Multi-agent event trigger control transient state and sesame phenomenon analysis method based on response characteristics

Abstract

The invention discloses a response characteristic-based multi-agent event trigger control transient state and sesame phenomenon analysis method, which comprises the following steps of: applying measurable input to a leader agent and each follower agent, acquiring output, identifying impulse response of the leader agent and the follower agent, and expressing the impulse response as a power function attenuation form; the convolution input and output relation is converted into an algebraic equation through orthogonal transformation, and a fractional order differential model of each agent is established; under an event trigger mechanism, control input is modeled as a segmented step function, impulse response is utilized to carry out convolution solution on output, a steady-state component and a transient component are separated, and a collaborative error model containing historical transient influence is constructed. And further constructing a positive definite Lyapunov function, deducing an additional threshold considering a historical transient component in combination with a fractional differential comparison principle, and solving a minimum safety triggering time interval. And when the adjacent triggering interval is smaller than the threshold value, false triggering caused by the transient state is judged, and the signal is shielded, so that the sesame phenomenon is effectively eliminated, and the communication overhead is reduced.

Description

Technical Field

[0001] This invention relates to a method for analyzing transient and Zeno phenomena in multi-agent event-triggered control based on response characteristics, belonging to the fields of artificial intelligence and robotics. Background Technology

[0002] Multi-agent systems consist of multiple autonomous agents that collaborate to complete a global task through local interactions and cooperation. Multi-agent technology holds great promise in fields such as autonomous driving, smart grids, and smart cities. Achieving multi-agent collaboration, improving execution efficiency, and ensuring task completion are key research areas in multi-agent systems.

[0003] Multi-machine collaboration refers to achieving multi-machine coordination and formation control through control strategies. Existing research methods almost all involve establishing a single-machine input-output differential model, designing a control strategy based on a reference signal, and synchronizing the agent with the reference signal to achieve collaborative control.

[0004] According to the input-output differential model: a change in input immediately changes the output; a stop in input immediately stops the change in the output signal. From a system perspective, no single machine is an ideal system; all have response characteristics. The output is the convolution of the input and the impulse response. When the input stops, the output will inevitably have a transient response process.

[0005] Event-triggered control transmits control signals only when triggering conditions are met, and it has been widely studied in multi-agent systems due to its low communication overhead. Clearly, when a control signal is triggered, it means that the input signal has changed. Due to response characteristics, any input change has a transient process, and multi-agent event-triggered control is no exception. Because of this transient process, event-triggered detectors inevitably mistake transient signals for multi-agent output signals, leading to false triggers, or even frequent triggers within a short period, resulting in the Zeno phenomenon. This not only fails to reduce communication overhead but may even increase it.

[0006] Therefore, by combining the response characteristics of multi-agent systems, this study investigates the transient process of event-triggered control to avoid the Zeno phenomenon. Based on this, designing multi-agent event-triggered control strategies is of great value in engineering applications. Summary of the Invention

[0007] The present invention provides a method for analyzing transient and Zeno phenomena in multi-agent event-triggered control based on response characteristics in order to solve the problems existing in the prior art.

[0008] The technical solutions adopted in this invention are as follows:

[0009] A method for analyzing transient and Zeno phenomena in multi-agent event-triggered control based on response characteristics includes the following steps:

[0010] Step 1: Apply measurable inputs to the leader agent and each follower agent respectively and collect output data. Independently identify the impulse response of the leader agent and each follower agent. Represent each impulse response as a power function in the form of a decay function. Transform the convolution input-output relationship of each agent into an algebraic equation through orthogonal transformation. Establish the fractional differential model of the leader agent and each follower agent.

[0011] Step 2: Under the event-triggered sequence, the zero-order hold control input of the follower agent is represented as a piecewise step function. The corresponding impulse response obtained in Step 1 is used to convolve the piecewise step function, and the output generated in each time period is decomposed into steady-state components and transient components to construct a cooperative error model that includes the influence of historical transients.

[0012] Step 3: Construct a positive definite function based on the cooperative error model, and give the upper bound expression of the positive definite function by combining the fractional differential comparison principle. Use the historical transient components in the upper bound expression as additional thresholds, solve for the minimum time interval that makes the triggering condition satisfied only on the steady-state component side, and forcibly block the triggering signal when the adjacent triggering interval is less than the minimum time interval, so as to realize multi-agent event triggering cooperative control and eliminate Zeno phenomenon.

[0013] Furthermore, in step 1, when identifying the impulse response for the leader agent and each follower agent, the applied measurable input is first synchronously recorded and combined with the collected output data to form input-output experimental data. Then, the convolution relationship between the agent input and the impulse response is transformed into an algebraic model and a cost function is constructed through the Legendre transformation. At the same time, a hybrid identification algorithm combining particle swarm optimization and gradient search is used to complete the parameter identification of the impulse response.

[0014] Furthermore, the specific expressions for the input-output kernel convolution relationship and impulse response of the agent are as follows:

[0015] ,

[0016] ,

[0017] in, For time variables, express Dimensional output, representing the agent's performance Moment Output status in each dimension; The output vector at the initial time, i.e., t=0, represents the initial state of the agent's output. express Dimensional input, representing the input applied to the agent Each dimension can measure the input signal;

[0018] for The diagonal matrix of the impulse response of the first-order system. , , Input the corresponding unit impulse response for each dimension; This is the convolution operator.

[0019] Further, in step 1, when establishing the fractional differential model, first construct the autonomous model of the driving agent, and then convert the autonomous model into a fractional differential model; the fractional differential expression of the autonomous model of the driving agent is:

[0020] ,

[0021] The fractional-order differential coupling model corresponding to the following multi-agent is:

[0022] ,

[0023] in, Let be the Caputo fractional differential operator, representing the expression for... The Caputo fractional derivative, where At the initial moment of the differential, Represents a fractional differential of the Caputo type. Indicates the order of the differential;

[0024] For the leader intelligent agent in The state output vector at time step; This is the agent's autonomous mapping function, which characterizes the mapping relationship between the agent's output state and the fractional-order differential state; For the first The state variables of each follower agent node; The total number of nodes in the follower agent; For the first The node and the first The coupling coefficient between nodes represents the strength of the interaction and association between nodes; For the first The state variables of each follower agent node.

[0025] Further, in step 2, the expression for the cooperative error is: And the Lipschitz condition satisfied by the cooperative error model is: ,in, For the first The collaborative error vector between the follower and the leader represents the state deviation between them; for The transpose of ; For the first The state variables of a follower agent; It is a nonlinear mapping of error correlation, representing the difference between the autonomous mapping functions of followers and leaders; This is the Lipschitz constant.

[0026] Furthermore, in step 2, when decomposing the output of each time period into steady-state and transient components, for The steady-state component of the output generated by the interval input. and transient components for:

[0027] ,

[0028] ,

[0029] in, This is the 0th trigger moment (i.e., the initial moment). This is the first trigger moment. For the first At each trigger moment, t i+1 For the first One trigger moment; is the gamma function, a fundamental special function in fractional calculus;

[0030] Coupling matrix The largest eigenvalue, Let be the positive definite error function of the i-th follower, representing the energy state of the cooperative error;

[0031] Let be the control gain of the i-th follower, which characterizes the strength of the control input's adjustment of the cooperative error;

[0032] For the first The collaborative error vector at each trigger moment;

[0033] It is a unit step function, with a function value of 1 when the independent variable is greater than or equal to 0, and a function value of 0 when the independent variable is less than 0;

[0034] for The steady-state component generated by the interval input represents the stable output component induced by the input during that period;

[0035] for The transient component generated by the interval input represents the attenuated transition output portion caused by the input during that period.

[0036] Furthermore, in step 3, the constructed positive definite function is:

[0037] ,

[0038] Furthermore, the fractional convergence constraint satisfied by the positive definite function at the triggering time is:

[0039] ,

[0040] in, For the first The error of a follower is a positive definite function; It is a constant greater than 0, representing the convergence rate of the positive definite function at the triggering time; For the first The event is triggered at the time. This indicates that the expression is in The value is retrieved at the trigger time.

[0041] Furthermore, in step 3, the transient state generated by the historical process within the current time period is defined by the invention. Its expression is:

[0042] ,

[0043] Furthermore, the correlation between measurement error and steady-state components and historical transient components is as follows:

[0044] ,

[0045] in, The trigger time sequence number; For the first One follower The total transient component caused by historical inputs within a given time period; For the first One follower Transient components generated by time-period input; For the first One follower Transient components of time-period input The impact of steady-state output over a given period;

[0046] For the first One follower Transient components of time-period input The impact of transient output over a period of time; For the first The measurement error of a follower represents the deviation between the actual detection error and the theoretical error; For the first One follower The steady-state output component generated by the input within a time period.

[0047] Furthermore, in step 3, the event triggering time constraint is set to avoid the Zeno phenomenon as follows:

[0048] ,

[0049] in, For the first The event is triggered at a specific time. This is the trigger time of the (k+1)th event; The infimum operator; The minimum trigger interval is the trigger time threshold set to avoid the Zeno phenomenon. Here, represents the trigger condition parameter, and represents the trigger threshold coefficient. For the first One follower The positive definite error function value at the trigger time; when When this occurs, it is determined to be a false trigger caused by a transient event, and the trigger signal is blocked. In the formula... For the first One follower The historical transient component at any given moment.

[0050] The present invention has the following beneficial effects:

[0051] This invention establishes the relationship between the system response model and the fractional-order model, and utilizes the memory characteristics of the fractional-order model to study the response characteristics of multi-agent systems. Combining the multi-agent fractional-order model, it establishes the relationship between the system output and the historical process, obtaining the relationship between the multi-agent event-triggered transient process and the historical process. Based on the transient process, the mechanism of Zeno's phenomenon is analyzed, and a method for analyzing Zeno's phenomenon is proposed. Furthermore, based on the transient process, time constraints are introduced to establish a multi-agent event-triggered control strategy to avoid Zeno's phenomenon and reduce communication overhead. Attached Figure Description

[0052] Figure 1 This is a schematic diagram of the control principle of the present invention.

[0053] Figure 2 for Simulation diagram of cooperative error.

[0054] Figure 3 for Simulation diagram of trigger time interval.

[0055] Figure 4 for Simulation diagram of cooperative error.

[0056] Figure 5 for Simulation diagram of trigger time interval.

[0057] Figure 6 for Simulation diagram of cooperative error.

[0058] Figure 7 for Simulation diagram of trigger time interval. Detailed Implementation

[0059] The invention will now be further described with reference to the accompanying drawings.

[0060] This invention discloses a method for analyzing transients and Zeno's phenomenon in multi-agent event-triggered control based on response characteristics. This method can be widely applied to multi-agent cooperative control scenarios in artificial intelligence and robotics. The specific implementation process can be carried out step-by-step according to the following technical flow to achieve stable multi-agent cooperation and avoid the increased communication overhead caused by Zeno's phenomenon. A schematic diagram is shown below. Figure 1 As shown, the follower detects the following error with the leader in real time. When the error exceeds a certain threshold, an event trigger is activated to change the follower's control input signal, enabling the follower to coordinate with the leader. Based on this, the present invention includes the following steps:

[0061] Step 1: Construct a multi-agent response model. The specific steps are as follows:

[0062] Step 1.1: Establish the leader input-output impulse response model.

[0063] Intelligent agents have complex structures and processes, making it virtually impossible to build models based on complex mechanisms. Instead, they are often built using experimental data to establish input-output models.

[0064] No intelligent agent is an ideal impulse-response system; every input has a response process. The system output is the convolution of the input and the impulse response. Let's assume the impulse response of the leader agent is: .

[0065] Based on this, the present invention proposes the following multi-agent impulse response model:

[0066] (1),

[0067] in, For time variables, The output vector at the initial time, i.e., t=0, represents the initial state of the agent's output. express Dimensional input, representing the input applied to the agent Each dimension can measure the input signal; express Dimensional output, representing the agent's performance Moment Output status in each dimension; for The diagonal matrix of the impulse response of the first-order system. , They represent The corresponding angular displacement as input The unit impulse response. The input-output relationship can be obtained:

[0068] (2),

[0069] Step 1.2: Establish the system impulse response :

[0070] According to the system stability condition, the agent's impulse response is always a function that decays with time, expressed as:

[0071] (3),

[0072] in, , , , Corresponding to , , , The parameters to be identified.

[0073] Step 1.3: Use the Legendre transform to convert the convolutional model into an algebraic model and construct the cost function. Experiments were conducted to collect multi-agent input and output data, and the particle swarm optimization algorithm and gradient search algorithm were combined to identify the unknown parameters in formula (3).

[0074] Step 1.4: Construct an autonomous model that drives intelligent agents.

[0075] Viewing the driving agent as an autonomous model, where the system output undergoes function computation and then feeds back to the input, we can obtain:

[0076] (4),

[0077] in, This indicates that the output signal has undergone function operations.

[0078] Step 1.5: Convert the autonomous model into a fractional-order model to facilitate research using fractional-order theory.

[0079] according to

[0080] (5),

[0081] The relationship can be obtained as follows:

[0082] (6),

[0083] express fractional derivative, Describing the order of the differential .

[0084] Combining formula (4), and using the order of the differential... and exponents, functions AND function The relationship allows us to obtain the differential order. And functions. Thus, a fractional-order model of the responding agent is obtained.

[0085] Step 1.6: Establish a fractional-order model of the following agent.

[0086] Similar to leader modeling, repeating steps 1.1 through 1.5 can establish a fractional-order model of a following single agent.

[0087] Step 1.7: Establish a fractional-order coupled model of a following multi-agent system.

[0088] There are coupling relationships among the multiple agents in the following model. Based on these coupling relationships, a multi-agent following model is established:

[0089] (7),

[0090] in, Let be the Caputo fractional differential operator, representing the expression for... The Caputo fractional derivative, where At the initial moment of the differential, Represents a fractional differential of the Caputo type. Indicates the order of the differential;

[0091] For the leader intelligent agent in The state output vector at time step; This is the agent's autonomous mapping function, which characterizes the mapping relationship between the agent's output state and the fractional-order differential state; For the first The state variables of each follower agent node; The total number of nodes in the follower agent; For the first The node and the first The coupling coefficient between nodes represents the strength of the interaction and association between nodes; For the first The state variables of each follower agent node.

[0092] Step 2: Analyze the multi-agent event-triggered control response process, specifically including the following steps:

[0093] Step 2.1: Assume that the multi-agent event triggering control is as follows: When the detector detects that the output signal has reached the trigger condition at the above moment, it transmits the trigger signal to the controller and changes the control input of the follower multi-agent. (8),

[0094] in, Indicates the first The collaboration error between followers and leaders Indicates control gain. Event-triggered controller. During the event trigger interval The input control remains unchanged.

[0095] Step 2.2: Represent the input signal using a piecewise function and establish the relationship between the system response and all historical inputs:

[0096] Introducing the unit step function Rewrite formula (8):

[0097] (9),

[0098] Step 2.3: Establish a follower-leader collaboration error model:

[0099] (10)

[0100] in,

[0101] Satisfying the Lipschitz condition , This is the Lipschitz constant.

[0102] Based on the memory characteristics of fractional-order models, the input is cut off, but the output is not immediately cut off. The output has memory characteristics of historical inputs, so the output is studied in conjunction with the historical process.

[0103] Step 2.4: Construct the positive definite error function and establish the relationship between the positive definite error function and the fractional derivative:

[0104] Construct positive definite functions:

[0105] (11),

[0106] in .

[0107] Establish the relationship between positive definite functions and fractional differentials:

[0108] (12)

[0109] definition: , for The largest eigenvalue.

[0110] Step 2.5: Establish the output relationship based on fractional integrals and the comparison principle.

[0111] Fractional integral of formula (12):

[0112] (13).

[0113] Step 2.6: Establish the relationship between output and historical input segment by segment, and analyze the transient process.

[0114] (1) Considering only When input is within a time interval, the output generated by the input within that time interval satisfies:

[0115] (14)

[0116] It should be noted that: Formula (14) reflects the fact that in The input within a time period produces the output, but due to response characteristics, this output... The timeframe does not end. There is also a transient process. This invention divides the above output into steady-state processes. and transient processes .in:

[0117] (15)

[0118] (16)

[0119] in, This is the 0th trigger moment (i.e., the initial moment). This is the first trigger moment. For the first At each trigger moment, t i+1 For the first One trigger moment; is the gamma function, a fundamental special function in fractional calculus;

[0120] Coupling matrix The largest eigenvalue, Let be the positive definite error function of the i-th follower, representing the energy state of the cooperative error;

[0121] Let be the control gain of the i-th follower, which characterizes the strength of the control input's adjustment of the cooperative error;

[0122] For the first The collaborative error vector at each trigger moment;

[0123] It is a unit step function, with a function value of 1 when the independent variable is greater than or equal to 0, and a function value of 0 when the independent variable is less than 0;

[0124] for The steady-state component generated by the interval input represents the stable output component induced by the input during that period;

[0125] for The transient component generated by the interval input represents the attenuated transition output portion caused by the input during that period.

[0126] (2) Consider only When inputting within a range:

[0127] Similar to sub-step (1) under step 2.6, only consider When input is within a time interval, the output generated by the input within that time interval satisfies:

[0128] (17)

[0129] Because in The input over a given time period produces not only a steady-state output but also a transient output, which in turn feeds back into the input, affecting subsequent processes. Therefore:

[0130] (18)

[0131] The above formula also includes steady-state output and transient output, where

[0132] (19)

[0133] (20)

[0134] (twenty one),

[0135] (twenty two),

[0136] (3) Only consider When the input is within the interval, its output satisfies:

[0137] (twenty three),

[0138] Similar to sub-step (2) in step 2.6, we can obtain:

[0139] (twenty four)

[0140] In the above formula, Indicates the first One follower Steady-state output generated by input over a time period Indicates the first One follower Input pairs within a time period Transient effects of time-limited output. Indicates the first One follower Input pairs within a time period Steady-state impact of output over a time period.

[0141] (4) Only consider When inputting within a range:

[0142] Similar to sub-steps (1)-(3) in step 2.6, we can obtain:

[0143] (25)

[0144] In the above formula, This indicates the impact of the steady-state output of historical inputs on the current output; This indicates the impact of the transient state generated by the current input segment on subsequent processes; This represents the impact of the transient output of historical inputs on the current output. For simplicity, this invention defines:

[0145] (26)

[0146] It represents a transient state generated by a historical process within the current time period.

[0147] Step 3: Propose a new time-constrained event triggering strategy to avoid the Zeno phenomenon, which includes the following steps:

[0148] Step 3.1: Design the feedback gain of the event-triggered controller.

[0149] The feedback gain is designed based on the stability condition of fractional-order systems using formula (10). , making ,in, For the first The error of a follower is a positive definite function; t is a constant greater than 0, representing the convergence rate of the positive definite function at the trigger time; kFor the k-th event trigger time, This indicates that the expression is in The value is retrieved at the trigger time.

[0150] Step 3.2: Define the measurement error and design event trigger control conditions based on the measurement error.

[0151] Define measurement error:

[0152] (27)

[0153] Set multi-agent event triggering conditions:

[0154] (28)

[0155] Where k is the trigger time number; For the first One follower The total transient component caused by historical inputs within a given time period; For the first One follower Transient components generated by time-period input; For the first One follower Transient components of time-period input The impact of steady-state output over a given period;

[0156] For the first One follower Transient components of time-period input The impact of transient output over a period of time; For the first The measurement error of a follower represents the deviation between the actual detection error and the theoretical error; For the first One follower The steady-state output component generated by the input within a time period.

[0157] Step 3.3: Calculate the trigger condition parameters .

[0158] according to This relationship, combined with parameters Solve the event trigger condition parameters Based on the triggering conditions and the boundedness of the state variables, we can obtain The lower bound makes it possible for... Internal constant This ensures that the collaboration error between any follower and leader converges over time.

[0159] Step 3.4: Analyze Zeno's phenomenon in conjunction with the transient process.

[0160] Based on the analysis of the transient process in step 2.6, calculate... The measurement error relationship can be obtained as follows:

[0161] (29)

[0162] express The steady-state output generated by the input within a time period. Equation (29) shows that the measurement error is not only related to the input within the current time period, but also to the transients generated by the historical process.

[0163] Obviously, when hour, .

[0164] (30)

[0165] if This inevitably triggers the time-based conditions again. Due to the transient effect of history, the detector mistakenly believes that the triggering conditions have been met again, leading to frequent triggering and even the Zeno phenomenon.

[0166] Step 3.5: In conjunction with transient processes, design an event-triggered control strategy to avoid Zeno's phenomenon.

[0167] Based on the event triggering conditions and the boundedness of the state variables of multiple agents, this invention posits that triggering is only initiated when the steady-state components of the state variables meet the triggering conditions. Based on the triggering conditions and the boundedness of the state variables, the minimum time interval for the event triggering conditions can be obtained. All triggers within this time period are considered false triggers and are ignored. Therefore, this invention proposes the following event trigger control measurement:

[0168] (31),

[0169] in, For the first The event is triggered at a specific time. This is the trigger time of the (k+1)th event; The infimum operator; The minimum trigger interval is the trigger time threshold set to avoid the Zeno phenomenon. Here, represents the trigger condition parameter, and represents the trigger threshold coefficient. For the first One follower The positive definite error function value at the trigger time; when When this occurs, it is determined to be a false trigger caused by a transient event, and the trigger signal is blocked. In the formula... For the first One follower The historical transient component at any given moment.

[0170] To verify the effectiveness of this method, a specific multi-agent model can be built for experiments, where the fractional-order differential model corresponding to the leader agent is as follows:

[0171] ,

[0172] The fractional-order differential model corresponding to the follower agent is:

[0173]

[0174] in The parameters are selected as follows:

[0175] , The follower has 6 nodes.

[0176] ,

[0177] Choose different Perform simulation.

[0178] , , Perform simulation.

[0179] The simulation results are as follows: Figures 2-7 As shown. Figure 2 yes Cooperative error, Figure 3 yes Simulation diagram of trigger time interval; Figure 4 yes Cooperative error, Figure 5 yes Simulation diagram of trigger time interval; Figure 6 yes Cooperative error, Figure 7 This is a simulation diagram of the trigger time interval.

[0180] Simulation results show that under the same conditions, different response characteristics result in different transient processes. It is necessary to analyze the transient processes in conjunction with the response characteristics of multiple agents, and on this basis, study event-triggered control strategies.

[0181] The above description is only a preferred embodiment of the present invention. It should be noted that those skilled in the art can make several improvements without departing from the principle of the present invention, and these improvements should also be considered within the scope of protection of the present invention.

Claims

1. A method for analyzing transient and Zeno phenomena in event-triggered control of multi-agent systems based on response characteristics, the method comprising: determining a response characteristic of each agent in the multi-agent system; and analyzing the transient and Zeno phenomena in the event-triggered control of the multi-agent system based on the response characteristics. The method comprises the following steps: Step 1: respectively applying measurable input to the leader agent and each follower agent and collecting output data, respectively identifying the impulse response of the leader agent and each follower agent, expressing each impulse response as a decay function in the form of a power function, converting the convolution input-output relationship of each agent into an algebraic equation through an orthogonal transformation, and establishing a fractional-order differential model of the leader agent and each follower agent; Step 2: under an event-triggered sequence, expressing the zero-order hold control input of the follower agent as a piecewise step function, convolving the piecewise step function with the corresponding impulse response obtained in step 1, decomposing the output generated in each period into a steady-state component and a transient-state component, and constructing a collaborative error model containing historical transient-state influence; Step 3: constructing a positive definite function based on the collaborative error model, giving an upper bound expression of the positive definite function by combining the fractional-order differential comparison principle, taking the historical transient-state component in the upper bound expression as an additional threshold, solving the minimum time interval at which the trigger condition is only satisfied on the steady-state component side, and forcibly shielding the trigger signal when the adjacent trigger interval is less than the minimum time interval, to realize multi-agent event-triggered collaborative control and eliminate Zeno phenomenon.

2. The response characteristic based multi-agent event-triggered control transient and Zeno phenomenon analysis method according to claim 1, wherein: In step 1, when identifying the impulse response of the leader agent and each follower agent, the measurable input applied is first recorded synchronously and combined with the collected output data to form input-output experimental data, then the convolution relationship between the agent input and the impulse response is converted into an algebraic model through Legendre transformation and a cost function is constructed, and a hybrid identification algorithm combining particle swarm algorithm and gradient search algorithm is used to complete the parameter identification of the impulse response.

3. The response characteristic based multi-agent event-triggered control transient and Zeno phenomenon analysis method according to claim 1, wherein: The specific expressions of the input-output core convolution relationship of the agent and the impulse response are as follows: ， ， in, For time variables, express Dimensional output, representing the agent's performance Moment Output status in each dimension; The output vector at the initial time, i.e., t=0, represents the initial state of the agent's output. express Dimensional input, representing the input applied to the agent Each dimension can measure the input signal; is a diagonal matrix of the system impulse response, , , are the unit impulse responses corresponding to each dimension input respectively; is the convolution operator notation.

4. The method according to claim 1, wherein: In step 1, when establishing the fractional-order differential model, an autonomous model of the driven agent is first constructed, and then the autonomous model is converted into a fractional-order differential model; the fractional-order differential expression of the autonomous model of the driven agent is: ， The fractional-order differential coupled model corresponding to the follower multi-agent is: ， wherein, is the Caputo fractional derivative operator, denotes the Caputo fractional derivative of wherein is the initial time of differentiation, denotes the Caputo fractional derivative, denotes the order of differentiation; For the leader intelligent agent in The state output vector at time step; This is the agent's autonomous mapping function, which represents the mapping relationship between the agent's output state and the fractional-order differential state; For the first The state variables of each follower agent node; The total number of nodes in the follower agent; For the first The node and the first The coupling coefficient between nodes represents the strength of the interaction and association between nodes; For the first The state variables of each follower agent node.

5. The response characteristic based multi-agent event-triggered control transient and Zeno phenomenon analysis method of claim 1, wherein: In Step 2, the expression of the coordination error is and the Lipschitz condition satisfied by the coordination error model is: where, is the coordination error vector of the th follower and leader, representing the state deviation of both; is the transpose vector of ; is the state variable of the th follower agent; is the error-related nonlinear mapping, representing the difference between the follower and leader autonomous mapping functions; is the Lipschitz constant.

6. The response characteristic based multi-agent event-triggered control transient and Zeno phenomenon analysis method of claim 1, wherein: In step 2, the output for each period is decomposed into a steady-state component and a transient component, where The output generated by the interval input, its steady-state component and transient component are: ， ， wherein, is the 0th trigger time, is the 1st trigger time, is the th trigger time, t i+1 is the th trigger time; is the gamma function, is the base special function in fractional calculus. the maximum eigenvalue of the coupling matrix the maximum eigenvalue of the coupling matrix the error positive definite function of the ith follower, representing the energy state of the cooperative error Ki is the control gain for the i-th follower, which characterizes the strength of the adjustment of the control input to the coordination error; the first coordinated error vector for the nth trigger instant; The unit step function is a function whose value is 1 for argument values greater than or equal to zero and whose value is zero for argument values less than zero. For The steady-state component generated by the interval input represents the stable output portion caused by the input in this period. For The transient component generated by the interval input represents the decaying transient output portion induced by the interval input.

7. The response characteristic based multi-agent event-triggered control transient and Zeno phenomenon analysis method of claim 1, wherein: In step 3, the constructed positive definite function is: ， The fractional-order convergence constraint satisfied by the positive definite function at the trigger time is: ， wherein, is a positive definite function of the error of the th follower; is a constant greater than 0, characterizing the convergence rate of the positive definite function at the triggering instant; is the th event-triggering instant, denotes the value of the expression at the 8. The response characteristic based multi-agent event-triggered control transient and Zeno phenomenon analysis method of claim 1, wherein: In step 3, the history process produces a transient for the current time period that is defined by the invention whose expression is ， The correlation relationship between the measurement error and the steady-state component and the historical transient-state component is: ， wherein, is a trigger time index; is a total transient component of the input to the th follower over the time period caused by the history input; is a transient component of the input to the th follower over the time period caused by the history input; is an influence of the transient component of the input to the th follower over the time period on the steady state output over the time period caused by the history input; For the first One follower Transient components of time-period input The impact of transient output over a period of time; For the first The measurement error of a follower represents the deviation between the actual detection error and the theoretical error; For the first One follower The steady-state output component generated by the input within a time period.

9. The response characteristic based multi-agent event-triggered control transient and Zeno phenomenon analysis method according to claim 1, wherein: In step 3, the event trigger time constraint set to avoid Zeno phenomenon is: ， in, For the first The event is triggered at a specific time. This is the trigger time of the (k+1)th event; The infimum operator; The minimum trigger interval is the trigger time threshold set to avoid the Zeno phenomenon. Here, represents the trigger condition parameter, and represents the trigger threshold coefficient. For the first One follower The positive definite error function value at the trigger time; when When this occurs, it is determined to be a false trigger caused by a transient event, and the trigger signal is blocked. In the formula... For the first One follower The total transient component of the history at any given moment.

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