Dynamic event-triggered consensus control method for multi-agent systems with communication delay

Abstract

The present invention discloses a method for controlling the dynamic event trigger consistency of a multi-agent system under communication delay, which belongs to the field of network communication technology of a multi-agent system. The control method includes: establishing a hybrid model including flow dynamics and jump dynamics to describe a closed-loop system; based on the hybrid model, a new Lyapunov function is proposed to establish a strict positive lower bound on the time between events and a stability condition of the maximum allowed delay, which can ensure that Zeno behavior does not occur; and an event trigger condition is designed to achieve asymptotic consistency. The hybrid dynamic event trigger mechanism proposed in the present invention can more effectively reduce the communication burden of the communication network; in addition, the proposed hybrid dynamic event trigger control strategy can guarantee a strict positive minimum trigger interval even in the presence of external disturbances, ensuring the exclusion of Zeno behavior, which is of great significance to the realization of physical control.

Description

Technical Field

[0001] The present invention relates to the field of multi-agent system network communication technology, and in particular to a multi-agent system dynamic event triggering consistency control method under communication delay. Background Art

[0002] In recent decades, multi-agent systems have been widely used in the fields of drones, robot system control, etc., and have attracted extensive attention from researchers. Among them, the leader-follower consistency problem of multi-agent systems has always been a hot research topic.

[0003] In order to achieve leader-follower consistency control of multi-agent systems, it is necessary for agents to communicate with each other. Generally speaking, agents rely on shared networks for communication. However, the communication resources (communication bandwidth and energy) of the shared network between agents are limited. Traditional continuous and periodic sampling control strategies will lead to excessive use of communication resources and may even cause network congestion. To solve this problem, researchers use event-triggered control strategies instead of periodic sampling control strategies.

[0004] Compared with traditional time-triggered control schemes, event-triggered control strategies usually require fewer communication resources because information exchange is performed only when necessary rather than in a periodic manner, while ensuring the desired system performance. In practice, when multi-agents propagate signals in a communication network, they are inevitably affected by communication delays, which may degrade the control performance or even lead to unstable system dynamics. Therefore, it is necessary to consider the impact of communication delays when designing multi-agent leader-follower consensus control protocols. In addition, if the system is subject to disturbances, even arbitrarily small, Zeno-triggered behavior (infinite triggering occurring in a finite time) may occur. If Zeno behavior occurs in the presence of disturbances, unpredictable system dynamics may undermine the stability of the system, which is undesirable in practice.

[0005] In summary, how to design a control protocol that can solve all the above problems and achieve leader-follower consistency has become an urgent problem that researchers in the field of multi-agents need to solve. Summary of the invention

[0006] The technical problem to be solved by the present invention is to provide a dynamic event-triggered consistency control method for a multi-agent system under communication delay. In order to realize the leader-follower consistency control of the multi-agent system under the condition of communication delay and disturbance, a hybrid dynamic event-triggered control strategy is proposed; firstly, the proposed control strategy can effectively reduce the communication burden of the network and avoid the possibility of network congestion due to excessive communication volume; secondly, a closed-loop system model with hybrid dynamics is constructed, which combines the proposed hybrid dynamic event-triggered control strategy with time-varying delay, and can explicitly calculate the maximum allowable delay; finally, a known and pre-specified lower bound of the trigger interval is obtained, and a new Lyapunov function is proposed, which helps to better analyze the relationship between the minimum event trigger interval and the maximum allowable delay.

[0007] In order to solve the above technical problems, the technical solution adopted by the present invention is:

[0008] A method for dynamic event-triggered consistency control of a multi-agent system under communication delay comprises the following steps:

[0009] Step 1, establish a multi-agent system model with communication delay;

[0010] Step 2: Reconstruct the multi-agent system model under the hybrid system framework;

[0011] Step 3, introduce auxiliary functions to obtain the strict positive lower bound of the inter-event time and the stability conditions of the maximum allowed delay, and build a dynamic event triggering mechanism;

[0012] Step 4: Design sufficient conditions for the multi-agent system to achieve leader-follower consistency control.

[0013] A further improvement of the technical solution of the present invention is that: in step 1, for a multi-agent system, the agents therein are divided into a leader agent and a follower agent; wherein the dynamic description of the leader agent is:

[0014]

[0015] The dynamic description of each follower agent is:

[0016]

[0017] in, and are the states of the leader agent and the follower agent, respectively. is the control input of follower agent i, represents the perturbation, i∈[1,N]; matrix A, B u and B wis a system matrix of appropriate dimensions, and assuming that (A,B u ) is stable;

[0018] The flow dynamics of the multi-agent system is described as:

[0019]

[0020]

[0021] in

[0022]

[0023]

[0024]

[0025]

[0026] ρ(t)=[ρ1(t)…ρ N (t)], e(t)=[e1(t)…e N (t)],w(t)=[w1(t)…w N (t)],ρ i (t) to follow

[0027] The consistency error between the agent i and the leader agent, e i (t) is the estimation error of follower agent i; is the Laplace matrix; θ=diag{θ1,θ2…θ N}, θ i Indicates whether the follower agent i can obtain reference information from the leader agent X0; k is the control gain; I N is the N-dimensional identity matrix.

[0028] A further improvement of the technical solution of the present invention is that in step 2, a hybrid system model is constructed for the multi-agent system:

[0029]

[0030] Among them, F(ν) is the flow dynamics, J(ν) is the jump dynamics, is a flow set, is a jump set; introduce auxiliary variable h i ∈{0,1}, Variable h i There are two values, which keep track of the agent's next event, which is the transmission event (h i =0) or update event (h i =1); variable si For storage exist The value at τ i Used to represent the time that has passed since the last trigger, and to ensure that Zeno behavior is completely excluded; introduce the state vector

[0031]

[0032] The flow dynamics of ν(t) is described as:

[0033]

[0034] in, in, It is the lower bound of the minimum event triggering interval;

[0035] The jump dynamics of ν(t) is described as:

[0036]

[0037] in,

[0038]

[0039] in, J 0,i (ν) indicates that agent i meets the event triggering condition and sends data to its neighbors; J 1,i (ν) indicates that after agent i sends data, its neighbors receive delayed data; represents a matrix with the i-th diagonal element equal to 1, and all other elements equal to 0.

[0040] A further improvement of the technical solution of the present invention is that in step 3, in order to analyze the stability of the multi-agent system, an auxiliary function is introduced:

[0041]

[0042] In order to obtain a strictly positive lower bound on the inter-event time and the maximum allowed delay, an auxiliary function is introduced:

[0043]

[0044]

[0045] b(τ i )=max{sign(τ METI -τ i ),0}

[0046] Among them, α i> 0, the trigger interval and time delay are constrained by Φ i and The time it takes to decrease to a smaller value is expressed as the time it takes to decrease to a smaller value, and the initial condition Φ needs to be specified i (0) and

[0047] For agent i, the dynamic event triggering condition is constructed as:

[0048]

[0049] in, When , it is the lower bound of the minimum event triggering interval; is an auxiliary variable; η i (t) Solve according to the following expression:

[0050]

[0051] Among them, i Indicates locally available information; when the above conditions are met, the controller updates.

[0052] A further improvement of the technical solution of the present invention is that in step 4, sufficient conditions for the multi-agent system to achieve leader-follower consistency control are designed, including:

[0053] 1) There is a constant τ MAD and τ METI , and τ MAD ≤τ METI , then it satisfies:

[0054]

[0055]

[0056] in, It is the upper bound of the maximum allowed delay;

[0057] 2) There exists a positive definite matrix Constant 0<ι<1, a>0, 0<ι1<1, 0<ι2<1, γ w >0, the following matrix inequality is satisfied:

[0058]

[0059]

[0060] in, C z and D z is a constant matrix, It consists of N sub-matrices, the i-th sub-matrix is ​​the identity matrix, and the remaining sub-matrices are zero matrices;

[0061] 3) There is a function For all The following conditions are met, where 0≤τ i <τ METI

[0062]

[0063]

[0064] Among them, the function Designed for:

[0065]

[0066] in, ι1>0, ι2>0;

[0067] In w i = 0, the dynamics (ρ, e, s, η) of the multi-agent system is uniformly globally asymptotically stable, that is, the follower agents in the multi-agent system are consistent with the leader agent; i ≠0, the multi-agent system goes from input w to output z - stable, - Gain is less than or equal to γ w ; and ensure that Zeno behavior will not occur.

[0068] Due to the adoption of the above technical solution, the technical progress achieved by the present invention is:

[0069] 1. The present invention mainly solves the leader-follower consistency problem of a multi-agent system with time-varying communication delay and external interference; the maximum allowable delay to ensure the stability of the multi-agent system is obtained, and the interval between any two events is known and designable; under the maximum allowable delay, the system can operate stably.

[0070] 2. Even if the multi-agent system is disturbed by external factors, the hybrid dynamic event triggering mechanism proposed in the present invention can still ensure the existence of a strictly positive minimum event triggering interval, realize Zeno-Free, and ensure the stability of the multi-agent system.

[0071] 3. The hybrid dynamic event triggering mechanism proposed in the present invention can effectively reduce the data transmission and communication burden of the network; in addition, the proposed hybrid dynamic event triggering control strategy can guarantee a strict positive minimum triggering interval even in the presence of external disturbances, ensuring the exclusion of Zeno behavior, which is of great significance for the realization of physical control. BRIEF DESCRIPTION OF THE DRAWINGS

[0072] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art are briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative labor.

[0073] Figure 1 It is a flow chart of a method for controlling consistency of dynamic event triggering of a multi-agent system under communication delay provided by the present invention;

[0074] Figure 2 is a block diagram of a miscellaneous event triggering mechanism in an embodiment of the present invention;

[0075] Figure 3 is a communication topology diagram including a leader agent and five follower agents in an embodiment of the present invention;

[0076] Figure 4 is the error signal between the follower agent and the leader agent in the embodiment of the present invention Figure 1 ;

[0077] Figure 5 is the error signal between the follower agent and the leader agent in the embodiment of the present invention Figure 2 ;

[0078] Figure 6 is the error signal between the follower agent and the leader agent in the embodiment of the present invention Figure 3 ;

[0079] Figure 7 is the error signal between the follower agent and the leader agent in the embodiment of the present invention Figure 4 ;

[0080] Figure 8 is the error signal between the follower agent and the leader agent in the embodiment of the present invention Figure 5 ;

[0081] Fig. 9 is an external disturbance graph of the multi-agent system in the embodiment of the present invention;

[0082] Fig.10 Schematic diagram of triggering moments and intervals of follower agents 1-5 in an embodiment of the present invention. DETAILED DESCRIPTION

[0083] It should be noted that the terms "including" and "having" and any variations thereof in the specification and claims of the present invention and the above-mentioned drawings are intended to cover non-exclusive inclusions. For example, a process, method, system, product or apparatus comprising a series of steps or units is not necessarily limited to those steps or units clearly listed, but may include other steps or units that are not clearly listed or inherent to these processes, methods, products or apparatus.

[0084] The present invention is further described in detail below with reference to the accompanying drawings and embodiments:

[0085] In this invention, it is assumed that the multi-agent system consists of N follower agents and 1 leader agent, and the communication network is represented by an undirected graph. To indicate that is the communication link between agents, is the vertex set, represents agent i, is the adjacency matrix. ij = 1, it means that agent i can receive information from agent j; when a ij = 0, agent i cannot receive information from agent j. is defined as the degree matrix, and The Laplacian matrix can be expressed as When agent i can obtain the reference information of leader X0, θ i =1, otherwise, θ i =0. And Θ=diag{θ1, θ2…θ N In order to solve the leader-follower consistency problem of multi-agent systems with communication delay and disturbance, such as Figure 1 As shown in the figure, a dynamic event-triggered consistency control method for a multi-agent system under communication delay is proposed, which includes the following steps:

[0086] Step 1: Establish a multi-agent system model with communication delay;

[0087] For a multi-agent system, the agents can be divided into leader agents and follower agents; the dynamics of the leader agent can be described as:

[0088]

[0089] The dynamics of each follower agent can be described as:

[0090]

[0091] in, and are the states of the leader agent and the follower agent, respectively. is the control input of follower agent i, represents the perturbation, i∈[1,N]. Matrix A, B u and B w is a system matrix of appropriate dimensions, and assuming that (A,B u ) is stable. To achieve leader-follower consistency,

[0092] Use below represents the triggering time of agent i, At this moment, agent i changes its state to its neighbor agent j. Under the influence of cannot reach agent j immediately, but is received by agent j. Assuming τ MAD ≤τ METI , where τ MAD is the maximum allowed delay, τ METI is the lower bound of the minimum event triggering interval, that is, the state of agent i is transferred to agent j before the next information transmission starts. So, satisfy Next, define:

[0093]

[0094] Under the influence of communication delay, the controller of the follower agent is designed as:

[0095]

[0096] Where k is the control gain.

[0097] The consistency error between follower agent i and leader agent is defined as:

[0098] ρ i (t) = x i (t)-x0(t) (5)

[0099] Define the estimation error of follower agent i as:

[0100]

[0101] According to (3) and (6), the estimated error e i (t) The jump dynamics at time is:

[0102]

[0103] According to (1), (2) and (4)-(6), ρ i (t) and e i The flow dynamics of (t) can be expressed as:

[0104]

[0105]

[0106] Then the flow dynamics of the multi-agent system can be expressed as:

[0107]

[0108]

[0109] in

[0110]

[0111]

[0112]

[0113]

[0114] ρ(t)=[ρ1(t)…ρ N (t)], e(t)=[e1(t)…e N (t)],w(t)=[w1(t)…w N (t)],ρ i (t) is the consistency error between follower agent i and leader agent, e i (t) is the estimation error of follower agent i.

[0115] Step 2: Reconstruct the multi-agent system model under the hybrid system framework;

[0116] Due to the existence of two types of error jump dynamics caused by transmission events and update events, in order to correctly describe the closed-loop dynamics and stability analysis, a hybrid system model of the multi-agent system is constructed:

[0117]

[0118] Among them, F(ν) is the flow dynamics, J(ν) is the jump dynamics, is a flow set, is a jump set. Introduce auxiliary variable h i ∈{0,1}, Variable h i There are two values, which keep track of the agent's next event, which is the transmission event (hi =0) or update event (h i =1). Variable s i For storage exist The value of τ i Used to represent the time that has passed since the last trigger, and to ensure that Zeno behavior is completely excluded. Introducing the state vector

[0119] The flow dynamics of ν(t) can be described as:

[0120]

[0121] in,

[0122] The jump dynamics of ν(t) can be described as:

[0123]

[0124] in,

[0125]

[0126] in, J 0,i (ν) indicates that agent i meets the event triggering condition and sends data to its neighbors. 1,i (ν) indicates that after agent i sends data, its neighbors receive delayed data. represents a matrix with the i-th diagonal element equal to 1, and all other elements equal to 0.

[0127] In the presence of disturbances, the performance of a multi-agent hybrid system can be defined as the attenuation of the disturbance relative to the output variable, which is expressed as follows:

[0128] z(t)=C z ρ(t)+D z w(t) (16)

[0129] Among them, C z and D z is a constant matrix.

[0130] The present invention uses the following definitions:

[0131] Definition 1: The hybrid model of multi-agent system composed of equations (13) and (14) is The given set is considered to be uniformly globally asymptotically stable if there exists a function So that for any initial condition and The following conditions hold:

[0132] ||ρ(t),e(t),s(t),η(t)||≤β(||ρ(0),e(0),s(0),η(0)||,t) (17)

[0133] Definition 2: The hybrid model of the multi-agent system composed of equations (13) and (14) is such that if there exists Function β and constant γ w > 0 so that for any initial condition and and any The following conditions hold:

[0134] ||z(t)||≤β(||ρ(0),e(0),s(0),η(0)||)+γ w ||w(t)|| (18)

[0135] in, w(t)|| is similar. Then, the multi-agent system from w(t) to z(t) is Stable.

[0136] Step 3, introduce relevant auxiliary functions, obtain the strict positive lower bound of the interval between events and the stability conditions of the maximum allowed delay, and construct a dynamic event triggering mechanism;

[0137] In order to analyze the stability of the multi-agent closed-loop system, an auxiliary function W is introduced. i (h i ,e i ,s i )as follows:

[0138]

[0139] According to (13) and (14), function (19) satisfies:

[0140]

[0141]

[0142] In order to obtain a strictly positive lower bound on the inter-event time and the maximum allowed delay, an auxiliary function is introduced:

[0143]

[0144]

[0145] b(τ i )=max{sign(τ METI -τi ),0} (24)

[0146] Among them, α i > 0, the trigger interval and time delay are constrained by Φ i and The time it takes to decrease to a smaller value is expressed as the time it takes to decrease to a smaller value, and the initial condition Φ needs to be specified i (0) and

[0147] For agent i, the dynamic event triggering condition is constructed as:

[0148]

[0149] in , it is the lower bound of the minimum event triggering interval. is an auxiliary variable. i (t) can be solved according to the following expression:

[0150]

[0151] Among them i Only locally available information is indicated. When the above conditions are met, the controller performs an update.

[0152] like Figure 2 As shown, in the present invention, each time When a trigger event occurs, at least τ METI The next event detection is performed after time, interval can be considered as an internal cycle, where event detection is not required. Then, from At the beginning, continuous event detection is performed until the next trigger event occurs. Therefore, the proposed event trigger mechanism is a "hybrid" of continuous event detection and periodic event detection, so it is called a hybrid event trigger mechanism.

[0153] In addition, according to (22) and (23), we can get and τ MAD :

[0154]

[0155]

[0156] Among them, l i is specified The lower bound of .

[0157] The present invention uses the following lemma:

[0158] Lemma 1: Undirected Graph are connected. yes The minimum eigenvalue of (A,B) is stable. There exists a solution P1>0 of the following Riccati inequality:

[0159] P1A+A T P1-2υP1BB T P1+υI n <0 (29)

[0160] Control gain k = B T P1.

[0161] Step 4: Design sufficient conditions for the multi-agent system to achieve leader-follower consistency control.

[0162] Theorem 1: According to the hybrid model (13) and (14) of multi-agent systems. If (20) and (21) hold, for a given constant α i >0, the following conditions are met.

[0163] 1) There is a constant τ MAD and τ METI , and τ MAD ≤τ METI , then it satisfies:

[0164]

[0165]

[0166] 2) There exists a positive definite matrix Constant 0<ι<1, a>0,0<ι1<1,0<ι2<1,satisfy the following matrix inequality:

[0167]

[0168]

[0169] in It consists of N sub-matrices, the i-th sub-matrix is ​​the identity matrix, and the remaining sub-matrices are zero matrices.

[0170] 3) There is a function For all The following conditions are met, where 0≤τ i <τ METI

[0171]

[0172]

[0173] The function Designed for:

[0174]

[0175] in ι1>0, ι2>0.

[0176] In w i = 0, the dynamics (ρ, e, s, η) of the multi-agent system is uniformly globally asymptotically stable, that is, the follower agents in the multi-agent system are consistent with the leader agent, that is, x i →x0. i ≠0, the multi-agent system goes from input w to output z - stable, - Gain is less than or equal to γ w . And it is guaranteed that Zeno behavior will not occur.

[0177] Proof: The Lyapunov function designed by the present invention is:

[0178]

[0179] where α i >0, for τ i ≥0 has Φ i (τ i )≥0. Use W 0i and W 1i To represent W i (0,e i ,s i ) and W i (1,e i ,s i ). Using (26), (34) and (35), when 0≤τ i <τ METI When η i ≥0.

[0180] When the system is not disturbed by external disturbances, w = 0, if it can be proved that the following conditions are met:

[0181]

[0182]

[0183] σ ρ and σ W is a positive definite function. ρ and σ ρ Asymptotically converges to zero, and the leader-follower consistency of the multi-agent system can be achieved.

[0184] When the system is disturbed by external disturbances, w≠0, if it can be proved that the following conditions are met:

[0185]

[0186]

[0187] Then the multi-agent system from input w to output z is - stable, - Gain is less than or equal to γ w .

[0188] First, consider that when the system is disturbed by external disturbance, w≠0, the time derivative of U(ν) is:

[0189]

[0190] According to (32), we have Let inequality (33) be multiplied by [ρ T e T w T ], multiply [ρ T e T w T ], so we have:

[0191]

[0192] Based on (42) and (43), we have:

[0193]

[0194] According to (24), we can get that for 0≤τ i <τ METI There is b(τ i )=1, for τ i ≥τ METI There is b(τ i )=0.

[0195]

[0196] Case 1: 0 ≤ τ i <τ METI , through (44) we have:

[0197]

[0198] Where L j :={i∈[1,N]|h i =j}.

[0199] Case 2: Due to τ i ≥τ METI ,h i = 0, through (44) we have:

[0200]

[0201] when And h i = 0, the next event is a transmission event, so τ i ≥τ METI , through (20), (30) and (31), we have:

[0202]

[0203] when And h i =1, the next event is an update event, so 0≤τ i ≤τ METI , through (20), (30) and (31), we have:

[0204]

[0205] Based on equations (45) to (48), using the standard Lyapunov stability theory of hybrid systems, the multi-agent system from input w to output z is - stable, - Gain is less than or equal to γ w .

[0206] When there is no external disturbance, that is, w = 0, we have:

[0207]

[0208] Similar to the case of w≠0, the jump conditions in equations (47) and (48) still hold. That is, when i∈[1,N], the leader-follower consistency control of the multi-agent system is realized, that is, x i →x0. So, the proof ends.

[0209] The present invention uses the spacecraft formation problem for MATLAB simulation. Each spacecraft can be regarded as an intelligent agent. Assume that there is a leader intelligent agent and five follower intelligent agents, with number 0 representing the leader intelligent agent and numbers 1-5 representing the follower intelligent agents. Their communication topology Figure 3 shown.

[0210] The dynamics of the i-th spacecraft can be described as:

[0211]

[0212]

[0213]

[0214] in represents the position of the i-th spacecraft in the rotating coordinate system, (u xi ,u yi ,u zi ) is the control input, and ω0 is the angular velocity of the spacecraft. Define the position vector Velocity Vector Control vector u i =[u xi ,u yi ,u zi ] T If their velocity vectors converge to the same value and their positions maintain a prescribed distance from each other, then a spacecraft formation is achieved, i.e., r i →h i →r j →h j , in represents the specified distance between spacecraft i and j. And define The dynamics of a multi-agent system can be described as

[0215] Leader Agent:

[0216] Follower Agent:

[0217]

[0218] where ω0 = 0.001 is the angular velocity of the spacecraft. Therefore, the spacecraft formation problem is transformed into a multi-agent consensus problem with agent 0 as the leader and the other agents as followers. In addition, it is assumed that there is external disturbance in the spacecraft dynamics, so the dynamics of each agent can be expressed as:

[0219]

[0220] Among them B w =[1,1,1,1,1,1] T .

[0221] Assume the initial condition is x0(0) = [0.1, 0, -0.1, 0.2, 0, -0.2] T ,x1(0)=[1,2,3,4,5,6] T , x2(0)=[2,4,6,8,10,12] T , x3(0)=[3,6,9,12,15,18]T , x4(0)=[4,8,12,16,20,24] T , x5(0)=[5,10,15,20,25,30] T Trigger parameters ι1=0.3,ι2=0.1,η i (0) = 0.1. The multi-agent system is subject to an upper bound of 2 (-2 ≤ w i ≤2). According to Theorem 1, the lower bound of the time between events and the maximum allowable delay can be calculated as τ MAD =0.03s.

[0222] The simulation results are as follows Figure 4-9 , Fig.10 The distributed hybrid dynamic event triggering control mechanism proposed in the present invention can be applied to multi-agent systems with disturbances and time delays. Fig.10 It is found that even in the presence of external disturbances, the trigger interval between events is still strictly positive and Zeno behavior will not occur. Finally, the leader-follower consistency control of the multi-agent system is realized, which means that the present invention is effective.

[0223] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or replace some or all of the technical features therein with equivalents. However, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for dynamic event-triggered consistency control of a multi-agent system under communication delay, characterized by: The following steps are involved: Step 1, establish a multi-agent system model with communication delay; Step 2: Reconstruct the multi-agent system model under the hybrid system framework; Constructing hybrid system models for multi-agent systems: Among them, F(ν) is the flow dynamics, J(ν) is the jump dynamics, is a flow set, is a jump set; introduce auxiliary variable h i ∈{0,1}, Variable h i There are two values, which keep track of the agent's next event, which is the transmission event (h i =0) or update event (h i =1); variable s i For storage exist The value at τ i Used to represent the time that has passed since the last trigger, and to ensure that Zeno behavior is completely excluded; introduce the state vector The flow dynamics of ν(t) is described as: in, in, It is the lower bound of the minimum event triggering interval; The jump dynamics of ν(t) is described as: in, in, J 0,i (ν) indicates that agent i meets the event triggering condition and sends data to its neighbors; J 1,i (ν) indicates that after agent i sends data, its neighbors receive delayed data; represents a matrix with the i-th diagonal element equal to 1, and all other elements equal to 0; Step 3, introduce auxiliary functions to obtain the strict positive lower bound of the inter-event time and the stability conditions of the maximum allowed delay, and build a dynamic event triggering mechanism; In order to analyze the stability of the multi-agent system, an auxiliary function is introduced: In order to obtain a strictly positive lower bound on the inter-event time and the maximum allowed delay, an auxiliary function is introduced: b(t i )=max{sign(τ METI -t i ),0} Among them, α i > 0, the trigger interval and time delay are constrained by Φ i and The time it takes to decrease to a smaller value is expressed as the time it takes to decrease to a smaller value, and the initial condition Φ needs to be specified i (0) and For agent i, the dynamic event triggering condition is constructed as: in, When , it is the lower bound of the minimum event triggering interval; is an auxiliary variable; η i (t) Solve according to the following expression: Among them, i Indicates locally available information; when the above conditions are met, the controller is updated; Step 4: Design sufficient conditions for the multi-agent system to achieve leader-follower consistency control.

2. According to the method of claim 1, the method is characterized by: In step 1, for the multi-agent system, the agents are divided into leader agents and follower agents; the dynamic description of the leader agent is: The dynamic description of each follower agent is: in, and are the states of the leader agent and the follower agent, respectively. is the control input of follower agent i, represents the perturbation, i∈[1,N]; matrix A, B u and B w is a system matrix of appropriate dimensions, and assuming that (A,B u ) is stable; The flow dynamics of the multi-agent system is described as: in ρ(t)=[ρ1(t)…ρ N (t)], e(t)=[e1(t)…e N (t)],w(t)=[w1(t)…w N (t)],ρ i (t) is the consistency error between follower agent i and leader agent, e i (t) is the estimation error of follower agent i; is the Laplace matrix; θ=diag{θ1,θ2…θ N }, θ i Indicates whether the follower agent i can obtain reference information from the leader agent X0; k is the control gain; I N is the N-dimensional identity matrix.

3. According to the method of claim 1, the method is characterized by: In step 4, sufficient conditions for the multi-agent system to achieve leader-follower consistency control are designed, including: 1) There is a constant τ MAD and τ METI , and τ MAD ≤τ METI , then it satisfies: in, It is the upper bound of the maximum allowed delay; 2) There exists a positive definite matrix Constant 0<ι<1, a>0, 0<ι1<1, 0<ι2<1, γ w >0, the following matrix inequality is satisfied: in, C z and D z is a constant matrix, It consists of N sub-matrices, the i-th sub-matrix is ​​the identity matrix, and the remaining sub-matrices are zero matrices; 3) There is a function For all The following conditions are met, where 0≤τ i <τ METI Among them, the function Designed for: in, In w i = 0, the dynamics (ρ, e, s, η) of the multi-agent system is uniformly globally asymptotically stable, that is, the follower agents in the multi-agent system are consistent with the leader agent; i ≠0, the multi-agent system goes from input w to output z - stable, - Gain is less than or equal to γ w ; and ensure that Zeno behavior will not occur.

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