Multi-agent output regulation method and device under joint connected switching topology condition

Abstract

The application provides a multi-agent output adjustment method and device under a joint connectivity handover topology condition, and belongs to the technical field of multi-agent collaborative output adjustment. The method comprises the following steps: researching a multi-agent system model and a communication topology of a generalized heterogeneous multi-agent system; designing a communication algorithm for communication with neighbor agents to obtain an external system matrix through a joint connectivity communication topology; designing a distributed controller with an external system switching compensator; substituting the distributed controller as a control input of the multi-agent system model into the multi-agent system model to make an error output converge to 0; when the agent is not connected with the external system, the external system switching compensator is enabled to offset the external system state; or when the agent is connected with the external system, the external system signal directly obtained is used to offset the external system state. The technical scheme of the application can solve the problem that each agent needs to know the external system matrix in advance in the prior art.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of multi-agent cooperative output regulation, and particularly relates to a multi-agent output regulation method and equipment under a joint connected switching topology condition. BACKGROUND

[0002] The concept of "agent" is an abstraction of various physical entities, and generally refers to individuals with perception, communication, calculation and execution capabilities. Compared with a single agent, a multi-agent system has a wider application field in modern engineering, such as mobile robots, mechanical arms, unmanned aerial vehicles and distributed energy systems. Due to the wide application of multi-agent systems in modern engineering and the advantages in completing scalable and robust group tasks, cooperative control of multi-agent systems has been a research hotspot for many years.

[0003] The cooperative control of multi-agent systems mainly aims to achieve the desired group behavior through the interaction between agents with information interaction function. Among them, as an important research field of multi-agent system control, the switching topology of multi-agent system refers to the case that the information interaction network structure between multi-agents in the multi-agent system changes dynamically over time or conditions. Switching topology has been increasingly concerned and systematically developed in the field of multi-agent systems: from the early requirement that each graph is connected and has a certain residence time to the current joint connectivity situation.

[0004] The current multi-agent output regulation method under the joint connectivity switching topology condition either does not consider the disturbance of the external system at all, or needs to have strong assumption conditions, that is, each agent knows the external system matrix in advance. For example, patent CN118778702A discloses a robust performance formation control method for discrete multi-agent systems, which includes: establishing a linear discrete multi-agent system dynamic model with external disturbance, and it is mentioned in the specification that is a function of x i ( k ), representing the external disturbance; represent disturbance matrices (equivalent to external system matrices) respectively. This method needs to have strong assumption conditions under the joint connectivity condition, that is, each agent knows the external system matrix in advance.

[0005] The reason for knowing the external system matrix in advance is that the prior art has not designed an effective acquisition scheme for external system matrix information. If a traditional consensus scheme is used for data acquisition, the error output of part of the agents will be in a discrete state for a period of time when the external system matrix is not acquired accurately enough, which forms the discrete multi-agent system described in the above patent, thereby causing the system convergence time to be greatly prolonged. SUMMARY

[0006] The technical solution of the present application provides a multi-agent output adjustment method and device under a joint connectivity switching topology, which is mainly aimed at providing a multi-agent output adjustment method and device under a joint connectivity switching topology. The multi-agent output adjustment method can obtain an external system matrix through communication with neighbor agents by means of the joint connectivity of the communication topology. An external system switching compensator is designed in combination with the external system matrix, and a distributed controller containing the external system switching compensator is designed. In this way, when the agents in the communication topology are not connected with the external system, the external system state of the multi-agent system model is offset by using the external system switching compensator, and when the agents are connected with the external system, the external system signal is directly obtained from the external system to offset the external system state, so that the error output of the multi-agent system model converges to 0. In summary, the communication method disclosed in the present application for the joint connectivity switching topology can effectively solve the problem that the previous method needs to obtain the known external system matrix under this condition. The controller design scheme and parameter design method disclosed in the present application directly use the external system signal when connected with the external system, without the need to calculate the external system switching compensator, which can save communication resources and computing resources, and make the multi-agent system model converge faster.

[0007] According to a first aspect of the present application, the embodiments of the present application provide a multi-agent output adjustment method under a joint connectivity switching topology, which comprises: researching a multi-agent system model and a communication topology of a generalized heterogeneous multi-agent system; wherein the multi-agent system model comprises an agent state, a control input and an error output caused by an external system state, and the communication topology satisfies the joint connectivity switching topology condition; designing a communication algorithm for communication with neighbor agents, and obtaining an external system matrix through the joint connectivity communication topology using the communication algorithm; designing a distributed controller in combination with the observation value of the agent state and the controller dynamics, wherein the distributed controller is built-in with an external system switching compensator, and the external system switching compensator is constructed using the external system matrix and the communication with the neighbor agents; taking the distributed controller as the control input of the multi-agent system model, and substituting it into the multi-agent system model, so that the error output of the multi-agent system model converges to 0; wherein when the agents in the communication topology are not connected with the external system, the external system switching compensator is enabled to offset the external system state of the multi-agent system model, so that the error output converges to 0; or when the agents are connected with the external system, the external system signal is directly obtained to offset the external system state of the multi-agent system model using the directly obtained external system signal, so that the error output converges to 0.

[0008] Preferably, the multi-agent output regulation method under the joint connectivity switching topology condition, the steps of researching the multi-agent system model and the communication topology of the generalized heterogeneous multi-agent system include: researching the multi-agent system model including the agent state space expression, the measurement output expression and the error output expression; wherein the agent state space expression, the measurement output expression and the error output expression all include the agent state, the control input, the external system state and the corresponding appropriate dimension matrix of each parameter; setting the multi-agent system model to exist the solution pair of the regulator equation, so that the multi-agent system model satisfies the model constraint equation, and the model constraint equation includes the external system matrix and the corresponding appropriate dimension matrix of each parameter; the communication topology researched is a switching topology, and the communication topology satisfies the joint connectivity assumption.

[0009] Preferably, the multi-agent output regulation method under the joint connectivity switching topology condition, the steps of designing the communication algorithm for communication with the neighbor agent, and using the communication algorithm to obtain the external system matrix through the joint connectivity communication topology include: initializing the auxiliary variable and the intermediate variable of the agent; wherein the auxiliary variable indicates whether the agent obtains the external system matrix; when the agent is connected with the external system, the intermediate variable is set as the external system matrix; with the help of the joint connectivity communication topology, the auxiliary variable and the intermediate variable are propagated to the neighbor agent; when the agent is not connected with the external system, the agent communicates with the neighbor agent through the joint connectivity communication topology; in the joint connectivity communication topology, the intermediate variable of the agent connected with the external system is obtained through the neighbor agent using the auxiliary variable as the external system matrix.

[0010] Preferably, the multi-agent output regulation method under the joint communication switching topology condition combines the observation value of the agent state and the controller dynamic to design a distributed controller, wherein the distributed controller is built-in with an external system switching compensator, the external system switching compensator uses the external system matrix and the steps of constructing the communication with the neighbor agent to include: constructing the compensator estimation value corresponding to the external system switching compensator according to the communication content of the agent with the neighbor agent at each trigger time, constructing the consistency error expression of the controller dynamic according to the compensator estimation value, the external system state and the connection of the agent with the external system; using the consistency error of the controller dynamic to combine the external system matrix to construct the differential equation group of the external system switching compensator; constructing the expression of the controller dynamic according to the external system switching compensator, the connection of the agent with the external system and the external system state; using the observation value of the agent state and the corresponding agent gain, and the controller gain corresponding to the controller dynamic to construct the expression of the distributed controller; wherein the controller gain is solved using the regulator equation solution pair of the multi-agent model and the agent gain; and using the controller dynamic, the distributed controller and the observation value of the agent state to construct the generalized observer of the agent; wherein the generalized observer represents the observation deviation between the theoretical output obtained by substituting the distributed controller into the multi-agent system model and the measured output of the agent.

[0011] Preferably, the multi-agent output regulation method under the condition of the jointly connected switching topology combines the observation value of the agent state and the controller dynamic design to design a distributed controller, wherein the distributed controller is internally provided with an external system switching compensator, the external system switching compensator is constructed using the external system matrix and the steps of communication with the neighbor agent, and further comprises: constructing a trigger mechanism of the distributed controller; wherein the trigger mechanism comprises a topology switching trigger mechanism corresponding to a topology switching time and a no switching trigger mechanism corresponding to a normal trigger time; when the trigger time of the distributed controller reaches the topology switching time, the distributed controller enters the topology switching trigger mechanism; in the topology switching trigger mechanism, the agent controls communication with the neighbor agent according to the communication algorithm, interacts with the neighbor agent through the intermediate communication variable as the communication content with the neighbor agent, wherein the intermediate communication variable is the true value of the external system state or the estimated value of the external system state; the communication content and the external system matrix are imported into the overall expression of the distributed controller to calculate the distributed controller and the external system state switching compensator; or when the trigger time of the distributed controller reaches the normal trigger time, the distributed controller enters the no switching trigger mechanism; in the no switching trigger mechanism, when the mode selector is 0, the distributed controller is controlled to enter the time triggered mode, and when the mode selector is not 0, the distributed controller is controlled to enter the event triggered mode; wherein the event triggered mode is constructed using the event triggered parameter and the trigger error term; in the event triggered mode, the trigger error term corresponding to the distributed controller continuously changes from 0 to eliminate the Zeno phenomenon of the distributed controller.

[0012] Preferably, the multi-agent output regulation method under the condition of the jointly connected switching topology directly acquires the external system signal when the agent has been connected with the external system, uses the directly acquired external system signal to offset the external system state of the multi-agent system model, so as to make the error output converge to 0, and the step of constructing the external system switching compensator using the external system matrix and the communication with the neighbor agent comprises: when the agent has been connected with the external system, stopping receiving the communication message from the neighbor agent and terminating the no switching trigger mechanism; only transmitting the external system state to the neighbor agent as the communication content; the neighbor agent estimates the current signal of the external system at the trigger moment; using the external system signal directly acquired from the external system to replace the external system switching compensator and substitute into the expression of the distributed controller to calculate the distributed controller; using the external system signal to offset the external system state of the multi-agent system model so as to make the error output converge to 0.

[0013] Preferably, in the multi-agent output regulation method under the joint communication switching topology condition, the distributed controller is taken as the control input of the multi-agent system model, and substituted into the multi-agent system model, so that the error output of the multi-agent system model converges to 0, and the step comprises: substituting the distributed controller into the multi-agent system model as the control input of the multi-agent system model; constructing an intermediate calculation function in combination with a matrix of appropriate dimensions; constructing a plurality of equivalent calculation functions in combination with a regulator equation solution pair, an agent state, an external system state and an external system switching compensator; wherein the equivalent calculation function comprises a cancellation bias function between the external system switching compensator and the external system state; using the intermediate calculation matrix and the plurality of equivalent calculation functions, rewriting the multi-agent system model after substituting the distributed controller, to obtain an equivalent form of a closed-loop system; wherein the equivalent form of the closed-loop system comprises a slow subsystem and a fast subsystem; according to the relationship between the fast subsystem and the slow subsystem, it is derived that when the cancellation bias function converges to 0, the error output of the multi-agent system model converges to 0; in combination with the trigger mechanism of the distributed controller, the external system switching compensator is enabled, and it is derived that the cancellation bias function converges to 0, so that the error output of the multi-agent system model converges to 0.

[0014] According to a second aspect of the present application, the present application also provides an electronic device comprising a memory, a processor and a computer program stored in the memory and run by the processor, wherein the processor implements the multi-agent output regulation method under the joint communication switching topology condition according to any one of the above technical solutions when executing the program.

[0015] The technical solution of the present application has at least the following technical effects:

[0016] The application provides a multi-integral output regulation scheme under a joint connectivity switching topology condition, studies a multi-agent system model and a communication topology of a generalized heterogeneous multi-agent system, the multi-agent system model includes an agent state, a control input and an error output caused by an external system state, and the communication topology satisfies a joint connectivity switching topology condition, that is, the type of the communication topology is a switching topology, and the joint connectivity assumption is satisfied. Specifically, to solve the problem that the prior art needs to know the external system matrix of each agent in advance, a communication algorithm for communicating with neighbor agents is constructed, through which the agent connected with the external system in the communication topology can directly obtain the external system matrix. Using the communication algorithm and combining the joint connectivity characteristics of the communication topology, the external system matrix can be obtained through relay communication between neighbor agents. Based on this, a distributed controller is designed, which has an external system switching compensator built-in, and the external system switching compensator is constructed using the external system matrix obtained by the above communication algorithm and the communication with neighbor agents. In this way, the above external system matrix can be obtained through communication with neighbor agents, and even the external system state can be obtained. Then, the above distributed controller is used as the control input of the multi-agent system model and is introduced into the multi-agent system model to offset the external system state, so that the error output of the multi-agent system model converges to 0. Specifically, when the agent in the communication topology is not connected with the external system, the above external system switching compensator is enabled, the external system switching compensator obtains the external system matrix through the joint connectivity communication topology according to the above communication algorithm, and calculates the external system matrix, so as to offset the external system state of the multi-agent system model, and make the error output converge to 0; when the agent is connected with the external system, the external system signal is directly obtained, and the external system signal is directly used to offset the external system state, so as to make the error output converge to 0. Through the above technical scheme, it can be known that the technical scheme of the application does not need to know the external system matrix of each agent in advance under the joint connectivity switching topology condition, but only needs to obtain the external system matrix through the communication algorithm with neighbor agents and the joint connectivity characteristics of the communication topology when the multi-agent actually runs and needs to offset the external system state. And the external system matrix is used to design an external system switching compensator to offset the external system state, or the external system signal is directly used to offset the external system state when directly connected with the external system, so as to control the error output of the multi-agent system model to converge to 0, thereby saving communication resources and calculation resources, and making the multi-agent system model converge faster. BRIEF DESCRIPTION OF DRAWINGS

[0017] The accompanying drawings, which are included to provide a further understanding of the application and are incorporated in and constitute a part of this application, illustrate embodiments of the application and together with the description serve to explain the application. In the drawings:

[0018] Figure 1 A flowchart of a multi-agent output adjustment method under a joint communication handover topology condition provided by an embodiment of the application is shown in the figure.

[0019] Figure 2 A communication topology graph of a generalized heterogeneous multi-agent system provided by an embodiment of the application is shown in the figure.

[0020] Figure 3 A convergence diagram of error outputs of multiple agents provided by an embodiment of the application is shown in the figure.

[0021] Figure 4 A structural diagram of an electronic device provided by an embodiment of the application is shown in the figure. DETAILED DESCRIPTION

[0022] In order to more clearly illustrate the overall concept of the application, the following will be described in detail with reference to the accompanying drawings.

[0023] Each of the embodiments in the specification is described in a progressive manner, and the same or similar parts of each of the embodiments can be referred to each other. Each of the embodiments focuses on the differences from other embodiments. The application can have various changes and modifications for those skilled in the art. Any modification, equivalent replacement, improvement, etc. within the spirit and principle of the application shall be included in the protection scope of the application. In the following description, many specific details are set forth in order to provide a thorough understanding of the application, but the protection scope of the application is not limited to the specific embodiments disclosed below. It should be noted that the embodiments of the application and the features in each of the embodiments can be combined with each other without conflict.

[0024] The prior art has the following defects:

[0025] The multi-agent output adjustment mode under the current joint connectivity switching topology condition either does not consider the interference of the external system at all, or needs to have a strong assumption condition, that is, each agent knows the external system matrix in advance. This mode needs to have a strong assumption condition under the joint connectivity condition, that is, each agent knows the external system matrix in advance. The reason for knowing the external system matrix in advance is that the prior art has not designed an effective acquisition scheme for external system matrix information. If a traditional consistency scheme is used for data acquisition, the error output of part of the agents will be in a discrete state for a period of time when the external system matrix is not acquired accurately enough, which forms a discrete multi-agent system, thereby causing the system convergence time to be greatly prolonged. Due to the joint connectivity characteristic of the communication topology, all agents cannot acquire the external system matrix at the same time in the communication process, and therefore the prior art needs the above strong assumption condition, that is, each agent knows the external system matrix in advance.

[0026] To solve the above problems, the following embodiments of the present application provide a multi-agent output adjustment scheme under a joint connectivity switching topology condition. For the joint connectivity switching topology, the communication propagation method provided by the technical scheme of the present application can acquire the external system matrix through mutual communication with neighbor agents by means of the joint connectivity communication topology. In this way, an external system switching compensator is built in the controller, the external system switching compensator is constructed using the external system matrix and the communication with the neighbor agents. When error output control is needed for the multi-agent system model, for a specific agent, if the agent is not connected with the external system, the external system switching compensator is started to offset the external system state of the multi-agent system model, so that the error output converges to 0. If the agent is connected with the external system, the external system signal acquired by the communication with the external system is directly used to offset the external system state, so that the error output converges to 0. Since the external system matrix can be acquired through the joint connectivity switching topology or directly acquired from the external system, it is not necessary for each agent in the multi-agent system to know the external system matrix in advance, and it is not necessary to use a consistency scheme for data acquisition. Therefore, the controller and parameters designed according to the method of the present application can effectively save communication resources and computing resources, so that the system converges quickly. The above method solves the problem that the traditional consistency scheme acquires the external system matrix, is prone to a discrete state, becomes a discrete multi-agent system, and the system convergence time is greatly prolonged.

[0027] To achieve the above object, referring to Figure 1 , Figure 1 A flowchart of a multi-agent output adjustment method under a joint connectivity switching topology condition provided by the embodiments of the present application is shown in Figure 1 , and the multi-agent output adjustment method comprises the following steps.

[0028] S110: research the multi-agent system model and the communication topology of the generalized heterogeneous multi-agent system; wherein the multi-agent system model comprises the agent state, the control input, and the error output caused by the external system state, and the communication topology satisfies the joint connectivity switching topology condition.

[0029] It should be noted that the generalized heterogeneous multi-agent system researched by the embodiments of the present application is not a discrete multi-agent system, nor is it an agent system with a fixed topology (for example, the neighbor agent is fixed or the agent is always connected to the external system). It is a switching topology under the joint connectivity assumption.

[0030] Under the joint connectivity assumption, the communication network between a group of agents does not need to be globally connected at any moment, but as long as the communication connection relationship of the entire network "puzzle" can form a connected graph within a continuous period of time, the system can achieve consistent goals (such as consensus, cooperation, formation, etc.). The embodiments of the present application utilize the structure of the switching topology under the joint connectivity assumption to obtain the external system matrix, and use the obtained external system matrix to design an external system switching compensator to compensate for the error output caused by the external system state.

[0031] Specifically, as a preferred embodiment, the multi-agent output regulation method under the joint connectivity switching topology condition described above, step S110: research the multi-agent system model and the communication topology of the generalized heterogeneous multi-agent system; comprising:

[0032] S111: research the multi-agent system model comprising the agent state space expression, the measurement output expression, and the error output expression; wherein the agent state space expression, the measurement output expression, and the error output expression all comprise the agent state, the control input, the external system state, and the corresponding appropriate dimension matrix of each parameter.

[0033] Specifically, the multi-agent system model corresponding to the generalized heterogeneous multi-agent system targeted by the present application is described as follows

[0034] (1)

[0035] wherein, xi, ui, yi, and ei represent the agent state, the control input, the measurement output, and the error output of the ith agent, respectively, v x0 represents the external system state; A i 、B i 、P i 、E i 、C i、D i 、F i 、C mi 、D mi and F mi All are matrices of appropriate dimensions. In the aforementioned multi-agent system model, This represents the state-space expression of the agent. This represents the expression for the measurement output. This represents the error output expression. Additionally, it needs to be specified... And it is assumed that the generalized heterogeneous multi-agent system is strongly stoic.

[0036] S112: Assume that the multi-agent system model has a pair of solutions to the regulator equation, such that the multi-agent system model satisfies the model constraint equation, which includes the external system matrix and the appropriate dimension matrix corresponding to each parameter.

[0037] Suppose that the regulator equation of the multi-agent system model provided in this application has a solution pair. The model constraint equations are as follows:

[0038] (2)

[0039] Among them, the external system state in the above multi-agent system model v It is generated by an external system. Its relationship with the external system matrix S is as follows: External system matrix The external system matrix is ​​neutral and stable, and is known in advance only to agents connected to the external system. Other agents not connected to the external system need to use certain communication algorithms, combined with the communication topology of the multi-agent system under the joint connectivity switching topology, to learn about the external system matrix through mutual communication between neighboring agents.

[0040] S113: The communication topology under study is a switching topology, and the communication topology satisfies the joint connectivity assumption.

[0041] The purpose of this application is to realize a multi-agent system and communication topology of the form (1). Design a distributed controller This ensures that for a generalized heterogeneous multi-agent system with arbitrary initial states, its error output... All converge to 0, and when the external system state... At that time, the closed-loop system is asymptotically stable. The communication topology... The joint connectivity assumption is satisfied. The communication topology studied in this application is as follows: Figure 2as shown. Figure 2 In the communication topology graph of the generalized heterogeneous multi-agent system as shown, the fixed topology is indicated by a solid line, and the random on-off of the agent is indicated by a dashed line, that is, the condition of the joint connectivity switching topology is met by Figure 2 It can be seen that the communication topology is a switching topology.

[0042] In the embodiment of the application, the joint connectivity assumption met by the communication topology of the multi-agent system is that there is a time sequence Satisfies the following two conditions:

[0043] So that ;

[0044] Is not connected; Is connected. Wherein, Indicates the total number of topology switching from the initial time To Time, here . That is, in continuous time, for any time, the communication connection of the communication topology exists in the disconnected state, but every time the communication topology switches, the union set of the communication topology graph is connected in the entire time set. If a long enough time period is considered, all different communication topology graphs in this time period are superimposed, and overall, it is connected.

[0045] The application aims to be realized by a communication algorithm and a controller. Through the communication algorithm, the external system matrix is obtained in combination with the agent structure of the joint connectivity switching topology condition, and the distributed controller with the built-in external system switching compensator is used. The external system switching compensator uses the external system matrix to compensate for the error output caused by the external system in the multi-agent system model, so that the error output of the entire multi-agent system model converges to 0; or when the agent is directly connected with the external system, the external system signal is directly obtained, and the error output caused by the external system is compensated.

[0046] Figure 1 The technical scheme provided by the embodiment as shown further comprises:

[0047] S120: Design a communication algorithm for communication with neighbor agents, and use the communication algorithm to obtain an external system matrix through the joint connectivity communication topology.

[0048] The technical scheme provided by the embodiments of the present application does not require each agent to know the communication algorithm in advance under the joint connectivity switching topology condition. The communication algorithm designed by the present application for communication with neighbor agents does not require each agent in the multi-agent system to know the external system matrix in advance, because after the agent directly connected with the external system obtains the external system matrix, the external system matrix can be effectively obtained through the transmission of signals between agents by communication with neighbor agents through the joint connectivity communication topology. The communication algorithm can be used for the controller design strategy and the matching parameter design method under the joint connectivity switching topology condition.

[0049] Specifically, as a preferred embodiment, the above Figure 1 The multi-agent output regulation method under the joint connectivity switching topology condition shown in the figure, step S120: design a communication algorithm for communication with neighbor agents, and use the communication algorithm to obtain the external system matrix through the joint connectivity communication topology, including:

[0050] S121: initialize the auxiliary variables and intermediate variables of the agent; wherein the auxiliary variable indicates whether the agent has obtained the external system matrix.

[0051] S122: when the agent is connected with the external system, set the intermediate variable as the external system matrix.

[0052] S123: through the joint connectivity communication topology, propagate the auxiliary variables and intermediate variables to the neighbor agents.

[0053] S124: when the agent is not connected with the external system, communicate with the neighbor agents through the joint connectivity communication topology, and the communication content includes the auxiliary variables of the interacting agent itself and the neighbor agents, and the intermediate variable of the neighbor agent with the largest auxiliary variable.

[0054] S125: in the joint connectivity communication topology, use the auxiliary variable to obtain the intermediate variable of the agent connected with the external system through the neighbor agent as the external system matrix.

[0055] The communication algorithm provided by the present application addresses the deficiencies of the prior art, and introduces an auxiliary variable to mark the agent i whether the correct external system matrix has been obtained S , and of course the external system state can also be obtained through the communication algorithm.

[0056] Specifically, the communication algorithm and parameter design are as follows:

[0057]

[0058] As can be seen from steps 1-3 of the algorithm above, the auxiliary variable = 0 indicates that the agent is intelligent. i The correct external system matrix was not obtained, and at this time the intermediate variables of agent i are... Time sequence t 1 = 0. From steps 4-7, we know that the signal... This indicates a connection to an external system. , representing intelligent agents i The intermediate variables become the external system matrix. w i = 1, indicating an intelligent agent i The correct external system matrix has been obtained. As shown in steps 8-12, under the assumption that the entire communication topology satisfies the joint connectivity hypothesis, the agent... i propagation to neighboring intelligent agents and S i Due to intelligent agents i The correct external system matrix has been obtained, therefore it can be transmitted to other neighboring agents. and S i This allows neighboring agents to also obtain the correct external system matrix. From steps 14-26 above, it can be seen that when an agent... i When there is no connection to external systems for a long time, that is == 0, propagate the intelligence to neighboring intelligent agents. i Auxiliary variables In jointly connected communication topologies, auxiliary variables are used. Auxiliary variables of neighboring agents w j To exchange, That is, the largest among neighboring intelligent agents w j Exchanges are conducted because if the neighboring intelligent agent is connected to an external system, then... w j That is, 1. w i It can then be 1, at which point we can calculate... w j The agent with the largest index l can communicate with its neighboring agents and set the intermediate variable of that neighboring agent as its intermediate variable, thus transforming the intermediate variable into the external system matrix. Because the communication topology is jointly connected, the neighbor agent can also communicate with other agents, so that the external system state can be finally obtained through the relay transmission among the multi-agents through the jointly connected communication topology. The intermediate variable of the agent finally obtained in communication with the external system is taken as the external system matrix.

[0059] It should be noted that the above , is an intermediate variable of the agent i , which will eventually be equal to the external system matrix after circulation. is an intermediate variable from the neighbor, l indicates the index, and arg indicates the index, which means finding w the largest neighbor.

[0060] In summary, the technical scheme provided by the embodiments of the application sets an auxiliary variable of the agent, which indicates whether the agent has obtained the external system matrix. In combination with the auxiliary variable, when the agent is in communication with the external system, the intermediate variable is set as the external system matrix, and the auxiliary variable serves as a signal that the agent is in communication with the external system. When the communication topology meets the joint connectivity, that is, the entire communication topology is connected at all times, the auxiliary variable and the intermediate variable are propagated to the neighbor agent, so that the neighbor agent can also obtain the external system matrix. Through the above-mentioned manner, under the condition of joint connectivity switching topology, other agents can also obtain the external system matrix. In addition, when the agent is not directly in communication with the external system, the intermediate variable (i.e., the external system matrix) of the agent in communication with the external system is obtained from the auxiliary variable of the neighbor agent, and then transmitted to the agent itself as the external system matrix obtained by the agent. Through the above-mentioned method, each agent in the generalized heterogeneous multi-agent system does not need to obtain the communication algorithm in advance or know the external system matrix in advance. Only by using the topology structure of the communication topology meeting the joint connectivity, the external system matrix can be obtained through the communication among the agents. Through the above-mentioned method, the agents of the entire system can quickly and effectively obtain the external system matrix, and the output error of the agent caused by the external system can be compensated in combination with the external system matrix, so that the entire multi-agent system quickly converges, and the convergence time of the multi-agent system is greatly shortened.

[0061] Figure 1 The technical scheme provided by the embodiments shown in the step S120: design a communication algorithm for communication with the neighbor agent, the communication algorithm is known by at least one agent in the communication topology, and after obtaining the external system matrix through the jointly connected communication topology, the technical scheme further includes:

[0062] S130: Combine the observations of the agent's state with the controller's dynamic design of a distributed controller. The distributed controller has a built-in external system switching compensator, which is constructed using the external system matrix and communication with neighboring agents.

[0063] The technical solution provided in this application combines the observed values ​​of the agent states and the controller dynamics to design a distributed controller. Because this distributed controller is obtained from the observed values ​​of the agent states and the external system matrix is ​​known, it can highly simulate the control input of a multi-agent system. Substituting this distributed controller into the aforementioned multi-agent system model allows it to serve as the control input, ensuring the stability and rapid convergence of the entire multi-agent system. Specifically, since the external system switching compensator communicates with neighboring agents and uses the aforementioned external system matrix, it can directly calculate the external system state using this matrix, accurately compensating for the error output caused by the external system state, thereby enabling the entire multi-agent system to converge rapidly.

[0064] Specifically, as a preferred embodiment, step S130 above: combining the observed values ​​of the agent's state and the controller to dynamically design a distributed controller, wherein the distributed controller has a built-in external system switching compensator, which is constructed using the external system matrix and communication with neighboring agents, specifically including: S131: constructing the compensator estimate corresponding to the external system switching compensator according to the communication content between the agent and neighboring agents at each trigger time, and constructing the controller's dynamic consistency error expression according to the compensator estimate, the external system state, and the connectivity between the agent and the external system.

[0065] In this embodiment, the calculation formula for the compensator estimate is set as follows: ;in, This represents the communication content between agent i and its neighboring agents at each trigger time. Using this communication content, the calculation formula for the compensator estimate mentioned above can be applied. The compensator estimate of agent i at time t is calculated. Similarly, the compensator estimate of neighbor agent j at time t... By combining the compensator estimate, the external system state, and the connectivity between the agent and the external system using the above method, a dynamic consistency error expression for the controller can be constructed:

[0066]

[0067] in, represents the connection status with the external system (1 for being connected, 0 for not being connected), v represents the actual external system state, z i represents the compensator, c io represents the historical connection status with the external system (1 for having been connected, 0 for not having been connected), represents the estimated value of the external system state, represents the connection status of the agent i with the agent j, represents the intermediate function of the communication content of the agent i, which is estimated by the compensator estimate value of the agent i at time t is calculated in combination with each time t, and for the same reason, represents the intermediate function of the communication content of the agent j, represents the consistency error of the controller dynamics.

[0068] As can be seen from the above, the intermediate function of the communication content of the agent i can be obtained from the compensator estimate value of the agent i at time t , and the formula is: It can be seen that the compensator estimate value of the agent i at time t is obtained from the communication content sent by the agent i to the neighbor at each triggering time . For the same reason, the intermediate function of the communication content of the agent j can be calculated from the compensator estimate value of the neighbor agent j at time t .

[0069] S132: Use the consistency error of the controller dynamics in combination with the external system matrix to construct the differential equation expression of the external system switching compensator.

[0070] The differential equation expression of the external system switching compensator is as follows: . Wherein, represents the external system switching compensator, is a constant; qi represents the above-mentioned consistency error of the controller dynamics, S represents the external system matrix, which can be obtained by the joint connected communication topology through the above-mentioned communication algorithm, represents the differential form of the external system switching compensator.

[0071] S133: According to the external system switching compensator, the connection status of the agent with the external system and the external system state, the expression of the controller dynamics is constructed.

[0072] The expression of the controller dynamics is as follows:

[0073] wherein, represents the controller dynamics of the agent i, which is switched by the above-mentioned external system switching compensator and the agent i and the connection condition of the external system and the external system state v are calculated.

[0074] S134: using the observation value of the agent state and the corresponding agent gain, and the controller gain corresponding to the controller dynamics, the expression of the distributed controller is constructed; wherein the controller gain is solved by using the regulator equation of the multi-agent model and the agent gain.

[0075] The expression of the distributed controller is as follows:

[0076] wherein, represents the distributed controller, the agent state estimation value of the agent i corresponds to the agent gain, represents the controller i corresponding to the controller gain of the controller dynamics of the controller. Wherein can make the closed-loop system satisfy the regular, stable and impulse-free conditions.

[0077] S135: using the controller dynamics, the distributed controller and the observation value of the agent state, a generalized observer of the agent is constructed; wherein the generalized observer represents the observation deviation between the theoretical output obtained by substituting the distributed controller into the multi-agent system model and the measured output of the agent.

[0078] The embodiment of the application uses the controller dynamics, the distributed controller and the observation value of the agent state to construct the generalized observer of the agent. Specifically, the generalized observer of the agent includes the use of the multi-agent system model in the generalized observer, and the application of the system output in the multi-agent system model. That is, the observation deviation is obtained by subtracting the detected actual output from the theoretical output calculated after the observation state is brought into the system, and the state observation value can be adjusted according to the observation deviation.

[0079] Specifically, as a preferred embodiment, step S135; using the controller dynamics, the distributed controller and the observation value of the agent state, a generalized observer of the agent is constructed, specifically including:

[0080] Substituting the controller dynamics, the distributed controller and the observation value of the agent state into the agent state space expression of the multi-agent system model, the system state observation value is obtained.

[0081] The observation value of the agent state, the controller dynamics and the distributed controller are substituted into the measurement output expression of the multi-agent system model to obtain an observation output of the agent.

[0082] The observation deviation between the observation output and the measurement output of the agent is calculated in combination with the controller gain.

[0083] The generalized observer of the agent is constructed in combination with the system state observation value and the observation deviation.

[0084] The generalized observer of the agent is constructed in combination with the system state observation value and the observation deviation.

[0085]

[0086] The expression form of the generalized observer is constructed by referring to the agent state space expression and the measurement output expression in the multi-agent system model, and the controller dynamics , the distributed controller and the observation value of the agent state are substituted into the original agent state space expression to obtain the system state observation value . The observation value of the agent state , the controller dynamics and the distributed controller are substituted into the original measurement output expression of the multi-agent system model to obtain the observation output of the agent. The observation deviation between the observation output and the policy output of the agent can be calculated in combination with the controller gain , the observation output of the agent and the measurement output of the agent, and the calculation formula is as follows: The generalized observer of the agent is constructed in combination with the system state observation value and the observation deviation as follows: After the generalized observer of the agent is constructed, the observation value of the agent state can be effectively adjusted according to the observation deviation.

[0087] In summary, the overall expression form of the distributed controller constructed in the embodiment of the application is as follows

[0088] (3)

[0089] Wherein, from top to bottom, the first term is the expression of the distributed controller, the second term is the expression of the controller dynamics, the third term is the expression of the generalized observer, the fourth term is the differential equation set of the external system switching compensator, and the fifth term is the consistency error expression of the controller dynamics. Here, several parameters to be explained are as follows:

[0090] ;

[0091] ;

[0092] ;

[0093] .

[0094] where, represents the controller dynamics of agent i , which can be estimated by the compensator value at time t , combined with the expression of the distributed controller above; represents the i th trigger time of agent k , is the communication content sent by agent i to its neighbors at each trigger time k . The communication content does not include the external system matrix, only the intermediate variable of the agent's calculation; the value of this intermediate variable can be the true value of the external system state, or the calculated value of the external system state estimated by the agent itself. represents the estimated value of the external system state, represents the time when agent i first connects with the external system, and the corresponding represents the external system state at that time. Ci0 is used to represent whether agent i has ever connected with the external system.

[0095] Here we assume and has . The controller gain makes the closed-loop system satisfy the regular, stable and impulse-free characteristics, and the selection method is given by Algorithm 8.1.1 in the book "Generalized System Theory" written by Jiang Guangren, which will not be repeated here. The compensator gain is a constant.

[0096] ​In summary, the technical scheme provided by the embodiments of the present application combines the observation value of the agent state and the controller dynamic to design a distributed controller, the distributed controller includes a compensator estimate value constructed according to the communication content of the agent with the neighbor agent at each triggering time, the communication content can be the direct external system state or the estimate value of the external system state, so that the external system switching compensator constructed using the compensator estimate value can accurately compensate the error output caused by the external system state. Among them, the connection condition of the agent and the external system is an important factor that needs to be considered when constructing the consistency error of the controller dynamic, when the agent is directly connected with the external system, the agent can directly obtain the external system signal, the signal includes the external system state and the external system matrix, and the distributed compensator calculated by substituting the above formula can directly use the directly obtained external system state to compensate the error output of the multi-agent system model. In addition, the above external system state can be obtained by communication with the neighbor agent, or the previously obtained external system state is applied. Because of the communication topology structure under the joint connectivity switching topology, if the topology is not switched, the external system state is unchanged. In addition, the differential equation set of the external system switching compensator is constructed by using the consistency error of the controller dynamic and the external system matrix, the value of the external system switching compensator can be directly obtained from the differential equation set, and then substituted into the expression of the controller dynamic, combined with the external system state, the controller dynamic can be calculated, and finally the controller dynamic is substituted into the expression of the distributed controller, and the above distributed controller is obtained. The distributed controller can be used as the control input of the multi-agent system model to balance the error output caused by the external system state.

[0097] In addition, the above distributed controller does not need to offset the external system state every moment, and the application designs two triggering mechanisms of the distributed controller: one is the topology switching triggering mechanism corresponding to the topology switching time, and the other is the no switching triggering mechanism corresponding to the normal triggering time. In the no switching triggering mechanism, the time triggering mode and the event triggering mode are included, and both triggering modes can avoid the Zeno phenomenon caused by the triggering of the distributed controller.

[0098] Specifically, as a preferred embodiment, the multi-agent output regulation method under the joint connectivity switching topology condition, S130: combine the observation value of the agent state and the controller dynamic to design a distributed controller, wherein the distributed controller is built-in with an external system switching compensator, and the external system switching compensator is constructed using the external system matrix and the communication with the neighbor agent, including:

[0099] S136: construct the triggering mechanism of the distributed controller; wherein the triggering mechanism includes the topology switching triggering mechanism corresponding to the topology switching time, and the no switching triggering mechanism corresponding to the normal triggering time.

[0100] S137: When the trigger time of the distributed controller reaches the topology switching time, the distributed controller enters the topology switching trigger mechanism.

[0101] S138: In the topology switching trigger mechanism, the agent communicates with the neighbor agent according to the communication algorithm, and interacts with the neighbor agent through the joint communication topology and the intermediate communication variable as the communication content of the agent at each trigger time. The intermediate communication variable is the true value of the external system state or the estimated value of the external system state.

[0102] S139: The communication content and the external system matrix are imported into the overall expression of the distributed controller, and the distributed controller and the external system state switching compensator are calculated. The external system matrix is obtained by the above communication algorithm.

[0103] The form of the overall expression of the distributed controller is shown in formula (3), and the method for calculating the distributed controller using the communication content and the external system matrix is described in steps S131-S135 above.

[0104] Or,

[0105] The distributed controller enters the no-switching trigger mechanism, which is as follows:

[0106] S1310: When the trigger time of the distributed controller reaches the normal trigger time, the distributed controller enters the no-switching trigger mechanism.

[0107] S1320: In the no-switching trigger mechanism, when the mode selector is 0, the distributed controller is controlled to enter the time trigger mode, and when the mode selector is not 0, the distributed controller is controlled to enter the event trigger mode; wherein the event trigger mode is constructed using the event trigger parameter and the trigger error term.

[0108] S1330: In the event trigger mode, the trigger error term corresponding to the distributed controller continuously changes from 0 to eliminate the Zeno phenomenon of the distributed controller.

[0109] The selection mode of the topology switching trigger mechanism and the no-switching trigger mechanism is as follows:

[0110]

[0111] Wherein, the selector represents the time trigger mode, and the selector represents the event trigger mode, both of which can avoid the Zeno phenomenon. In addition, when the trigger time reaches the switching topology time If the condition is satisfied, the trigger mode adjustment of the switching topology is performed, at which the external system matrix is obtained through the above communication algorithm, and the current signal of the external system is obtained through the communication between the agent and the neighbor agent, which can include the estimated value of the external system state or the true value of the external system state.

[0112] It should be noted that the time trigger parameter in the expression of the above trigger mechanism is as follows: , wherein, α is a time trigger intermediate parameter, β is an event trigger parameter, λ M The maximum eigenvalue of the Laplacian matrix in the communication topology graph at the current moment is represented. The trigger error term is designed as follows: ; is the compensator value corresponding to t; the selector is designed as follows: is the selector, is the topology switching moment, and the right lower subscript l represents the switching number.

[0113] The design concept of this distributed controller is to use more accurate signals as much as possible. That is, when the agent is connected with the external system, the distributed controller will directly use the external system state v . In this way, when directly connected with the external system, the entire trigger mechanism is no longer run, because the calculation of the external switching compensator z i is not needed, and the external system state v is directly substituted for z i , which is substituted into the above expression of the first item of the distributed controller and the expression of the second item of the controller dynamics, so that the most accurate distributed controller is obtained. The error output caused by the external system state in the above multi-agent system model is compensated using the directly obtained external system state, which can make the error output quickly converge to 0, thereby improving the convergence efficiency of the entire system model.

[0114] The main advantage of the above scheme design of the application is to fully utilize the information of the external system and use more accurate signals as much as possible. At the same time, this method reduces the communication and calculation between agents.

[0115] At the same time, the trigger mechanism is only for the case that the agent cannot directly obtain the external system state v . That is, when the agent i can communicate with the external system, it will not only stop receiving information from the neighbors (such as the above controller dynamics Furthermore, it will also terminate its own event-triggered and time-triggered calculations. Therefore, in this way, communication and computation between intelligent agents can be reduced to some extent.

[0116] The trigger condition will be met when the agent and the external system switch from an unconnected state to a connected state. At this time, the agent... i It will only transmit external system status to its neighbors. v As the content of communication. In this case, the intelligent agent... i The neighbor can estimate the current signal of the external system (the agent) at the moment of each trigger. i Transmit external system status only to neighbors v As communication content, there are prerequisites: intelligent agent i It needs to connect to an external system to propagate directly. v However, its neighboring intelligence is unaware that what agent i is emitting is... v Therefore, intelligent agents i The neighbors still need to be estimated v Although they do not know whether the estimated signal is the current real external signal.

[0117] For example, if the intelligent agent i Always connected to external systems, it will not perform event-triggered or time-triggered computations, and will only send communication data to neighboring agents during topology changes. This communication data includes the actual controller dynamics used by agent i. The dynamic expression of the controller described above: It can be seen that if agent i is always connected to the external system, then its topology switching compensator... This is equivalent to the state of the external system. v， That is, the distributed controller actually transmits the state of the external system. v This also makes it easier for neighboring agents to use the external system state to accurately calculate the distributed controller, enabling the multi-agent system model to converge quickly.

[0118] Furthermore, since the external system is in the form of It can be assumed that as long as the external system and the intelligent agent... i Once connected, information from the external system can be directly accessed by the intelligent agent indefinitely. i Obtaining the consistency error in the dynamic design of the controller. When using estimates of the external system state. To fill the gap in intelligent agents i A blank space indicating that external system information cannot be obtained when disconnected from the external system. The estimated value of this external system state has been given by the calculation formula above and will not be repeated here. Of course, to make the estimate closer to reality, when the intelligent... iWhen connected with the external system, The update will be made. Even from a theoretical point of view, this will result in the same as only once information acquisition and estimation.

[0119] The technical scheme provided by the embodiments of the present application is to construct a trigger mechanism of the distributed controller, which includes a topology switching trigger mechanism corresponding to a topology switching time and a no-switching trigger mechanism corresponding to a normal departure time. When the trigger time of the distributed controller reaches the topology switching trigger time, the distributed controller enters the topology switching trigger mechanism. At this time, the agent and the neighbor agent are controlled to communicate through the above communication algorithm, so that the current signal of the external system is obtained through the joint connected communication topology (the current signal can be the controller dynamic of the neighbor node, and from the above content, the controller dynamic can be the external system state or its estimated value, and includes the external system matrix). At this time, the current signal of the external system is used to calculate according to the expression of the distributed controller to obtain the estimated value of the external system state of the agent, and the current signal (including the external system matrix) is introduced into the expression of the distributed controller to construct the distributed controller and the external system state switching compensator. When the trigger time reaches the normal trigger time, the distributed controller enters the no-switching trigger mechanism. When the mode selector is 0, the controller enters the time trigger mode, and when the mode selector is not 0, the controller enters the event trigger mode. The selector is 0, and the time trigger mode naturally has no Zeno phenomenon. The event trigger mode is constructed using the event trigger parameter and the trigger error term, and the corresponding trigger error term continuously changes from 0, so that the Zeno phenomenon of the distributed controller can be eliminated.

[0120] Figure 1 The technical scheme provided by the embodiments shown in the present application further includes the following steps after S130: designing the distributed controller by combining the observation value of the agent state and the controller dynamic.

[0121] S140: The distributed controller is taken as a control input of the multi-agent system model, and is substituted into the multi-agent system model, so that the error output of the multi-agent system model converges to 0. When the agent in the communication topology is not connected with the external system, the external system switching compensator is enabled to offset the external system state of the multi-agent system model, so that the error output converges to 0. Or, when the agent is connected with the external system, the external system signal is directly obtained, and the directly obtained external system signal is used to offset the external system state of the multi-agent system model, so that the error output converges to 0.

[0122] Specifically, as shown in the present application Figure 3 The communication topology shown in the present application Figure 2 The error outputs of the four agents in the communication topology shown in the present application , , and ) convergent case. It can be seen from Figure 3 that although the above four agent error outputs are not synchronous convergence, they can achieve fast convergence of error output. Among them, the agent 1 is directly connected with the external system (i.e. circle 0 in Figure 2 ), and uses the directly obtained external system matrix and external system signal (i.e. the true value of the external system state) to offset the external system state in the multi-agent system model, so that the agent error output of the agent 1 converges the fastest.

[0123] It can be seen from the above trigger mechanism that the distributed controller is used as the control input of the multi-agent system model, and is substituted into the multi-agent system model. Since the above external system switching compensator is constructed using the external system matrix and the communication with the neighbor agent, the external system state can be accurately estimated or accurately obtained through the communication of the neighbor node. The external system switching compensator can effectively offset the external system state of the multi-agent system model, so that the error output converges to 0. If the agent is directly connected with the external system, the agent can directly obtain the external system information, and then use the external system signal to directly offset the external system state in the model, so as to quickly converge the error output to 0. In summary, using the external system switching compensator or directly obtaining the external system signal compensation method can promote the fast convergence of the multi-agent system model. Through the above method, each agent in the multi-agent system does not need to know the external system matrix in advance. The problem that the existing traditional consistency scheme obtains data, causing part of the agent error output to be in a divergent state for a period of time when the external system matrix is not accurate enough, and greatly prolonging the system convergence time is solved.

[0124] In addition, as a preferred embodiment, the multi-agent output adjustment method under the joint connected switching topology condition, when the agent has been connected with the external system, directly obtains the external system signal, uses the directly obtained external system signal to offset the external system state of the multi-agent system model, so that the error output converges to 0. The step comprises:

[0125] S141: When the agent has been connected with the external system, stop receiving the communication message from the neighbor agent, and terminate the switching trigger mechanism. The trigger mechanism is only for the case that the agent cannot directly obtain the external system state v. That is, when the agent can communicate with the external system, it will not only stop receiving information from the neighbor, but also terminate its own event trigger and time trigger calculation. Therefore, through this way, the communication and calculation between agents can be reduced to a certain extent.

[0126] S142: Only the external system state is transmitted to the neighboring agent as communication content; the neighboring agent estimates the current signal of the external system at the moment of triggering. The triggering condition will be met when the agent and the external system switch from an unconnected state to a connected state. At this time, the agent... i It will only transmit to its neighbors. v As the content of communication. In this case, the intelligent agent... i The neighboring systems can estimate the current signal of the external system at each trigger, even though they do not know whether the estimated signal is the actual current external signal. For example, if agent i is always connected to the external system, it will not perform event-triggered or time-triggered calculations and will only send data to its neighbors when the topology changes.

[0127] S143: Using external system signals obtained directly from the external system to replace the external system switching compensator, and substituting them into the expression of the distributed controller, the distributed controller is calculated.

[0128] S144: Use external system signals to cancel out the external system state of the multi-agent system model, so that the error output converges to 0. The specific time-varying agent error output curve is shown in the figure below. Figure 3 As shown.

[0129] The technical solution provided in this application embodiment stops receiving communication messages from neighboring agents and terminates the no-handover trigger mechanism when the agent is connected to an external system. This avoids interference from neighboring agent communication messages. At this time, external system signals, including the external system state, can be directly obtained. Only the external system state is transmitted to the neighboring agent as communication content. The neighboring agent can estimate the current signal of the external system by this communication content. Combining the dynamic expression of the controller and the expression of the distributed controller mentioned above, a highly accurate distributed controller can be obtained. Substituting this distributed controller into the multi-agent system model, the external system signals (including the external system state) can be directly used to cancel out the external system state in the multi-agent system model, and the error loss can quickly and accurately converge to 0. The design philosophy of this controller is to use the most accurate signals possible. That is, when the agent is connected to an external system (when the agent can connect to an external system, the entire trigger mechanism is no longer run because no handover triggering is needed at this time),... (Calculations), the controller will directly use the external system state. v The advantage of this approach is that it makes full use of external information and utilizes as many accurate signals as possible. At the same time, this method reduces communication and computation between agents.

[0130] After obtaining the above technical solution, the effectiveness of the above design needs to be demonstrated. Specifically, as a preferred embodiment, the multi-agent output adjustment method under the joint connected switching topology condition, step S140: the distributed controller is taken as the control input of the multi-agent system model, and substituted into the multi-agent system model, so that the error output of the multi-agent system model converges to 0, including:

[0131] S145: Substitute the distributed controller into the multi-agent system model as the control input of the multi-agent system model.

[0132] S146: Combine the appropriate dimension matrix to construct an intermediate calculation function; combine the regulator equation solution pair, agent state, external system state and external system switching compensator to construct multiple equivalent calculation functions; wherein the equivalent calculation function includes a cancellation bias function between the external system switching compensator and the external system state.

[0133] S147: Use the intermediate calculation matrix and multiple equivalent calculation functions to rewrite the multi-agent system model after substituting the distributed controller to obtain the equivalent form of the closed-loop system; wherein the equivalent form of the closed-loop system includes a slow subsystem and a fast subsystem.

[0134] S148: According to the relationship between the fast subsystem and the slow subsystem, it is derived that when the cancellation bias function converges to 0, the error output of the multi-agent system model converges to 0.

[0135] S149: Enable the external system switching compensator in combination with the trigger mechanism of the distributed controller, and derive that the cancellation bias function converges to 0, so that the error output of the multi-agent system model converges to 0.

[0136] Specifically, assume that there is an intermediate calculation matrix And , ; in combination with the above appropriate dimension matrix (such as A i 、B i 、E i 、C i And C mi 、 ) to construct an intermediate calculation function: , and . Here , , and as auxiliary calculation, no exact physical meaning; represents the dimension ofn il The identity matrix. and They are respectively The bottom left corner block and The upper right corner of the block; among which, the above The top left block matrix I The dimension is The dimension of the bottom right block is ; The top left block dimension is The dimension of the bottom right block is .

[0137] After performing linear and coordinate transformations on the closed-loop system corresponding to the multi-agent system model, and combining this with the regulator equations, we obtain the agent states. The following are equivalent computation functions: The error between the observed and actual values ​​of the agent's state. : External system state switching compensator and external system state cancellation deviation function : ; corresponding controller gain : Note the external system status. v There exist equivalent computation functions of the following form: , Indicates that agent i is in the first... k The external system state is obtained at each trigger moment, and based on the intelligent agent i Cases of connection to external systems And whether the agent is currently connected to an external system. From the definition, we can know .

[0138] Therefore, after substituting the above distributed controller, the equivalent form of the closed-loop system corresponding to the multi-agent system model is as follows:

[0139]

[0140] Among them, the state parameters or dimension matrices of the above variables. , , , , , No. i The estimated values ​​of the offsetting bias function for each agent are as follows: , This represents the offsetting deviation of agent i at the k-th trigger moment.

[0141] make , , , , ; where, , , , and are the overall states of the respective functions. The slow subsystem (the 1, 3 and 5 terms of the equivalent form of the above closed loop system) can then be rewritten in compact form as follows:

[0142]

[0143] where the history connection state function of each agent is defined as , the intermediate derivation function is: , the offset deviation function is: , and the estimated offset deviation function is: . I q represents the q dimensional identity matrix, I N represents the N dimensional identity matrix, represents the connection matrix of the agent with the external system.

[0144] Taking out the fast subsystem of the above closed loop system, we have:

[0145]

[0146] , and are the state parameters of the respective variables. It can be found that the second row has been substituted into the slow subsystem, while the term in the first row is only determined by the variables that have dynamic processes in the other three terms in the equation, and does not have an independent dynamic. At this point, the model conversion has been completed, and it is easy to obtain is a sufficient condition for solving the original problem (making the error output of the multi-agent system model converge to 0). The following needs to be demonstrated .

[0147] Specifically, as a preferred embodiment, the multi-agent output adjustment method under the joint communication handover topology condition combines the trigger mechanism of the distributed controller to enable the external system handover compensator, derives the offset cancellation function converging to 0, and makes the error output of the multi-agent system model converge to 0, including: designing an intermediate cancellation vector corresponding to the offset cancellation function, and calculating a Lyapunov function corresponding to the intermediate cancellation vector; designing an augmented vector composed of the trigger error items of the agent, using the augmented vector in combination with the selector of the agent and the connection condition of the agent and the external system, proving that the limit convergence value of the Lyapunov function exists and the intermediate cancellation vector is bounded; according to the Cauchy convergence criterion, designing an intermediate function of the offset cancellation vector corresponding to the Lyapunov function, and proving by reductio ad absurdum that the limit of the intermediate function of the offset cancellation vector converges to 0; according to the relationship between the intermediate function of the offset cancellation vector and the offset cancellation function, deriving that the offset cancellation function converges to 0, and obtaining that the error output of the multi-agent system model converges to 0.

[0148] Specifically, let the intermediate cancellation vector of the i-th agent be: Then, Wherein, is an augmented vector composed of trigger error items, and the intermediate cancellation vector Similarly. Consider the Lyapunov function Then its derivative with respect to time is as follows:

[0149] ; wherein,

[0150] .

[0151] The plurality of agents of the multi-agent system will be dynamically divided into ; If the selector and for any , there is , then If for any , there is , then .

[0152] Therefore , . Let the Boolean parameter be true if and only if , and the Boolean parameter be true if and only if , wherein , and define the functions or connection matrices corresponding to the above S2(t) and S3(t): , . Thus The augmented vector consisting of the triggering error term is thus given by .

[0153] First consider the first and the formula on the right side of the equation:

[0154]

[0155] And for There are two cases: And To analyze both, the derived intermediate cancellation vector is rewritten as follows:

[0156]

[0157] Note that When , then for the agent i can be simplified to Thus when the history has not connected to , then , which means . That is, the triggering error term . And when the history has connected to , , that is, the triggering error term: .

[0158] From the above, it can be derived that: ; Thus it can be known that: When no agent satisfies , the above inequality takes equality. And the topology switching moment can only make the triggering earlier, which means will not exceed the boundary set by the triggering mechanism. Thus there is the following relationship:

[0159] That is ;

[0160] Using the time-triggered intermediate parameter α and the event-triggered parameter β , the two intermediate functions and corresponding to them are substituted into , to the above formula, which can be obtained:

[0161] Where, λ M represents the largest eigenvalue of the Laplacian matrix in the current moment of the communication topology graph. Thus it has the following form:

[0162] , then where the intermediate function .

[0163] This means exists, so is bounded. Further, it is derived that is bounded, so is bounded.

[0164] Since the limit exists, according to the Cauchy convergence criterion, it is derived that: , so .

[0165] Let the cancellation vector intermediate function , so is bounded.

[0166] Then next, by reductio ad absurdum, it is proved that for there exists limit, and .

[0167] Suppose the cancellation vector intermediate function limit does not exist, then , and . Then , so that then so , , which contradicts the original condition. So for there exists . In the following, for the sake of simple expression, the .

[0168] then . Note that , so it is equivalent to .

[0169] According to the relationship between the cancellation vector intermediate function and the cancellation bias function , it is derived that the cancellation bias function converges to 0, and it is obtained that the error output of the multi-agent system model converges to 0, that is .

[0170] It is also noted that , which means . Therefore ; according to the definition of limit, it is known that , , so that if , then . So m can be found such that , so that , , m and are intermediate quantities defined in terms of the limits referred to above (e.g. T and ).

[0171] i.e. which means that . So we have

[0172] , . Note that so . In combination with we know that which means that the bias function is cancelled out. Also, it was mentioned above that , In combination with the previous conclusions we can conclude that the original problem is solved without Zeno phenomenon.

[0173] In addition, the following embodiments of the present application provide product embodiments, which have the same beneficial effects as the above-mentioned embodiments of the method for adjusting the output of multiple agents under the condition of joint connected switching topology, and other technical features in the product embodiments are the same as the features disclosed in the above-mentioned embodiments of the method, which will not be repeated here.

[0174] Referring to Figure 4 , Figure 4 is a structural schematic diagram of an electronic device provided by an embodiment of the present application. As Figure 4 shown, the electronic device includes a memory, a processor, and a computer program stored in the memory and run by the processor, and the processor implements the method for adjusting the output of multiple agents under the condition of joint connected switching topology when executing the program. As Figure 4As shown, the electronic device can include a processing device 1001 (e.g., a central processing unit or a graphics processing unit) that can perform various appropriate actions and processes in accordance with programs stored in a read-only memory ROM 1002 or loaded from a storage device 1003 into a random access memory RAM 1004. In the RAM 1004, various programs and data required for operation of the electronic device described above are also stored. The processing device 1001, the ROM 1002, and the RAM 1004 are connected to each other through a bus 1005. An I / O interface 1006 is also connected to the bus. Generally, the following systems can be connected to the I / O interface 1006: input devices 1007 including, for example, a touch screen, a touch pad, a keyboard, a mouse, an image sensor, a microphone, an accelerometer, and / or a gyroscope; output devices 1008 including, for example, a liquid crystal display (LCD), a speaker, a vibrator; and a communication device 1009. While a model construction device having various systems is shown in the figure, it should be understood that all of the systems shown are not required to be implemented or provided. More or fewer systems can be alternatively implemented or provided.

Claims

1. A method for adjusting the output of multiple agents under a jointly connected switching topology, characterized in that, The method comprises the following steps: Researching a multi-agent system model and a communication topology of a generalized heterogeneous multi-agent system; wherein, the multi-agent system model comprises an agent state, a control input, and an error output caused by an external system state, and the communication topology satisfies a joint connectivity switching topology condition; Designing a communication algorithm for communication with neighbor agents, and using the communication algorithm to obtain an external system matrix through the jointly connected communication topology; Designing a distributed controller in combination with an observation value of the agent state and a controller dynamic, wherein the distributed controller is built-in with an external system switching compensator, and the external system switching compensator is constructed using the external system matrix and communication with neighbor agents; Substituting the distributed controller as a control input of the multi-agent system model into the multi-agent system model to make the error output of the multi-agent system model converge to 0; wherein, When the agent in the communication topology is not connected with the external system, the external system switching compensator is enabled to offset the external system state of the multi-agent system model to make the error output converge to 0; or when the agent has been connected with the external system, an external system signal is directly obtained, and the external system signal directly obtained is used to offset the external system state of the multi-agent system model to make the error output converge to 0; The step of designing a communication algorithm for communication with neighbor agents and using the communication algorithm to obtain an external system matrix through the jointly connected communication topology comprises: Initializing an auxiliary variable and an intermediate variable of the agent; wherein, the auxiliary variable represents whether the agent has obtained the external system matrix; When the agent is connected with the external system, the intermediate variable is set as the external system matrix; With the aid of the jointly connected communication topology, the auxiliary variable and the intermediate variable are propagated to neighbor agents; When the agent is not connected with the external system, the agent communicates with neighbor agents through the jointly connected communication topology, and the communication content comprises interaction of the auxiliary variables of the agent and neighbor agents, and the intermediate variable of the neighbor agent with the largest auxiliary variable is obtained; In the jointly connected communication topology, the intermediate variable of the agent connected with the external system is obtained through the neighbor agent using the auxiliary variable as the external system matrix; The step of designing a distributed controller in combination with an observation value of the agent state and a controller dynamic, wherein the distributed controller is built-in with an external system switching compensator, and the external system switching compensator is constructed using the external system matrix and communication with neighbor agents comprises: According to the communication content of the agent with neighbor agents at each trigger time, a compensator estimation value corresponding to the external system switching compensator is constructed, and a consistency error expression of the controller dynamic is constructed according to the compensator estimation value, an external system state, and a connection condition of the agent with the external system. using the controller dynamics and the external system matrix, constructing a differential equation expression of an external system switching compensator; constructing an expression of the controller dynamics according to the external system switching compensator, the connection of the agent with the external system, and the state of the external system; using the observation of the agent state and the corresponding agent gain, and the controller gain corresponding to the controller dynamics, constructing an expression of the distributed controller; wherein the controller gain is solved using a regulator equation solution pair of the multi-agent system model and the agent gain; and using the controller dynamics, the distributed controller, and the observation of the agent state, constructing a generalized observer of the agent; wherein the generalized observer represents the observation deviation between the theoretical output of the multi-agent system model into which the distributed controller is substituted, and the measured output of the agent.

2. The method of claim 1, wherein, The steps of researching the multi-agent system model and the communication topology of the generalized heterogeneous multi-agent system include: researching a multi-agent system model including an agent state space expression, a measured output expression, and an error output expression; wherein the agent state space expression, the measured output expression, and the error output expression all include the agent state, the control input, the external system state, and the corresponding appropriate dimension matrix of each parameter; setting that the multi-agent system model has a regulator equation solution pair, so that the multi-agent system model satisfies a model constraint equation, and the model constraint equation includes the external system matrix and the corresponding appropriate dimension matrix of each parameter; The communication topology researched is a switching topology, and the communication topology satisfies the joint connectivity assumption.

3. The method of claim 1, wherein, The steps of using the controller dynamics, the distributed controller, and the observation of the agent state to construct the generalized observer of the agent include: substituting the controller dynamics, the distributed controller, and the observation of the agent state into the agent state space expression of the multi-agent system model to obtain a system state observation; substituting the observation of the agent state, the controller dynamics, and the distributed controller into the measured output expression of the multi-agent system model to obtain an observed output of the agent; combining the controller gain to calculate the observation deviation between the observed output of the agent and the measured output; combining the system state observation and the observation deviation to construct the generalized observer of the agent.

4. The method of claim 2, wherein, The steps of combining the observation of the agent state and the controller dynamics to design the distributed controller, wherein the distributed controller has an external system switching compensator, and the external system switching compensator is constructed using the external system matrix and the communication with the neighbor agent, further include: constructing a trigger mechanism of the distributed controller; wherein the trigger mechanism includes a topology switching trigger mechanism corresponding to a topology switching time, and a no-switching trigger mechanism corresponding to a normal trigger time; When the trigger time of the distributed controller reaches the topology switching time, the distributed controller enters the topology switching trigger mechanism; In the topology switching trigger mechanism, the agent communicates with neighbor agents according to the communication algorithm, and interacts with neighbor agents through a joint communication topology to obtain an intermediate communication variable as the communication content of the agent at each trigger time; wherein the intermediate communication variable is a true value of an external system state or an estimated value of the external system state; The communication content and the external system matrix are introduced into the overall expression of the distributed controller to calculate the distributed controller and the external system state switching compensator; Or, when the trigger time of the distributed controller reaches the normal trigger time, the distributed controller enters the no-switching trigger mechanism; In the no-switching trigger mechanism, when the mode selector is 0, the distributed controller enters the time-triggered mode, and when the mode selector is not 0, the distributed controller enters the event-triggered mode; wherein the event-triggered mode is constructed using an event-triggered parameter and a trigger error term; In the event-triggered mode, the trigger error term corresponding to the distributed controller continuously changes from 0 to eliminate the Zeno phenomenon of the distributed controller.

5. The method of claim 4, wherein, The step of directly obtaining the external system signal when the agent has communicated with the external system, and using the directly obtained external system signal to offset the external system state of the multi-agent system model to make the error output converge to 0, comprises: When the agent has communicated with the external system, stop receiving communication messages from neighbor agents and terminate the no-switching trigger mechanism; Only transmit the external system state to neighbor agents as communication content; neighbor agents estimate the current signal of the external system at the trigger moment; Use the external system signal directly obtained from the external system to replace the external system switching compensator and substitute into the expression of the distributed controller to calculate the distributed controller; Use the external system signal to offset the external system state of the multi-agent system model to make the error output converge to 0.

6. The method of claim 5, wherein, The step of substituting the distributed controller as the control input of the multi-agent system model into the multi-agent system model to make the error output of the multi-agent system model converge to 0, comprises: Substitute the distributed controller as the control input of the multi-agent system model into the multi-agent system model; Combine the appropriate dimension matrix to construct an intermediate calculation function; combine the regulator equation solution pair, the agent state, the external system state and the external system switching compensator to construct multiple equivalent calculation functions; wherein the equivalent calculation function includes a cancellation bias function between the external system switching compensator and the external system state; Rewrite the multi-agent system model after substituting the distributed controller using the intermediate calculation function and the plurality of equivalent calculation functions, to obtain an equivalent form of a closed-loop system; wherein the equivalent form of the closed-loop system includes a slow subsystem and a fast subsystem; According to the relationship between the fast subsystem and the slow subsystem, it is deduced that when the offset deviation function converges to 0, the error output of the multi-agent system model converges to 0; Combine the trigger mechanism of the distributed controller to enable the external system switching compensator, and deduce that the offset deviation function converges to 0, so that the error output of the multi-agent system model converges to 0.

7. The method of claim 6, wherein, The step of combining the trigger mechanism of the distributed controller to enable the external system switching compensator, and deducing that the offset deviation function converges to 0, so that the error output of the multi-agent system model converges to 0, comprises: Design the intermediate offset vector corresponding to the offset deviation function, and calculate the Lyapunov function corresponding to the intermediate offset vector; Design an augmented vector composed of the trigger error items of the agent, and use the augmented vector to combine the selector of the agent and the connection condition of the agent and the external system to prove that the limit convergence value of the Lyapunov function exists and the intermediate offset vector is bounded; According to the Cauchy convergence criterion, design the offset vector intermediate function corresponding to the Lyapunov function, Prove by reductio ad absurdum that the limit of the offset vector intermediate function converges to 0; According to the relationship between the offset vector intermediate function and the offset deviation function, it is deduced that the offset deviation function converges to 0, and the error output of the multi-agent system model converges to 0.

8. An electronic device comprising a memory, a processor, and a computer program stored on the memory and run on the processor, characterized in that, The processor executes the program to realize the multi-agent output adjustment method under the joint communication handover topology condition as claimed in any one of claims 1 to 7.

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