Event triggering fixed time inclusion control method for nonlinear multi-agent system with time delay

Abstract

The invention provides a non-linear multi-agent system event triggering fixed time inclusion control method with time delay, which comprises the following steps: establishing a first-order non-linear multi-agent dynamic model with external disturbance and input time delay, and representing a collaborative interaction relationship between agents; then, an auxiliary state variable is introduced, and the state of the intelligent agent is updated to eliminate the delay effect; on the basis, a self-adaptive distributed fixed-time event trigger control protocol is designed to carry out inclusion control on multiple agents; and then, constructing a dynamic event triggering mechanism, dynamically adjusting a communication threshold value based on a state error and an adaptive gain, and triggering control update only when a conditional expression is met, thereby reducing event triggering times, optimizing energy and bandwidth consumption, and remarkably reducing communication frequency.

Description

Technical Field

[0001] This invention relates to the field of cooperative control technology for multi-agent systems, and more specifically to a fixed-time event-triggered control method for nonlinear multi-agent systems with time delay. Background Technology

[0002] With the rapid development of applications such as drone swarms, vehicle-to-everything (V2X) communication, and robot clusters, multi-agent systems have attracted much attention due to their distributed collaborative capabilities. However, a common challenge they face in working together to accomplish various complex tasks is how to achieve efficient coordination and comprehensive control to ensure optimal system stability and performance.

[0003] In multi-agent systems, efficient communication and coordination among agents are crucial for stable system operation. However, real-world systems often face multiple challenges: 1. Time delays disrupt system real-time performance: Input time delays introduced by factors such as sensor response delays and communication link transmission delays significantly aggravate state tracking errors, disrupt the real-time performance of control signals, and thus reduce the system's convergence speed and robustness. 2. Limited communication bandwidth resources: Limited communication bandwidth may limit the speed and capacity of information exchange between agents, thus limiting system performance. 3. Excessive consumption of communication resources: Traditional periodic communication or static event triggering mechanisms may lead to excessively frequent information exchange, not only wasting valuable communication bandwidth resources but also easily triggering a large number of redundant triggering events, further increasing the network burden.

[0004] To address these challenges, researchers have been seeking innovative control methods and communication strategies. On one hand, adaptive control methods are being used to allow systems to adjust their control strategies based on environmental changes and uncertainties, thus maintaining system stability and performance. On the other hand, event-triggered strategies, where the system updates control signals when it deviates from a preset threshold, effectively replace the continuous exchange of state information.

[0005] Existing event triggering strategies can be divided into two categories: static event triggering, where the threshold is fixed and preset, making it difficult to adapt to dynamic changes in the system and lacking flexibility; and dynamic event triggering, which significantly reduces the number of triggers and improves efficiency by introducing a threshold that adapts to the system state.

[0006] However, in nonlinear multi-agent systems with input time delays, existing strategies still face limitations: dynamic triggering mechanisms fail to effectively meet convergence requirements within a fixed time, making it difficult to guarantee containment control within a preset time limit; time delay disturbances can disrupt trigger synchronization and exacerbate tracking errors. Therefore, an innovative control method is urgently needed to optimize triggering efficiency while ensuring the stability and convergence of the system under strict time constraints. Summary of the Invention

[0007] To address the problems of poor convergence, difficulty in ensuring control within a preset time limit, and high consumption of communication resources in existing methods, this invention proposes a time-delayed event-triggered fixed-time control method for nonlinear multi-agent systems.

[0008] To achieve the above-mentioned technical effects, the technical solution of the present invention is as follows: A fixed-time event-triggered control method for a nonlinear multi-agent system with time delay includes the following steps: S1: Establish a first-order nonlinear multi-agent dynamic model, and obtain the initial state value, initial value of dynamic variables and adaptive initial value in the first-order nonlinear multi-agent dynamic model through simulation. S2: Determine whether the actual simulation time of the model is greater than or equal to the preset simulation deadline. If yes, end the simulation; otherwise, execute S3. S3: Calculate the error vector, dynamic variable update value, and adaptive update value based on the initial state value, initial value of dynamic variable, and adaptive initial value in the first-order nonlinear multi-agent dynamic model; S4: Determine whether the triggering condition is met based on the event triggering function. If not, return to execute S2. If yes, update the agent state based on the error vector, dynamic variable update value, and adaptive update value. S5: Based on the updated agent state value, obtain the adaptive distributed fixed-time event-triggered control protocol, perform inclusion control on multiple agents, and then continue to execute S2.

[0009] Compared with the prior art, the beneficial effects of the technical solution of the present invention are: This invention proposes a fixed-time inclusion control method for event-triggered nonlinear multi-agent systems with time delays. It establishes a first-order nonlinear multi-agent dynamic model incorporating external disturbances and input time delays to characterize the cooperative interaction relationships between agents. Subsequently, auxiliary state variables are introduced to update the agent states and eliminate delay effects. Based on this, an adaptive distributed fixed-time event-triggered control protocol is designed to perform inclusion control on the multi-agent system. Then, a dynamic event-triggered mechanism is constructed, dynamically adjusting the communication threshold based on state error and adaptive gain, triggering control updates only when conditional conditions are met. This reduces the number of event triggers, optimizes energy and bandwidth consumption, and significantly reduces communication frequency. Attached Figure Description

[0010] Figure 1 The flowchart illustrates a control method for a fixed-time event triggering process in a nonlinear multi-agent system with time delay, as shown in an embodiment of the present invention.

[0011] Figure 2This is a communication topology diagram illustrating an embodiment of the present invention.

[0012] Figure 3 This is a state trajectory diagram under no-delay conditions shown in an embodiment of the present invention.

[0013] Figure 4 This is a state trajectory diagram under an input delay of 0.5s as shown in an embodiment of the present invention.

[0014] Figure 5 This is a control input trajectory diagram under the event triggering mechanism shown in an embodiment of the present invention.

[0015] Figure 6 This is an example of an error trajectory diagram shown in an embodiment of the present invention.

[0016] Figure 7 This is an adaptive gain trajectory diagram shown in an embodiment of the present invention.

[0017] Figure 8 The diagram illustrates the trajectory of measurement error and trigger threshold in an embodiment of the present invention.

[0018] Figure 9 This is a diagram showing the triggering times of each intelligent agent in an embodiment of the present invention. Detailed Implementation

[0019] Exemplary embodiments will now be described in detail, examples of which are illustrated in the accompanying drawings. When the following description relates to the drawings, unless otherwise indicated, the same numerals in different drawings denote the same or similar elements. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with the present invention. Rather, they are merely examples of apparatuses and methods consistent with some aspects of the invention as detailed in the appended claims.

[0020] The terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of the invention. The singular forms “a,” “the,” and “the” used in this invention and the appended claims are also intended to include the plural forms unless the context clearly indicates otherwise. It should also be understood that the term “and / or” as used herein refers to and includes any or all possible combinations of one or more of the associated listed items.

[0021] It should be understood that although the terms first, second, third, etc., may be used in this invention to describe various information, this information should not be limited to these terms. These terms are only used to distinguish information of the same type from one another. For example, first information may also be referred to as second information without departing from the scope of this invention, and similarly, second information may also be referred to as first information. Depending on the context, the word "if" as used herein may be interpreted as "when," "when," or "in response to a determination."

[0022] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.

[0023] Example 1 This embodiment proposes a fixed-time event-triggered control method for a nonlinear multi-agent system with time delay, the flowchart of which is shown below. Figure 1 As shown, it includes the following steps: S1: Establish a first-order nonlinear multi-agent dynamic model, and obtain the initial state value, initial value of dynamic variables and adaptive initial value in the first-order nonlinear multi-agent dynamic model through simulation. S2: Determine whether the actual simulation time of the model is greater than or equal to the preset simulation deadline. If yes, end the simulation; otherwise, execute S3. S3: Calculate the error vector, dynamic variable update value, and adaptive update value based on the initial state value, initial value of dynamic variable, and adaptive initial value in the first-order nonlinear multi-agent dynamic model; S4: Determine whether the triggering condition is met based on the event triggering function. If not, return to execute S2. If yes, update the agent state based on the error vector, dynamic variable update value, and adaptive update value. S5: Based on the updated agent state value, obtain the adaptive distributed fixed-time event-triggered control protocol, perform inclusion control on multiple agents, and then continue to execute S2.

[0024] In this embodiment, a first-order nonlinear multi-agent dynamic model containing external disturbances and input time delays is established to characterize the cooperative interaction relationship between agents. Subsequently, auxiliary state variables are introduced to update the agent states to eliminate delay effects. Based on this, an adaptive distributed fixed-time event-triggered control protocol is designed to control the multiple agents. Then, a dynamic event-triggered mechanism is constructed to dynamically adjust the communication threshold based on state error and adaptive gain, triggering control updates only when conditional conditions are met, thereby reducing the number of event triggers, optimizing energy and bandwidth consumption, and significantly reducing communication frequency.

[0025] Example 2 This embodiment provides a detailed explanation of Embodiment 1.

[0026] A nonlinear first-order multi-agent system is modeled, considering the dynamic interactions and coordination among the agents. A nonlinear first-order dynamic model is established to describe the position changes of the agents: In one optional embodiment, the establishment of a first-order nonlinear multi-agent dynamic model is expressed as follows: (1) in, Equations representing multi-agent systems, Represents an inherently nonlinear continuous function. Indicates the first The location of each agent. Indicates control input, Indicates external interference. Indicates a group of followers. Represents the set of leaders. This represents a positive input delay. The first-order nonlinear multi-agent dynamic model includes There are 10 intelligent agents, of which 10 are intelligent agents. One follower, with One leader.

[0027] Furthermore, the follower group is... The leaders are grouped as .

[0028] In one alternative embodiment, the graph is obtained based on the network connections within the first-order nonlinear multi-agent dynamic model. Since the leader has no neighbors, the diagram... The Laplacian matrix can be decomposed into:

[0029] Where L represents the Laplacian matrix, express A matrix related to the information flow of each follower. , express One follower to A matrix related to the information flow of each leader. , R Represents all real numbers, and represents n Viocli, Indicates the number of rows and columns. m OK n List, Indicates the number of rows and columns. m OK m List.

[0030] Furthermore, by introducing auxiliary state variables, the time-delay system is converted into an equivalent time-delay-free form in real time and a compensation signal is generated to eliminate the delay effect.

[0031] In one optional embodiment, the error vector is calculated based on the initial state value, initial value of dynamic variables, and adaptive initial value in the first-order nonlinear multi-agent dynamic model. First, the desired state is defined: (2) in, This represents the target position that followers expect to reach using the Laplacian matrix. Indicates a leader; in The error vector is then: (3) in, This represents the difference between the follower's position and the desired position. It indicates a follower.

[0032] In one alternative embodiment, an auxiliary variable is defined: (4) in, Represents auxiliary variables. Indicates the first The location of each agent. t express t time, Indicates controller, This represents a positive input delay. The multi-agent equation is rewritten based on the auxiliary variables; its expression is: (5) in, This represents the rewritten multi-agent equation. Indicates control input, Represents nonlinear terms, Indicates external interference. Represents the set of followers; The rewritten error vector is obtained based on the rewritten multi-agent equations and the error vector; its expression is: (6) in, This represents the rewritten error vector, where j represents... The set of edges, Represents the set of all follower neighbor nodes. This represents the weighting coefficient between followers. Indicates follower j, This represents the weighting coefficient between followers and leaders. Indicates the leader l, f represents the follower.

[0033] In one optional embodiment, the updated value of the dynamic variable is calculated based on the initial state value, initial value of the dynamic variable, and adaptive initial value in the first-order nonlinear multi-agent dynamic model; its expression is: (7) in, Represents a dynamic variable equation. Represents the coefficient. Represents the power exponent. Represents dynamic variables. Represents the coefficient. Represents the power exponent. , , .

[0034] In one optional embodiment, the adaptive update value is calculated based on the initial state value, initial value of dynamic variables, and adaptive initial value in the first-order nonlinear multi-agent dynamic model; its expression is:

[0035] in, Represents the adaptive coupling strength equation. This represents the positive coefficient in the adaptive law. This represents the inclusion error after rewriting the agent dynamics equations.

[0036] In one optional embodiment, the agent state is updated based on the error vector, dynamic variable update value, and adaptive update value. An adaptive distributed fixed-time event-triggered control protocol is then obtained based on the updated agent state value to perform inclusive control over multiple agents; its expression is: (8) in, Indicates control input, All represent the parameters to be designed. Representing the first The first agent of the intelligent agent Next trigger moment This represents the rewritten error vector. Represents the power exponent. Represents the power exponent. , For adaptive coupling strength.

[0037] Furthermore, the measurement error is defined as: (9) In one alternative embodiment, the first The triggering condition for each agent is defined as follows: (10) in, Representing the first The first agent of the intelligent agent Next trigger moment Representing the first The first agent of the intelligent agent Next trigger moment This indicates the trigger function.

[0038] Furthermore, (11) In one alternative embodiment, the method proves the system stability using Lyapunov functions.

[0039] Furthermore, the Lyapunov function is constructed as follows: (12) in, (13) (14) (15) right Taking the derivative, we get: (16) Furthermore, the third term in equation (16) simplifies to: (17) The fourth term in equation (16) simplifies to: (18) make ,but (19) The first term in equation (16) simplifies to: (20) exist If the triggering time has not yet been reached, then the second term in equation (16) can be simplified to: (twenty one) According to the young inequality, and the existence of , , If the value is greater than 1, then equation (21) can be rewritten as: (twenty two) (twenty three) (twenty four) From equation (16) to equation (24), we can simplify to obtain: (25) right Differentiating gives (26) right Differentiating, we get: (27) Combining equations (25) and (27), and rearranging, we get: (28) Further refinement, setting , Then there is , Therefore, we can conclude that: (29) make , , To further express: (30) According to equations (18)-(21), by applying inequality scaling, we can obtain: (31) Given a positive parameter , , then make ,but , If the system converges to zero within a fixed time, then control can be achieved within that fixed time, and the upper bound of the fixed time is: (32) Further Zeno behavioral analysis was conducted: No. The event triggering time sequence of each agent is composed of , , ... to indicate, and Indicates the first The first agent of the intelligent agent At the next trigger time, assuming there is Then there will be .

[0040] From equation (9), we can have (33) In the formula , , , , .

[0041] From equation (33), we can see that Therefore there is (34) In the At the next trigger time, there are It is not difficult to see that Greater than or equal to positive numbers .

[0042] The above formulas contradict the assumption. Therefore, the system strictly excludes Zeno behavior.

[0043] Therefore, this is proven.

[0044] In this embodiment, by combining a fixed-time controller design, an adaptive compensation law, and a time-delay order reduction strategy, effective containment control of a first-order nonlinear multi-agent system with input time delay can be achieved within a preset fixed time. By constructing an appropriate Lyapunov function, it is rigorously proven that the system converges to the convex hull region formed by the leader within a fixed time, thereby significantly improving the system's convergence, stability, and robustness.

[0045] To reduce communication overhead, the proposed event-triggered mechanism introduces dynamic variables that can dynamically adjust the trigger threshold, updating the control input only when necessary. This effectively avoids frequent communication and redundant calculations caused by periodic sampling. This mechanism significantly reduces the number of communication triggers, lowers communication bandwidth and energy consumption, while ensuring coordinated control within a fixed timeframe, thereby improving communication efficiency and the system's sustainable operation.

[0046] The designed coupled gain law with online adaptive adjustment capability can dynamically optimize the control strategy during system operation. As the system state error changes, the adaptive parameters are adjusted in real time, which avoids the performance degradation caused by conservative parameter selection, and effectively controls the control input amplitude while ensuring convergence speed. This ensures that the system maintains good stability and control performance under various complex environments.

[0047] The proposed control method is applicable to collaborative and inclusive control tasks in various multi-agent systems, including but not limited to robot collaboration, social networks, and traffic flow control. Its innovative control strategy, which combines time delay compensation with event triggering mechanisms, can provide a more stable, efficient, and reliable collaborative control solution in scenarios with limited communication resources and high system response speed requirements.

[0048] Example 3 This embodiment is illustrated by way of example based on Embodiment 1 and Embodiment 2.

[0049] The communication topology diagram of the model is as follows: Figure 2 As shown, Figure 2 The communication topology of a multi-agent system consisting of two leaders (triangles) and five followers (circles) is presented. Each edge represents the direction of information transmission. The communication relationships are as follows: Leader 1 communicates with follower 3, follower 3 communicates with follower 4, follower 4 communicates with follower 5, follower 5 communicates with follower 6, follower 6 communicates with follower 7, and leader 2 communicates with follower 7. This forms a complex network structure that includes both leader-follower hierarchical links and internal interconnections among followers.

[0050] Set the variable parameter as follows: It consists of five followers and two leaders, with 1-2 being the leaders and 3-7 being the leaders.

[0051] The initial states of the five followers and three leaders are set as follows: ,

[0052] The nonlinear term of the design is

[0053] The designed interference items are ,

[0054] Laplace matrix , Designed as

[0055] Communication topology such as Figure 2 As shown, nodes 1-2 correspond to the leader, and nodes 3-7 represent the leader. ,,but , . , , , The event triggering includes a range of controller count parameters, which is selected as follows. , , , , , , , , , .

[0056] The system simulation time is set to The sampling time is set to .

[0057] Figure 3 This is the state trajectory diagram under the no-delay condition in this embodiment. Under no input delay, the trajectories of the five followers' states over time show that the five agents enter the convex hull formed by the two leader states. Subsequently, each follower's state remains within the convex hull, demonstrating that the employed containment control method exhibits significant effectiveness and superior stability in this nonlinear first-order multi-agent system.

[0058] Figure 4 This is the state trajectory diagram under the condition of an input delay of 0.5s in this embodiment. After introducing a fixed input delay of 0.5s, the follower state curve shows a brief lag, but it still maintains a bounded convergence trend and eventually stably enters the leader convex hull, verifying the robustness of the proposed algorithm to network latency.

[0059] Figure 5 This is the control input trajectory diagram under the event-triggered mechanism in this embodiment. Applying a sliding dynamic event trigger condition, the control inputs of the five followers are updated only at the trigger moment and gradually converge to near zero. The control input amplitude remains within a small range, satisfying the requirement for rapid convergence while avoiding unnecessary energy consumption.

[0060] Figure 6 This is the inclusion error trajectory diagram in this embodiment. The evolution of the inclusion error defined for each follower over time shows that all errors rapidly decrease to near-zero values ​​within a fixed time frame, further demonstrating that the algorithm can still achieve inclusion control under event-triggered influence.

[0061] Figure 7 This is the adaptive gain trajectory diagram in this embodiment. The online update process of the adaptive coupling gain in the controller dynamically adjusts according to the tracking error and eventually converges to its constant value, ensuring a balance between fixed-time convergence and control input amplitude.

[0062] Figure 8This is a trajectory diagram of measurement error and trigger threshold in this embodiment. The curves showing the change of the follower's measurement error and dynamic event threshold over time demonstrate that when the error is large, the threshold rises to suppress excessively frequent triggering, and when the error decreases, the threshold gradually decreases to meet the triggering requirements.

[0063] Figure 9 This is a diagram showing the triggering times of each agent in this embodiment. The five follower agents triggered a limited number of times within a finite time. Under the control of the event triggering function, the number of triggers was effectively reduced, ensuring convergence performance while alleviating communication and computational burdens and improving the stability of the algorithm.

[0064] The various embodiments in this invention are described in a progressive manner. Similar or identical parts between embodiments can be referred to mutually. Each embodiment focuses on describing the differences from other embodiments. In particular, the device embodiments are basically similar to the method embodiments, so the description is relatively simple; relevant parts can be referred to the descriptions in the method embodiments. The device embodiments described above are merely exemplary. The modules described as separate components may or may not be physically separate. When implementing the present invention, the functions of each module can be implemented in one or more software and / or hardware. Alternatively, some or all of the modules can be selected to achieve the purpose of this embodiment according to actual needs.

[0065] Obviously, the above embodiments of the present invention are merely examples for clearly illustrating the present invention, and are not intended to limit the implementation of the present invention. Those skilled in the art can make other variations or modifications based on the above description. It is neither necessary nor possible to exhaustively describe all embodiments here. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the claims of the present invention.

Claims

1. A fixed-time event-triggered control method for a nonlinear multi-agent system with time delay, characterized in that, Includes the following steps: S1: Establish a first-order nonlinear multi-agent dynamic model, and obtain the initial state value, initial value of dynamic variables and adaptive initial value in the first-order nonlinear multi-agent dynamic model through simulation. S2: Determine whether the actual simulation time of the model is greater than or equal to the preset simulation deadline. If yes, end the process; otherwise, execute S3. S3: Calculate the error vector, dynamic variable update value, and adaptive update value based on the initial state value, initial value of dynamic variable, and adaptive initial value in the first-order nonlinear multi-agent dynamic model; S4: Determine whether the triggering condition is met based on the event triggering function. If not, return to execute S2. If yes, update the agent state based on the error vector, dynamic variable update value, and adaptive update value. S5: Based on the updated agent state value, obtain the adaptive distributed fixed-time event-triggered control protocol, perform inclusion control on multiple agents, and then continue to execute S2.

2. The event-triggered fixed-time control method for a nonlinear multi-agent system with time delay according to claim 1, characterized in that, The first-order nonlinear multi-agent dynamic model is established; its expression is: in, Equations representing multi-agent systems, Represents an inherently nonlinear continuous function. Indicates the first The location of each agent. Indicates control input, Indicates external interference. Indicates a group of followers. Represents the set of leaders. This represents a positive input delay. The first-order nonlinear multi-agent dynamic model includes There are 10 intelligent agents, of which 10 are intelligent agents. One follower, with One leader.

3. The event-triggered fixed-time control method for a nonlinear multi-agent system with time delay according to claim 2, characterized in that, The graph is obtained based on the network connections within the first-order nonlinear multi-agent dynamic model. The diagram The Laplacian matrix can be decomposed into: Where L represents the Laplacian matrix, express A matrix related to the information flow of each follower. , express One follower to A matrix related to the information flow of each leader. , R Represents all real numbers, and represents n Viocli, Indicates the number of rows and columns. m OK n List, Indicates the number of rows and columns. m OK m List.

4. A fixed-time event-triggered control method for a nonlinear multi-agent system with time delay according to any one of claims 1 to 3, characterized in that, The error vector is calculated based on the initial state value, initial value of dynamic variables, and adaptive initial value in the first-order nonlinear multi-agent dynamic model. First, the desired state is defined: in, This represents the target position that followers expect to reach using the Laplacian matrix. Indicates a leader; in The error vector is then: in, This represents the difference between the follower's position and the desired position. It indicates a follower.

5. A fixed-time event-triggered control method for a nonlinear multi-agent system with time delay as described in claim 4, characterized in that, a definition is provided. Auxiliary variables: in, Represents auxiliary variables. Indicates the first The location of each agent. t express t time, Indicates controller, This represents a positive input delay. The multi-agent equation is rewritten based on the auxiliary variables; its expression is: in, This represents the rewritten multi-agent equation. Indicates control input, Represents nonlinear terms, Indicates external interference. Represents the set of followers; The rewritten error vector is obtained based on the rewritten multi-agent equations and the error vector; its expression is: in, This represents the rewritten error vector, where j represents... The set of edges, Represents the set of all follower neighbor nodes. This represents the weighting coefficient between followers. Indicates follower j, This represents the weighting coefficient between followers and leaders. Indicates the leader l, f represents the follower.

6. A fixed-time event-triggered control method for a nonlinear multi-agent system with time delay according to claim 1, characterized in that, Calculate the updated value of the dynamic variable based on the initial state value, initial value of the dynamic variable, and adaptive initial value in the first-order nonlinear multi-agent dynamic model; Its expression is: in, Represents a dynamic variable equation. Represents the coefficient. Represents the power exponent. Represents dynamic variables. Represents the coefficient. It represents the power exponent.

7. A fixed-time event-triggered control method for a nonlinear multi-agent system with time delay according to claim 1, characterized in that, The adaptive update value is calculated based on the initial state value, initial value of dynamic variables, and adaptive initial value in the first-order nonlinear multi-agent dynamic model; its expression is: in, Represents the adaptive coupling strength equation, This represents the positive coefficient in the adaptive law. This represents the inclusion error after rewriting the agent dynamics equations.

8. A fixed-time event-triggered control method for a nonlinear multi-agent system with time delay according to claim 1, characterized in that, The agent state is updated based on the error vector, dynamic variable update value, and adaptive update value. An adaptive distributed fixed-time event-triggered control protocol is obtained based on the updated agent state value to perform inclusive control of multiple agents. Its expression is: in, Indicates control input, All represent the parameters to be designed. Representing the first The first agent of the intelligent agent Next trigger moment This represents the rewritten error vector. Represents the power exponent. Represents the power exponent. For adaptive coupling strength.

9. A fixed-time event-triggered control method for a nonlinear multi-agent system with time delay according to claim 1, characterized in that, The triggering condition is defined as follows: in, Representing the first The first agent of the intelligent agent Next trigger time Representing the first The first agent of the intelligent agent Next trigger time This indicates the trigger function.

10. A fixed-time event-triggered control method for a nonlinear multi-agent system with time delay according to claim 1, characterized in that, The method described above proves the stability of the system using Lyapunov functions.

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