Multi-agent collaborative output adjustment method and device based on fully distributed strategy

Abstract

The present application provides a multi-agent collaborative output regulation method and device based on a fully distributed strategy, which belongs to the field of multi-agent collaborative output regulation technology, wherein the multi-agent collaborative output regulation method includes: studying a multi-agent system model for describing a multi-agent system, wherein the multi-agent system model includes an agent state, an external system state, a controller, and an error output; according to a fully distributed strategy, using the agent state in combination with the controller to dynamically construct a fully distributed controller of a non-adaptive method, the controller has a built-in external system state compensator; substituting the fully distributed controller into the multi-agent system model, and using the external system state compensator to offset the external system state, so that the error output of the multi-agent system converges to 0. The present application can solve the problem in the prior art of using adaptive methods, i.e., differential equations, to solve dynamic controller parameters, which requires a large amount of computing resources.

Description

Technical Field

[0001] The present application belongs to the technical field of multi-agent collaborative output regulation, and specifically relates to a multi-agent collaborative output regulation method and device based on a fully distributed strategy. Background Art

[0002] The concept of "agent" is an abstraction of various physical entities. Generally speaking, it refers to individuals with perception, communication, computation, and execution capabilities, such as robots, unmanned vehicles, and aircraft. Compared to single agents, multi-agent systems have a wider range of applications, such as mobile robots, robotic arms, space satellites, and distributed energy systems. Due to their widespread application in modern engineering (e.g., in specific scenarios where multiple devices collaborate to achieve a control objective) and their advantages in scalability and robustness in accomplishing group tasks, the coordinated control of multi-agent systems has been a research hotspot for many years.

[0003] The primary goal of cooperative control of multi-agent systems is to achieve desired group behavior through interactions between agents with information exchange capabilities. Research on cooperative control of multi-agent systems typically encompasses specific issues such as consensus, formation, and clustering. Consensus control, a fundamental issue in cooperative control, involves designing distributed controllers so that all agents in the system can reach consensus on certain quantities of interest through local interactions. Furthermore, cooperative output regulation of multi-agents, or the problem of coordinated output regulation, has also garnered considerable attention from scholars worldwide. Its goal is to enable multiple agents to track a given reference signal under certain disturbances.

[0004] Most existing multi-agent collaborative output regulation methods incorporate event-triggered mechanisms. These mechanisms are primarily categorized into two types: dynamic event triggering and static event triggering. However, most multi-agent collaborative output regulation methods employ adaptive strategies, specifically dynamic controller parameters solved by differential equations. This approach is equivalent to dynamic event triggering. This approach relies on global information, and therefore requires significant computational resources to solve the adaptive dynamic controller parameters. This introduces a significant additional computational burden, and currently, there is no other method to circumvent this burden in order to achieve a fully distributed strategy. Summary of the Invention

[0005] The following technical solution of this application is intended to provide a method and device for multi-agent collaborative output regulation based on a fully distributed strategy. By optimizing the dynamic control parameters introduced by the traditional sampling adaptive strategy method into static parameters, the edge weights of the communication topology graph are adjusted in disguise, achieving the goal of not relying on global information such as the eigenvalues ​​of the Laplace matrix by the controller parameters (including the trigger mechanism parameters), thereby reducing the amount of computation. By implementing a fully distributed strategy, the dependence of multiple agents on global information is reduced, thereby solving the problem of the traditional model adopting an adaptive strategy method, that is, the large amount of computation introduced by the dynamic controller parameters to solve the differential equation.

[0006] According to the first aspect of the present application, an embodiment of the present application provides a multi-agent collaborative output adjustment method based on a fully distributed strategy, comprising:

[0007] Study the multi-agent system model used to describe the multi-agent system, which includes the agent state, external system state, controller and error output;

[0008] According to the fully distributed strategy, a fully distributed controller of a non-adaptive method is constructed dynamically using the agent state combined with the controller, wherein the fully distributed controller has a built-in external system state compensator;

[0009] The fully distributed controller is substituted into the multi-agent system model, and the external system state compensator is used to offset the external system state so that the error output in the multi-agent system model converges to 0.

[0010] Preferably, in the above-mentioned multi-agent collaborative output adjustment method, the multi-agent system model includes an agent state space expression and an error output expression;

[0011] The agent state space expression includes the agent state and the corresponding matrix of appropriate dimensions, the controller and the corresponding matrix of appropriate dimensions, and the external system state and the corresponding matrix of appropriate dimensions; the error output expression includes the agent state and the corresponding matrix of appropriate dimensions, the controller and the corresponding matrix of appropriate dimensions, and the external system state and the corresponding matrix of appropriate dimensions;

[0012] The steps of the multi-agent system model used in the above study to constrain the multi-agent system include:

[0013] Using a matrix of appropriate dimensions and an external system matrix, a model constraint equation is constructed; wherein the model constraint equation is used to constrain the multi-agent system model, and the model constraint equation includes a pair of solutions for the regulator equation;

[0014] Constrained multi-agent system models using pairs of regulator equations with solutions.

[0015] Preferably, in the above-mentioned multi-agent collaborative output adjustment method, the step of dynamically constructing a fully distributed controller of a non-adaptive method using the agent state combined with the controller according to the fully distributed strategy includes:

[0016] Obtaining the communication state between adjacent agents in the multi-agent system, using the communication state in combination with the external system state or an estimate of the external system state to construct a compensator intermediate function for the controller dynamics, and using the compensator intermediate function in combination with the controller dynamics and the corresponding external system matrix to construct a set of differential equations for the controller dynamics as a compensator for the external system state;

[0017] Using the controller dynamics and the corresponding controller gains, combined with the agent states and the corresponding controller gains, a fully distributed controller is constructed.

[0018] Preferably, in the above-mentioned multi-agent collaborative output adjustment method, the steps of using the communication state in combination with the external system state or the external system state estimate to construct a compensator intermediate function about the controller dynamics, and using the compensator intermediate function in combination with the controller dynamics and the corresponding external system matrix to construct a differential equation system about the controller dynamics as the external system state compensator include:

[0019] Obtain the communication content, number of neighbors, and connection status between adjacent agents in a multi-agent system as the communication status;

[0020] Use the communication state, compensator gains, and controller dynamics, combined with the external system state or with an estimate of the external system state, to construct a compensator intermediate function:

[0021]

[0022] in, represents the compensator intermediate function, represents the compensator gain, represents the state of the external system or an estimate of the state of the external system, Representing an agent The controller dynamics, Representing an agent and The connection status, Representing an agent The number of neighbors, Representing an agent The number of neighbors, Representing an agent The intermediate function of the communication content ， Representing an agent The intermediate function of the communication content;

[0023] Using the compensator intermediate function, combined with the controller dynamics and the corresponding external system matrix, we construct a set of differential equations for the controller dynamics:

[0024]

[0025] As the external system state compensator, wherein, represents the derivative of the controller dynamics, represents the compensator intermediate function, represents the controller dynamics and S represents the external system matrix.

[0026] Preferably, in the above-mentioned multi-agent collaborative output adjustment method, the step of dynamically constructing a fully distributed controller of a non-adaptive method using the agent state in combination with the controller according to the fully distributed strategy specifically further includes:

[0027] Get the triggering moment of the controller dynamics;

[0028] A time-triggered mode is constructed using the trigger moment in combination with the time trigger parameter, and an event-triggered mode is constructed using the event trigger parameter in combination with the controller error, wherein in the event-triggered mode, the controller error changes continuously from 0;

[0029] Use the mode selector to combine the time trigger mode and the event trigger mode to build a Zeno-free trigger mechanism corresponding to the trigger moment;

[0030] Among them, when the mode selector is 0, the Zeno trigger mechanism enters the time trigger mode, and when the mode selector is not 0, the Zeno trigger mechanism enters the event trigger mode.

[0031] Preferably, in the above-mentioned multi-agent collaborative output adjustment method, the step of substituting the fully distributed controller into the multi-agent system model and using the external system state compensator to offset the external system state so that the error output in the multi-agent system model converges to 0 includes:

[0032] Substituting the fully distributed controller into the multi-agent system model, we obtain a compact form of the closed-loop system, where the closed-loop system includes the overall state of all agents in the multi-agent system and the cancellation function of the external system compensator and the external system state.

[0033] According to the definition of input-to-state stability and the compact form of the closed-loop system, the error output of the agent is derived when the overall state converges to 0. The compact form of the closed-loop system is a single expression that represents the status of all agents. The system state corresponding to the compact form of the closed-loop system is the combined state of all agents.

[0034] According to the relationship between the offset function and the overall state, it is deduced that when the offset function converges to 0, the convergence value of the error output is 0;

[0035] Combined with the Zeno-free trigger mechanism of the external system state compensator, according to the relationship between the external system state and the offset function, it is deduced that when the external system state compensator offsets the external system state, the convergence value of the offset function is 0;

[0036] The offset function is converged to 0 so that the error output of the multi-agent system converges to 0.

[0037] Preferably, in the above-mentioned multi-agent collaborative output adjustment method, according to the definition of input-to-state stability and based on the compact form of the closed-loop system, the step of deriving the error output of the agent when the overall state converges to 0 includes:

[0038] Compact form using closed loop system:

[0039]

[0040] The calculation equation for the convergence value of the error output of the intelligent agent is derived:

[0041]

[0042] in, represents the overall state of all agents in the multi-agent system after the states of all agents are combined, represents the derivative of the overall state, represents the cancellation function of the external system compensator and the external system state, represents the derivative of the cancellation function, represents the compensator gain, is the connection matrix between the agent and the external system, represents the derivation of the intermediate function, express dimensional identity matrix, represents the controller gain; and represents the solution pair of the controller;

[0043] When the convergence value of the offset function and When bounded, ;

[0044] when When the convergence value of the error output is calculated according to the equation, the convergence value of the error output is .

[0045] Preferably, in the above-mentioned multi-agent collaborative output adjustment method, in combination with the Zeno-free trigger mechanism of the external system state compensator, according to the relationship between the external system state and the offset function, the step of deducing that when the external system state compensator offsets the external system state, the convergence value of the offset function is 0 includes:

[0046] Constructing the Lyapunov function of the external system state;

[0047] Use the Lyapunov function of the external system state to classify all acquired agents and obtain the sets of agents that rely on event-triggered strategies and time-triggered strategies;

[0048] Combined with the Zeno-free triggering mechanism of the external system state compensator, the agent sets that rely on event-triggered strategies and time-triggered strategies are solved respectively, and the relationship between the external system state and the compensation function is obtained;

[0049] According to the relationship between the external system state and the offset function, the convergence value of the offset function is derived to be 0.

[0050] Preferably, the multi-agent collaborative output adjustment method further comprises, after the step of using the external system state compensator to offset the external system state so that the error output of the multi-agent system converges to 0:

[0051] The actual controller dynamics of the controller in the multi-agent system are sampled using a Zeno-free triggering mechanism, and the sampled controller dynamics are substituted into the external system state compensator;

[0052] Under the control of a fully distributed controller, an external system state compensator is used to offset the external system state to achieve collaborative output regulation of the multi-agent system.

[0053] According to the second aspect of the present application, the present application also provides an electronic device, including a memory, a processor, and a computer program stored on the memory and runnable on the processor. When the processor executes the program, it implements a multi-agent collaborative output adjustment method based on a fully distributed strategy as provided in any of the above technical solutions.

[0054] The technical solution of this application has at least the following technical effects:

[0055] The technical solution provided in this application studies a multi-agent system model for describing a multi-agent system, wherein the multi-agent system model includes an agent state and an external system state (if directly obtainable) or an estimated value of the external system state (if not directly obtainable), a controller, and an error output. The entire agent system model and the communication topology of the multi-agent system are taken as research objects, and a compensation mechanism of the controller is designed to compensate for the external state of the multi-agent system, thereby offsetting the external system state and achieving zero error output of the multi-agent system. Specifically, according to a fully distributed strategy, a fully distributed controller of a non-adaptive method is dynamically constructed using the agent state in combination with the controller. The fully distributed controller can implement a fully distributed strategy, thereby reducing dependence on global information, and abandoning the traditional adaptive method that relies on dynamic control parameters. By optimizing the original dynamic control parameters into static parameters, it is possible to achieve the purpose of not relying on global information such as the eigenvalues ​​of the Laplace matrix for static controller parameters (including trigger mechanism parameters), thereby reducing the amount of computation. In addition, the controller has a built-in external system state compensator. By substituting the fully distributed controller into the multi-agent system model, the external system state compensator is used to offset the external system state, so that the error output of the multi-agent system converges to 0, thus achieving a stable output of the multi-agent system. Through the above method, the external system compensator can offset the influence of the external system state on the multi-agent system, so that the error output of the multi-agent system converges to 0, and a stable output of the multi-agent system is achieved.

[0056] In summary, the above technical solution can solve the problem that most existing multi-agent collaborative output adjustment methods adopt an adaptive strategy, that is, the dynamic controller parameters are obtained through the differential equation method, which results in the adaptive dynamic controller parameter solution process requiring a large amount of computing resources and introducing a large amount of additional computing burden. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] The drawings described herein are used to provide a further understanding of the present application and constitute a part of the present application. The illustrative embodiments of the present application and their descriptions are used to explain the present application and do not constitute an improper limitation on the present application. In the drawings:

[0058] Figure 1 A flow chart of a multi-agent collaborative output adjustment method based on a fully distributed strategy provided in an embodiment of the present application;

[0059] Figure 2 for Figure 1 A flowchart of a method for constructing constraint conditions for a multi-agent system model provided by the illustrated embodiment;

[0060] Figure 3 for Figure 1A schematic flow chart of a first method for constructing a fully distributed controller provided by the illustrated embodiment;

[0061] Figure 4 for Figure 1 A schematic flow chart of a second method for constructing a fully distributed controller provided by the illustrated embodiment;

[0062] Figure 5 for Figure 1 The illustrated embodiment provides a flow chart of a method for using a compensator to offset an external system state;

[0063] Figure 6 for Figure 5 A schematic flow chart of a method for deriving convergence of a cancellation function provided by the illustrated embodiment;

[0064] Figure 7 A flowchart of a second multi-agent collaborative output adjustment method based on a fully distributed strategy provided in an embodiment of the present application;

[0065] Figure 8 A flowchart of a third multi-agent collaborative output adjustment method based on a fully distributed strategy provided in an embodiment of the present application;

[0066] Figure 9 A topological structure diagram provided in an embodiment of the present application;

[0067] Figure 10 A graph showing changes in adaptive parameters involved in the adaptive method used in the prior art;

[0068] Figure 11 A schematic diagram of the error output curves of the four intelligent agents provided in the embodiment of the present application;

[0069] Figure 12 A schematic diagram of the structure of an electronic device provided in an embodiment of the present application. DETAILED DESCRIPTION

[0070] In order to more clearly illustrate the overall concept of the present application, a detailed description is given below in an illustrative manner in conjunction with the accompanying drawings.

[0071] Each embodiment in this specification is described in a progressive manner. Similar portions between the embodiments can be referenced to each other. Each embodiment focuses on the differences from other embodiments. For those skilled in the art, various modifications and variations are possible. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of this application shall be included within the scope of protection of this application.

[0072] The following description sets forth many specific details to facilitate a thorough understanding of the present application. However, the present application may also be implemented in other ways than those described herein, and therefore, the scope of protection of the present application is not limited by the specific embodiments disclosed below. It should be noted that the embodiments of the present application and the features of each embodiment may be combined with each other unless there is a conflict.

[0073] In this application, unless otherwise clearly specified and limited, a first feature "above" or "below" a second feature may be that the first and second features are in direct contact, or the first and second features are in indirect contact through an intermediate medium. In the description of this specification, the description with reference to the terms "one embodiment", "some embodiments", "example", "specific example", or "some examples" means that the specific features, structures, materials or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present application. In this specification, the schematic representation of the above terms does not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described may be combined in an appropriate manner in any one or more embodiments or examples.

[0074] The existing technology has the following defects:

[0075] Existing multi-agent output regulation models based on adaptive strategies require significant computational resources to solve for adaptive parameters. In scenarios where topology changes, especially changes in the number of agents, are possible, the parameters of conventional distributed strategies are determined by global information. These parameters often need to be determined before networking. Once the system is operational, these parameters are difficult to modify and obtain, otherwise the system may degenerate into a centralized control strategy. Therefore, in scenarios where the number of agents is highly flexible, conventional distributed solutions struggle to cope with changes in the global structure. Time-varying parameters are almost inevitably required, which introduces a significant computational burden.

[0076] To solve the above problems, the following embodiment of the present invention provides a multi-agent collaborative output adjustment scheme based on a fully distributed strategy. It uses fixed parameters, but its time-varying nature is still retained, that is, the relevant parameters change with the number of its neighbors and "secondary neighbors" and are not completely fixed. When the topology structure, especially the total number of agents, changes, it will inevitably cause some of the agent controller parameters to be adjusted accordingly, but the amount of computation required for this adjustment is only reflected in replacing the original value with a new value obtained by the communication process. Compared with adaptive strategies that require continuous calculations, this method almost eliminates this part of the computational requirements.

[0077] To achieve the above purpose, see Figure 1 , the embodiment of the present application provides a multi-agent collaborative output adjustment method based on a fully distributed strategy, including:

[0078] S110: Study the multi-agent system model used to describe the multi-agent system. The multi-agent system model includes agent state, external system state, controller and error output.

[0079] The present application embodiment combines the communication topology diagram of the multi-agent system (such as Figure 9 As shown, the communication topology diagram represents the abstract mathematical representation of the communication connection relationship between multiple agents, the label is the name of the agent, and 0 represents the external system), and the multi-agent system model under the joint triggering mechanism of time and events is studied. The multi-agent system model studies heterogeneous multi-agent systems, including multiple agents. The purpose of the embodiment of the present application is to implement a given multi-agent system and communication topology, and to design a controller based on distributed information so that the error output of the system converges to 0 for any initial state; and when the state of the external system is 0, the entire multi-agent system model with a fully distributed controller is brought in, and the closed-loop system it constitutes is asymptotically stable.

[0080] S120: According to the fully distributed strategy, a fully distributed controller of a non-adaptive method is dynamically constructed using the agent state combined with the controller, wherein the fully distributed controller has a built-in external system state compensator.

[0081] The fully distributed controller provided by the present application's embodiments eliminates the need for traditional adaptive strategy-based controllers, which require the design of differential equations to solve dynamic controller parameters. This fully distributed controller optimizes existing dynamic control parameters into static parameters, effectively adjusting the edge weights of the communication topology graph. This ensures that controller parameters (including trigger mechanism parameters) are independent of global information such as the Laplace matrix eigenvalues, significantly reducing computational complexity.

[0082] S130: Substitute the fully distributed controller into the multi-agent system model, and use the external system state compensator to offset the external system state so that the error output in the multi-agent system model converges to 0.

[0083] The multi-agent collaborative output adjustment method provided in the embodiment of the present application studies a multi-agent system model used to describe a multi-agent system, and the multi-agent system model includes the agent states, external system states, controllers, and error outputs of multiple agents. The entire agent system model and the communication topology of the multi-agent system are taken as research objects, and the compensation mechanism of the controller is designed to compensate for the external state of the multi-agent system, thereby offsetting the external system state and achieving zero error output of the multi-agent system. Specifically, according to a fully distributed strategy, a fully distributed controller of a non-adaptive method is constructed using the agent state in combination with the controller dynamics. The fully distributed controller can implement a fully distributed strategy, thereby reducing the dependence of the system model on global information. In addition, the traditional adaptive method that depends on dynamic control parameters is abandoned, and the original dynamic control parameters are optimized into static parameters, so that the controller parameters (including the trigger mechanism parameters) do not depend on global information such as the eigenvalues ​​of the Laplace matrix, thereby reducing the purpose of computational complexity. In addition, the fully distributed controller designed in the embodiment of the present application has a built-in external system state compensator. By substituting the fully distributed controller into the multi-agent system model, the external system state compensator is used to offset the external system state, so that the error output of the multi-agent system converges to 0, thereby achieving a stable output of the multi-agent system. Through the above method, the external system compensator can offset the influence of the external system state on the multi-agent system, thereby causing the error output of the multi-agent system to converge to 0 and achieving a stable output of the multi-agent system.

[0084] In summary, the above technical solution can solve the problem that most existing multi-agent collaborative output adjustment methods adopt adaptive strategies, that is, the dynamic controller parameters of differential equations (equivalent to dynamic event triggering), which leads to dependence on global information, and then the adaptive dynamic controller parameter solution process requires a large amount of computing resources, which introduces a large amount of additional computing burden.

[0085] Among them, as a preferred embodiment, the multi-agent system model includes an agent state space expression and an error output expression; wherein, the agent state space expression includes the agent state and the corresponding appropriate dimension matrix, the controller and the corresponding appropriate dimension matrix, and the external system state and the corresponding appropriate dimension matrix; the error output expression includes the agent state and the corresponding appropriate dimension matrix, the controller and the corresponding appropriate dimension matrix, and the external system state and the corresponding appropriate dimension matrix.

[0086] Specifically, the error output expression includes the agent state, controller and external system state, and the corresponding matrices of appropriate dimensions.

[0087] In the embodiment of the present application, the multi-agent system model includes the agent state space expression and error output expression, which are as follows:

[0088]

[0089] in, is a matrix of appropriate dimensions corresponding to each parameter in the model. The specific value or proportion can be obtained by the following constraint equation; For the The derivative of the state of each agent, Respectively represent The state, controller, and error output of each agent. v Generated by an external system, its derivative , S is the external system matrix and has no positive real part.

[0090] In addition, when studying the multi-agent system model of the multi-agent system, it is necessary to consider the actual situation of the multi-agent system and the interference of the external system, consider the constraints of the multi-agent system model, and specifically construct the model constraint equation of the multi-agent system model. Therefore, the specific construction of the model constraint equation is as follows Figure 2 As shown, the above step S110: the step of studying the multi-agent system model for describing the multi-agent system specifically includes:

[0091] S111: Use a matrix of appropriate dimensions and an external system matrix to construct a model constraint equation; wherein the model constraint equation is used to constrain the multi-agent system model, and the model constraint equation includes a regulator equation with a solution pair.

[0092] Here, it is assumed that the matrix of appropriate dimensions includes .

[0093] S112: Constraining multi-agent system models using pairs of regulator equations with solutions.

[0094] Using matrices of appropriate dimensions and external system matrices, the constraint equations of the multi-agent system model are constructed.

[0095] The constraint equations of the multi-agent system model constructed in the embodiment of the present application are as follows:

[0096]

[0097] in, is a matrix of appropriate dimension, is the external system matrix, has no positive real part, and is known in advance by each agent. The embodiment of the present application assumes that the multi-agent system is stabilizable and that the constraint equation has a solution to the regulator equation. ,In this application, the regulator equation has a solution pair, which will be used in designing a fully distributed controller.

[0098] The purpose of the technical solution provided in the embodiment of the present application is to provide a multi-agent system model and communication topology as shown above, so as to design a controller based on distributed information. , so that the error output of the system for any initial state is All converge to 0, and when the external system state When , the closed-loop system of the multi-agent is asymptotically stable. This solution can solve the problem that most existing multi-agent collaborative output regulation methods use adaptive strategies, that is, dynamic controller parameters solved by differential equations, which is equivalent to using dynamic event triggering, resulting in reliance on global information. In turn, the adaptive dynamic controller parameter solution process requires a large amount of computing resources, introducing a large additional computational burden.

[0099] In addition, as a preferred embodiment, Figure 3 As shown, the above step S120: the step of dynamically constructing a fully distributed controller of a non-adaptive method using the agent state in combination with the controller according to the fully distributed strategy, includes:

[0100] S121: Obtain the communication state between adjacent agents in the multi-agent system. Use this communication state in combination with the external system state (if available) or an estimate of the external system state (if not available) to construct a compensator intermediate function for the controller dynamics. Use this compensator intermediate function, combined with the controller dynamics and the corresponding external system matrix, to construct a system of differential equations for the controller dynamics, which serves as a compensator for the external system state. It should be noted that for agents that have a communication connection with the external system, the external system state is known and available.

[0101] The communication status of each agent provided in this embodiment includes information such as the communication content, number of neighbors and connection status between adjacent agents.

[0102] Specifically, as a preferred embodiment, the steps of using the communication state in combination with the external system state or an estimated value of the external system state to construct a compensator intermediate function regarding the controller dynamics, and using the compensator intermediate function in combination with the controller dynamics and the corresponding external system matrix to construct a set of differential equations regarding the controller dynamics as the external system state compensator, specifically include:

[0103] Obtain the communication content, number of neighbors, and connection status between adjacent agents in a multi-agent system as the communication status;

[0104] Using the communication state, compensator gains, and controller dynamics, combined with the external system state or an estimate of the external system state, a compensator intermediate function is constructed:

[0105]

[0106] in, represents the compensator intermediate function, represents the compensator gain, represents the state of the external system or an estimate of the state of the external system, Representing an agent The controller dynamics, Representing an agent and The connection status, Representing an agent The number of neighbors, Representing an agent The number of neighbors, Representing an agent The intermediate function of the communication content ， Representing an agent The intermediate function of the communication content;

[0107] Using the compensator intermediate function, combined with the controller dynamics and the corresponding external system matrix, we construct a set of differential equations for the controller dynamics:

[0108]

[0109] As an external system state compensator. As the external system state compensator, wherein, represents the derivative of the controller dynamics, represents the compensator intermediate function, represents the controller dynamics, represents the external system matrix, S does not have a positive real part, and is known in advance by each agent.

[0110] S122: Using the controller dynamics and corresponding controller gains, combined with the agent state and corresponding controller gains, a fully distributed controller is constructed.

[0111] The technical solution provided by the embodiment of this application, the intelligent body i The fully distributed controller is as follows:

[0112]

[0113] in, is the expression for a fully distributed controller, Representing an agent i The controller dynamics, its intermediate function:

[0114] ,

[0115] Representing an agent i The kth triggering moment of Representing an agent i The content of the communication sent to its neighbors at each triggering instant. Represents the compensator gain, which is any positive number.

[0116] represents the number of neighbors of agent i, Similarly; Indicates the connection between agents i and j. If there is communication, then ;otherwise In addition, the controller gain make sure Located in the left half of the complex plane, the controller gain , both are controller gains. In addition, Depends on whether there is communication between agent i and the external system, which is 1 if there is communication and 0 if not.

[0117] Using the communication state, compensator gain, external system state and controller dynamics, the external system state compensator is solved. In a fully distributed controller, a dynamic variable is designed about the controller dynamics. The embodiment of this application solves the The differential equation of is obtained. This differential equation , which is the external system state compensator.

[0118] In addition, as a preferred embodiment, Figure 4 As shown, in the above-mentioned multi-agent collaborative output adjustment method, step S120: the step of dynamically constructing a fully distributed controller of a non-adaptive method using the agent state combined with the controller according to the fully distributed strategy, further includes:

[0119] S123: Obtain the triggering moment of the controller dynamics.

[0120] S124: constructing a time trigger mode using the trigger moment in combination with the time trigger parameter, and constructing an event trigger mode using the event trigger parameter in combination with the controller error, wherein in the event trigger mode, the controller error changes continuously from 0.

[0121] S125: Use the mode selector to combine the time trigger mode and the event trigger mode to construct a Zeno-free trigger mechanism corresponding to the trigger moment; wherein, when the mode selector is 0, the Zeno-free trigger mechanism enters the time trigger mode, and when the mode selector is not 0, the Zeno-free trigger mechanism enters the event trigger mode. The advantage of the Zeno-free trigger is that the Zeno phenomenon is avoided at the beginning of the design. The existing event triggering method requires additional mathematical proof, but if there are loopholes in the proof, the Zeno phenomenon may still exist in practical applications. The method provided in the embodiment of the present application fundamentally eliminates the Zeno phenomenon.

[0122] Specifically, it can be seen from the above embodiments that Representing an agent i No. k A trigger moment, the trigger moment Determined by the following triggering mechanisms:

[0123]

[0124] in, is the error term, It is the time trigger parameter.

[0125] is called a selector, is the event trigger parameter, is the event trigger parameter β, and its upper limit is the trigger mechanism parameter. If the trigger mechanism has the Zeno phenomenon, then the trigger mechanism can only be Not equal to 0; otherwise, when the selector When is 0, the trigger mechanism will enter the time-triggered mode, and the Zeno phenomenon will not occur. The introduction of the trigger mechanism can significantly reduce the amount of computation and communication between multiple agents.

[0126] When the selector When it is not 0, the error term will change continuously from 0, that is, the trigger condition will be met after a period of time, so the Zeno phenomenon will no longer exist. It should be noted that if the selector , then until agent j triggers ( ), it will always be 0. Although the expression While continuous, it doesn't actually change over time; it only changes when triggered. The triggering time here includes the triggering order of agent i itself and its neighbors, so the selector doesn't need to run continuously, eliminating the need for continuous computation. The fully distributed controller provided by the present embodiment can select a time or event strategy (determined by whether the selector is 0) at each trigger instant, rather than requiring constant judgment.

[0127] The main advantage of the trigger strategy provided by the embodiment of the present application is that it reduces the required calculation amount by optimizing the parallel operation of time triggering and event triggering to serial operation while retaining the Zeno-free characteristics. Auxiliary variables are set in the trigger mechanism, that is, selectors that do not require continuous calculations. This variable organically connects the two existing mechanisms, with the selector determining whether to execute them. The selector itself intermittently calculates and judges based on its own data and neighbor data at the time of triggering, eliminating the need for continuous solving. Traditional Zeno-free schemes rely on real-time calculations and parallel judgments of both, selecting the larger interval as the final time interval and triggering. This embodiment reduces this computational overhead.

[0128] In addition, as a preferred embodiment, Figure 5 As shown, in the above-mentioned multi-agent collaborative output adjustment method, step S130: substituting the fully distributed controller into the multi-agent system model and using the external system state compensator to offset the external system state so that the error output in the multi-agent system model converges to 0, specifically includes:

[0129] S131: Substitute the fully distributed controller into the multi-agent system model to obtain a compact form of the closed-loop system, where the closed-loop system includes the overall state of all agents in the multi-agent system and the cancellation function of the external system compensator and the external system state.

[0130] In the embodiment of the present application, the above-mentioned intelligent agent i The formula of the fully distributed controller is introduced into the expression of the above multi-agent system model , which is a closed-loop system. Rewriting it into a compact form means writing the N agents in the multi-agent system together instead of listing them separately.

[0131] In the embodiment of the present application, the above fully distributed controller is substituted into the multi-agent system model to obtain a compact form of the closed-loop system as follows:

[0132]

[0133] in, This is the cancellation function obtained during the derivation process and does not represent the actual meaning. represents the overall state after the states of all agents are combined, represents the derivative of the overall state. It is an item proposed in the derivation process after rewriting it into compact form. is the connection matrix between the agent and the external system, is an item obtained in the derivation process, express dimensional identity matrix. Specifically, , , , and With similar Definition of; , L is the Laplace matrix, D is the in-degree matrix, , From the compact form of the closed-loop system above, we can see that: By controller gain The selection of can make it located in the left half plane. According to the definition of input to state stability, if and Bounded, then , thus obtaining the error output of agent i. In this application, the multi-agent system is input-state stable. "Input-state stability" is an inherent property of a system. If a system is input-state stable, then when its input is stable, its output is also stable; when its input diverges, its output also diverges. Substituting the above fully distributed controller, the multi-agent system possesses this property.

[0134] S132: According to the definition of input-to-state stability and the compact form of the closed-loop system, the error output of the intelligent agent is derived when the overall state converges to 0; the compact form of the closed-loop system is to show the status of all intelligent agents through an expression, and the system state corresponding to the compact form of the closed-loop system is the merger of all intelligent states.

[0135] S133: According to the relationship between the offset function and the overall state, it is deduced that when the offset function converges to 0, the convergence value of the error output is 0.

[0136] As a preferred embodiment, step S133: deducing that when the offset function converges to 0, the convergence value of the error output is 0 based on the relationship between the offset function and the overall state, specifically includes:

[0137] Compact form using closed loop system:

[0138] The convergence equation of the agent's error output can be derived:

[0139] ;

[0140] When the convergence value of the offset function and When bounded, ;

[0141] when Then according to the error output of the above agent The convergence equation of the derivation shows that: when the convergence value of the offset function When the error output will also converge to 0.

[0142] S134: Combining the Zeno-free trigger mechanism of the external system state compensator and the relationship between the external system state and the offset function, it is deduced that when the external system state compensator offsets the external system state, the convergence value of the offset function is 0;

[0143] S135: Converge the offset function to 0 so that the error output of the multi-agent system converges to 0.

[0144] The convergence equation of the error output of the above agent is It can be seen that:

[0145] When the external system status When, obviously there is , which means that the closed-loop system is stable when the state of the external system is always zero. , the output regulation problem of the original system is solved. Therefore, it can be found that if , then for any initial condition, the error output will converge to zero. Therefore, we will is considered as a sufficient condition for the original problem.

[0146] This converts the problem into a compact form of the closed-loop system mentioned above The derivative of the cancellation function in The stability problem of the second equation. Next, we need to perform stability analysis on this second equation:

[0147] Specifically, as a preferred embodiment, Figure 6 As shown, in the above multi-agent collaborative output adjustment method, step S134: combining the Zeno-free trigger mechanism of the external system state compensator, according to the relationship between the offset function and the external system state, it is deduced that when the external system state compensator offsets the external system state, the convergence value of the offset function is 0, specifically including:

[0148] S1341: Constructing Lyapunov functions of external system states;

[0149] S1342: Use the Lyapunov function of the external system state to classify all acquired agents to obtain a set of agents that rely on event-triggered strategies and time-triggered strategies;

[0150] S1343: Combined with the Zeno-free triggering mechanism of the external system state compensator, solve the set of agents that rely on event triggering strategies and time triggering strategies respectively, and obtain the relationship between the external system state and the compensation function;

[0151] S1344: According to the relationship between the external system state and the offset function, derive that the convergence value of the offset function is 0.

[0152] The technical solution provided in the embodiment of this application can be known from the existing lemma ,therefore ,and , noting , , easy to get ,thus .

[0153] Based on the above analysis, the following form of the Lyapunov function of the external system state is constructed:

[0154]

[0155] The external system state V The time derivative is

[0156] .

[0157] Notice ,then

[0158] For analysis and The inequality relationship between them, all agents are divided into two parts, named and If for any , with a selector ,So If for any ,have ,So . It can be found and are sets of agents that rely on event-triggered and time-triggered strategies, respectively.

[0159] set up If and only if , If and only if .set up Among them, the definition , .but , It should be noted that and Respectively represent that for agent i, if the current selector is not 0, then ,on the contrary . In an agent system consisting of N agents, if we define and , then the above and Satisfies such a property.

[0160] for , according to the above trigger mechanism, it can be seen that there are the following forms:

[0161]

[0162] Notice and similar, which means that they have exactly the same eigenvalues; and according to Gerschgorin's theorem All eigenvalues ​​of are located in the set , noting is a real symmetric matrix, so its eigenvalues ​​are all real numbers, so we can get Combined with the previous formula, it has the following form:

[0163]

[0164] for , note that combined with the original system So when hour , or when hour .Right now

[0165]

[0166] Combine We can get:

[0167] Then we can get the external system state in the following form:

[0168]

[0169] This means that the convergence value of the cancellation function is 0, that is, =0, combined with the above analysis, we can see that the original problem has been solved.

[0170] In addition, as a preferred embodiment, Figure 7 As shown, the multi-agent collaborative output adjustment method further includes, after the step of using the external system state compensator to offset the external system state so that the error output of the multi-agent system converges to 0:

[0171] S140: Using a Zeno-free trigger mechanism, the actual controller dynamics of the controller in the multi-agent system are sampled, and the sampled controller dynamics are substituted into the external system state compensator;

[0172] S150: Under the control of a fully distributed controller, an external system state compensator is used to offset the external system state to achieve collaborative output regulation of the multi-agent system.

[0173] The technical solution provided by the embodiment of the present application is difficult to cope with once the global structure changes in scenarios with a flexible number of agents. In this case, time-varying parameters are almost inevitably required to cope with it. At this time, the introduction of adaptive parameter solutions is particularly reasonable. Although fixed parameters are adopted in the solution of this article, its time-varying nature is still retained, that is, the relevant parameters change with the changes in the number of its neighbors and "secondary neighbors" and are not completely fixed. When the topology structure, especially the total number of agents, changes, it will inevitably cause some of the parameters of the agent controllers to be adjusted accordingly, but the amount of calculation required for such adjustments is only reflected in replacing the original value with a new value obtained by the communication process. Compared with adaptive strategies that require continuous calculations, this method almost eliminates this part of the calculation requirements.

[0174] Also, see Figure 8 , Figure 8 This is a flow chart of a multi-agent collaborative output adjustment method based on a fully distributed strategy provided in an embodiment of the present application. Figure 8 As shown, the multi-agent collaborative output adjustment method includes:

[0175] S201: The external system state cannot be directly obtained by all agents.

[0176] S202: Construct a serial time and event combined trigger mechanism.

[0177] S203: Constructing a fully distributed controller structure that does not adopt an adaptive solution.

[0178] S204: indirectly cancelling the disturbance of the external system through the compensator signal, and estimating the reference signal therein.

[0179] S205: Design a controller using compensation signals to achieve collaborative output regulation of heterogeneous multi-agent systems.

[0180] In addition, in combination with the technical solutions provided in the above embodiments, it is necessary to further consider the situation where the number of agents varies over time:

[0181] The present application embodiment first considers a simple case. We add or subtract M agents at a time, assuming that if we add new agents, they meet the aforementioned assumptions; if we subtract agents, we assume that the deleted agents are not bridges in the original graph, i.e., connectivity is not destroyed. The output regulation problem for the augmented multi-agent system can be equivalently described as follows:

[0182] Considering linear heterogeneous multi-agent systems and external systems, design controllers To achieve output regulation of the system:

[0183]

[0184] Among them, the intelligent i The initial state is , or , other agents have arbitrary initial states, Indicates that the original system For the initial conditions Status at the moment. Mapping Represents the agent in the initial system i exist The label of the time.

[0185] It should be noted that for a system where the number of agents changes, their numbers are no longer unique on a time scale.

[0186] For time intervals with different numbers of agents, agents i The rationale behind possibly referring to different physical entities is as follows. First, for real networks, the physical addresses of nodes are often very complex. After the network is built, the normal communication between agents will not confuse each other. The impact of the increase or decrease of agents on the network can be avoided through the underlying communication rules. Therefore, the naming of the agent model in the network can be manually specified, that is, i It can be considered part of the corresponding agent model, and it's perfectly acceptable to name agents differently at different time intervals. In short, having duplicate names for different agents at different time intervals after modeling does not affect system analysis. The significance of allowing the numbering of different time intervals to change is to simplify the expression of the system model. For systems with added agents, the names of the existing agents do not need to be changed. However, for systems with fewer agents, if the initial names of the agents leaving the network are not sequentially from NM to N, the analysis and expression of the overall system will be very confusing and inconvenient.

[0187] In a real network, if a network node stops connecting to the network at a certain moment, a network address vacancy may appear in the network, and subsequently a newly added node may take over the address. However, for the modeled system, when describing the system at each moment, we always hope that its name is sequentially from 1 to the total number of nodes, even if the names at different moments correspond to different entities.

[0188] The new problem above essentially expresses two issues: whether adding or removing M agents, the system under consideration must achieve output regulation. The system with fewer non-bridge agents clearly still meets the assumptions of the original problem, so the controller proposed in this technique can solve it. For systems with N+M agents, the controller is also effective, as the previous results show that it can handle any initial state. The controller parameters in the original system will change with the addition of new agents, and these modified parameters will remain consistent with the initial parameters of the multi-agent system in the equivalent problem.

[0189] Similarly, for a finite number of increases and decreases, it is always possible to iterate to the situation described in the new problem. Therefore, for a multi-agent system with a finite number of expansions or reductions, the controller given by this technique is always effective.

[0190] Compared to static parameter controllers and triggering mechanisms used in previous literature, when the agent scales up or down, the parameters designed based on pre-known graph information are often difficult to adjust in real time, making "plug-and-play" timeliness impossible. In other words, when the agent scales up or down, the resulting new problem cannot be iteratively adapted to the corresponding theorem of the original problem, and parameters at risk of failure must be recalculated.

[0191] in addition, Figure 10 The figure shows a curve diagram of adaptive parameter changes involved in the adaptive method used in the prior art; Figure 11 A schematic diagram of the error output curves of the four agents provided in the embodiment of the present application is shown. Figure 10 and Figure 11 It can be seen that the parameters given by the existing adaptive scheme will be dynamically adjusted over time, but they will eventually converge to a fixed value, that is, they do not fluctuate continuously. Therefore, this indirectly confirms the feasibility of the above method of this application.

[0192] In addition, the following embodiments of this application provide product embodiments, the beneficial effects of which are the same as the beneficial effects of the multi-agent collaborative output adjustment method based on a fully distributed strategy provided in the above embodiments, and the other technical features in the product embodiments are the same as the features disclosed in the above embodiment methods, which will not be repeated here.

[0193] See also Figure 12 , Figure 12 This is a schematic diagram of the structure of an electronic device provided in an embodiment of the present application. The electronic device includes:

[0194] At least one processor; and a memory communicatively connected to the at least one processor; wherein the memory stores instructions executable by the at least one processor, and the instructions are executed by the at least one processor so as to enable the at least one processor to execute the multi-agent collaborative output adjustment method based on a fully distributed strategy of any of the above embodiments.

[0195] Reference below Figure 12 , which shows a schematic diagram of the structure of an electronic device suitable for implementing the embodiments of the present application. The electronic devices in the embodiments of the present application can include, but are not limited to, mobile terminals such as mobile phones, laptop computers, digital broadcast receivers, PDAs (Personal Digital Assistants), PADs (Portable Application Descriptions), PMPs (Portable Media Players), in-vehicle terminals (such as in-vehicle navigation terminals), and fixed terminals such as digital TVs and desktop computers. Figure 12 The device shown is only an example and should not limit the functions and scope of use of the embodiments of the present application.

[0196] like Figure 12 As shown, the electronic device may include a processing device 1001 (e.g., a central processing unit, a graphics processing unit, etc.), which can perform various appropriate actions and processes based on programs stored in a read-only memory (ROM) 1002 or programs loaded from a storage device 1003 into a random access memory (RAM) 1004. RAM 1004 also stores various programs and data required for the operation of the electronic device. Processing device 1001, ROM 1002, and RAM 1004 are interconnected via a bus 1005. An input / output (I / O) interface 1006 is also connected to the bus. Typically, the following systems can be connected to I / O interface 1006: input devices 1007 including, for example, a touchscreen, touchpad, keyboard, mouse, image sensor, microphone, accelerometer, gyroscope, etc.; output devices 1008 including, for example, a liquid crystal display (LCD), speaker, vibrator, etc.; storage device 1003 including, for example, a magnetic tape or hard disk; and communication device 1009. The communication device 1009 can enable the above-mentioned electronic devices to communicate with other devices wirelessly or by wire to exchange data. Although the figure shows a model building device with various systems, it should be understood that it is not required to implement or have all the systems shown. More or fewer systems can be implemented or provided instead.

Claims

1. A multi-agent collaborative output adjustment method based on a fully distributed strategy, characterized in that: include: Studying a multi-agent system model for describing a multi-agent system, wherein the multi-agent system model includes agent states, external system states, a controller, and error outputs; According to a fully distributed strategy, a fully distributed controller of a non-adaptive method is dynamically constructed using the agent state in combination with the controller, wherein the fully distributed controller has a built-in external system state compensator; the fully distributed controller is optimized to static parameters, so that the static controller parameters do not depend on global information; Substituting the fully distributed controller into the multi-agent system model, and using the external system state compensator to offset the external system state, so that the error output in the multi-agent system model converges to 0; The fully distributed controller is as follows: in, is the expression for a fully distributed controller, x i Indicates the i The state of an agent, Representing an agent The controller dynamics, and K 2i Both are controller gains; represents the derivative of the controller dynamics, S Expressed as the external system matrix, represents the compensator intermediate function, represents the state of the external system or an estimate of the state of the external system, Represents the compensator gain, which is any positive number. Representing an agent and The connection status, Representing an agent The number of neighbors, Representing an agent The number of neighbors, Representing an agent The intermediate function of the communication content, Representing an agent The intermediate function of the communication content, Indicates whether there is communication between agent i and the external system.

2. The method according to claim 1, characterized in that The multi-agent system model includes an agent state space expression and an error output expression; wherein the agent state space expression includes the agent state and the corresponding appropriate dimension matrix, the controller and the corresponding appropriate dimension matrix, and the external system state and the corresponding appropriate dimension matrix; the error output expression includes the agent state and the corresponding appropriate dimension matrix, the controller and the corresponding appropriate dimension matrix, and the external system state and the corresponding appropriate dimension matrix; The steps of the multi-agent system model used in the study to describe the multi-agent system include: Using the appropriate dimension matrix and the external system matrix, constructing a model constraint equation; wherein the model constraint equation is used to constrain the multi-agent system model, and the model constraint equation includes a regulator equation with a solution pair; The multi-agent system model is constrained using the solution pairs of the regulator equations.

3. The method according to claim 1, characterized in that The step of dynamically constructing a fully distributed controller of a non-adaptive method using the agent state in combination with the controller according to the fully distributed strategy includes: Acquiring communication states between adjacent agents in the multi-agent system, using the communication states in combination with an external system state or an estimate of the external system state to construct a compensator intermediate function for controller dynamics, and using the compensator intermediate function in combination with the controller dynamics and a corresponding external system matrix to construct a set of differential equations for the controller dynamics as the external system state compensator; The fully distributed controller is constructed using the controller dynamics and corresponding controller gains, combined with the agent state and corresponding controller gains.

4. The method according to claim 3, characterized in that The steps of constructing a compensator intermediate function related to controller dynamics using the communication state in combination with an external system state or an estimated value of the external system state, and constructing a differential equation system related to the controller dynamics using the compensator intermediate function in combination with the controller dynamics and a corresponding external system matrix as the external system state compensator include: Acquire communication content, number of neighbors, and connection status between adjacent agents in the multi-agent system as the communication status; Using the communication state, compensator gain, and controller dynamics, combined with the external system state or an estimate of the external system state, a compensator intermediate function is constructed: in, represents the compensator intermediate function, represents the compensator gain, represents the state of the external system or an estimate of the state of the external system, Representing an agent The controller dynamics, Representing an agent and The connection status, Representing an agent The number of neighbors, Representing an agent The number of neighbors, Representing an agent The intermediate function of the communication content ， Representing an agent The intermediate function of the communication content; Using the compensator intermediate function, combined with the controller dynamics and the corresponding external system matrix, a set of differential equations for the controller dynamics is constructed: As the external system state compensator, wherein, represents the derivative of the controller dynamics, represents the compensator intermediate function, represents the controller dynamics and S represents the external system matrix.

5. The method according to claim 3, characterized in that The step of dynamically constructing a fully distributed controller of a non-adaptive method using the agent state in combination with the controller according to the fully distributed strategy further includes: Obtaining a dynamic triggering moment of the controller; Using the trigger moment in combination with a time trigger parameter to construct a time trigger mode, and using the event trigger parameter in combination with a controller error to construct an event trigger mode, wherein in the event trigger mode, the controller error changes continuously from 0; Using a mode selector to combine the time trigger mode and the event trigger mode to construct a Zeno-free trigger mechanism corresponding to the trigger moment; When the mode selector is 0, the Zeno-free trigger mechanism enters a time trigger mode; when the mode selector is not 0, the Zeno-free trigger mechanism enters an event trigger mode.

6. The method according to claim 1, characterized in that The step of substituting the fully distributed controller into the multi-agent system model and using the external system state compensator to offset the external system state so that the error output in the multi-agent system model converges to 0 includes: Substituting the fully distributed controller into the multi-agent system model to obtain a compact form of a closed-loop system, wherein the closed-loop system includes the overall state of all agents in the multi-agent system and a cancellation function of the external system compensator and the external system state; According to the definition of input-to-state stability, and based on the compact form of the closed-loop system, the error output of the agent is derived when the overall state converges to 0; wherein the compact form of the closed-loop system is a single expression representing the state of all agents in the multi-agent system, and the system state corresponding to the compact form of the closed-loop system is the combined state of all agents; According to the relationship between the offset function and the overall state, it is deduced that when the offset function converges to 0, the convergence value of the error output is 0; Combined with the Zeno-free trigger mechanism of the external system state compensator, according to the relationship between the external system state and the offset function, it is deduced that when the external system state compensator offsets the external system state, the convergence value of the offset function is 0; The compensation function is converged to 0 so that the error output of the multi-agent system converges to 0.

7. The method according to claim 6, characterized in that The step of deriving the error output of the agent when the overall state converges to 0 according to the input-to-state stability definition and the compact form of the closed-loop system comprises: Using the compact form of the closed loop system: The calculation equation for the convergence value of the error output is derived as follows: ； in, represents the overall state of all agents in the multi-agent system after the states of all agents are combined, represents the derivative of the overall state, represents the cancellation function of the external system compensator and the external system state, represents the derivative of the cancellation function, represents the compensator gain, is the connection matrix between the agent and the external system, represents the derivation of the intermediate function, express dimensional identity matrix, represents the controller gain; and represents the solution pair of the controller; When the convergence value of the offset function and When bounded, ; when When the convergence value of the error output is calculated according to the equation, the convergence value of the error output is .

8. The method according to claim 6 or 7, characterized in that The step of combining the Zeno-free trigger mechanism of the external system state compensator and deriving, based on the relationship between the external system state and the offset function, that the convergence value of the offset function is 0 when the external system state compensator offsets the external system state includes: Constructing the Lyapunov function of the external system state; Classify all acquired agents using the Lyapunov function of the external system state to obtain a set of agents that rely on event-triggered strategies and a set that rely on time-triggered strategies; In combination with the Zeno-free triggering mechanism of the external system state compensator, the agent sets of the event-dependent triggering strategy and the time-dependent triggering strategy are solved respectively to obtain the relationship between the external system state and the compensation function; According to the relationship between the external system state and the offset function, it is deduced that the convergence value of the offset function is 0.

9. The method according to claim 1, characterized in that After the step of using the external system state compensator to offset the external system state so that the error output of the multi-agent system converges to 0, the method further includes: sampling actual controller dynamics of a controller in the multi-agent system using a Zeno-free trigger mechanism, and substituting the sampled controller dynamics into the external system state compensator; Under the control of the fully distributed controller, the external system state compensator is used to offset the external system state to achieve collaborative output regulation of the multi-agent system.

10. An electronic device comprising a memory, a processor, and a computer program stored in the memory and running on the processor, characterized in that: When the processor executes the program, it implements the multi-agent collaborative output adjustment method based on a fully distributed strategy as described in any one of claims 1 to 9.

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