Multi-agent system index cluster synchronous control method and system and medium

Abstract

The invention discloses a multi-agent system index cluster synchronization control method and system, and a medium. The method comprises the following steps: S101, obtaining system model parameters, cluster division information, a target trajectory model and time-varying topology information; s102, checking whether a system can be checked, whether inter-cluster coupling meets specific conditions or not and whether an average communication topology # imgabs0 # contains a spanning tree or not; step S103, calculating a feedback gain matrix K; step S104, determining a lower bound of in-cluster coupling strength # imgabs1 # and an upper limit of a switching time scale factor according to system characteristics and average topological information; s105, selecting a condition which meets the determination in the step S104; step S106, constructing a controller, and obtaining fast switching topology information according to the current time t and the selected # imgabs2 # during implementation; and step S107, applying the controller to each agent # imgabs3 # to realize index cluster synchronization. According to the method, the fast switching characteristic is clearly considered and utilized, and synchronization can be guaranteed even when the topology is instantaneously disconnected.

Description

Technical Field

[0001] The present invention relates to the technical field of multi-agent system control, and specifically to an exponential cluster synchronization control method, system and medium for multi-agent systems. Background Art

[0002] Multi-agent systems (MAS) have attracted much attention due to their wide application potential in fields such as robotics, communication networks, and autonomous systems. A fundamental problem in multi-agent cooperative control is to achieve consensus or synchronization, that is, to enable multiple autonomous agents to eventually reach a unified state or decision based on their interactions.

[0003] Existing research has widely focused on the consensus problem of multi-agent systems, including second-order systems, synchronization under directed graphs, heterogeneous nonlinear systems, and the case of communication delays. In recent years, cluster synchronization (or called group synchronization, clustering synchronization) has become a research hotspot, that is, the agents in the system are divided into several clusters, and the goal is to achieve the state synchronization of the agents within each cluster, while the states of the agents between different clusters are not necessarily synchronized.

[0004] However, in many practical application scenarios, the communication topology structure between multi-agent systems is dynamically changing, and may even be rapidly switched. The rapid switching topology poses a great challenge to cluster synchronization control. For example, the network may be disconnected at some moments, and traditional control methods based on instantaneous connectivity may fail. In addition, some existing methods may have strong requirements on the topology switching speed, system controllability, and network connectivity. How to find the (as weak as possible) conditions to ensure that the system achieves exponential cluster synchronization under a rapidly switching and possibly instantaneously disconnected network topology, and design an effective controller, is a technical problem to be solved urgently. Summary of the Invention

[0005] The purpose of the present invention is to provide an exponential cluster synchronization control method, system and medium for multi-agent systems, so as to solve the technical problem proposed in the above background art that it is difficult to ensure the robust and exponential cluster synchronization of multi-agent systems under the condition of rapidly switching network topologies, especially the problem of how to design a controller and determine the conditions for the system to achieve cluster synchronization when the topology may be instantaneously disconnected but satisfies certain average characteristics.

[0006] To achieve the above purpose, the present invention provides the following technical solution: An exponential cluster synchronization control method for multi-agent systems, including the following steps:

[0007] Step S101: Obtain system model parameters ( , ), cluster division information , target trajectory model and time-varying topology information ;

[0008] Step S102: Check whether the system stabilizability, the inter-cluster coupling satisfies specific conditions, and whether the average communication topology contains a spanning tree;

[0009] Step S103: Calculate the feedback gain matrix K;

[0010] Step S104: Determine the lower bound of the intra-cluster coupling strength and the upper bound of the switching time scale factor according to the system characteristics and the average topology information; the upper bound of ;

[0011] Step S105: Select and ;

[0012] Step S106: Construct a controller, and when implementing, obtain the fast-switching topology information according to the current time t and the selected ;

[0013] Step S107: Apply the controller to each agent , and achieve exponential cluster synchronization.

[0014] The multi-agent system includes agents, which are divided into clusters , and the dynamic model of each agent is:

[0015] where is the state, is the control input, is a constant matrix and is stabilizable, and each cluster corresponds to a target trajectory satisfies:

[0016] The communication topology among agents is described by a fast-switching directed graph , and the method includes: designing and applying a controller to each agent , and the form of the controller is:

[0017] where: is the feedback gain matrix; is a positive constant of the time scale characterizing the speed of topology switching; is the number of the cluster to which the agent belongs; is the coupling coefficient. When belongs to the same cluster and when belongs to different clusters ; is the traction coefficient between the agent and the leader , indicating the existence of a connection, otherwise it is 0; is an element of the adjacency matrix ; and the parameters and and are selected to satisfy a predetermined condition related to the system matrix , the feedback gain K, and the time-average characteristics of the communication topology such that the states of all agents belonging to the same cluster exponentially converge to the target trajectory ;

[0018] The feedback gain matrix K is determined by solving an algebraic Riccati equation related to A and B. For example , where P is a positive definite solution satisfying a specific Lyapunov inequality or Riccati equation.

[0019] The time-average characteristics of the communication topology require that for each cluster , its associated leader 's average communication topology contains a directed spanning tree with as the root node.

[0020] The predetermined condition for selecting the parameter is that is greater than a threshold depending on the corresponding principal sub-block of the average Laplacian matrix derived from the average adjacency matrix and the predefined positive definite weighted matrix related to the cluster

[0021] The predetermined condition for selecting the parameter is that is less than a positive upper bound determined by system stability analysis , and the value of is related to the system matrix and the average topology Related to properties.

[0022] A multi-agent system exponential cluster synchronization control system, comprising: a processor and a memory, the memory storing instructions executable by the processor; when the processor executes the instructions, the steps of the multi-agent system exponential cluster synchronization control method are implemented.

[0023] A computer-readable storage medium, on which computer program instructions are stored, and when the instructions are executed by a processor, the steps of the multi-agent system exponential cluster synchronization control method are implemented.

[0024] The present invention further discloses the key parameter conditions for achieving exponential cluster synchronization: it is necessary to select a sufficiently large intra-cluster coupling strength (greater than a threshold determined by the average topological characteristics) and a sufficiently small time-scale factor (less than an upper bound determined by the system stability analysis ). Through such design and parameter selection, the method of the present invention can drive the system to achieve exponential cluster synchronization under fast-switching topologies.

[0025] Compared with the prior art, the beneficial effects of the present invention are:

[0026] I. Adapt to fast-switching topologies: Clearly consider and utilize the fast-switching characteristics, and ensure synchronization even when the topology is instantaneously disconnected.

[0027] II. Exponential convergence: The exponential convergence rate is theoretically guaranteed, and the synchronization speed is fast.

[0028] III. Clear conditions: Sufficient conditions directly related to system controllability, average connectivity, coupling strength, and switching rate are given to guide the design.

[0029] IV. Solid theoretical foundation: Based on mature theories such as Lyapunov stability and averaging method.

[0030] V. Wide application potential: Applicable to distributed control scenarios such as UAV formations and robot group cooperation. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] Figure 1 is an example diagram of the state one Figures 3 to 6 of the fast-switching communication topology used in simulation scenarios 1 and 2 (corresponding to the simulation results) according to an embodiment of the present invention, showing the traction relationship between two interacting clusters ( , ) and their respective leaders ( );

[0032] Figure 2is the state two of the fast-switching communication topology used in simulation scenarios 1 and 2 (corresponding to Figures 3 to 6 the simulation results), where the agents, clusters, and leaders are the same as , and the system switches periodically between this state and state one ( Figure 1 ); );

[0033] Figure 3 is the first simulation result graph of the cluster synchronization error varying with time under the action of the controller according to an embodiment of the present invention ( , , );

[0034] Figure 4 is the second simulation result graph of the cluster synchronization error varying with time under the action of the controller according to an embodiment of the present invention ( , , );

[0035] Figure 5 is the first simulation result graph of the cluster synchronization error varying with time under the action of the controller according to another embodiment of the present invention ( , , );

[0036] Figure 6 is the second simulation result graph of the cluster synchronization error varying with time under the action of the controller according to another embodiment of the present invention ( , , );

[0037] Figure 7 is the first simulation comparison graph of the divergence of the cluster synchronization error when the average topology spanning tree condition is not satisfied;

[0038] Figure 8 is the second simulation comparison graph of the divergence of the cluster synchronization error when the average topology spanning tree condition is not satisfied;

[0039] Figure 9 is the first simulation comparison graph of the inability to achieve cluster synchronization when the system model ( , ) is uncontrollable;

[0040] Figure 10 is the second simulation comparison graph of the inability to achieve cluster synchronization when the system model ( , ) is uncontrollable;

[0041] Figure 11 is Figure 7State 1 of the fast-switching communication topology that is simulated and does not satisfy the average topological spanning tree condition ( ) Example diagram;

[0042] Figure 12 Is Figure 7 State 2 of the fast-switching communication topology that is simulated and does not satisfy the average topological spanning tree condition ( ), and the system switches periodically between this state and State 1 ( );

[0043] Figure 13 Is the process schematic diagram of the method of the present invention. Detailed implementation manners

[0044] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

[0045] Please refer to Figures 1-13 , the present invention provides a technical solution: a multi-agent system exponential cluster synchronization control method, system and medium, which can be specifically implemented according to the following steps S101 to S107:

[0046] Step S101: Obtain system model parameters, cluster partitioning, target trajectories and topological information

[0047] Specific implementation manners:

[0048] System model parameters ( ): Determined by system identification or physical modeling, and regarded as known and fixed in the design stage. These parameters are constant matrices And .

[0049] Cluster partitioning ( ): The cluster structure of the system is preset according to application requirements. Agents are divided into Non-empty and non-overlapping clusters ( ). Each agent Needs to store the cluster number To which it belongs.

[0050] Target trajectory ( ): Generated by a specified source (central node or leader within the cluster). Agent Needs to have the ability to obtain the target trajectory Of its corresponding cluster. Target trajectory Satisfy the dynamic equation .

[0051] Time-varying topological information ( ): The adjacency matrix describing the communication relationship between agents is time-varying and is obtained through one of the following means:

[0052] Neighbor discovery mechanism: Agents construct and update their adjacency relationships in real time through periodic communication .

[0053] Preset switching rules: Agents determine the current topology according to the global time or external events based on known rules .

[0054] Centralized information distribution: The central node monitors the global topology and distributes it to each agent. The frequency of obtaining topological information must be higher than the switching time scale defined by .

[0055] Summary: This step is to establish the mathematical model of the problem. The linear dynamics model is the basis for applying linear control theory. The cluster structure and the target trajectory define the specific goal of "cluster synchronization" - the states of the agents within each cluster eventually need to track . The time-varying topology represents the main challenge faced by the system - the communication constraints are dynamic and rapidly changing. Clearly defining this information is a prerequisite for subsequent analysis and design .

[0056] Step S102: Check the system preconditions

[0057] Specific implementation method: Completed during the controller design stage (offline):

[0058] Check for stabilizability: Use standard control theory methods to verify the stabilizability of ( , ).

[0059] Check the inter-cluster coupling conditions: Analyze whether the inter-cluster connection elements of satisfy the specific algebraic conditions (such as in-degree balance) used in the theoretical derivation of this method

[0060] Check the average communication topology spanning tree:

[0061] Calculate the time-averaged adjacency matrix . For periodic switching (period ), ; for random switching, is in the desired form:

[0062] Construct a graph that includes , and an enhanced graph with average connectivity .

[0063] Apply graph theory algorithms (BFS or DFS) to verify that there exists a directed path from to all in

[0064] Summary: This step verifies the necessary conditions for applying this method. If the conditions are not met, this method is not applicable.

[0065] Step S103: Calculate the feedback gain matrix K

[0066] Specific implementation method:

[0067] Select a positive constant as a design parameter.

[0068] Use numerical calculation software to solve the algebraic Riccati inequality: to obtain a symmetric positive definite solution .

[0069] Calculate the feedback gain according to the formula :

[0070] Store the calculated in the controller parameter set of each agent (completed offline).

[0071] Summary: This step determines the basic gain matrix for state feedback.

[0072] Step S104: Determine the lower bound of the intra-cluster coupling strength and the switching time scale factor upper bound

[0073] Specific implementation method: Completed in the design stage (offline):

[0074] Lower bound determination: Based on the inequality conditions derived from Lyapunov stability analysis (involving the average Laplacian matrix sub-block and the weighted matrix calculate the minimum numerical threshold that each must satisfy.

[0075] Upper bound determination: Based on the Lyapunov derivative Boundary estimation, using averaging or singular perturbation theory, to derive the upper limit .

[0076] Summary: Output parameter range and .

[0077] Step S105: Select the and

[0078] Specific implementation method:

[0079] According to the result of step S104, select the value of each to ensure that .

[0080] Select the value to ensure that , and at the same time, evaluate the requirements of the selected for system communication and computing resources.

[0081] Take the selected and values as the controller parameters (design phase completed).

[0082] Summary: On the premise of meeting the theoretical conditions, determine the final parameter values considering the actual constraints.

[0083] Step S106: Construct the controller and obtain the real-time / fast-switching topology information

[0084] Specific implementation method: During the real-time operation phase of the controller:

[0085] The controller of each agent loads the pre-determined , (corresponding to its own ), parameters.

[0086] In each control execution cycle:

[0087] Sample or obtain its own state .

[0088] Obtain the current target trajectory value .

[0089] Obtain the topology information at the current effective time through the communication mechanism: adjacency weights and the corresponding neighbor states (if ), and the connection status with the leader .

[0090] Calculate the control input for the current period according to the controller formula :[[]] where According to whether in the same cluster and the selected determine( if , otherwise).

[0091] Summary: This step describes the actual calculation process of the controller on the agent.

[0092] Step S107: Apply the controller to achieve exponential cluster synchronization

[0093] Specific implementation method:

[0094] Transfer the control input calculated in step S106 to the underlying actuator of the agent .

[0095] Continuously execute the closed-loop control law composed of steps S106 and S107.

[0096] The system state will evolve according to the theoretical analysis results, so that the states of the agents within each cluster exponentially converge to , satisfying:

[0097] The convergence can be verified by monitoring the state error .

[0098] Summary: The system reaches and maintains the exponential cluster synchronization state.

[0099] Example:

[0100] This example aims to specifically illustrate the application process and effect of the exponential cluster synchronization control method under fast-switching topologies proposed by the present invention.

[0101] Application of step S101: Obtain the system model, cluster partition, target trajectory, and topology information

[0102] Consider a multi-agent system composed of agents. The state of each agent is , and its dynamics follow the linear time-invariant equation . The system matrix and The specific definitions are as follows: , These 7 agents are divided into clusters: Cluster and Cluster . Target trajectories and are respectively set for these two clusters, and they satisfy and . The communication topology among the agents switches rapidly between two different directed graph states (denoted as and , as shown in Figure 1 and Figure 2 ).

[0103] Figure 1 Figure 2 Meanwhile, it shows the traction relationships of the leader with some of the agents within their respective clusters. In this embodiment, it is set that the switching is periodic, and the switching period is 0.1 second.

[0104] Application of Step S102: Checking the system preconditions

[0105] Before designing the controller, check the settings of this embodiment:

[0106] Stabilizability: After calculation, the given system matrix pair ( , ) is controllable, so the stabilizability requirement is satisfied.

[0107] Inter-cluster coupling condition: Assume that the coupling effect among the agents in this embodiment satisfies the specific conditions required by the theoretical derivation of the present invention.

[0108] Average communication topology spanning tree: Analyze and the average topology formed by the periodic switching. The calculation shows that for the average enhanced graph formed by Cluster and its leader , there exists a directed spanning tree with as the root node;

[0109] Similarly, for the average enhanced graph formed by Cluster and its leader , there also exists a directed spanning tree with as the root node. The average communication topology connectivity condition is satisfied. All preconditions are satisfied, and the subsequent steps can be continued.

[0110] Application of Step S103: Calculate the feedback gain matrix K

[0111] Select design parameters . Solve the algebraic Riccati inequality related to ( , ), and obtain a symmetric positive definite solution . In this embodiment, a matrix that meets the conditions is: According to , calculate the feedback gain matrix : :

[0112] Application of Step S104: Determine the lower bound of the intra-cluster coupling strength and the upper bound of the switching time scale factor Lower bound and switching time scale factor Upper bound

[0113] Based on the system matrix ( , ) of this embodiment, the calculated feedback gain , and the average topological characteristics, determine the parameter range through theoretical analysis:

[0114] Lower bound of the intra-cluster coupling strength: It is calculated that it needs to satisfy and .

[0115] Upper bound of the switching time scale factor: There theoretically exists a positive number such that when , the system is stable.

[0116] Application of Step S105: Select and

[0117] According to the range determined in Step S104, select parameter values for simulation verification:

[0118] Simulation scenario 1 (meeting the conditions): Select the intra-cluster coupling strength and . Select the switching time scale factor . Assume .

[0119] Simulation scenario 2 (meeting the conditions, slower switching): Keep . Select the switching time scale factor . Assume .

[0120] Simulation scenario 3 (for comparison, does not satisfy the condition of the average spanning tree): Keep the parameters , but use the topology shown in Figure 11 for switching (this topology does not satisfy condition 3 of step S102).

[0121] Simulation scenario 4 (for comparison, does not satisfy the controllability condition): Keep the topology switching of parameters and Figure 1 , but replace the system matrix with an uncontrollable (A', B') (does not satisfy condition 1 of step S102).

[0122] Application of step S106: Construct the controller and obtain the real-time / rapid switching topology information

[0123] According to the calculated in step S103 and the selected in step S105, construct the controller. For the agent ( ), the controller is:[[]] where if , if . For the agent ( ), the controller is:[[]] where if , if . In the simulation, according to the selected value (0.5 or 0.8) and a switching period of 0.1 seconds, determine the effective topology information corresponding to each moment and and (derived from or ).

[0124] Application of step S107: Apply the controller to achieve exponential cluster synchronization

[0125] Apply the controller constructed in step S106 to the system dynamics model for simulation.[[]]

[0126] Results of simulation scenario 1 ( Figure 3 ): When , define the cluster error and 。 Figure 3 and Figure 4 display and both converge to 0 rapidly exponentially. The system successfully achieves exponential cluster synchronization.

[0127] Results of simulation scenario 2 ( Figure 5 ): When , Figure 5 and Figure 6 display and still converge to 0 exponentially, but the convergence speed is significantly slower compared to Figure 3 . This verifies the influence of the switching rate on the convergence performance.

[0128] Results of simulation scenario 3 ( Figure 7 ): When using the topology (not satisfying the average spanning tree), Figure 7 and Figure 8 display and diverge over time. The necessity of prerequisite 3 is verified.

[0129] Results of simulation scenario 4 ( Figure 9 ): When the system model is uncontrollable, Figure 9 and Figure 10 display and diverge over time. The necessity of prerequisite 1 is verified.

[0130] This embodiment, through specific parameter settings, controller construction, and simulation verification, fully demonstrates the process of implementing the method of the present invention according to the S101 - S107 process, and verifies its effectiveness and the necessity of the key conditions.

[0131] Further explanation regarding parameter selection:

[0132] Feedback gain : Although the method based on is given in the embodiment, the present invention is not limited to this way of obtaining . Any feedback gain , that can stabilize the system ( ), if it can cooperate with the subsequent coupling and switching conditions to ensure overall stability, is applicable. Other control design methods such as pole placement, LQR (linear quadratic regulator), etc. can be used to obtain .

[0133] Coupling strength : In the embodiment, all clusters use the same lower - bound calculation method and selected value ( ), but in practical applications, different clusters may have different average topological properties, resulting in different calculated lower bounds. Therefore, each needs to be calculated and selected independently, as long as each meets its corresponding lower bound condition. Selecting a value much larger than the lower bound will improve the robustness of the system, but increase the control energy consumption and the system's sensitivity to noise.

[0134] Time scale factor : should be selected while ensuring it is less than the upper bound and considering the physical limitations of the actual system. A very small means extremely fast topological switching, which poses high requirements on the communication bandwidth of the network, the computing power of the nodes, and the response speed. In practical applications, a feasible value needs to be selected according to the limitations of the hardware capabilities and communication protocols. If cannot be selected small enough to meet , then the coupling strength needs to be enhanced, or the connectivity of the average topology needs to be improved to relax the requirement for (i.e., increase ).

[0135] Extensions to the system model:

[0136] Although the present invention has been mainly described and verified for linear time-invariant (LTI) systems, its core idea (achieving synchronization by using fast switching, average topological properties, and strong enough coupling) is applicable to a wider range of system models.

[0137] Nonlinear systems: For nonlinear systems that meet specific conditions (meeting the Lipschitz condition or having incremental quadratic constraints), the controller can be designed and the stability can be analyzed by similar methods. The form of the controller needs to be adjusted, and non-quadratic Lyapunov functions or tools such as contraction theory are required for stability analysis.

[0138] Time-varying systems: If the system matrix and / or varies slowly with time (relative to the topological switching rate), this method can be applied under the quasi-static assumption, or more complex time-varying system control theories need to be used for analysis.

[0139] Systems with perturbations / uncertainties: Bounded external perturbations or model uncertainties can be considered in the controller design and stability analysis. By using robust control techniques (such as control), is designed and the parameter range is determined to ensure robust cluster synchronization under perturbations (the error converges to a bounded neighborhood).

[0140] Regarding the topology switching mode:

[0141] The method of the present invention does not depend on a specific topology switching mode, as long as the switching meets the condition of "fast" ( ), and its time-average characteristics meet the spanning tree requirements. The switching can be periodic, random (following a certain Markov chain, and the average graph corresponding to its stationary distribution meets the conditions), or event-triggered. The key lies in the average behavior and the switching rate.

[0142] System implementation:

[0143] The cluster synchronization control system proposed by the present invention can be implemented on a distributed computing platform. Each agent can be equipped with a local processor and a memory to store model information, status, cluster information, target trajectory, and control algorithms. The agents need to exchange status information through a communication network (according to the topology ) and receive leader information (according to ).

[0144] The functions of the system definition unit, condition check unit, and parameter calculation unit are completed in the design stage before system deployment, calculating the necessary 、 lower bounds, upper bounds.

[0145] The control signal generation unit and the execution unit run in real time on the local processor of each agent. The control signal generation unit determines the topological connection according to the current time and the selected , , , obtains the neighbor status , its own status and the target trajectory , and calculates the control input . The execution unit applies to the actuator.

[0146] The acquisition of topological information is a key link. It can be achieved through global broadcast, neighbor discovery protocol, or preset switching logic. For fast switching, it is necessary to ensure that the update frequency of topological information is high enough.

[0147] It should be noted that in this article, relational terms such as first and second are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any actual relationship or order between these entities or operations. Moreover, the term "comprising", "including" or any other variant thereof is intended to cover non-exclusive inclusion, so that a process, method, article or device comprising a series of elements not only includes those elements, but also includes other elements not expressly listed, or also includes elements inherent to such process, method, article or device.

Claims

1. A method for synchronous control of exponential clusters of a multi-agent system, characterized by: The steps include: Step S101: Obtain system model parameters ( , ), cluster partition information , target trajectory model and time-varying topological information ; Step S102: Checking system stability, whether inter-cluster coupling meets specific conditions, and average communication topology Whether to include a spanning tree; Step S103: Calculate the feedback gain matrix K; Step S104: Determine the intra-cluster coupling strength based on system characteristics and average topology information The lower bound and switching time scale factor Upper limit ; Step S105: Select the one that meets the conditions determined in step S704 and ; Step S106: Construct a controller, which needs to be implemented according to the current time t and the selected Get fast switching topology information; Step S107: Apply the controller to each agent , achieving index cluster synchronization.

2. A method for synchronous control of exponential clusters of a multi-agent system according to claim 1, characterized in that: The multi-agent system includes N agents, and the cluster partition information is divided into Cluster , each agent The kinetic model is: in For status, is the control input, ( , ) is a constant matrix, , , each cluster Corresponding target trajectory satisfy: The communication topology between agents is a directed graph with fast switching. Description, the controller form is: in: is the feedback gain matrix; A positive constant that characterizes the time scale of topological switching speed; For intelligent agents The number of the cluster to which it belongs; is the coupling coefficient, when Belong to the same cluster hour ,when Belong to different clusters ; For intelligent agents With leaders The traction coefficient, Indicates that there is a connection, otherwise it is 0; is the adjacency matrix The feedback gain matrix K is solved by ( , ) is determined by the related algebraic Riccati equation.

3. A method for synchronous control of exponential clusters of a multi-agent system according to claim 1, characterized in that: The communication topology The time average characteristic requirement is: for each cluster , its associated leaders Average communication topology Contains a is a directed spanning tree with as root node.

4. The method for controlling the synchronization of exponential clusters of a multi-agent system according to claim 1, characterized in that: The selection parameters The reservation conditions are: is greater than one depending on the average adjacency matrix The derived mean Laplacian matrix The corresponding main sub-block and cluster The associated predefined positive definite weight matrix The threshold for the minimum eigenvalue of .

5. The method for controlling the synchronization of exponential clusters of a multi-agent system according to claim 1, characterized in that: The selection parameters The reservation conditions are: is less than a positive upper bound determined by system stability analysis , The value of and system matrix and average topology Nature related.

6. A multi-agent system exponential cluster synchronization control system, characterized in that: include: A processor and a memory, the memory storing instructions executable by the processor; When the processor executes the instructions, the method according to any one of claims 1 to 5 is implemented.

7. A computer-readable storage medium having computer program instructions stored thereon, characterized in that: When the instructions are executed by a processor, the method according to any one of claims 1 to 5 is implemented.

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