Consistency control method in fixed-switching topology based on event-triggered mechanism

Abstract

The present application relates to a consistency control method under a fixed-switching topology based on an event-triggered mechanism, which includes the following steps: constructing an adjacency matrix A and a communication matrix B according to the communication relationship between followers and between followers and leaders in each cluster of the multi-agent system, and a second-order nonlinear dynamic model of the leader and followers; taking the consistency of the follower state in each cluster with the leader state as the control target; constructing the state error of the followers in the current cluster; obtaining the control input of the followers in the current cluster based on the state error, and designing an event-triggered controller, which updates the control input and realizes consistency control of the followers in the current cluster. The present invention solves the limitations of existing fixed topology structures when facing complex tasks, overcomes the defect that some existing switching topology structures only focus on structural changes within a single cluster, and enhances the collaboration and control capabilities of multi-agent systems in dynamic environments.

Description

Technical Field

[0001] The present application relates to the field of collaborative control of multi-agent systems, and specifically to a consistency control method under a fixed-switching topology based on an event-triggered mechanism. Background Art

[0002] A multi-agent system (MAS) is a system composed of multiple agents, each with a degree of autonomy and capabilities, capable of perceiving the environment, making decisions, and interacting with other agents. Relying on communication, information exchange, and collaborative work to form a unified whole, they can replace expensive single systems and solve large-scale, complex real-world problems. Currently, most research considers implementations based on fixed network topologies. In real-world settings, the widespread use of multi-agent systems has led to increasingly complex external environments. For example, in high-temperature and high-pressure environments, agents are initially divided into multiple clusters to repair facilities. During the repair process, agents in one cluster may be insufficient, necessitating the use of agents from other clusters, or agents may suddenly malfunction, requiring them to operate in a new topology. Multi-agent systems with fixed topologies often cannot meet the demands of complex tasks, and some switching topologies often only consider structural changes within a single cluster. Summary of the Invention

[0003] The purpose of the present invention is to provide a consistency control method under a fixed-switching topology based on an event-triggered mechanism, which is applicable to a multi-agent system with a switching topology structure. It solves the limitations of the existing fixed topology structure when facing complex tasks, and overcomes the defect that some existing switching topology structures only focus on structural changes within a single cluster, thereby enhancing the collaboration and control capabilities of the multi-agent system in a dynamic environment.

[0004] The technical solution adopted by the present invention is: a consistency control method under a fixed-switching topology based on an event trigger mechanism, comprising the following steps:

[0005] S1: For a multi-agent leader-follower system, denote the number of clusters in the multi-agent leader-follower system as n; construct an adjacency matrix A and a communication matrix B based on the communication relationships between followers in each cluster and the communication relationships between followers and leaders, and establish a second-order nonlinear dynamic model of leaders and followers in a single cluster, as well as followers in adjacent clusters;

[0006] S2: The control goal is to make the follower state and the leader state consistent in each cluster;

[0007] S3: Introduce and establish communication management between followers in adjacent clusters and followers in the current cluster, and construct the state error of followers in the current cluster;

[0008] S4: Obtaining the control input of the followers in the current cluster according to the state error, and designing an event-triggered controller. The event-triggered controller updates the control input to achieve consistency control of the followers in the current cluster.

[0009] Furthermore, the specific steps of step S1 are:

[0010] S101: There are M followers and one leader l in the current cluster, and N followers in the adjacent cluster. For the current cluster, a weight graph G and an adjacency matrix A are established based on the communication relationships between the M followers. ij ], the adjacency matrix A is an M×M matrix, a ij Indicates the communication relationship between the i-th follower and the j-th follower in the current cluster; if there is a communication relationship between the i-th follower and the j-th follower in the current cluster, a directed edge is added between the i-th follower and the j-th follower in the weighted graph G, and a is recorded. ij >0, and if there is no communication relationship between the i-th follower and the j-th follower in the current cluster, there is no edge relationship between the i-th follower and the j-th follower in the weighted graph G, and record a ij =0, a in the adjacency matrix A ii =0;

[0011] S102: Perform Laplace transformation on the adjacency matrix A to obtain the Laplace matrix L corresponding to the adjacency matrix A, L = DA, where D is the degree matrix, D = diag{d1, d2, ..., d M},

[0012] S103: Establish a communication matrix B based on the communication relationship between the followers and the leader in the current cluster, B = diag{b1, b2, ..., b N}, b i Indicates the communication relationship between the ith follower and the leader in the current cluster; if there is a communication relationship between the ith follower and the leader in the current cluster, then b i >0, if there is no communication relationship between the i-th follower and the leader in the current cluster, then b i =0;

[0013] S104: Establish a second-order nonlinear dynamic model of the leader, followers in the current cluster, and followers in adjacent clusters. The specific expression is:

[0014]

[0015] in, Represents the location information s of the i-th follower in the current cluster i The first derivative of vi represents the speed information of the i-th follower in the current cluster, Represents the speed information v of the i-th follower in the current cluster i The first-order derivative of , F(·) represents a nonlinear function that satisfies the Lipschiz condition, u i represents the control input of the i-th follower in the current cluster, represents the first-order derivative of the position information s0 of the current cluster leader, v0 represents the velocity information of the current cluster leader, Represents the first-order derivative of the velocity information v0 of the current cluster leader, Indicates the adjacent cluster Location information of followers The first derivative of Indicates the adjacent cluster The speed information of each follower, Indicates the adjacent cluster Speed ​​information of each follower The first derivative of , t represents time.

[0016] Furthermore, the specific expression of the control target in step S2 is:

[0017]

[0018] Where T represents the convergence time under a specific initial state.

[0019] Furthermore, the specific steps of step S3 are:

[0020] S301: Construct a weight graph based on the communication relationship between followers in the current cluster and followers in adjacent clusters And the adjacent matrix C, the adjacent matrix C is an M×M matrix, Elements in the neighbor matrix C Indicates the adjacent cluster The communication relationship between the follower and the i-th follower in the current cluster; if the i-th follower in the neighboring cluster There is a communication relationship between the follower and the i-th follower in the current cluster, and the weight graph Middle A directed edge is added between the follower and the ith follower, and it is recorded If the adjacent cluster There is no communication relationship between the follower and the i-th follower in the current cluster. The weight graph Middle There is no edge relationship between the follower and the ith follower, and record c in the proximity matrix C ii=0;

[0021] S302: In a multi-agent system with a fixed topology, the state error χ of the i-th follower in the current cluster i The expression is:

[0022] χ i (t) = k1χ si (t)+k2χ vi (t)

[0023] Wherein, k1 represents the first coupling parameter, k2 represents the second coupling parameter, and χ si represents the position error of the i-th follower in the current cluster under fixed topology, χ vi represents the velocity error of the i-th follower in the current cluster under a fixed topology;

[0024] Therefore, the expression of the state error χ of the multi-agent system under fixed topology is:

[0025]

[0026] Among them, χ s represents the position error of the multi-agent system under fixed topology, χ v represents the velocity error of the multi-agent system under a fixed topology, represents the augmented Laplace matrix under fixed topology, represents the augmentation matrix under fixed topology, Θ(·) represents the disturbance function that changes with time t;

[0027] In a multi-agent system under switching topology, the state error χ of the i-th follower in the current cluster is ρ i The expression is:

[0028] χ ρ i (t) = k1χ ρ si (t)+k2χ ρ vi (t);

[0029] Among them, χ ρ si represents the position error of the i-th follower in the current cluster under the switching topology, χ ρ vi represents the speed error of the i-th follower in the current cluster under the switching topology;

[0030] Then the state error χ of the multi-agent system under the switching topology is ρ The expression is:

[0031]

[0032] in, represents the position error of the multi-agent system under the switching topology, represents the velocity error of the multi-agent system under switching topology, represents the augmented Laplace matrix under the switching topology, represents the position error between the i-th follower and the leader in the current cluster, represents the speed error between the i-th follower and the leader in the current cluster.

[0033] Furthermore, the specific steps of step S4 are:

[0034] S401: In a multi-agent system with a fixed topology, the specific expression of the control input of the i-th follower is:

[0035]

[0036] Among them, u i represents the control input of the ith follower under a fixed topology, r1, r2, and r3 are all constants greater than 0, represents the kth time triggering moment of the i-th follower; represents the αth power of the state error of the i-th follower under a fixed topology, represents the β-power of the state error of the i-th follower under a fixed topology, χ i represents the state error of the i-th follower under a fixed topology;

[0037] In a multi-agent system under a switching topology, the specific expression of the control input of the i-th follower is:

[0038]

[0039] in, represents the control input of the ith follower in the switching topology, represents the αth power of the state error of the i-th follower under the switching topology, represents the β-power of the state error of the i-th follower under the switching topology, represents the state error of the i-th follower under the switching topology;

[0040] S402: In a multi-agent system with a fixed topology, the event triggering function of the event triggering controller of the i-th follower is:

[0041]

[0042] Among them, f irepresents the event triggering function of the event triggering controller of the i-th follower under a fixed topology, e i represents the measurement error of the ith follower under a fixed topology, Indicates event trigger parameters,

[0043] In a multi-agent system with a switching topology, the event triggering function of the event triggering controller of the i-th follower is:

[0044]

[0045] in, represents the event triggering function of the event triggering controller of the i-th follower in the switching topology, represents the measurement error of the i-th follower under the switching topology;

[0046] S403: When the event of the i-th follower in the fixed topology triggers the event triggering function f of the controller i >0 or switch the event trigger function of the controller for the event of the i-th follower in the topology When the event triggers the controller to control the control input u of the i-th follower under the fixed topology i Or switch the control input of the ith follower in the topology Update to achieve consistency control of followers in the current cluster.

[0047] The beneficial effects of the present invention are:

[0048] (1) This paper addresses the challenges of task complexity and collision risk during dynamic topology switching faced by multi-agent systems in leader-follower control by introducing an improved clustering control strategy, fusing neighboring state errors, and adopting an event-triggered controller.

[0049] (2) The present invention achieves adaptive adjustment through clustering control strategy, which can dynamically cluster agents according to task complexity, effectively improving the system's adaptability and control efficiency in complex environments;

[0050] (3) The present invention incorporates the information of neighboring agents in neighboring clusters into the state error calculation to achieve neighboring state error fusion, ensuring that the system can avoid collision risks in advance when switching between clusters and when the topology changes dynamically, thereby enhancing the security and stability of the system.

[0051] (4) The present invention designs an event-triggered controller and uses the event-triggered mechanism to determine the update timing of the control input, which significantly reduces the frequency of unnecessary control law calculations, thereby reducing computing resource consumption and improving the real-time response capability of the system. BRIEF DESCRIPTION OF THE DRAWINGS

[0052] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the following briefly introduces the drawings required for use in the embodiments. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0053] Figure 1 is a flow chart of a method according to an embodiment of the present invention;

[0054] Figure 2 A communication network diagram under a fixed topology according to an embodiment of the present invention;

[0055] Figure 3 This is a location state diagram of an embodiment of the present invention under a fixed topology;

[0056] Figure 4 This is a speed state diagram of an embodiment of the present invention under a fixed topology;

[0057] Figure 5 This is a control input diagram of an embodiment of the present invention under a fixed topology;

[0058] Figure 6 for Figure 5 A local enlarged view near t=0s;

[0059] Figure 7 This is a triggering time sequence diagram of an embodiment of the present invention under a fixed topology;

[0060] Figure 8 A communication network diagram under a switching topology according to an embodiment of the present invention;

[0061] Figure 9 This is a position state diagram of an embodiment of the present invention under a switching topology;

[0062] Figure 10 This is a speed state diagram of an embodiment of the present invention under a switching topology;

[0063] Figure 11 This is a control input diagram of an embodiment of the present invention under a switching topology;

[0064] Figure 12 for Figure 11 A local enlarged view near t=0s;

[0065] Figure 13 for Figure 11 A local enlarged view near t = 5s;

[0066] Figure 14 This is a triggering time sequence diagram of an embodiment of the present invention under a switching topology. DETAILED DESCRIPTION

[0067] In order to more clearly understand the above-mentioned objects, features and advantages of the present invention, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments. In the following description, many specific details are set forth to facilitate a full understanding of the present invention. However, the present invention may also be implemented in other ways different from those described herein. Therefore, the present invention is not limited to the specific embodiments disclosed below.

[0068] like Figure 1 As shown, the embodiment of the present invention proposes a consistency control method in a fixed-switching topology based on an event trigger mechanism, comprising the following steps:

[0069] S1: For a multi-agent leader-follower system, denote the number of clusters in the multi-agent leader-follower system as n; construct an adjacency matrix A and a communication matrix B based on the communication relationships between followers in each cluster and the communication relationships between followers and leaders, and establish a second-order nonlinear dynamic model of leaders and followers in a single cluster, as well as followers in adjacent clusters; the specific steps are as follows:

[0070] S101: There are M followers and one leader l in the current cluster, and N followers in the adjacent cluster. For the current cluster, a weight graph G and an adjacency matrix A are established based on the communication relationships between the M followers. ij ], the adjacency matrix A is an M×M matrix, a ij Indicates the communication relationship between the i-th follower and the j-th follower in the current cluster; if there is a communication relationship between the i-th follower and the j-th follower in the current cluster, a directed edge is added between the i-th follower and the j-th follower in the weighted graph G, and a is recorded. ij >0, and if there is no communication relationship between the i-th follower and the j-th follower in the current cluster, there is no edge relationship between the i-th follower and the j-th follower in the weighted graph G, and record a ij =0, a in the adjacency matrix A ii =0.

[0071] S102: Perform Laplace transformation on the adjacency matrix A to obtain the Laplace matrix L corresponding to the adjacency matrix A, L = DA, where D is the degree matrix, D = diag{d1, d2, ..., d M},

[0072] S103: Establish a communication matrix B based on the communication relationship between the followers and the leader in the current cluster, B = diag{b1, b2, ..., b N}, b i Indicates the communication relationship between the ith follower and the leader in the current cluster; if there is a communication relationship between the ith follower and the leader in the current cluster, then bi >0, if there is no communication relationship between the i-th follower and the leader in the current cluster, then b i =0.

[0073] S104: Establish a second-order nonlinear dynamic model of the leader, followers in the current cluster, and followers in adjacent clusters. The specific expression is:

[0074]

[0075] in, Represents the location information s of the i-th follower in the current cluster i The first derivative of v i represents the speed information of the i-th follower in the current cluster, Represents the speed information v of the i-th follower in the current cluster i The first-order derivative of , F(·) represents a nonlinear function that satisfies the Lipschiz condition, u i represents the control input of the i-th follower in the current cluster, represents the first-order derivative of the position information s0 of the current cluster leader, v0 represents the velocity information of the current cluster leader, Represents the first-order derivative of the velocity information v0 of the current cluster leader, Indicates the adjacent cluster Location information of followers The first derivative of Indicates the adjacent cluster The speed information of each follower, Indicates the adjacent cluster Speed ​​information of each follower The first derivative of , t represents time.

[0076] S2: The control goal is to make the follower state and the leader state consistent in each cluster. The specific expression of the control goal is:

[0077]

[0078] Where T represents the convergence time under a specific initial state.

[0079] When t>T, the m followers in the current cluster will be consistent with the leader in the current cluster in position and speed, that is, the position error and speed error will remain zero. The convergence time T is bounded, that is, For any initial state of the agent, the system convergence time is T <T max Established, T max It represents the maximum convergence time for any initial state.

[0080] S3: Introduce and establish communication management between followers in adjacent clusters and followers in the current cluster, and construct the state error of followers in the current cluster; the specific steps are:

[0081] S301: Construct a weight graph based on the communication relationship between followers in the current cluster and followers in adjacent clusters And the adjacent matrix C, the adjacent matrix C is an M×M matrix, Elements in the neighbor matrix C Indicates the adjacent cluster The communication relationship between the follower and the i-th follower in the current cluster; if the i-th follower in the neighboring cluster There is a communication relationship between the follower and the i-th follower in the current cluster, and the weight graph Middle A directed edge is added between the follower and the ith follower, and it is recorded If the adjacent cluster There is no communication relationship between the follower and the i-th follower in the current cluster. The weight graph Middle There is no edge relationship between the follower and the ith follower, and record c in the proximity matrix C ii =0.

[0082] S302: In a multi-agent system with a fixed topology, the state error χ of the i-th follower in the current cluster i The expression is:

[0083] χ i (t) = k1χ si (t)+k2X vi (t);

[0084]

[0085] Where k1 represents the first coupling parameter, k2 represents the second coupling parameter, and X si represents the position error of the i-th follower in the current cluster under a fixed topology, X vi represents the speed error of the i-th follower in the current cluster under a fixed topology, s j represents the location information of the jth follower in the current cluster under a fixed topology, v j Represents the speed information of the j-th follower in the current cluster under a fixed topology.

[0086] The position error X of the i-th follower in the current cluster under the fixed topology si and the speed error X of the i-th follower in the current cluster under fixed topology viSubstitute the expression into the state error X of the i-th follower in the current cluster under the fixed topology i In the expression of , we can get:

[0087]

[0088]

[0089] Among them, χ s represents the position error of the multi-agent system under a fixed topology, X v represents the velocity error of the multi-agent system under a fixed topology, represents the augmented Laplace matrix under fixed topology, represents the augmentation matrix under fixed topology, Θ(·) represents the disturbance function that changes with time t, represents the position error between the i-th follower and the leader in the current cluster, represents the speed error between the i-th follower and the leader in the current cluster.

[0090] In a multi-agent system, if the original clusters cannot handle complex task allocation, it is necessary to adjust the number of agents in certain clusters or the number of clusters according to the distribution of task scheduling. To this end, it is necessary to consider a set of weight graphs G(ω(t))∈{G1,G2,…,G r}, where ω(t) represents a continuous-time Markov process, the value of ω(t) is obtained in a finite set R∈{1,2,…,r}, r represents the number of possible situations after switching the topology, G r Represents the weight graph for the rth case. The transition probability P for the rth case r The definition is as follows:

[0091]

[0092] Where, Δt>0,lim Δt→0 o(Δt)=0,ρ pq represents the transition probability from state p to state q, ρ pq ≥0, Δt represents the time interval from the current state to the next state, ρ pp represents the probability of maintaining state p, o represents a high-order infinitesimal, represents the set of real numbers, and there exists H ρ =H(ω(t))∈{H1,H2,…,H r}, H ρ represents the Laplace matrix in the switching state, H r represents the Laplace matrix in the rth case under the switching state, represents the augmented Laplace matrix in the switching state, represents the augmented Laplace matrix in the rth case under the switching state.

[0093] Therefore, in a multi-agent system under a switching topology, the state error χ of the i-th follower in the current cluster is ρ i The expression is:

[0094]

[0095] Among them, χ ρ si represents the position error of the i-th follower after switching topology, χ ρ vi represents the speed error of the ith follower after switching, Indicates the number of followers in the current cluster after switching the topology. represents the number of followers in the adjacent cluster after switching the topology, It represents the communication relationship between the i-th follower and the j-th follower in the current cluster after switching the topology. Represents the communication relationship between the i-th follower and the leader in the current cluster after switching the topology, Indicates the first The communication relationship between the follower and the i-th follower in the current cluster.

[0096] Then the state error χ of the multi-agent system under the switching topology is ρ The expression is:

[0097]

[0098]

[0099] in, represents the position error of the multi-agent system under the switching topology, represents the velocity error of the multi-agent system under switching topology, represents the augmented Laplace matrix.

[0100] S4: Obtain the control input of the followers in the current cluster based on the state error, and design an event-triggered controller to update the control input to achieve consistency control of the followers in the current cluster. The specific steps are:

[0101] S401: In a multi-agent system with a fixed topology, the specific expression of the control input of the i-th follower is:

[0102]

[0103] Among them, u i represents the control input of the ith follower under a fixed topology, r1, r2, and r3 are all constants greater than 0, represents the kth time triggering moment of the i-th follower; represents the αth power of the state error of the i-th follower under a fixed topology, represents the β-power of the state error of the i-th follower under a fixed topology, X i represents the state error of the i-th follower under a fixed topology, and the exponent α∈(0,1) and β∈(1,+∞) are the ratios of positive odd numbers.

[0104] In a multi-agent system under a switching topology, the specific expression of the control input of the i-th follower is:

[0105]

[0106] in, represents the control input of the ith follower in the switching topology, represents the αth power of the state error of the i-th follower under the switching topology, represents the β-power of the state error of the i-th follower under the switching topology, represents the state error of the i-th follower under the switching topology.

[0107] S402: In a multi-agent system with a fixed topology, the event triggering function of the event triggering controller of the i-th follower is:

[0108]

[0109] Among them, f i represents the event triggering function of the event triggering controller of the i-th follower under a fixed topology, e i represents the measurement error of the ith follower under a fixed topology, Indicates event trigger parameters, is a discrete quantity, representing the state error of the i-th follower at the k-th trigger moment under a fixed topology, χ i (t) is a continuous quantity, which represents the state error of the i-th follower at time t under a fixed topology.

[0110] In a multi-agent system with a switching topology, the event triggering function of the event triggering controller of the i-th follower is:

[0111]

[0112] in, represents the event triggering function of the event triggering controller of the i-th follower in the switching topology, represents the measurement error of the ith follower under the switching topology, is a discrete quantity, representing the state error of the i-th follower at the k-th time trigger moment under the switching topology, It is a continuous quantity, which represents the state error of the i-th follower at time t under the switching topology.

[0113] S403: When the event of the i-th follower in the fixed topology triggers the event triggering function f of the controller i >0 or switch the event trigger function of the controller for the event of the i-th follower in the topology When the event triggers the controller to control the control input u of the i-th follower under the fixed topology i Or switch the control input of the ith follower in the topology Update to achieve consistency control of followers in the current cluster. That is, for the i-th follower, the i-th follower control input is no longer a continuous signal, and the i-th follower only controls the event at the time of triggering. Updating the control input signal reduces the frequency of unnecessary control law calculations, reduces computing resource consumption and improves the real-time response capability of the system.

[0114] In the embodiment of the present invention, even after switching the topology, the communication relationship between the i-th follower and the j-th follower in the current cluster remains unchanged. The communication relationship between the i-th follower and the leader in the current cluster after switching the topology and the adjacent cluster after switching topology The communication relationship between the follower and the i-th follower in the current cluster is a dynamically changing non-negative constant, and the number of followers in the current cluster after switching the topology and the number of followers in the adjacent cluster after switching the topology is also dynamically changing, but the nonlinear perturbation function Θ(x,y,t) in the state error is hour, Where γ is the communication link threshold vector. Therefore, only the topology changes within the cluster under the switching topology can be considered at this time. Then consider the adjacent cluster Followers are incorporated into the current cluster for control, among which, is the safety distance coefficient vector. The size of the non-negative elements in the proximity matrix C is inversely proportional to the distance, and the distance can be indirectly reflected by the communication frequency between agents. According to the above analysis, there is still the equation The augmented Laplace matrix in the switching state Although the elements of are dynamically changing, their positive definiteness is guaranteed. Therefore, Lyapunov stability theory can be used to prove that the event-triggered strategy under the switching topology still converges, and the same method can be used to prove that the Zeno phenomenon does not occur.

[0115] by Figure 2 The fixed topology state shown and Figure 8 As an example of the switching topology state shown in FIG, a control simulation experiment is performed using the method described in the embodiment of the present invention, and the following can be obtained: Figures 3 to 7 and Figures 9 to 14 The experimental results are shown in FIG. 1 . The experimental results show that based on the existing multi-agent system leader-follower consistency control method under fixed topology, the control method proposed by the present invention under switching topology is still effective.

[0116] The foregoing description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Those skilled in the art will readily appreciate that various modifications and variations of the present invention are possible. Any modifications, equivalent substitutions, or improvements made within the spirit and principles of the present invention are intended to be within the scope of protection of the present invention.

Claims

1. A consistency control method in a fixed-switching topology based on an event-triggered mechanism, characterized in that: The steps include: S1: For a multi-agent leader-follower system, denote the number of clusters in the multi-agent leader-follower system as n; construct an adjacency matrix A and a communication matrix B based on the communication relationships between followers in each cluster and the communication relationships between followers and leaders, and establish a second-order nonlinear dynamic model of leaders and followers in a single cluster, as well as followers in adjacent clusters; S2: The control goal is to make the follower state and the leader state consistent in each cluster; S3: Introduce and establish communication management between followers in adjacent clusters and followers in the current cluster, and construct the state error of followers in the current cluster; S4: Obtaining a control input of the followers in the current cluster according to the state error, and designing an event-triggered controller, which updates the control input to achieve consistency control of the followers in the current cluster; The specific steps of step S1 are: S101: There are M followers and one leader in the current cluster , there are N followers in the adjacent cluster; for the current cluster, the weight graph G and adjacency matrix are established based on the communication relationship between the M followers , the adjacency matrix A is an M×M matrix, Indicates the first The communication relationship between the jth follower and the jth follower; if the current cluster There is a communication relationship between the jth follower and the jth follower. A directed edge is added between the jth follower and the jth follower, and it is recorded , and if the current cluster There is no communication relationship between the jth follower and the jth follower. There is no edge relationship between the jth follower and the jth follower, and record , in the adjacency matrix A ; S102: Perform Laplace transformation on the adjacency matrix A to obtain the Laplace matrix L corresponding to the adjacency matrix A, L=DA, where D is the degree matrix, , ; S103: Establish a communication matrix B based on the communication relationship between the followers and the leader in the current cluster. , Indicates the current cluster The communication relationship between the follower and the leader; if the current cluster There is a communication relationship between the follower and the leader, then , if the current cluster There is no communication relationship between the follower and the leader, then ; S104: Establish a second-order nonlinear dynamic model of the leader, followers in the current cluster, and followers in adjacent clusters. The specific expression is: ； ； ； in, Indicates the current cluster Location information of followers The first derivative of Indicates the current cluster The speed information of each follower, Indicates the current cluster Speed ​​information of each follower The first derivative of represents a nonlinear function that satisfies the Lipschiz condition, Indicates the current cluster The control input of each follower, Indicates the location information of the current cluster leader The first derivative of Indicates the speed information of the current cluster leader, Indicates the speed information of the current cluster leader The first derivative of Indicates the adjacent cluster Location information of followers The first derivative of Indicates the adjacent cluster The speed information of each follower, Indicates the adjacent cluster Speed ​​information of each follower The first derivative of , t represents time.

2. The consistency control method in a fixed-switching topology based on an event-triggered mechanism according to claim 1, characterized in that: The specific expression of the control target in step S2 is: ； Where T represents the convergence time under a specific initial state.

3. The consistency control method in a fixed-switching topology based on an event-triggered mechanism according to claim 1, characterized in that: The specific steps of step S3 are: S301: Construct a weight graph based on the communication relationship between followers in the current cluster and followers in adjacent clusters And the adjacent matrix C, the adjacent matrix C is an M×M matrix, , the elements in the neighbor matrix C Indicates the adjacent cluster Followers and the current cluster The communication relationship between followers; if the Followers and the current cluster There is a communication relationship between followers, and the weight graph Middle Followers and A directed edge is added between followers, and , , if the adjacent cluster Followers and the current cluster There is no communication relationship between followers, and the weight graph Middle Followers and There is no edge relationship between followers, and record , , in the proximity matrix C ; S302: In a multi-agent system with a fixed topology, the current cluster The state error of the follower The expression is: ;in, represents the first coupling parameter, represents the second coupling parameter, Indicates the number of The position error of each follower, Indicates the number of The velocity error of each follower; Therefore, the state error of the multi-agent system under a fixed topology The expression is: ； in, represents the position error of the multi-agent system under a fixed topology, represents the velocity error of the multi-agent system under a fixed topology, represents the augmented Laplace matrix under fixed topology, , represents the augmentation matrix under fixed topology, , , Indicates that over time Changing disturbance function; In a multi-agent system under a switching topology, the current cluster The state error of the follower The expression is: ； in, Indicates the number of The position error of each follower, Indicates the number of The velocity error of each follower; Then the state error of the multi-agent system under the switching topology is The expression is: ;in, represents the position error of the multi-agent system under the switching topology, represents the velocity error of the multi-agent system under switching topology, represents the augmented Laplace matrix under the switching topology, Indicates the current cluster The position error between the follower and the leader, Indicates the current cluster The velocity error between the follower and the leader.

4. The consistency control method in a fixed-switching topology based on an event-triggered mechanism according to claim 1, characterized in that: The specific steps of step S4 are: S401: Multi-agent systems under fixed topology, The specific expression of the control input of a follower is: ； in, Indicates the fixed topology The control input of each follower, 、 and are all constants greater than 0. Indicates the The kth time trigger moment of a follower; Indicates the fixed topology The state error of the follower Power, Indicates the fixed topology The state error of the follower Power, Indicates the fixed topology The state error of each follower; Multi-agent systems under switching topology, The specific expression of the control input of a follower is: ； in, Indicates the switching topology The control input of each follower, Indicates the switching topology The state error of the follower Power, Indicates the switching topology The state error of the follower Power, Indicates the switching topology The state error of each follower; S402: Multi-agent systems under fixed topology, The event triggering function of the event triggering controller of each follower is: ； ； in, Indicates the fixed topology The event triggering function of the controller is triggered by the event of each follower. Indicates the fixed topology The measurement error of each follower, Indicates event trigger parameters, ; Multi-agent systems under switching topology, The event triggering function of the event triggering controller of each follower is: ； ； in, Indicates the switching topology The event triggering function of the controller is triggered by the event of each follower. Indicates the switching topology The measurement error of each follower; S403: When the fixed topology The event triggering function of the controller is triggered by the event of each follower Or switch topology The event triggering function of the controller is triggered by the event of each follower When the event triggers the controller to The control input of a follower Or switch topology The control input of a follower Update to achieve consistency control of followers in the current cluster.

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