of interaction with adjacent agents.

[0039] denotes the neighborhood set of the i-th agent, i.e., the set of other agents that are directly connected to the i-th agent.

[0040] ψ i and ψ j denotes the norm of the reference signal of the i-th and j-th agent, which is a combination of the reference position, velocity and acceleration,

[0041] h is a heterogeneous non-linear function.

[0042] denotes the reference acceleration of the i-th agent, which is used to provide desired acceleration information in the dynamic model.

[0043] Further, the heterogeneous non-linear function h is defined as follows:

[0044]

[0045] where ε and are specified as positive constants, which is an exponential decay function, and ω is a vector used to describe the state or control policy of the agent.

[0046] Further, the specific settings of the step S104 of implementing distributed average tracking of multiple time-varying signals by the adaptive parameter include:

[0047] The setting of the control input u i :

[0048]

[0049] where η is a gain parameter that controls the degree of influence of the control error on the control input.

[0050] denotes the error between the actual position of the i-th agent and its estimated position, i.e., denotes the error between the actual velocity of the i-th agent and its estimated velocity, i.e., denotes the rate of change of the estimated velocity of the i-th agent, i.e., the estimated change of the reference velocity.

[0051] denotes the estimate of the unknown non-linear dynamic function f i (x i ,v i ).

[0052] denotes the estimate of the external disturbance d iestimation of the disturbance. This part is used to compensate the influence of external disturbance on the motion of agents.

[0053] Further, the step S104 further includes:

[0054] A control algorithm is designed to ensure that all signals in the closed-loop system are bounded while the distributed average tracking error converges to a neighborhood of the origin.

[0055] where e xi represents the position tracking error of the i-th agent.

[0056] x i (t) represents the actual position of the i-th agent at time t.

[0057] represents the reference position of the j-th agent at time t. The reference position is the position that the system expects the agent to reach.

[0058] n represents the total number of agents.

[0059] e vi represents the velocity tracking error of the i-th agent.

[0060] v i (t) represents the actual velocity of the i-th agent at time t.

[0061] represents the reference velocity of the j-th agent at time t.

[0062] The present application also discloses a distributed average tracking control system, which can be used to implement the above-mentioned distributed average tracking control method, specifically comprising:

[0063] Network topology construction module: responsible for constructing and maintaining the network structure of the multi-agent system, including the definition of nodes (agents) and edges (communication connections).

[0064] State equation setting module: according to the dynamic characteristics of the multi-agent system, define the position and velocity state equations of each agent, and set the corresponding reference signal.

[0065] Adaptive neural network control module: design and implement a control strategy based on adaptive neural network, which is used to process the control input of each agent and realize the tracking of time-varying signals.

[0066] Parameter adaptive module: design and optimize adaptive parameters to adapt to different time-varying signals, ensure the effectiveness and stability of the distributed average tracking.

[0067] Information exchange module: enables information exchange and data sharing among agents, supporting real-time communication between adjacent nodes.

[0068] Error evaluation module: calculates and evaluates the tracking error of each agent, monitors system performance, and provides feedback for control strategy adjustment.

[0069] Control input calculation module: calculates the control input of each agent according to the designed control strategy and parameters to achieve tracking of the target reference signal.

[0070] System monitoring and feedback module: real-time monitoring of system state, including the position, speed and error of the agent, and providing feedback to optimize the control effect.

[0071] Simulation and test module: used to verify and test the effectiveness of the control strategy, and evaluate the performance of the system under various conditions through simulation experiments.

[0072] User interface module: provides a friendly user interface for users to set parameters, start / stop the system, and view system status and performance indicators.

[0073] The application also discloses a computer device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to realize the above-mentioned distributed average tracking control method.

[0074] The application also discloses a computer readable storage medium having a computer program stored thereon, wherein the program is executed by a processor to realize the above-mentioned distributed average tracking control method.

[0075] Compared with the prior art, the application has the following advantages:

[0076] 1. Online approximation capability: through adaptive neural networks, the unknown system dynamics and external disturbances are approximated online, effectively addressing distributed average tracking problems in nonlinear and uncertain environments.

[0077] 2. Precise tracking capability: combined with local information exchange, the multi-agent system can accurately track the average value of time-varying input signals, improving the tracking accuracy of the system.

[0078] 3. Nonlinear processing: the application fully considers the nonlinear dynamics and complex external disturbances of the multi-agent system, optimizes the control strategy, and compared with traditional linear control algorithms, can significantly improve the tracking accuracy while ensuring system stability.

[0079] 4. Enhanced adaptability: adding a disturbance observer to compensate for external disturbances enhances the system's adaptability to uncertainties in complex environments.

[0080] 5. Synergistic task optimization: can be applied to solve the state tracking problem in the dynamic environment of multi-robot synergistic task, effectively alleviate the low efficiency caused by insufficient information sharing between robots, so as to improve the performance and efficiency of multi-agent system in practical application. BRIEF DESCRIPTION OF DRAWINGS

[0081] Figure 1 is a flowchart of the distributed average tracking control method of the embodiment of the present application

[0082] Figure 2 is a network topology diagram of the distributed average tracking control method of the embodiment of the present application;

[0083] Figure 3 is a position tracking error diagram of the tracking agent system of the embodiment of the present application;

[0084] Figure 4 is a speed tracking error diagram of the tracking agent system of the embodiment of the present application;

[0085] Figure 5 is a trajectory evolution diagram of the agent system of the embodiment of the present application. DETAILED DESCRIPTION

[0086] In order to make the purpose, technical scheme and advantages of the present application clearer and more apparent, the following will further describe the present application in detail according to the drawings and examples.

[0087] As shown in Figure 1 , a distributed average tracking control method based on an adaptive neural network comprises the following steps:

[0088] S101, construct a network structure topology of a heterogeneous nonlinear multi-agent system, each node represents an agent, obtain the point set, edge set and neighbor information of each node of the graph;

[0089] The step S101 specifically comprises:

[0090] For a multi-agent system composed of n agents, its communication topology can be described by an undirected connected graph , wherein, N represents a set of N nodes, ε represents a set of edges, the adjacency set N of node i in the graph i contains all nodes j satisfying (i,j)∈ε and i≠j. The adjacency matrix A[a ij ] represents a set of N×N real number matrices, a ijis an element of the adjacency matrix; in the adjacency matrix, if there is an edge between nodes i, j, then a ij = a ij = 1, otherwise a ij = 0.

[0091] In this example, a system with 8 agents is used, and the network topology is as shown in Figure 2 .

[0092] S102, given the state equation of the system, set the reference signal of each node;

[0093] The step S102 specifically includes:

[0094] Consider a multi-agent system containing n agents, which interact on an undirected graph, where the agent is described by the following double integrator dynamics state equation:

[0095]

[0096] x i (t),v i (t) respectively represent the position and velocity of the agent, and the control input is represented as u i (t). In addition, f i represents an unknown nonlinear vector-valued function, and the external disturbance is represented by d i .

[0097] The dynamics of the reference signal are represented by the following:

[0098]

[0099]

[0100] Where represent the reference position, velocity and acceleration respectively.

[0101] In this example, the nonlinearity is represented by f i (x i ,v i ) = v i sinx i , and the dynamics equation of the reference object is given by:

[0102]

[0103] S103, design a distributed average tracking method based on adaptive neural network for each node;

[0104] The step S103 specifically includes the following steps:

[0105] (1) Since each agent can only access its own reference signal, an averaged reference estimator was designed to obtain the averaged reference signal. An estimation filter was designed for each agent to effectively retrieve the averaged time-varying reference signal, ensuring accurate and reliable performance. The filter design is as follows:

[0106]

[0107] in k, β are the gains that will be determined later, ξ i , ζ i This is the output of the filter. Furthermore, the heterogeneous nonlinear function is defined as follows:

[0108]

[0109] Where ε and It is specified as a positive number.

[0110] (2) Control input u i The settings are as follows:

[0111]

[0112] in And η is specified as a positive constant. and They represent f respectively i (x i ,v i ) and d i The estimated value.

[0113] In this example, k = 1, β = 5, and η = 10.

[0114] S104. Design adaptive parameters to achieve distributed averaging tracking of multiple time-varying signals.

[0115] Step S104 specifically includes:

[0116] Consider a multi-agent system with a given system state. Design a control algorithm that ensures all signals in the closed-loop system are bounded, while simultaneously averaging the tracking error using a distributed method. It converges to the neighborhood of the origin.

[0117] like Figure 2 As shown, the network topology of the multi-agent system consists of eight agents, with solid lines representing communication links for information exchange between agents.

[0118] Figure 3 and Figure 4 This is a diagram showing the position and velocity tracking error of the experimental intelligent agent system of this invention.Figure 5 The trajectory evolution graph of the intelligent agent system shows that the positions and velocities of the intelligent agents converge to the average value of all time-varying reference signals, and the control target is achieved by applying the designed distributed weighted average tracking control algorithm.

[0119] In another embodiment of the present application, a distributed average tracking control system is provided, which can be used to implement the distributed average tracking control method described above. Specifically, it includes:

[0120] Network topology construction module: responsible for constructing and maintaining the network structure of the multi-agent system, including the definition of nodes (agents) and edges (communication connections).

[0121] State equation setting module: according to the dynamic characteristics of the multi-agent system, define the position and velocity state equation of each agent, and set the corresponding reference signal.

[0122] Adaptive neural network control module: design and implement the control strategy based on adaptive neural network, which is used to process the control input of each agent and realize the tracking of time-varying signal.

[0123] Parameter adaptive module: design and optimize adaptive parameters to adapt to different time-varying signals, ensure the effectiveness and stability of distributed average tracking.

[0124] Information exchange module: realize the information exchange and data sharing between agents, support real-time communication between adjacent nodes.

[0125] Error evaluation module: calculate and evaluate the tracking error of each agent, monitor the system performance, and provide feedback for the adjustment of control strategy.

[0126] Control input calculation module: according to the designed control strategy and parameters, calculate the control input of each agent to realize the tracking of target reference signal.

[0127] System monitoring and feedback module: real-time monitoring of system state, including the position, velocity and error of agent, and providing feedback to optimize the control effect.

[0128] Simulation and test module: used to verify and test the effectiveness of the control strategy, and evaluate the performance of the system under various conditions through simulation experiment.

[0129] User interface module: provide a friendly user interface, which is convenient for users to set parameters, start / stop the system, and view system status and performance indicators.

[0130] In still another embodiment of the present application, a terminal device is provided, which comprises a processor and a memory, the memory is configured to store a computer program, the computer program comprises program instructions, and the processor is configured to execute the program instructions stored in the computer storage medium. The processor can be a central processing unit (CPU), and can also be other general-purpose processors, digital signal processors (DSP), application specific integrated circuits (ASIC), field-programmable gate arrays (FPGA) or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc., which are the computing core and control core of the terminal, and are suitable for implementing one or more instructions, and are particularly suitable for loading and executing one or more instructions to implement a corresponding method flow or a corresponding function; the processor in the embodiments of the present application can be used for the operation of the distributed average tracking control method, comprising the following steps:

[0131] S101, constructing a network structure topology of a heterogeneous nonlinear multi-agent system, wherein each node represents an agent, and obtaining a point set, an edge set and adjacency information of each node of the graph, so as to facilitate information interaction in the network;

[0132] S102, setting a reference signal for each node based on a state equation of the multi-agent system, the state equation comprising a dynamic description of the position and velocity of each agent;

[0133] S103, designing a distributed average tracking control strategy based on an adaptive neural network for each agent, using the strategy to process the control input of the agent and track the time-varying signal;

[0134] S104, designing an adaptive parameter, using the parameter to perform distributed average tracking on multiple time-varying signals, and ensuring that the tracking error of all agents converges to a predetermined range.

[0135] In another embodiment of the present application, a storage medium, specifically a computer readable storage medium (Memory) is provided, which is a memory device in the terminal equipment, used for storing programs and data. It can be understood that the computer readable storage medium herein can include the built-in storage medium in the terminal equipment, and of course can also include the expansion storage medium supported by the terminal equipment. The computer readable storage medium provides a storage space, which stores the operating system of the terminal. Moreover, one or more instructions suitable for being loaded and executed by the processor are also stored in the storage space, and the instructions can be one or more computer programs (including program codes). It should be noted that the computer readable storage medium herein can be a high-speed RAM memory, or a non-volatile memory such as at least one disk memory.

[0136] The one or more instructions stored in the computer readable storage medium can be loaded and executed by the processor to implement the corresponding steps of the distributed average tracking control method in the above embodiments; the one or more instructions in the computer readable storage medium are loaded and executed by the processor to perform the following steps:

[0137] S101, constructing a network structure topology of a heterogeneous nonlinear multi-agent system, wherein each node represents an agent, and obtaining a point set, an edge set and adjacency information of each node of the graph, so as to facilitate information interaction in the network;

[0138] S102, setting a reference signal of each node based on a state equation of the multi-agent system, wherein the state equation includes a dynamic description of the position and velocity of each agent;

[0139] S103, designing a distributed average tracking control strategy based on an adaptive neural network for each agent, using the strategy to process the control input of the agent, and tracking a time-varying signal;

[0140] S104, designing an adaptive parameter, using the parameter to perform distributed average tracking on multiple time-varying signals, and ensuring that the tracking error of all agents converges to a predetermined range.

[0141] Those skilled in the art should understand that the embodiments of the present application can be provided as a method, a system, or a computer program product. Therefore, the present application can take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware aspects. Moreover, the present application can take the form of a computer program product implemented on one or more computer usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer usable program code.

[0142] The embodiments of the present application are described with reference to the flowchart illustrations and / or block diagrams of the methods, apparatus (systems) and computer program products according to embodiments of the present application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart illustrations and / or block diagrams block or blocks. Figure 1 one or more functions specified in the flowchart illustrations and / or block diagrams block or blocks. Figure 1 one or more functions specified in the flowchart illustrations and / or block diagrams block or blocks.

[0143] These computer program instructions can also be stored in a computer- readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instructions which implement the function specified in the flowchart illustrations and / or block diagrams block or blocks. Figure 1 one or more functions specified in the flowchart illustrations and / or block diagrams block or blocks. Figure 1 one or more functions specified in the flowchart illustrations and / or block diagrams block or blocks.

[0144] These computer program instructions can also be loaded into a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart illustrations and / or block diagrams block or blocks. Figure 1 one or more functions specified in the flowchart illustrations and / or block diagrams block or blocks. Figure 1 one or more functions specified in the flowchart illustrations and / or block diagrams block or blocks.

[0145] Those skilled in the art will realize that the embodiments described herein are for illustrative purposes only and that various modifications and combinations of elements can be made without departing from the scope of the present application. Accordingly, other embodiments are within the scope of the present application.

Claims

1. A distributed average tracking control method based on an adaptive neural network, characterized in that, Includes the following steps: S101. Construct a network structure topology graph of a heterogeneous nonlinear multi-agent system, wherein each node represents an agent, and obtain the point set, edge set and adjacency information of each node in the graph to facilitate information interaction in the network. S102. Based on the state equation of the multi-agent system, set the reference signal for each node. The state equation includes a dynamic description of the position and velocity of each agent. S103. Design a distributed average tracking control strategy based on an adaptive neural network for each agent, and use this strategy to process the control input of the agent and track time-varying signals. Specifically, this includes the following steps: Design an average reference estimator to obtain an averaged reference signal, specifically including designing an estimation filter, the design of which is as follows: ， ， in, This represents the state estimate of the i-th agent, which is regarded as the estimated position of the agent's reference signal and is used to track the position of the reference signal. It is continuously updated through a filter. express The time derivative of the estimated position, i.e., the rate of change of the estimated position, can be understood as an estimated velocity. This represents the rate of change of the state estimate of the i-th agent, used to estimate the reference velocity, reflecting the rate of change of the agent's position estimate, and is continuously updated through a filter; express The time derivative of the velocity is the estimated rate of change of velocity, which can be understood as the estimated acceleration. It is a gain parameter used to adjust the system's response speed and stability; This represents the reference position of the i-th agent at time t; This represents the reference velocity of the i-th agent at time t; It is another gain parameter used to adjust the strength of the interaction with neighboring agents; This represents the neighbor set of the i-th agent, that is, the set of other agents directly connected to the i-th agent; Let represent the norm of the reference signal for the i-th and j-th agents, which is a combination of reference position, velocity, and acceleration. ; It is a heterogeneous nonlinear function; This represents the reference acceleration of the i-th agent, used to provide the desired acceleration information in the dynamic model; S104. Design adaptive parameters to obtain an adaptive control strategy. Use the adaptive control strategy to perform distributed averaging tracking of multiple time-varying signals to ensure that the tracking error of all agents converges to a predetermined range. The specific settings for the adaptive parameters in step S104 to achieve distributed averaging tracking of multiple time-varying signals include: Control input Settings: ， in, It is a gain parameter, representing the degree of influence of control error on control input; This represents the error between the actual position and the estimated position of the i-th agent, i.e. ; This represents the error between the actual velocity and the estimated velocity of the i-th agent, i.e. ; This represents the rate of change of the estimated velocity of the i-th agent, i.e., the estimated change of the reference velocity; Represents an unknown nonlinear dynamic function The estimate; Indicates external interference The estimate; this part is used to compensate for the impact of external disturbances on the agent's motion; Step S104 also includes: Design a control algorithm that ensures all signals in the closed-loop system are bounded, while simultaneously averaging the tracking error using a distributed approach. , It converges to the neighborhood of the origin; in, This represents the position tracking error of the i-th agent; This represents the actual position of the i-th agent at time t; This represents the reference position of the j-th agent at time t; the reference position is the position that the system expects the agent to reach. This represents the total number of intelligent agents; This represents the velocity tracking error of the i-th agent; This represents the actual velocity of the i-th agent at time t; This represents the reference velocity of the j-th agent at time t.

2. The distributed average tracking control method according to claim 1, characterized in that, Step S101 specifically includes: Using an undirected connected graph Description by A multi-agent system consisting of several agents; express A set of nodes, Let represent the set of edges, where A diagram is used to describe the communication topology of a multi-agent system. This represents a set of nodes, where each node represents an agent. This represents a set of edges, defining the connections between nodes; The total number of nodes is represented by ; i and j represent the index or identifier of the node.

3. The distributed average tracking control method according to claim 1, characterized in that, Step S102 specifically includes: The motion of the agent is described by the following dual integrator dynamic state equations: ， ， in, This represents the position vector of the i-th agent at time t; The time derivative of the position of the i-th agent is represented, i.e., its velocity; This represents the velocity vector of the i-th agent at time t; The time derivative of the velocity of the i-th agent, i.e., acceleration; Let represent an unknown nonlinear vector-valued function that describes the dynamic characteristics of the i-th agent; This indicates external interference or disturbance; This represents the control input of the i-th agent at time t; Indicates that i is a set of nodes One of the elements; The dynamics of the reference signal are represented as follows: ， ， in , , , representing the reference position, velocity, and acceleration, respectively; This represents the time derivative of the reference position of the i-th agent; Let represent the time derivative of the reference velocity of the i-th agent.

4. The distributed average tracking control method according to claim 1, characterized in that, The heterogeneous nonlinear function The definition is as follows: ， in and Designated as a positive number, This is an exponentially decaying function. It is a vector used to describe the state or control policy of an agent.

5. A distributed average tracking control system, characterized in that: This system can be used to implement the distributed average tracking control method according to any one of claims 1 to 4, specifically including: Network topology construction module: responsible for building and maintaining the network structure of the multi-agent system, including the definition of nodes and edges; State equation setting module: Based on the dynamic characteristics of the multi-agent system, define the position and velocity state equations for each agent and set the corresponding reference signals; Adaptive Neural Network Control Module: Designs and implements a control strategy based on an adaptive neural network to process the control input of each agent and achieve tracking of time-varying signals; Parameter Adaptive Module: Designs and optimizes adaptive parameters to adapt to different time-varying signals, ensuring the effectiveness and stability of distributed average tracking; Information interaction module: Enables information exchange and data sharing between intelligent agents, and supports real-time communication between neighboring nodes; Error assessment module: Calculates and evaluates the tracking error of each agent, monitors system performance, and provides feedback for adjusting the control strategy; Control input calculation module: Based on the designed control strategy and parameters, calculates the control input for each agent to achieve tracking of the target reference signal; System monitoring and feedback module: Monitors system status in real time, including the position, speed and error of the agent, and provides feedback to optimize control performance; User interface module: Provides a user-friendly interface, making it easy for users to set parameters, start / stop the system, and view system status and performance metrics.

6. A computer device, characterized in that: It includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor, when executing the program, implements the distributed average tracking control method according to any one of claims 1 to 4.

7. A computer-readable storage medium, characterized in that: It stores a computer program that, when executed by a processor, implements the distributed average tracking control method according to any one of claims 1 to 4.

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