Group consensus control method for multi-agent systems based on dynamic event triggering

Abstract

The present invention discloses a group consistency control method for a multi-agent system based on dynamic event triggering. For a second-order nonlinear multi-agent system with unknown disturbances and actuator failures, a finite-time observer is proposed to achieve real-time observation of disturbances and fault information experienced by the agents. Based on the relative state information between the multi-agents, a consistency error variable is defined. Then, based on non-singular terminal sliding mode control, a dynamic event triggering mechanism is introduced, and a fixed-time sliding mode fault-tolerant control method is designed. The present invention can eliminate the impact of faults and unknown disturbances on the system, effectively reducing the consumption of communication resources while achieving a consistent state among the multi-agent subsystems.

Description

Technical Field

[0001] The present invention relates to a group consistency control method for a multi-agent system based on dynamic event triggering, and belongs to the technical field of consistency control of multi-agent systems. Background Art

[0002] In recent years, inspired by the swarming behavior of organisms in nature, researchers have applied the consistency of multi-agent systems to the coordinated control of complex systems. This problem holds significant promise in areas such as robotic collaboration, drone fleets, sensor networks, and group decision-making. In multi-agent systems, group consistency refers to the ability of agents within the same group to converge to a consistent value, while agents in different groups may reach different convergence values. Achieving group consistency can better address the parallel processing of complex tasks.

[0003] However, in practical engineering applications, since multi-agent systems multiply the hardware scale of a single agent, their vulnerability to unknown disturbances and failures is also multiplied. For example, in a drone swarm system, each drone is subject to varying degrees of noise interference during a mission. These disturbances affect both the individual's posture and the information exchange between them and other agents, ultimately impacting the control of the entire system. Therefore, it is crucial to quickly and effectively achieve group consistency in multi-agent systems and design more efficient controllers to improve system robustness.

[0004] Furthermore, in traditional control methods, each agent periodically samples its neighbors. While this approach is theoretically easy to analyze and implement, it also presents challenges such as requiring large communication bandwidth and lengthy computation times. To address this issue, event-triggered control has been introduced as an alternative to traditional periodic clock-triggered control. This is because its triggering mechanism is on-demand, meaning that controller updates are only executed when the agent "needs" to do so. This reduces communication bandwidth and power consumption. However, the threshold of the static triggering mechanism is pre-set and cannot be flexibly adjusted based on actual conditions. In some cases, this can lead to frequent event triggering, resulting in a large amount of unnecessary information transmission.

[0005] In response to the above problems, developing more flexible event triggering conditions to reduce communication costs and control update times, and designing more efficient controllers to enable the system to achieve group consensus under the influence of faults and disturbances have become urgent issues to be solved. Summary of the Invention

[0006] Purpose of the Invention: In light of the aforementioned research background, a novel group-consistency control method for multi-agent systems based on dynamic event triggering is proposed. A finite-time observer is designed to enable rapid and accurate estimation of unknown disturbances and fault information. Dynamic variables are introduced to design a dynamic event triggering mechanism, allowing for adaptive adjustment of the triggering interval, thereby further improving the triggering interval and reducing the controller update frequency. Furthermore, a non-singular terminal sliding mode controller is designed, combining the relative state errors between agents, to achieve group-consistency control of the multi-agent system within a fixed timeframe.

[0007] Technical solution:

[0008] The group consistency control method of a multi-agent system based on dynamic event triggering includes the following specific steps:

[0009] Step 1): Determine a multi-agent system dynamics model, where the multi-agent system includes q leaders and N followers;

[0010] Step 2): Determine the communication topology of the multi-agent system;

[0011] Step 3): Construct a finite-time observer;

[0012] Step 4): Design a consistency control law based on dynamic event triggering. According to Lyapunov stability theory, verify that the multi-agent system achieves fixed-time consistency under the action of the consistency control law based on dynamic event triggering.

[0013] The implementation process of step 1) is:

[0014] Step 1.1): Determine the dynamic model of the leader p (p = 1, 2, ..., q) as shown in (1):

[0015]

[0016] in, Represent the position and velocity states of the p-th leader respectively; is the control input of the p-th leader; m is the spatial dimension;

[0017] Step 1.2): Determine the dynamic model of follower i (i = 1, 2, ..., n) with unknown disturbances and actuator failures as shown in (2):

[0018]

[0019] in, Respectively represent the position and velocity state of the i-th follower; f i (x i (t),v i(t),t) represents the intrinsic nonlinear dynamic function of the i-th follower; d i (t) represents the unknown disturbance of the i-th follower; is the actual control input of the ith follower; its expression is shown in (3):

[0020]

[0021] in, is the ideal control input of the i-th follower; 0≤ρ i <1 indicates the actuator failure factor;

[0022] Define the aggregate fault of the ith follower as w i (t), the lumped fault includes unknown disturbances and actuator faults, and its expression is shown in (4):

[0023] w i (t) = d i (t)-ρ i u i (t) (4)

[0024] Rewrite equation (2) as shown in (5):

[0025]

[0026] Step 1.3): For the inherent nonlinear dynamic function f i (x i (t),v i (t),t) and the lumped fault w i (t) Make assumptions:

[0027]

[0028] in, are all non-negative constants.

[0029] Preferably, the implementation process of step 2) is:

[0030] In a multi-agent system, the leader is marked as p (p = 1, 2, ..., q), and the follower is marked as i (i = 1, 2, ..., n); the communication topology between followers is described by a topology graph G = {W, E, A}, where W = {w1, w2, ..., w N} represents a node set, w i Represents a node, Represents an edge set, A=[a ij ]∈R N×N represents the adjacency matrix, a ij Used to determine node w i and node wj Is there an edge between them? If there is a directed edge from node w j Points to node w i , that is, node w i Can be from node w j Get information, then (w j ,w i )∈E,a ij ≠0; otherwise, a ij =0;

[0031] G is a topological graph consisting of q sub-networks, each of which contains n1, n2, ..., n q followers, G1, G2, …, G q Represents the topology of each sub-network, satisfying n1+n2+…+n q =N, G1={W1,E1,A1}, G2={W2,E2,A2},…,G q ={W q ,E q ,A q};W p ,E p ,A p Represent the node set, edge set and adjacency matrix of the p-th sub-network topology graph respectively;

[0032] G1,G2,…,G q The subscript sets of the nodes are:

[0033] N1∈{1,2,…,n1},

[0034] N2∈{n1+1,n1+2,…,n1+n2},

[0035] ...,

[0036] N q ∈{n1+n2+…+n q-1 +1,n1+n2+…+n q-1 +2,…,n1+n2+…+n q -1,N};

[0037] and Represents the subscript set of all nodes; define node w i The degree is Then the degree matrix of the topological graph G is expressed as D=diag{d1,d2,...,d N}∈R N×N ; Laplace matrix is ​​expressed as L = [l ij ]∈R N×N =DA;

[0038] Define the adjacency matrix between the p-th leader and follower as B p =diag(b 1p ,b 2p ,…,b ip ,...,b np )∈R N×N , b ip Used to determine whether follower i can accept the information of leader p; if follower i can obtain information directly from leader p, then b ip =1; otherwise, b ip =0; define the adjacency matrix between the leader and the follower as H=L+B, where H describes the impact of interactions between followers and information transfer between leaders and followers on the multi-agent system.

[0039] Preferably, the implementation process of step 3 is:

[0040] Step 3.1): First, design a finite-time observer for each follower as shown in (7):

[0041]

[0042] in, represents the aggregate fault estimate of the ith follower; a, c i is a positive constant, 0<α<1, h i (t) represents auxiliary variables;

[0043] Step 3.2): Define the estimated error of the lumped fault As shown in (8):

[0044]

[0045] Step 3.3): Construct two auxiliary variables h i (t) and q i (t), in q i (t) with the help of the auxiliary variable h i (t) is designed as the integral of the lumped fault estimation error:

[0046]

[0047] Adjust a, c i , the value of α makes the estimation error The multi-agent system is eventually uniformly bounded and finite-time stable, that is:

[0048]

[0049] Where T1 is the finite convergence time, V1(0) is the value of the selected Lyapunov function at t=0; adjust a, c i , the value of α will estimate the error Adjust to a very small value of 0.

[0050] Preferably, the implementation process of step 4) is:

[0051] Step 4.1): Define the consistency tracking position error variable e xi (t) and the consistent speed error variable e vi (t), which has the following form:

[0052]

[0053]

[0054] definition:

[0055]

[0056]

[0057]

[0058]

[0059]

[0060]

[0061] e x is the consistent tracking position error variable e xi (t) vector set, e v is the consistency tracking speed error variable e vi (t) is a vector set, is the position error between each group of followers and the corresponding group leader Vector collection of is the speed error between each group of followers and the corresponding group leader If we consider the vector set of , then (12) can be rewritten into vector form as shown in (13):

[0062]

[0063] Among them, I m represents the m-dimensional identity matrix;

[0064] Step 4.2): Design the non-singular terminal sliding surface function as shown in (14):

[0065]

[0066] Among them, k0, k1, μ1, μ2 are non-negative constants, 0<σ<1, β>1, 0<r<1 and satisfies k0μ1r+k0μ2=k0r σ +k1r β ;

[0067] Step 4.3): Design a consistency control law based on dynamic event triggering for the follower subsystem as shown in (15):

[0068]

[0069] in g ij is the matrix H -1 The element in row i and row j of is the k-th triggering moment of the i-th agent, p represents the p-th leader, k2, k3, k4, k5 are positive constants;

[0070] The measurement error is defined as shown in (16):

[0071]

[0072] Step 4.4): Combined with the measurement error, design the dynamic event trigger function ψ i (t) and dynamic variable η i (t) As shown in (17):

[0073]

[0074] Among them, k6>0, k7>0, η i (t)>0,

[0075] The event triggering conditions are shown in (18):

[0076]

[0077] Step 4.5): Estimate the upper bound of convergence time:

[0078] According to Lyapunov stability theory, it is verified that the multi-agent system achieves fixed-time consistency under the action of the consistency control law (15) based on dynamic event triggering. The upper bound of the convergence time is shown as (19):

[0079]

[0080] in ο is a constant introduced after applying Young's inequality and satisfies ο>0; function function parameter parameter

[0081] Beneficial Effects: A novel group-consistency control method for nonlinear multi-agent systems with unknown disturbances and actuator failures is designed based on dynamic event triggering. A finite-time observer is designed to rapidly estimate and compensate for disturbances and fault information. Based on the observer's estimated values ​​and combined with a dynamic event triggering function, a non-singular terminal sliding mode controller is designed to achieve the fixed-time group-consistency control objective. Overall, the present invention has the following advantages:

[0082] 1) A finite-time observer is designed to achieve rapid estimation and compensation of disturbance and fault information.

[0083] 2) A dynamic event triggering mechanism is designed, and the triggering time interval can be adaptively adjusted, thereby further improving the triggering interval and reducing the update frequency of the controller.

[0084] 3) The non-singular terminal sliding mode control method designed in this paper can solve the problem of achieving group consistency in a class of nonlinear multi-agent systems with unknown disturbances and actuator failures. This method ensures that the system converges within a fixed time, which improves equipment efficiency and reduces costs to a certain extent, while enhancing the system's robustness and stability, and is more suitable for handling complex tasks.

[0085] 4) The group consistency control method of the multi-agent system based on dynamic event triggering proposed in the present invention has high accuracy, strong security, high efficiency, moderate hardware requirements, saves communication resources, has certain application significance, and can be widely used in the group consistency implementation problem of a class of nonlinear multi-agent systems with unknown disturbances and actuator failures. BRIEF DESCRIPTION OF THE DRAWINGS

[0086] Figure 1 is a flow chart of the method of the present invention;

[0087] Figure 2 It is the communication topology network of multiple Qball-X4 quadrotor helicopter systems;

[0088] Figure 3 are the estimation curves of the two observers for the disturbance and failure of follower 3;

[0089] Figure 4 are the estimation curves of the two observers for the disturbance and failure of follower 5;

[0090] Figure 5 It is the position tracking curve under the control method designed by the present invention;

[0091] Figure 6 It is the speed tracking curve under the control method designed by the present invention;

[0092] Figure 7 It is the position tracking curve under the traditional terminal sliding mode control method;

[0093] Figure 8 It is the speed tracking curve under the traditional terminal sliding mode control method;

[0094] Figure 9 is the trigger time interval under the control method designed by the present invention;

[0095] Figure 10 is the trigger time interval under the traditional control method. DETAILED DESCRIPTION

[0096] The present invention will be further explained below with reference to the accompanying drawings.

[0097] like Figure 1 As shown in the figure, a finite-time observer is designed for the case where the second-order system interference and actuator failure are unknown, so as to realize the real-time observation of the disturbance and fault information of the agent. On the basis of non-singular terminal sliding mode control, a dynamic event triggering mechanism is designed to solve the problem of waste of communication resources, which greatly reduces unnecessary information interaction. Compared with the conventional non-singular terminal sliding mode control, this control law has a faster convergence speed, and the convergence time is independent of the initial value of the system. It has higher robustness, lower triggering frequency, effectively saves communication resources, and is more suitable for processing complex tasks. A group consistency control of a multi-agent system based on dynamic event triggering includes the following specific steps:

[0098] Step 1) Determine the multi-agent system dynamics model, including the following steps:

[0099] Step 1.1) Determine the dynamic model of the leader p (p = 1, 2, ..., q) as shown in (1):

[0100]

[0101] in, Represent the position and velocity states of the p-th leader respectively; is the control input of the p-th leader;

[0102] Step 1.2) Determine the dynamic model of follower i (i = 1, 2, ..., n) with unknown disturbances and actuator failures as shown in (2):

[0103]

[0104] in, Respectively represent the position and velocity state of the i-th follower; f i (x i (t),v i (t),t) represents the intrinsic nonlinear dynamic function of the i-th agent; d i (t) represents the unknown disturbance of the i-th agent; is the actual control input of the ith agent; its expression is shown in (3):

[0105]

[0106] in, is the ideal control input of the i-th agent; 0≤ρ i <1 indicates the failure factor of the actuator. Define the aggregate failure of the i-th agent as w i (t), including unknown disturbances and actuator failures, is expressed as shown in (4):

[0107] w i (t) = d i (t)-ρ i u i (t) (4)

[0108] Then (2) can be rewritten into a dynamic model as shown in (5):

[0109]

[0110] Step 1.3) For the inherent nonlinear dynamic function f i (x i (t),v i (t),t) and the sum of fault and disturbance w i (t) Make reasonable assumptions:

[0111]

[0112] in, are all non-negative constants;

[0113] Step 2) Determine the communication topology of the multi-agent system:

[0114] In a multi-agent system, the leader is marked as p (p = 1, 2, ..., q), and the follower is marked as i (i = 1, 2, ..., N); the communication network of the followers is described by a topological graph G = {W, E, A}, where W = {w1, w2, ..., w N} represents a node set, w i Represents a node, Represents an edge set, A=[a ij]∈R N×N represents the adjacency matrix, a ij Used to determine node w i and node w j Is there an edge between them? If there is a directed edge from node w j Points to node w i , that is, node w i Can be from node w j Get information, then (w j ,w i )∈E,a ij ≠0; otherwise, a ij =0; G is a topological graph consisting of q sub-networks, each of which contains n1, n2, ..., n q followers, G1, G2, …, G q Represents the topology of each sub-network, satisfying n1+n2+…+n q =N, G1={W1,E1,A1}, G2={W2,E2,A2},…,G q ={W q ,E q ,A q};W p , E p , A p Respectively represent the node set, edge set and adjacency matrix of the p-th sub-network topology graph; G1, G2, ..., G q The subscript sets of the nodes are: N1∈{1,2,…,n1}, N2∈{n1+1,n1+2,…,n1+n2},…,N q ∈{n1+n2+…+n q-1 +1,n1+n2+…+n q-1 +2,…,n1+n2+…+n q -1,N}; and Represents the subscript set of all nodes; define node w i The degree is Then the degree matrix of the topological graph G is expressed as D=diag{d1,d2,...,d N}∈R N×N ; Laplace matrix is ​​expressed as L = [l ij ]∈R N×N =DA; define the adjacency matrix between the p-th leader and follower as B p =diag(b 1p ,b 2p ,…,b ip ,...,b np )∈R N×N , b ipUsed to determine whether follower i can accept the information of leader p; if follower i can obtain information directly from leader p, then b ip =1; otherwise, b ip =0; define the adjacency matrix between the leader and the follower as H=L+B, where H describes the impact of interactions between followers and information transfer between leaders and followers on the multi-agent system.

[0115] Step 3) Construct a finite-time observer, including the following steps:

[0116] Step 3.1) First, design a finite-time observer for each follower as shown in (7):

[0117]

[0118] in, represents the aggregate fault estimate of the i-th agent; a, c i is a positive constant, 0<α<1,

[0119] Step 3.2) Define the estimated error of the lumped fault as shown in (8):

[0120]

[0121] Step 3.3) Construct two auxiliary variables, auxiliary variable h i (t) is designed as the integral of the lumped fault estimation error:

[0122]

[0123] By choosing appropriate parameters, the estimation error (8) is eventually uniformly bounded and the system is finite-time stable, that is:

[0124]

[0125] Where T1 is the finite convergence time, V1(0) is the value of the selected Lyapunov function at t = 0; by a, c i ,αselects a suitable value, which can adjust the estimation error to a very small value;

[0126] Step 4) Design a fixed-time sliding mode fault-tolerant control method based on a dynamic event trigger mechanism, including the following steps:

[0127] Step 4.1) Define the consistency tracking position error variable e based on the neighbor information obtained by the i-th agent xi and the speed error variable e vi , in order to write concisely, the function variables are omitted, and the form is as follows:

[0128]

[0129]

[0130] definition Then (12) can be rewritten into vector form as shown in (13):

[0131]

[0132] Among them, I m represents the m-dimensional identity matrix;

[0133] Step 4.2): Design the non-singular terminal sliding surface function as shown in (14):

[0134]

[0135] Among them, k0, k1, μ1, μ2 are non-negative constants, 0<σ<1, β>1, 0<r<1 and satisfies k0μ1r+k0μ2=k0r σ +k1r β ;

[0136] Step 4.3): Design a consistency control law based on dynamic event triggering for the follower subsystem as shown in (15):

[0137]

[0138] in g ij is the matrix H -1 The element in row i and row j of is the k-th triggering moment of the i-th agent, p represents the p-th leader, k2, k3, k4, k5 are positive constants;

[0139] The measurement error is defined as shown in (16):

[0140]

[0141] Step 4.4): Combined with the measurement error, design the dynamic event trigger function ψ i (t) and dynamic variable η i (t) As shown in (17):

[0142]

[0143] Among them, k6>0, k7>0, η i (t)>0,

[0144] The event triggering conditions are shown in (18):

[0145]

[0146] Step 4.5): Estimate the upper bound of convergence time:

[0147] According to Lyapunov stability theory, it is verified that the multi-agent system composed of equations (1) and (5) achieves fixed-time consistency under the action of the consistency control law (15). The upper bound of the convergence time is shown in (19):

[0148]

[0149] in ο is a constant introduced after applying Young's inequality and satisfies ο>0;

[0150] The effectiveness of the implementation plan is illustrated by a real case simulation below.

[0151] The flight control system of the Qball-X4 quadrotor helicopter developed by the Canadian Quanser Company is used as the research object. The multi-agent system consists of 8 Qball-X4 quadrotor helicopters, each with a leader labeled θ1 and θ2 and followers labeled i (i = 1, 2, 3, 4, 5, 6). Its communication topology is as follows: Figure 2 As shown. Among them, the leader of the agents marked 1, 2, 3, and 4 is θ1, and the leader of the agents marked 5 and 6 is θ2. In the communication topology graph, the weight of each edge in the same group is 1, and the weight of each edge in different groups is -1. According to the communication topology structure, the specific expressions of the Laplace matrix L and the adjacency matrix B can be calculated as follows:

[0152] B=diag(1,1,0,0,1,0)

[0153] For the model of the multi-agent system, the control inputs of the leader are The initial state values ​​are

[0154] The nonlinear dynamics of the follower are f i (x i (t),v i (t),t)=-sin(x i (t))-sin(v i (t)),i=1,2,3,4,fi (x i (t),v i (t),t)=-cos(x i (t))-cos(v i (t)), i=5,6, obviously ||f i (x i (t),v i (t),t)||≤2; the perturbation equations are d i (t)=0.1+0.2sin(0.5πt),i=1,2,3,4,d i (t)=0.1+0.2cos(0.5πt),i=5,6; the initial state values ​​are x1(0)=2.2,x2(0)=2.55,x3(0)=0.7,x4(0)=-2.4,x5(0)=-1.8,x6(0)=1.6, v1(0)=3.2, v2(0)=1.98, v3(0)=-2.1, v4(0)=1.8 v5(0)=-1.2, v6(0)=0.6.

[0155] To illustrate the effectiveness and superiority of the fault-tolerant control method designed in this invention in solving the consistency control problem of a multi-agent system with actuator failures, assume that followers 3 and 5 experience actuator failures, while the other followers are not faulty. ρ3 = 0.1, ρ5 = 0.3.

[0156] Select the observer parameters as: a=1, c i =0.6, α=0.5. In order to better demonstrate the rapidity and accuracy of the observer designed in the present invention in disturbance and fault estimation, a traditional observer is selected for comparison, and the comparison curves of the present observer and the traditional observer in disturbance and fault estimation are obtained as follows: Figure 3 and Figure 4 By comparison, it can be seen that the observer designed by the present invention has a faster convergence speed, a smoother curve, and a lower peak value than the traditional observer. Therefore, the observer designed by the present invention has a better effect.

[0157] The controller parameters are selected as follows: σ = 0.5, β = 1.5, r = 0.47, k0 = 0.8, k1 = 2, k2 = 8, k3 = 10, k4 = 2.5, k5 = 2, k6 = 0.4, k7 = 1.8, μ1 = 0.6, μ2 = 1.2. To better demonstrate the higher robustness of the non-singular terminal sliding mode controller designed in this paper, a traditional terminal sliding mode controller is selected for comparison. Figure 5 and Figure 6 They are the position and velocity curves of the follower under the action of the controller designed by the present invention, Figure 7 and Figure 8 The curves show the position and velocity of the follower under the action of the traditional terminal sliding mode controller. As can be seen from the curves, both methods can achieve the goal of consistent convergence of the multi-agent system under disturbances and failures, but it is obvious that the controller designed by the present invention has a shorter convergence time. In addition, the traditional method cannot handle complex tasks and can only execute a set of tasks. In order to more clearly compare the communication resource consumption of the two controllers, Figure 9 and Figure 10 The triggering intervals for the two control methods are shown. Clearly, the controller designed by this invention has a longer triggering interval than the traditional terminal sliding mode controller, effectively saving communication resources. Therefore, this case demonstrates the effectiveness of this control method.

[0158] This method designs a fixed-time group consistency fault-tolerant control method for second-order multi-agent systems based on a dynamic event triggering mechanism. For situations where second-order system interference and actuator failures are unknown, a finite-time observer is designed to achieve real-time observation of the disturbances and fault information experienced by the agent. Based on non-singular terminal sliding mode control, a dynamic event triggering mechanism is designed to address the problem of wasted communication resources, greatly reducing unnecessary information interaction. Compared with conventional non-singular terminal sliding mode control, this control law has a faster convergence speed, and the convergence time is independent of the system initial value. It has higher robustness, a lower triggering frequency, effectively saves communication resources, and is more suitable for processing complex tasks.

[0159] The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principles of the present invention. These improvements and modifications should also be regarded as within the scope of protection of the present invention.

Claims

1. A group consistency control method for a multi-agent system based on dynamic event triggering, characterized in that: The specific steps include: Step 1): Determine a multi-agent system dynamics model, where the multi-agent system includes q leaders and N followers; Step 2): Determine the communication topology of the multi-agent system; Step 3): Construct a finite-time observer; Step 4): Design a consistency control law based on dynamic event triggering. Based on Lyapunov stability theory, verify that the multi-agent system can achieve fixed-time consistency under the action of the consistency control law based on dynamic event triggering. The implementation process of step 4) is: Step 4.1): Define the consistency tracking position error variable e xi (t) and the consistent speed error variable e vi (t), which has the following form: in, Represent the position and velocity states of the i-th follower respectively; Represent the position and velocity state of the pth leader respectively; in the multi-agent system, the leader is marked as p (p = 1, 2, ..., q) and the follower is marked as i (i = 1, 2, ..., n); the communication topology between followers is described by the topology graph G = {W, E, A}, where W = {w1, w2, ..., w N } represents a node set, w i Represents a node, represents the edge set, represents the adjacency matrix, a ij Used to determine node w i and node w j Is there an edge between them? If there is a directed edge from node w j Points to node w i , that is, node w i Can be from node w j Get information, then (w j ,w i )∈E,a ij ≠0; otherwise, a ij =0; G is a topological graph consisting of q sub-networks, each of which contains n1, n2, ..., n q followers, G1, G2, …, G q Represents the topology of each sub-network, satisfying n1+n2+…+n q =N,G1,G2,…,G q The subscript sets of the nodes are: N1∈{1,2,…,n1}, N2∈{n1+1,n1+2,…,n1+n2}, ……， N q ∈{n1+n2+…+n q-1 +1,n1+n2+…+n q-1 +2,…,n1+n2+…+n q -1,N}; and represents the subscript set of all nodes; the adjacency matrix between the p-th leader and follower is defined as b ip Used to determine whether follower i can accept the information of leader p; if follower i can obtain information directly from leader p, then b ip =1; otherwise, b ip =0; define the adjacency matrix between the leader and the follower as H = L + B, where L is the Laplace matrix and H describes the effects of the interactions between followers and the information transfer between leaders and followers on the multi-agent system; definition: e x is the consistent tracking position error variable e xi (t) vector set, e v is the consistency tracking speed error variable e vi (t) is a vector set, is the position error between each group of followers and the corresponding group leader Vector collection of is the speed error between each group of followers and the corresponding group leader If we consider the vector set of , then (2) can be rewritten into vector form as shown in (3): Among them, I m represents the m-dimensional identity matrix; Step 4.2): Design the non-singular terminal sliding surface function as shown in (4): Among them, k0, k1, μ1, μ2 are non-negative constants, 0<σ<1, β>1, 0<r<1 and satisfies k0μ1r+k0μ2=k0r σ +k1r β ; Step 4.3): Design a consistency control law based on dynamic event triggering for the follower subsystem as shown in (5): in is the ideal control input of the ith follower; g ij is the matrix H -1 The prime in row i and column j of is the k-th triggering moment of the i-th agent, p represents the p-th leader, k2, k3, k4, k5 are positive constants; represents the aggregate fault estimate of the ith follower; is the control input of the p-th leader; m is the spatial dimension; The measurement error is defined as shown in (6): Step 4.4): Combined with the measurement error, design the dynamic event trigger function ψ i (t) and dynamic variable η i (t) As shown in (7): Among them, k6>0, k7>0, η i (t)>0, The event triggering conditions are shown in (8): Step 4.5): Estimate the upper bound of convergence time: According to Lyapunov stability theory, it is verified that the multi-agent system achieves fixed-time consistency under the action of the consistency control law (5) based on dynamic event triggering. The upper bound of the convergence time is shown in (9): in ο is a constant introduced after applying Young's inequality and satisfies ο>0; function function parameter parameter 2. The group consistency control method of a multi-agent system based on dynamic event triggering according to claim 1, characterized in that: The implementation process of step 1) is: Step 1.1): Determine the dynamic model of the leader p (p = 1, 2, ..., q) as shown in (10): Step 1.2): Determine the dynamic model of follower i (i = 1, 2, ..., n) with unknown disturbances and actuator failures as shown in (11) Among them, f i (x i (t),v i (t),t) represents the intrinsic nonlinear dynamic function of the i-th follower; d i (t) represents the unknown disturbance of the i-th follower; is the actual control input of the ith follower; its expression is shown in (12): Where 0≤ρ i <1 indicates the actuator failure factor; Define the aggregate fault of the ith follower as w i (t), the lumped fault includes unknown disturbances and actuator faults, and its expression is shown in (13): w i (t)=d i (t)-ρ i u i (t) (13) Rewrite equation (11) as shown in (14): Step 1.3): For the inherent nonlinear dynamic function f i (x i (t),v i (t),t) and the lumped fault w i (t) Make assumptions: in, are all non-negative constants.

3. The group consistency control method of a multi-agent system based on dynamic event triggering according to claim 2, characterized in that: The implementation process of step 2) is: Define G1 = {W1, E1, A1}, G2 = {W2, E2, A2}, ..., G q ={W q ,E q ,A q };W p ,E p ,A p Represent the node set, edge set and adjacency matrix of the p-th sub-network topology graph respectively; Define node w i The degree is Then the degree matrix of the topological graph G is expressed as The Laplace matrix is ​​expressed as 4. The group consistency control method of a multi-agent system based on dynamic event triggering according to claim 3 is characterized in that: The implementation process of step 3 is: Step 3.1): First, design a finite-time observer for each follower as shown in (16): Among them, a, c i is a positive constant, 0<α<1, h i (t) represents auxiliary variables; Step 3.2): Define the estimated error of the lumped fault As shown in (17): Step 3.3): Construct two auxiliary variables h i (t) and q i (t), in q i (t) with the help of the auxiliary variable h i (t) is designed as the integral of the lumped fault estimation error: Adjust a, c i , the value of α makes the estimation error The multi-agent system is eventually uniformly bounded and finite-time stable, that is: Where T1 is the finite convergence time, V1(0) is the value of the selected Lyapunov function at t=0; adjust a, c i , the value of α will estimate the error Adjust to a very small value of 0.

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