Consensus control method for random time-delay multi-agent systems under directed topology

Abstract

The present invention relates to the technical field of multi-agent systems, and discloses a consistency control method for a random time-delay multi-agent system under a directed topology. The method comprises: constructing a random time-delay multi-agent system under a directed communication topology and introducing random nonlinear time delay; determining a controller according to the states of different agents in the random time-delay multi-agent system; determining a dynamic event triggering mechanism according to a consistency error and a dynamic signal function, and controlling the update of the controller based on the dynamic event triggering mechanism, so as to realize dynamic event triggering consistency control of the random time-delay multi-agent system under the directed topology, effectively suppressing Zeno behavior, reducing the amount of system calculation and power consumption, solving the mean square exponential consistency problem under the directed communication topology, ensuring that the proposed dynamic event triggering mechanism can control the influence of sampling errors, and ensuring the random consistency of the consistent error system, so as to facilitate the promotion and use of the method.

Description

Technical Field

[0001] The present invention relates to the technical field of multi-agent systems, and in particular to a consistency control method for a random time-delay multi-agent system under a directed topology. Background Art

[0002] For decades, the consistency problem of multi-agent systems (MAS) has attracted widespread attention from scholars due to its wide application in various engineering systems, such as the construction of spacecraft, vehicles, and unmanned aerial vehicle systems. In order to achieve system consistency, an effective control protocol or algorithm must be designed so that each agent in the MAS can continuously adjust its behavior based on the information sent by its neighbors. To implement such a control protocol in practice, periodic sampling techniques are usually used. However, in actual multi-agent systems, individual agents may be equipped with small embedded microprocessors and onboard communication and execution modules with limited capabilities to save installation costs. The use of periodic sampling usually wastes a lot of energy, thereby shortening the service life of the system. In order to extend the life of the system, an effective way is to reduce the triggering frequency of electronic components. It is worth noting that an alternative strategy called event-triggered consistency control is an effective approach that can reduce control updates and energy consumption and guarantee the required performance.

[0003] So far, there have been abundant research results and great attention on the analysis of random MAS. However, the issues related to event-triggered consistency in random MAS have not been sufficiently studied, mainly due to difficulties in random convergence analysis and the design of appropriate event-triggered mechanisms. Specifically, methods related to deterministic systems cannot be generalized to random MAS to estimate and control sampling errors to avoid infinitely fast sampling and analyze system performance. In recent years, some research results on event-triggered consistency of random MAS have been reported, but the existing research results are more about studying the consistency problem under undirected topology, which mainly relies on the symmetric properties of the relevant Laplacian matrix and is therefore invalid when dealing with directed interaction topology settings. In practice, the information exchange between agents may be unidirectional, thus leading to a directed interaction topology. In addition, in the framework of directed topology, the Laplacian matrix associated with the interaction topology is not symmetric, spanning the time interval [t i , t i+1 ), the dynamics of the system whose union of interaction topologies has a directed spanning tree may be different for different i, where i=1, 2, ..., N, N represents the number of agents, and i represents the i-th agent. It can be seen that there are few research results on random MAS of directed graphs, which is a motivation of the present invention.

[0004] Recently, dynamic event-triggered mechanism (DETM) has become an important research area, which introduces an auxiliary dynamic variable with beneficial properties, which can reduce the number of triggers compared with static mechanisms in most cases. So far, there have been several studies on DETM for stochastic systems, however, these studies have not considered the effect of time delay. In fact, due to the physical limitations of electronic devices, the occurrence of time delay in information transmission is inevitable, which will lead to richer dynamic behaviors. Similar to most time-delay system analysis techniques, multiple Lyapunov-Krasovskii function methods are used to analyze switched stochastic time-delay systems with unstable subsystems, but so far, there are relatively few studies on the application of DETM to analyze the consistency of random time-delay MAS under directed topology, which is a research gap that inspired the development of the current invention. Therefore, how to achieve dynamic event-triggered consistency control of random time-delay multi-agent systems under directed topology has become an urgent problem to be solved.

[0005] The above contents are only used to assist in understanding the technical solution of the present invention and do not constitute an admission that the above contents are prior art. Summary of the invention

[0006] The main purpose of the present invention is to provide a consistency control method for a random time-delay multi-agent system under a directed topology, aiming to solve the technical problem that the existing technology cannot achieve dynamic event-triggered consistency control of a random time-delay multi-agent system under a directed topology.

[0007] To achieve the above object, the present invention provides a consistency control method for a random time-delay multi-agent system under a directed topology, the method comprising the following steps:

[0008] Construct a random time-delay multi-agent system with random nonlinear time delay under directed communication topology;

[0009] Determining a controller according to the states of different agents in the random time-delay multi-agent system;

[0010] A dynamic event triggering mechanism is determined according to the consistency error and the dynamic signal function, and the update of the controller is controlled based on the dynamic event triggering mechanism to achieve dynamic event triggered consistency control of the random time-delay multi-agent system under a directed topology.

[0011] Optionally, the step of constructing a random time-delay multi-agent system with random nonlinear time delay introduced under a communication topology comprises:

[0012] The random time-delay multi-agent system with random nonlinear time delay under directed communication topology is constructed by the following formula;

[0013] dx i (t) = [Af(x i (t))+Bg(x i (t-τ(t)))+Cu i (t)]dt+Dx i (t)dω(t)

[0014] In the formula, represents the real-time state of the ith agent, represents n-dimensional Euclidean space, t represents time, τ(t) represents time lag, and satisfies 0≤τ(t)≤τ (τ is a preset constant). represents an n×n real matrix, A, B, and represents a known real matrix, represents an n×m real matrix, m <n,u i (t) represents the controller of the control input corresponding to the ith agent, and ω(t) represents the controller defined in The standard Brownian motion on , Ω is a non-empty set, representing the sample space, is a non-empty subset of the Q power set, represents a non-empty subset of the Q power set for time t ≥ 0, represents a non-singular matrix, It means that the dimension of matrix P is N×N, and represent continuous vector functions, represents an m-dimensional vector, i = 1, 2, ..., N, where N represents the number of agents, i represents the i-th agent, and the interconnection topology between agents is a directed graph. describe, represents a set of vertices, Represents a set of edges, the adjacency matrix j represents the jth agent, a ij represents the element in the i-th row and j-th column of the adjacency matrix, that is, the connection relationship between the i-th agent and the j-th agent, a ij =0 means no connection, a ij ≠0 means there is a connection.

[0015] Optionally, the step of determining the controller according to the states of different agents in the random time-delay multi-agent system comprises:

[0016] The controller is determined by the following formula according to the states of different agents in the random time-delay multi-agent system;

[0017]

[0018] In the formula, ui (t) represents the controller of the control input corresponding to the ith agent, represents an m-dimensional vector, t represents time, t∈[t k ,t k+1 ), is the trigger time series defined by DETM, t 1 =0,t k represents the kth triggering moment, t k+1 represents the k+1th triggering moment, N represents the number of agents, i represents the i-th agent, j represents the j-th agent, a ij represents the element in the i-th row and j-th column of the adjacency matrix, that is, the connection relationship between the i-th agent and the j-th agent, a ij =0 means no connection, a ij ≠0 means there is a connection, c means a preset constant, c>0, x j (t k ) indicates that the jth agent is at t k The state at this moment, x i (t k ) represents the i-th agent at t k The state of the moment.

[0019] Optionally, the step of determining a dynamic event triggering mechanism according to a consistency error and a dynamic signal function, and controlling the update of the controller based on the dynamic event triggering mechanism to achieve dynamic event triggered consistency control of a random time-delay multi-agent system under a directed topology includes:

[0020] Determine the dynamic event triggering mechanism according to the consistency error and the dynamic signal function through the following formula, and control the update of the controller based on the dynamic event triggering mechanism to achieve dynamic event triggered consistency control of the random time-delay multi-agent system under the directed topology;

[0021] t k+1 = inf{t≥t k +δ|||e i (t)-e i (t k )|| 2 ≥α||e i (t)|| 2 +βη i (t)}

[0022] In the formula, α, β represent preset constants, α>0, β>0, δ represents the pause time, δ>0, inf represents the infimum function, t represents time, is the trigger time series defined by DETM, t 1 =0,tk represents the kth triggering moment, e i (t) represents the real-time consistency error, e i (t k ) indicates that at t k The consistency error at this moment, η i (t) represents the dynamic signal function.

[0023] Optionally, the dynamic signal function is determined by the following formula;

[0024]

[0025] Where η i (t) represents the dynamic signal function, Represents η i (t) is derived, that is, η i (t), t represents time, t∈[t k , t k+1 ), is the trigger time series defined by DETM, t 1 =0,t k represents the kth triggering moment, t k+1 represents the k+1th triggering moment, i represents the i-th agent, e i (t) represents the real-time consistency error, e i (t k ) indicates that at t k The consistency error at this moment, η i (0) = η 0 Satisfy 0<η 0 ≤||e i (0)|| 2 , t≥0,η i (t)≥0.

[0026] Optionally, the consistency error is determined by the following formula;

[0027]

[0028]

[0029] In the formula, e i (t) represents the real-time consistency error, represents the real-time state of the ith agent, represents n-dimensional Euclidean space, represents the average state, t represents time, i represents the i-th agent, j represents the j-th agent, N represents the number of agents, ξ j Represents a preset constant, x j(t) represents the real-time state of the j-th agent.

[0030] Optionally, the consistency error forms a closed-loop system under the dynamic event-triggering mechanism through the following formula;

[0031]

[0032]

[0033]

[0034] where de i (t) represents the closed-loop system, with an initial value of e i (0) = ξ, where ξ represents a random variable, represents an n×n real matrix, A, B, and represents a known real matrix, represents an n×m real matrix, where m < n, i represents the i-th agent, j represents the j-th agent, N represents the number of agents, u i (t) represents the controller of the control input corresponding to the i-th agent, represents an m-dimensional vector, ξ j represents a preset constant, u j (t) represents the controller of the control input corresponding to the j-th agent, e i (t) represents the real-time consistency error, ω(t) represents a standard Brownian motion defined on , Ω is a non-empty set representing the sample space, is a non-empty subset of the power set of Ω, represents the time t ≥ 0 of the non-empty subset of the power set of Ω, represents a non-singular matrix, represents that the dimension of matrix P is N×N, and represent continuous vector functions respectively, represents the real-time state of the i-th agent, represents the n-dimensional Euclidean space, t represents time, τ(t) represents the time delay, satisfying 0 ≤ τ(t) ≤ τ (τ is a preset constant), x j (t) represents the real-time state of the j-th agent.

[0035] In the present invention, a random time-delay multi-agent system with random nonlinear time delay is constructed under a directed communication topology; a controller is determined according to the states of different agents in the random time-delay multi-agent system; a dynamic event triggering mechanism is determined according to the consistency error and the dynamic signal function, and the update of the controller is controlled based on the dynamic event triggering mechanism to achieve dynamic event triggering consistency control of the random time-delay multi-agent system under the directed topology. By establishing a DETM based on relative information in a random time-delay MAS, and studying MSEC according to Lyapunov's theorem and Halanay inequality, the proposed event is intermittently executed, and the Zeno behavior can be effectively suppressed by enforcing a strictly positive fixed time between any two consecutive execution times, reducing the system's computational load and power consumption, and solving the MSEC problem under a more general directed communication topology. In addition, the present invention provides an accurate estimate of the sampling error in the expected sense, ensuring that the proposed DETM can control the influence of the sampling error. By adopting a general random convergence analysis technique, the random consistency of the consistent error system is guaranteed. Different from the single time-delay system in the prior art, the present invention takes into account multiple systems and utilizes a more general stochastic analysis strategy to facilitate the promotion and use of the dynamic event-triggered consistency control method of the random time-delay multi-agent system under the directed topology described in the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] Figure 1 It is a flow chart of the first embodiment of the consistency control method of the random time-delay multi-agent system under the directed topology of the present invention;

[0037] The realization of the purpose, functional features and advantages of the present invention will be further explained in conjunction with embodiments and with reference to the accompanying drawings. DETAILED DESCRIPTION

[0038] It should be understood that the specific embodiments described herein are only used to explain the present invention, and are not used to limit the present invention.

[0039] The embodiment of the present invention provides a consistency control method for a random time-delay multi-agent system under a directed topology, referring to Figure 1 , Figure 1 Schematic diagram of the flow of the first embodiment of the consistency control method of the random time-delay multi-agent system under the directed topology of the present invention.

[0040] In this embodiment, the consistency control method of the random time-delay multi-agent system under the directed topology includes the following steps:

[0041] Step S10: constructing a random time-delay multi-agent system with random nonlinear time delay introduced under a directed communication topology;

[0042] In the specific implementation, the random time-delay multi-agent system with random nonlinear time delay introduced under the directed communication topology can be constructed by the following formula;

[0043] dx i (t) = [Af(x i (t))+Bg(x i (t-τ(t)))+Cu i (t)]dt+Dx i (t)dω(t)

[0044] In the formula, represents the real-time state of the ith agent, represents n-dimensional Euclidean space, t represents time, τ(t) represents time lag, and satisfies 0≤τ(t)≤τ (τ is a preset constant). represents an n×n real matrix, A, B, and represents a known real matrix, represents an n×m real matrix, m <n,u i (t) represents the controller of the control input corresponding to the ith agent, and ω(t) represents the controller defined in The standard Brownian motion on , Ω is a non-empty set, representing the sample space, is a non-empty subset of the Ω power set, The time t ≥ 0 represents a non-empty subset of the Ω power set, represents a non-singular matrix, It means that the dimension of matrix P is N×N, and represent continuous vector functions, represents an m-dimensional vector, i = 1, 2, ..., N, where N represents the number of agents, i represents the i-th agent, and the interconnection topology between agents is a directed graph. describe, represents a set of vertices, Represents a set of edges, the adjacency matrix j represents the jth agent, a ij represents the element in the i-th row and j-th column of the adjacency matrix, that is, the connection relationship between the i-th agent and the j-th agent, a ij =0 means no connection, a ij ≠0 means there is a connection.

[0045] Step S20: determining a controller according to the states of different agents in the random time-delay multi-agent system;

[0046] In a specific implementation, the controller may be determined by the following formula according to the states of different agents in the random time-delay multi-agent system;

[0047]

[0048] In the formula, u i (t) represents the controller of the control input corresponding to the ith agent, represents an m-dimensional vector, t represents time, t∈[t k , t k+1 ), is the trigger time series defined by DETM, t 1 =0,t k represents the kth triggering moment, t k+1 represents the k+1th triggering moment, N represents the number of agents, i represents the i-th agent, j represents the j-th agent, a ij represents the element in the i-th row and j-th column of the adjacency matrix, that is, the connection relationship between the i-th agent and the j-th agent, a ij =0 means no connection, a ij ≠0 means there is a connection, c means a preset constant (which can be set according to actual needs), c>0, x j (t k ) indicates that the jth agent is at t k The state at this moment, x i (t k ) represents the i-th agent at t k The state of the moment.

[0049] Step S30: Determine a dynamic event triggering mechanism according to the consistency error and the dynamic signal function, and control the update of the controller based on the dynamic event triggering mechanism to achieve dynamic event triggered consistency control of the random time-delay multi-agent system under a directed topology.

[0050] In a specific implementation, the dynamic event triggering mechanism can be determined by the following formula according to the consistency error and the dynamic signal function, and the update of the controller can be controlled based on the dynamic event triggering mechanism to realize the dynamic event triggered consistency control of the random time-delay multi-agent system under the directed topology;

[0051] t k+1 = inf{t≥t k +δ|||e i (t)-e i (t k )|| 2 ≥α||e i (t)|| 2 +βη i (t)}

[0052] In the formula, α, β represent preset constants (which can be set according to actual needs), α>0, β>0, δ represents the pause time, δ>0, inf represents the infimum function, t represents time, is the trigger time series defined by DETM, t 1 =0,t k represents the kth triggering moment, e i (t) represents the real-time consistency error, e i (t k ) indicates that at t k The consistency error at this moment, η i (t) represents the dynamic signal function.

[0053] It should be noted that the trigger function in the equation is constructed by the sampling error between the current value and the control update. Although similar triggering methods are discussed in the prior art, the consistency problem under directed topology is the focus of the present invention, and the results in the prior art are not applicable in this case of the present invention.

[0054] It is easy to understand that under this equation, once the trigger condition is met, the trigger will remain suspended for a period of time (i.e., δ). Only after the suspension can the equation be continuously evaluated to determine the next execution time. Therefore, the event is executed intermittently. In addition, the mandatory positive time between any two executions is not less than δ, i.e., t k+1 -t k ≥δ. That is, when t k+1 -t k When ≥δ, the control information is updated and Zeno behavior is avoided (which can be understood as the number of event triggers is infinite within a finite time interval). The DETM proposed in this embodiment does not use the expected value of the system signal, but only uses the online signal to determine its execution time.

[0055] In a specific implementation, the dynamic signal function can be determined by the following formula:

[0056]

[0057] Where η i (t) represents the dynamic signal function, Represents η i (t) is derived, that is, η i (t), t represents time, t∈[t k , t k+1 ), is the trigger time series defined by DETM, t 1 =0,t k represents the kth triggering moment, t k+1represents the k+1th triggering moment, i represents the i-th agent, e i (t) represents the real-time consistency error, e i (t k ) indicates that at t k The consistency error at this moment, η i (0) = η 0 Satisfy 0<η 0 ≤||e i (0)|| 2 , t≥0, η i (t)≥0.

[0058] It should be noted that the initial value of the dynamic signal is assumed to be appropriate. The purpose of designing the dynamic signal is to increase or adjust the threshold of the trigger function to reduce the use of communication resources. The introduction of the dynamic signal here can further reduce the number of triggers and reduce the consumption of communication resources. In addition, the initial value of this signal can be preset according to actual conditions. Therefore, for η i (0) It is reasonable to make this assumption. When t ≥ 0, η i (t) satisfies η i (t)≥0, which makes the equation solvable and ensures that it is a continuously changing value. i When =0, DETM transforms into a static state.

[0059] In a specific implementation, the consistency error can be determined by the following formula:

[0060]

[0061]

[0062] In the formula, e i (t) represents the real-time consistency error, represents the real-time state of the ith agent, represents n-dimensional Euclidean space, represents the average state, t represents time, i represents the i-th agent, j represents the j-th agent, N represents the number of agents, ξ j Indicates preset constant (can be set according to actual needs), x j (t) represents the real-time state of the j-th agent.

[0063] In a specific implementation, the consistency error can form a closed-loop system under the dynamic event triggering mechanism through the following formula:

[0064]

[0065]

[0066]

[0067] In the formula, de i (t) represents a closed-loop system, and its initial value is e i (0) = ξ, ξ represents a random variable, represents an n×n real matrix, A, B, and represents a known real matrix, represents an n×m real matrix, m<n, i represents the i-th agent, j represents the j-th agent, N represents the number of agents, u i (t) represents the controller of the control input corresponding to the ith agent, represents an m-dimensional vector, ξ j Indicates preset constant (can be set according to actual needs), u j (t) represents the controller of the control input corresponding to the jth agent, e i (t) represents the real-time consistency error, ω(t) represents the The standard Brownian motion on , Ω is a non-empty set, representing the sample space, is a non-empty subset of the Ω power set, The time t ≥ 0 represents a non-empty subset of the Ω power set, represents a non-singular matrix, Indicates that the dimension of matrix P is NxN, and represent continuous vector functions, represents the real-time state of the ith agent, represents n-dimensional Euclidean space, t represents time, τ(t) represents time lag, and satisfies 0≤τ(t)≤τ (τ is a preset constant, which can be set according to actual needs), x j (t) represents the real-time state of the j-th agent.

[0068] This embodiment establishes a DETM based on relative information in random time-delay MAS, and studies the mean-square exponential consistency (MSEC) problem according to Lyapunov theorem and Halanay inequality. With the help of the integral form of Halanay inequality and Lyapunov theorem framework, some conditions for guaranteeing the exponential stability of random time-delay MASs under directed topology are given to ensure the stability of the closed-loop system. The main breakthroughs include avoiding infinite fast sampling and random stability analysis. The proposed event is intermittently executed, and Zeno behavior can be effectively suppressed by enforcing a strictly positive fixed time (i.e., δ) between any two consecutive execution times (which can be understood as the number of event triggers is infinite within a finite time interval). That is, the controller update is reduced by designing a DETM that does not involve system signal expectations, and a certain positive lower bound is imposed in the DETM to effectively exclude Zeno behavior and reduce system computation and power consumption. Unlike the prior art, the proposed solution solves the MSEC problem under a more general directed communication topology. Unlike most directed topologies that only consider a specific MAS, this embodiment considers a random time-delay MAS, which is beneficial to further improve the versatility of the system based on the DETM involved. In addition, this embodiment provides an accurate estimate of the sampling error in the expected sense, ensuring that the proposed DETM can control the impact of the sampling error, that is, ensuring that the constant control of each execution time has sufficient feedback capability to control the impact of the sampling error. By adopting a general random convergence analysis technique, the random consistency of the consistent error system is guaranteed. Unlike the single time-delay system in the prior art, this embodiment considers multiple systems and utilizes a more general random analysis strategy to facilitate the promotion and use of the dynamic event-triggered consistency control method of the random time-delay multi-agent system under the directed topology described in this embodiment.

[0069] In this embodiment, a random time-delay multi-agent system with random nonlinear time delay is constructed under a directed communication topology; a controller is determined according to the states of different agents in the random time-delay multi-agent system; a dynamic event triggering mechanism is determined according to the consistency error and the dynamic signal function, and the update of the controller is controlled based on the dynamic event triggering mechanism to achieve dynamic event triggering consistency control of the random time-delay multi-agent system under a directed topology. By establishing a DETM based on relative information in a random time-delay MAS, and studying MSEC according to Lyapunov's theorem and Halanay inequality, the proposed event is intermittently executed, and the Zeno behavior can be effectively suppressed by enforcing a strictly positive fixed time between any two consecutive execution times, reducing the system's computational load and power consumption, and solving the MSEC problem under a more general directed communication topology. In addition, this embodiment provides an accurate estimate of the sampling error in the expected sense, ensuring that the proposed DETM can control the influence of the sampling error. By adopting a general random convergence analysis technique, the random consistency of the consistent error system is guaranteed. Different from the single time-delay system in the prior art, this embodiment takes into account multiple systems and utilizes a more general random analysis strategy to facilitate the promotion and use of the dynamic event-triggered consistency control method of the random time-delay multi-agent system under the directed topology described in this embodiment.

[0070] It should be noted that, in this article, the terms "include", "comprises" or any other variations thereof are intended to cover non-exclusive inclusion, so that a process, method, article or system including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, article or system. In the absence of further restrictions, an element defined by the sentence "comprises a ..." does not exclude the existence of other identical elements in the process, method, article or system including the element.

[0071] The serial numbers of the above embodiments of the present invention are only for description and do not represent the advantages or disadvantages of the embodiments.

[0072] Through the description of the above implementation methods, those skilled in the art can clearly understand that the above-mentioned embodiment methods can be implemented by means of software plus a necessary general hardware platform, and of course can also be implemented by hardware, but in many cases the former is a better implementation method. Based on such an understanding, the technical solution of the present invention, or the part that contributes to the prior art, can be embodied in the form of a software product, which is stored in a storage medium (such as a read-only memory / random access memory, a magnetic disk, or an optical disk), and includes a number of instructions for a terminal device (which can be a mobile phone, a computer, a server, an air conditioner, or a network device, etc.) to execute the methods described in each embodiment of the present invention.

[0073] The above are only preferred embodiments of the present invention, and are not intended to limit the patent scope of the present invention. Any equivalent structure or equivalent process transformation made using the contents of the present invention specification and drawings, or directly or indirectly applied in other related technical fields, are also included in the patent protection scope of the present invention.

Claims

1. A consistency control method for a random time-delay multi-agent system under directed topology, characterized in that: The consistency control method of the random time-delay multi-agent system under the directed topology comprises the following steps: Construct a random time-delay multi-agent system with random nonlinear time delay under directed communication topology; Determining a controller according to the states of different agents in the random time-delay multi-agent system; Determine a dynamic event triggering mechanism according to the consistency error and the dynamic signal function, and control the update of the controller based on the dynamic event triggering mechanism to achieve dynamic event triggered consistency control of the random time-delay multi-agent system under the directed topology; The method of determining a dynamic event triggering mechanism according to a consistency error and a dynamic signal function, and controlling the update of the controller based on the dynamic event triggering mechanism to realize dynamic event triggered consistency control of a random time-delay multi-agent system under a directed topology, includes: Determine the dynamic event triggering mechanism according to the consistency error and the dynamic signal function through the following formula, and control the update of the controller based on the dynamic event triggering mechanism to achieve dynamic event triggered consistency control of the random time-delay multi-agent system under the directed topology; In the formula, , β represents the preset constant, , Indicates the pause time. , inf represents the infimum function, t represents time, is the trigger time series defined by DETM, 0, represents the kth triggering moment, represents the real-time consistency error, Indicated in The consistency error at this moment is Represents a dynamic signal function.

2. The consistency control method of a random time-delay multi-agent system under a directed topology as claimed in claim 1, characterized in that: The method for constructing a random time-delay multi-agent system with random nonlinear time delay under a directed communication topology includes: The random time-delay multi-agent system with random nonlinear time delay under directed communication topology is constructed by the following formula; In the formula, represents the real-time state of the ith agent, express dimensional Euclidean space, t represents time, Indicates time lag, satisfies ( is a preset constant), , express Real matrix, , as well as represents a known real matrix, represents an n×m real matrix, m <n, represents the controller of the control input corresponding to the ith agent, Indicates that the definition is The standard Brownian motion on is a non-empty set, representing the sample space, is a non-empty subset of the Ω power set, The time t ≥ 0 represents a non-empty subset of the Ω power set, represents a non-singular matrix, Indicates that the dimension of matrix P is N N, and represent continuous vector functions, represents an m-dimensional vector, , i = 1, 2, ...., N, N represents the number of agents, i represents the i-th agent, and the interconnection topology between agents is represented by a directed graph describe, represents a set of vertices, Represents a set of edges, the adjacency matrix , j represents the jth agent, represents the element in the i-th row and j-th column of the adjacency matrix, that is, the connection relationship between the i-th agent and the j-th agent. =0 means no connection, ≠0 means there is a connection.

3. The consistency control method of a random time-delay multi-agent system under a directed topology as claimed in claim 1, characterized in that: The controller is determined according to the states of different agents in the random time-delay multi-agent system, comprising: The controller is determined by the following formula according to the states of different agents in the random time-delay multi-agent system; In the formula, represents the controller of the control input corresponding to the ith agent, , represents an m-dimensional vector, t represents time, , is the trigger time series defined by DETM, 0, represents the kth triggering moment, represents the k+1th triggering moment, N represents the number of agents, i represents the i-th agent, j represents the j-th agent, represents the element in the i-th row and j-th column of the adjacency matrix, that is, the connection relationship between the i-th agent and the j-th agent. =0 means no connection, ≠0 means there is a connection, c means a preset constant, c>0, Indicates that the jth agent is The state of this moment, Indicates that the i-th agent is The state of the moment.

4. The consistency control method of a random time-delay multi-agent system under a directed topology as claimed in claim 1, characterized in that: The dynamic signal function is determined by the following formula; In the formula, represents the dynamic signal function, Express To perform the derivation, The derivative form of , t represents time, , is the trigger time series defined by DETM, 0, represents the kth triggering moment, represents the k+1th triggering moment, i represents the i-th agent, represents the real-time consistency error, Indicated in The consistency error at this moment is satisfy , hour, .

5. The consistency control method of a random time-delay multi-agent system under a directed topology as claimed in claim 1, characterized in that: The consistency error is determined by the following formula; In the formula, represents the real-time consistency error, represents the real-time state of the ith agent, express dimensional Euclidean space, represents the average state, t represents the time, i represents the i-th agent, j represents the j-th agent, N represents the number of agents, Represents a preset constant, Represents the real-time state of the jth agent.

6. The consistency control method of a random time-delay multi-agent system under a directed topology as claimed in claim 5, characterized in that: The consistency error forms a closed-loop system under the dynamic event triggering mechanism through the following formula: wherein, represents a closed-loop system with an initial value of , represents a random variable, , represents a real matrix, , and represent known real matrices, represents an n×m real matrix, where m < n, i represents the i-th agent, j represents the j-th agent, N represents the number of agents, represents the controller for the control input corresponding to the i-th agent, , represents an m-dimensional vector, represents a preset constant, represents the controller for the control input corresponding to the j-th agent, represents the real-time consensus error, represents a standard Brownian motion defined on , is a non-empty set representing the sample space, is a non-empty subset of the power set of Ω, represents the time t≥0 of a non-empty subset of the power set of Ω, represents a non-singular matrix, represents that the dimension of matrix P is N N, and respectively represent continuous vector functions, represents the real-time state of the i-th agent, represents a d-dimensional Euclidean space, t represents time, represents the time delay, satisfying ( is a preset constant), represents the real-time state of the j-th agent.​

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