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

Abstract

The invention discloses a distributed average tracking control method and system based on an adaptive neural network, and the method comprises the steps: firstly, constructing a network structure topological graph of a heterogeneous nonlinear multi-agent system, each node representing one agent, and obtaining a point set and an edge set of the graph and the neighbor information of each node; secondly, based on a state equation of the system, setting a reference signal for each node; thirdly, designing a distributed average tracking method based on an adaptive neural network; and finally, designing adaptive parameters so as to realize distributed average tracking of a plurality of time-varying signals. By combining a radial basis function neural network and an internal model driven external disturbance observer, the method successfully realizes average tracking of a plurality of time-varying reference signals under the conditions of system uncertainty and external disturbance. Therefore, the method has important theoretical and practical values in the fields of multi-robot collaboration and the like.

Description

Technical Field

[0001] The present invention relates to the field of control and information technology, and in particular to a distributed average tracking control method and system based on an adaptive neural network. Background Art

[0002] In recent years, multi-agent systems have received extensive attention in practical applications such as autonomous driving, sensor networks, drone formations, and multi-robot collaboration. The core advantage of multi-agent systems is that they can achieve global collaborative task goals through local information interaction, such as distributed estimation, collaborative tracking, and consistency control. However, since each agent in a multi-agent system can only obtain local information and the input signal of the system is usually time-varying and uncertain, it is very challenging to track the global goal. In order to address this problem, distributed average tracking control methods have gradually become a hot topic of research, aiming to enable the state of the 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 application, distributed average tracking can be used in drone formation control to coordinate flight paths and ensure the stability of the formation; in smart grids, it can achieve dynamic balancing of the power of each node; in multi-robot collaborative tasks, this method can effectively realize information sharing and task allocation, and improve overall work efficiency. 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, which require the 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 the agents are often nonlinear and uncertain, which further increases the difficulty of distributed average tracking. To this end, in recent years, control methods based on adaptive neural networks have been introduced into multi-agent systems, which achieve accurate tracking of time-varying signals by online approximation of unknown system dynamics and external disturbances. Compared with traditional linear control methods, control strategies based on adaptive neural networks 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 in multi-robot collaborative tasks, and can effectively alleviate the low efficiency of collaboration caused by insufficient information sharing between 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, thereby significantly improving the collaborative ability and overall performance of multi-robot systems. In addition, this control strategy can significantly improve the overall efficiency and response speed in task allocation and collaborative execution in multi-robot systems. Therefore, studying a distributed average tracking control method based on adaptive neural network has important application value and practical significance. Summary of the invention

[0004] In view of the defects of the prior art, the present invention provides a distributed average tracking control method and system based on an adaptive neural network.

[0005] In order to achieve the above invention object, the technical solution adopted by the present invention is as follows:

[0006] A distributed average tracking control method based on an adaptive neural network comprises the following steps:

[0007] S101, constructing a network structure topology graph 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;

[0008] 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;

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

[0010] S104, designing adaptive parameters to obtain an adaptive control strategy, and performing 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] Furthermore, the step S101 specifically includes:

[0012] Using an undirected connected graph Describe a multi-agent system consisting of n agents; represents a set of N nodes, represents a set of edges, where Representation graph used to describe the communication topology of a multi-agent system. represents a set of nodes, each of which represents an agent. ε represents a set of edges, which defines the connection relationship between nodes. N represents the total number of nodes. i and j represent the index or identifier of the node.

[0013] Furthermore, the step S102 specifically includes:

[0014] The following double integrator dynamic state equation is used to describe the motion of the agent:

[0015]

[0016]

[0017] Among them, x i (t) represents the position (state) vector of the ith agent at time t.

[0018] represents the time derivative of the position of the ith agent, that is, its velocity.

[0019] v i (t) represents the velocity vector of the ith agent at time t.

[0020] Represents the time derivative of the velocity of the ith agent, i.e., acceleration.

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

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

[0023] u i (t) represents the control input of the ith agent at time t.

[0024] Indicates that i is a node set An element in .

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

[0026]

[0027] in Represent the reference position, velocity and acceleration respectively. represents the time derivative of the reference position of the ith agent. Represents the time derivative of the reference velocity of the ith agent.

[0028] Furthermore, the step S103 specifically includes the following steps:

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

[0030]

[0031] Among them, ξ i Represents the state estimate of the i-th agent, which is regarded as the estimated position of the agent's reference signal. It is used to track the position of the reference signal and is continuously updated through the filter.

[0032] Indicates i The time derivative of , that is, the rate of change of the estimated position, is understood as the estimated velocity.

[0033] ζ i It represents the rate of change of the state estimate of the ith agent, which is used to estimate the reference speed and reflects the rate of change of the agent's position estimate, which is continuously updated through the filter.

[0034] Indicates i The time derivative of , that is, the rate of change of the estimated velocity, 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 ith agent at time t.

[0037] represents the reference speed of the ith agent at time t.

[0038] β is another gain parameter that adjusts the strength of interactions with neighboring agents.

[0039] represents the neighbor set of the ith agent, that is, the set of other agents directly connected to the ith agent.

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

[0041] h is a heterogeneous nonlinear function.

[0042] Represents the reference acceleration of the ith agent, which is used to provide the expected acceleration information in the dynamic model.

[0043] Furthermore, the heterogeneous nonlinear function h is defined as follows:

[0044]

[0045] where ε and is specified as a positive constant, This is an exponential decay function, and ω is a vector that describes the state or control policy of the agent.

[0046] Furthermore, the specific setting of the adaptive parameters in step S104 to implement distributed average tracking of multiple time-varying signals includes:

[0047] Control input u i Settings:

[0048]

[0049] Among them, η is a gain parameter, which is the degree of influence of the control error on the control input.

[0050] represents the error between the actual position of the ith agent and its estimated position, that is, represents the error between the actual speed of the ith agent and its estimated speed, that is, It represents the rate of change of the estimated speed of the ith agent, that is, the estimated change of the reference speed.

[0051] Represents the unknown nonlinear dynamic function f i (x i ,v i )’s estimate.

[0052] Indicates external interference d iThis part is used to compensate for the impact of external disturbances on the movement of the agent.

[0053] Furthermore, the step S104 also includes:

[0054] Design a control algorithm that ensures that all signals in the closed-loop system are bounded and that the average tracking error is distributed Converges to a neighborhood of the origin.

[0055] Among them, e xi represents the position tracking error of the ith agent.

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

[0057] represents the reference position of the jth 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 ith agent.

[0060] v i (t) represents the actual speed of the ith agent at time t.

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

[0062] The present invention 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 building module: responsible for building 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 signals.

[0065] Adaptive neural network control module: Design and implement control strategies based on adaptive neural networks to process the control input of each intelligent agent and track time-varying signals.

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

[0067] Information interaction module: realizes information exchange and data sharing between intelligent agents, and supports 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 adjustment of control strategies.

[0069] Control input calculation module: According to the designed control strategy and parameters, the control input of each intelligent agent is calculated to achieve tracking of the target reference signal.

[0070] System monitoring and feedback module: monitors the system status in real time, including the position, speed and error of the agent, and provides feedback to optimize the control effect.

[0071] Simulation and testing 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 present invention also discloses a computer device, including a memory, a processor and a computer program stored in the memory and executable on the processor, wherein the processor implements the above-mentioned distributed average tracking control method when executing the program.

[0074] The present invention also discloses a computer-readable storage medium on which a computer program is stored. When the program is executed by a processor, the above-mentioned distributed average tracking control method is implemented.

[0075] Compared with the prior art, the advantages of the present invention are:

[0076] 1. Online approximation capability: Through adaptive neural networks, online approximation of unknown system dynamics and external disturbances can be achieved, which can effectively deal with distributed average tracking problems in nonlinear and uncertain environments.

[0077] 2. Accurate tracking capability: Combined with local information interaction, the multi-agent system can accurately track the average value of the time-varying input signal, improving the tracking accuracy of the system.

[0078] 3. Nonlinear processing: The present invention fully considers the nonlinear dynamics and complex external interference of the multi-agent system and optimizes the control strategy. Compared with the traditional linear control algorithm, it can greatly improve the tracking accuracy while ensuring the stability of the system.

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

[0080] 5. Collaborative task optimization: It can be applied to solve the state tracking problem in dynamic environment in multi-robot collaborative tasks, effectively alleviate the low collaboration efficiency caused by insufficient information sharing between robots, and thus improve the performance and efficiency of multi-agent systems in practical applications. BRIEF DESCRIPTION OF THE DRAWINGS

[0081] Figure 1 Flow chart of the distributed average tracking control method according to an embodiment of the present invention

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

[0083] Figure 3 is a position tracking error graph of a system for tracking an intelligent agent according to an embodiment of the present invention;

[0084] Figure 4 is a velocity tracking error diagram of a tracking agent system according to an embodiment of the present invention;

[0085] Figure 5 This is a trajectory evolution diagram of the intelligent agent system according to an embodiment of the present invention. DETAILED DESCRIPTION

[0086] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below with reference to the accompanying drawings and examples.

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

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

[0089] The step S101 specifically includes:

[0090] For a multi-agent system consisting of n agents, its communication topology can be represented by an undirected connected graph To describe, represents a set of N nodes, Represents a set of edges, node i in the graph The adjacent set N in i ={j|(i,j)∈ε,i≠j} contains all nodes j that satisfy (i,j)∈ε and i≠j. The adjacency matrix A[a ij ] represents the set of N×N dimensional real number matrices, a ijis an element of the adjacency matrix; in the adjacency matrix, if there is an edge connecting nodes i and j, then there is a ij =a ij =1, otherwise there is a ij =0.

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

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

[0093] The step S102 specifically includes:

[0094] Consider a multi-agent system consisting of n agents that exchange information on an undirected graph, where the agents are described by the following double integrator dynamics state equation:

[0095]

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

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

[0098]

[0099]

[0100] in 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 The dynamic equation of the reference object is given by:

[0102]

[0103] S103, designing a distributed average tracking method based on an 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 average reference estimator is designed to obtain the average reference signal. An estimation filter designed for each agent can effectively retrieve the average time-varying reference signal, ensuring accurate and reliable performance. The filter is designed as follows:

[0106]

[0107] in k, β is a gain to be determined later, ξ i , i is the output of the filter. In addition, the heterogeneous nonlinear function is defined as follows:

[0108]

[0109] where ε and is specified as a positive constant.

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

[0111]

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

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

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

[0115] The step S104 specifically includes:

[0116] Consider a multi-agent system with a given system state. Design a control algorithm that ensures that all signals in the closed-loop system are bounded and that the distributed average tracking error Converges to a neighborhood of the origin.

[0117] like Figure 2 As shown, it can be seen that the network topology of the multi-agent system consists of 8 agents, where the solid lines represent the communication links for information exchange between agents.

[0118] Figure 3 and Figure 4 is the position and velocity tracking error diagram of the experimental intelligent agent system of the present invention, Figure 5 It is a trajectory evolution diagram of the intelligent agent system, showing that by applying the distributed weighted average tracking control algorithm designed by the present invention, the position and velocity of each intelligent agent eventually converge to the average value of all time-varying reference signals, thus achieving the control target.

[0119] In yet another embodiment of the present invention, a distributed average tracking control system is provided. The system can be used to implement the above-mentioned distributed average tracking control method, specifically including:

[0120] Network topology building module: responsible for building 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 equations of each agent and set the corresponding reference signals.

[0122] Adaptive neural network control module: Design and implement control strategies based on adaptive neural networks to process the control input of each intelligent agent and track time-varying signals.

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

[0124] Information interaction module: realizes information exchange and data sharing between intelligent agents, and supports real-time communication between adjacent nodes.

[0125] Error Evaluation Module: Calculates and evaluates the tracking error of each agent, monitors system performance, and provides feedback for adjustment of control strategies.

[0126] Control input calculation module: According to the designed control strategy and parameters, the control input of each intelligent agent is calculated to achieve tracking of the target reference signal.

[0127] System monitoring and feedback module: monitors the system status in real time, including the position, speed and error of the agent, and provides feedback to optimize the control effect.

[0128] Simulation and testing 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.

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

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

[0131] S101, constructing a network structure topology graph 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 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;

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

[0134] S104, designing adaptive parameters, using which distributed average tracking is performed on multiple time-varying signals to ensure that the tracking errors of all intelligent agents converge to a predetermined range.

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

[0136] The processor may load and execute one or more instructions stored in a computer-readable storage medium to implement the corresponding steps of the distributed average tracking control method in the above embodiment; the processor may load and execute the following steps:

[0137] S101, constructing a network structure topology graph 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 intelligent agent, using the strategy to process the control input of the intelligent agent and track the time-varying signal;

[0140] S104, designing adaptive parameters, using which distributed average tracking is performed on multiple time-varying signals to ensure that the tracking errors of all intelligent agents converge to a predetermined range.

[0141] Those skilled in the art will appreciate that embodiments of the present invention may be provided as methods, systems, or computer program products. Therefore, the present invention may take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware. Moreover, the present invention may 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 present invention is described with reference to flowcharts and / or block diagrams of methods, devices (systems), and computer program products according to embodiments of the present invention. It should be understood that each process and / or block in the flowchart and / or block diagram, as well as the combination of processes and / or blocks in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0143] These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer-readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0144] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process. Figure 1 A process or multiple processes and / or boxes Figure 1 The steps for the functions specified in one or more boxes.

[0145] Those skilled in the art will appreciate that the embodiments described herein are intended to help readers understand the implementation methods of the present invention, and should be understood that the protection scope of the present invention is not limited to such special statements and embodiments. Those skilled in the art can make various other specific variations and combinations that do not deviate from the essence of the present invention based on the technical revelations disclosed by the present invention, and these variations and combinations are still within the protection scope of the present invention.

Claims

1. A distributed average tracking control method based on adaptive neural network, characterized in that: The following steps are involved: S101, constructing a network structure topology graph 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; 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; S103, designing a distributed average tracking control strategy based on an adaptive neural network for each intelligent agent, using the strategy to process the control input of the intelligent agent and track the time-varying signal; S104, designing adaptive parameters to obtain an adaptive control strategy, and performing 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.

2. The distributed average tracking control method according to claim 1, characterized in that: The step S101 specifically includes: Using an undirected connected graph Describe a multi-agent system consisting of n agents; represents a set of N nodes, represents a set of edges, where Representation graph, used to describe the communication topology of a multi-agent system; represents a set of nodes, each of which represents an agent; ε represents a set of edges, which defines the connection relationship between nodes; N represents the total number of nodes; 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: The step S102 specifically includes: The following double integrator dynamic state equation is used to describe the motion of the agent: Among them, x i (t) represents the position (state) vector of the ith agent at time t; represents the time derivative of the position of the ith agent, i.e., its velocity; v i (t) represents the velocity vector of the ith agent at time t; represents the time derivative of the velocity of the ith agent, i.e., acceleration; f i (x i (t), v i (t)) represents an unknown nonlinear vector-valued function that describes the dynamic characteristics of the i-th agent; d i (t) indicates external interference or disturbance; u i (t) represents the control input of the ith agent at time t; Indicates that i is a node set An element in The dynamics of the reference signal is represented by: in represent the reference position, velocity and acceleration respectively; represents the time derivative of the reference position of the ith agent; Represents the time derivative of the reference velocity of the ith agent.

4. The distributed average tracking control method according to claim 1, characterized in that: The step S103 specifically includes the following steps: Design an average reference estimator to obtain an average reference signal, specifically including designing an estimation filter, the design of which is as follows: Among them, ξ i represents the state estimate of the i-th agent, which is regarded as the estimated position of the agent's reference signal, used to track the position of the reference signal, and is continuously updated through the filter; Represents ξ i The time derivative of , i.e. the rate of change of the estimated position, is understood as the estimated velocity; ζ i It represents the rate of change of the state estimate of the i-th agent, which is used to estimate the reference speed and reflects the rate of change of the agent's position estimate, which is continuously updated through the filter; Indicates i The time derivative of , i.e. the rate of change of the estimated velocity, is understood as the estimated acceleration; K is a gain parameter used to adjust the response speed and stability of the system; represents the reference position of the ith agent at time t; represents the reference speed of the ith agent at time t; β is another gain parameter that adjusts the strength of interactions with neighboring agents; represents the neighbor set of the ith agent, that is, the set of other agents directly connected to the ith agent; ψi and ψ j represents the norm of the reference signal of the i-th and j-th agents, which is a combination of the reference position, velocity and acceleration, h is a heterogeneous nonlinear function; Represents the reference acceleration of the ith agent, which is used to provide the expected acceleration information in the dynamic model.

5. The distributed average tracking control method according to claim 1, characterized in that: The heterogeneous nonlinear function h is defined as follows: where ε and is specified as a positive constant, This is an exponential decay function, and ω is a vector that describes the state or control policy of the agent.

6. The distributed average tracking control method according to claim 1, characterized in that: The specific setting of the adaptive parameters in step S104 to implement distributed average tracking of multiple time-varying signals includes: Control input u i Settings: Among them, η is a gain parameter, which is the degree of influence of the control error on the control input; represents the error between the actual position of the ith agent and its estimated position, that is, represents the error between the actual speed of the ith agent and its estimated speed, that is, represents the rate of change of the estimated speed of the ith agent, that is, the estimated change of the reference speed; Represents the unknown nonlinear dynamic function f i (x i , v i ) Indicates external interference d i This part is used to compensate for the impact of external disturbances on the movement of the agent.

7. The distributed average tracking control method according to claim 1, characterized in that: The step S104 also includes: Design a control algorithm that ensures that all signals in the closed-loop system are bounded and that the average tracking error is distributed Converge to the neighborhood of the origin; Among them, e xi represents the position tracking error of the i-th agent; x i (t) represents the actual position of the i-th agent at time t; represents the reference position of the jth agent at time t; the reference position is the position that the system expects the agent to reach; n represents the total number of agents; e vi represents the speed tracking error of the i-th agent; v i (t) represents the actual speed of the ith agent at time t; represents the reference speed of the j-th agent at time t.

8. A distributed average tracking control system, characterized in that: The system can be used to implement the distributed average tracking control method described in any one of claims 1 to 7, specifically comprising: Network topology building 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: 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; Adaptive neural network control module: Design and implement control strategies based on adaptive neural networks to process the control input of each intelligent agent and track time-varying signals; Parameter Adaptation Module: Design and optimize adaptive parameters to adapt to different time-varying signals and ensure the effectiveness and stability of distributed average tracking; Information interaction module: realizes information exchange and data sharing between intelligent agents, and supports real-time communication between adjacent nodes; Error evaluation module: calculates and evaluates the tracking error of each agent, monitors system performance, and provides feedback for the adjustment of control strategies; Control input calculation module: Calculate the control input of each agent according to the designed control strategy and parameters to achieve tracking of the target reference signal; System monitoring and feedback module: monitors the system status in real time, including the position, speed and error of the agent, and provides feedback to optimize the control effect; User interface module: provides a friendly user interface for users to set parameters, start / stop the system, and view system status and performance indicators.

9. A computer device, characterized in that: The invention comprises a memory, a processor and a computer program stored in the memory and executable on the processor, wherein when the processor executes the program, the distributed average tracking control method according to one of claims 1 to 7 is implemented.

10. A computer-readable storage medium, characterized in that: A computer program is stored thereon, and when the program is executed by a processor, the distributed average tracking control method described in one of claims 1 to 7 is implemented.

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