Method and system for controlling dynamic event triggering consistency of multi-agent system

Abstract

The embodiment of the invention provides a dynamic event trigger consistency control method and system for a multi-agent system, and the method comprises the steps: setting a dual-threshold line based on a Lyapunov function, dividing a system state function into an activation time period, a holding time period and an idle time period, and dynamically switching the working mode of the controller, namely inputting a non-zero control quantity in an activation period to quickly converge a state, performing input zero setting in an idle period to save resources, maintaining control input at the previous moment in a keeping period to avoid frequent switching, and forcibly performing zero setting control input in a DoS attack period. Secondly, monitoring a measurement error (a deviation between a current state of the intelligent agent and a historical trigger state), a consistency error (a state deviation between the intelligent agent and a leader) and an auxiliary variable in real time, and if the weighted contribution of the measurement error in an activation time period exceeds the sum of the weighted contribution of the consistency error and the auxiliary variable, triggering a communication update state and reducing redundant communication;

Description

Technical Field

[0001] The embodiments of the present invention relate to the technical fields of distributed system control and network security control, and in particular to a method and system for dynamic event-triggered consistency control of a multi-agent system. Background Art

[0002] Consensus control, as a core topic in the research field of multi-agent systems (MAS), has long attracted widespread attention. Traditional consensus methods are mostly based on continuous control strategies, requiring agents to continuously exchange state information. This results in frequent communication even when the system state changes slightly, resulting in high communication overhead.

[0003] To address this issue, intermittent communication mechanisms have been introduced, which reduce the communication burden and energy consumption by presetting active and idle periods. For example, some studies have proposed intermittent communication schemes to achieve consistency control of second-order nonlinear multi-agent systems. Others have explored the consistency issues of nonlinear multi-agent systems with time delays and intermittent communication. Others have proposed solutions to distributed collaborative optimization problems for heterogeneous, uncertain, high-order nonlinear multi-agent systems in intermittent communication networks, and designed consistency protocols that incorporate aperiodic intermittent effects to address clustering consistency issues.

[0004] In addition, the Distributed Event-Triggered Control (DETC) strategy, as an efficient method for optimizing communication resource utilization, effectively reduces communication frequency while ensuring system stability by setting specific trigger conditions and rationally determining the timing of data sampling and control updates. Related research involves the semi-global bipartite consistency problem in linear MASs subject to input saturation, solving the consistency problem of MASs with general linear dynamics without using global data, the consistency challenges in linear MASs with directed communication networks, and the output consistency problem of uncertain non-strict feedback MASs.

[0005] There has also been considerable research on security issues in communication, particularly denial of service (DoS) attacks. For example, some studies have proposed an event-triggered control method based on input information, which avoids the need for continuous sampling through link state estimation; studied the impact of uncertain non-homogeneous Markov switching and time-varying delay on MAS, and analyzed the effect of DoS attacks on leader-follower consistency; proposed a distributed security consistency control method based on an event-triggered mechanism to deal with DoS attacks; and used a multi-Lyapunov function method to study the leader-follower consistency problem in a nonlinear MAS affected by uncertain non-homogeneous Markov switching and DoS attacks.

[0006] Although existing research has made some progress in optimizing communication mechanisms, improving MAS performance, and responding to DoS attacks, the following technical issues still exist:

[0007] Insufficient integration of intermittent communication and dynamic event triggering: In existing research, the integration of intermittent communication mechanism and DETC is still insufficient, and the potential synergistic effect of the two in optimizing communication efficiency and enhancing system security has not been fully explored, making it impossible to achieve efficient communication resource scheduling and security control in complex network environments.

[0008] Static strategies have poor adaptability: Current research focuses on simple attack scenarios or static communication strategies. There is a lack of comprehensive methods to deal with DoS attacks in complex network environments. It is difficult to dynamically adjust communication strategies based on the real-time status of the system and the attack situation, resulting in insufficient stability and reliability of the system when facing changing attack modes.

[0009] Imbalance between communication efficiency and security: Under DoS attacks, existing methods fail to strike a good balance between communication efficiency and system security. They either increase unnecessary communication overhead due to over-protection of communication, or make it difficult to maintain system consistency due to unreasonable scheduling of communication resources.

[0010] Zeno behavior affects practicality: Some event-triggered control strategies may induce Zeno behavior, that is, infinite event triggering occurs within a finite time, resulting in continuous communication, which seriously affects the practical application feasibility of the control scheme. Summary of the Invention

[0011] An embodiment of the present invention provides a dynamic event-triggered consistency control method and system for a multi-agent system to solve the problem in the existing field of industrial big data and electronic equipment safety technology, where the chain from perception to prediction to control is broken, making it difficult for charging protection schemes to achieve precise protection in complex scenarios.

[0012] In a first aspect, an embodiment of the present invention provides a method for dynamic event-triggered consistency control of a multi-agent system, wherein the multi-agent system includes multiple agents, wherein the multiple agents include a leader and the rest are followers, and the method includes:

[0013] S100. Setting a dual threshold line based on the Lyapunov function divides the system state function into an activation period region, a holding period region, and an idle period region, and switches the controller operating mode in different period regions; wherein the controller input corresponding to the activation period region is non-zero, the controller input corresponding to the idle period region is zero, and the controller corresponding to the holding period region maintains the control input of the previous moment unchanged, and the control input is forced to zero during a DoS attack; wherein the system state function represents the consistency error between the follower and the leader, and the degree of global consistency of the multi-agent system;

[0014] S200 : Determine a trigger condition based on the error term and the auxiliary variable, and determine whether to perform communication according to the trigger condition during the activation period.

[0015] Preferably, in step S100, setting a double threshold line based on the Lyapunov function specifically includes:

[0016] In each safe communication interval, two straight lines that decay over time are generated according to the initial state and attenuation parameter of the system state function, namely the first threshold line and the second threshold line. The attenuation parameter of the first threshold line is smaller than the attenuation parameter of the second threshold line, and the initial proportional coefficient of the first threshold line is larger than the initial proportional coefficient of the second threshold line.

[0017] As an example, the kth secure communication area [s k-1 , s k ] is the time from the end of the k-1th DoS attack to the start of the kth DoS attack;

[0018] The first threshold line is:

[0019]

[0020] The second threshold line is:

[0021]

[0022] In the above formula, a1 is the initial proportional coefficient of the first threshold line, a2 is the initial proportional coefficient of the second threshold line, and they satisfy 1>a1>a2>0; t represents the current time, Ω1 represents the first threshold line, and Ω2 represents the second threshold line; W represents the system state function; α1 is the decay rate of the first threshold line, α2 is the decay rate of the second threshold line, and α2≥α1>0.

[0023] Preferably, in S100, dividing the system state function into an activation period, a holding period, and an idle period includes:

[0024] By comparing the size relationship between the system state function and the first threshold line and the second threshold line, the communication interval is divided into three areas:

[0025] When the system state function is greater than or equal to the first threshold line, it is the activation period area

[0026] When the system state function is less than the second threshold line, it is the idle period area

[0027] When the system state function is between the second threshold line and the first threshold line, it is the holding period area, which maintains the area of ​​the control input at the previous moment

[0028] Preferably, in step S100, the controller input corresponding to the activation period area is non-zero, the controller input corresponding to the space period area is zero, and the controller input corresponding to the holding period area remains unchanged. Specifically,

[0029]

[0030] In the above, u i (t) represents the controller input at time t, represents the gain matrix; t_ represents the previous moment, u i (t_) represents the controller input at time t; W(t) represents the system state function at time t; subscript i represents the index of the current agent, subscript j represents the index of the neighboring agent, i = 1, 2, ..., N, j = 1, 2, ..., N; subscript 0 represents the leader agent; is the state of agent i at the time of the most recent event triggering, The state of agent j at the time of the most recent event triggering, x0(t) is the real-time state of the leader at time t; d i represents the connection weight between agent i and the leader.

[0031] Preferably, the step S200 includes:

[0032] Based on the real-time state x(t) of agent i at time t and the state at the most recent time trigger The deviation of determines the measurement error:

[0033]

[0034] Determine the consistency error based on the current state x(t) of agent i and the real-time state x0(t) of the leader at time t:

[0035] δ i (t) = x i (t)-x0(t)

[0036] Determine the trigger conditions:

[0037]

[0038] In the above formula, is the k+1th event triggering time of agent i, inf represents the minimum time to meet the departure conditions; f i represents the trigger weight coefficient of agent i; r1>0, r2>0, is the weight coefficient of the error term; η i (t) is an auxiliary variable, and the auxiliary variable η i(t) satisfies the initial value condition η i (t)>0;

[0039]

[0040] In the above formula, 1>ω i ≥0, m i is the attenuation coefficient of the auxiliary variable, ω i is the error feedback coefficient.

[0041] As a preference, it also includes:

[0042] Step S300: Construct a Lyapunov function including the system state function and auxiliary variables, determine the derivative of the Lyapunov function in the safe communication interval and the DoS attack interval, and obtain the ratio constraint of the attack duration to the total time through inequality transformation and parameter setting.

[0043] In a second aspect, an embodiment of the present invention provides a dynamic event-triggered consistency control system for a multi-agent system, the multi-agent system comprising a plurality of agents, wherein the plurality of agents include a leader and the remaining agents are followers, the system comprising:

[0044] The intermittent communication control module sets a dual threshold line based on the Lyapunov function, divides the system state function into an activation period region, a holding period region, and an idle period region, and switches the controller operating mode in different period regions. The controller input corresponding to the activation period region is non-zero, the controller input corresponding to the idle period region is zero, and the controller input corresponding to the holding period region remains unchanged. During a DoS attack, the control input is forced to zero. The system state function represents the consistency error between the follower and the leader, and the degree of global consistency of the multi-agent system.

[0045] The dynamic event trigger control module determines the trigger condition based on the error term and the auxiliary variable, and determines whether to communicate during the activation period based on the trigger condition.

[0046] In a third aspect, an embodiment of the present invention provides an electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the program, the steps of the dynamic event-triggered consistency control method for a multi-agent system as described in the embodiment of the first aspect of the present invention are implemented.

[0047] In a fourth aspect, an embodiment of the present invention provides a non-transitory computer-readable storage medium on which a computer program is stored. When the computer program is executed by a processor, the steps of the dynamic event-triggered consistency control method of the multi-agent system as described in the embodiment of the first aspect of the present invention are implemented.

[0048] Embodiments of the present invention provide a dynamic event-triggered consistency control method, system, electronic device, and storage medium for multi-agent systems. This method dynamically divides active / hold / idle periods based on a Lyapunov function and dual threshold lines, enabling intelligent scheduling that actively communicates when state deviations are large and hibernates to save energy when deviations are small. Compared with traditional fixed-time intermittent communication, this method reduces communication frequency by 30%-50%, significantly reducing network load and energy consumption. Communication is triggered only when measurement error (state hysteresis) exceeds a dynamic threshold, avoiding redundant transmission of periodic sampling. By comparing the weighted error terms (measurement error and consistency error) with auxiliary variables in real time, "on-demand triggering" is achieved, and the communication efficiency is improved by about 40% while ensuring consistency accuracy; attack interval analysis and Lyapunov function constraints are introduced to derive the critical conditions for attack duration; ensure that the growth of state deviation during the attack does not exceed the system recovery capability; through the three-layer technical architecture of "dynamic scheduling-event triggering-attack robustness", the communication efficiency, security, and engineering practicality of the multi-agent system are improved to a new level, which is especially suitable for distributed scenarios with limited communication resources and the risk of network attacks, such as industrial Internet of Things, unmanned system clusters, smart grids, etc., providing a solution with both theoretical innovation and engineering value for multi-agent collaborative control in complex network environments. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following is a brief introduction to the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0050] Figure 1 This is a flowchart of a method for dynamic event-triggered consistency control of a multi-agent system according to an embodiment of the present invention;

[0051] Figure 2 is a framework diagram of a multi-agent system according to an embodiment of the present invention;

[0052] Figure 3 is the state change of w(t) according to an embodiment of the present invention;

[0053] Figure 4 is a communication topology diagram according to an embodiment of the present invention;

[0054] Figure 5 is x according to an embodiment of the present invention i (t) state change diagram;

[0055] Figure 6 are the error functions and threshold functions of agents 1-6 according to an embodiment of the present invention;

[0056] Figure 7 is a schematic diagram of triggering timing of a method according to an embodiment of the present invention;

[0057] Figure 8 is a schematic diagram of triggering timing according to the prior art in an embodiment of the present invention;

[0058] Figure 9 Schematic diagram of the physical structure according to an embodiment of the present invention. DETAILED DESCRIPTION

[0059] To make the objectives, technical solutions, and advantages of the embodiments of the present invention more clear, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention without making any creative efforts shall fall within the scope of protection of the present invention.

[0060] In the embodiments of the present application, the term "and / or" is merely a description of the association relationship between associated objects, indicating that three relationships may exist. For example, A and / or B may represent three situations: A exists alone, A and B exist at the same time, and B exists alone.

[0061] The terms "first" and "second" in the embodiments of the present application are only used for descriptive purposes and are not to be understood as indicating or implying relative importance or implicitly indicating the number of the indicated technical features. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one of the features. In the description of the present application, the terms "include" and "have" and any variations thereof are intended to cover non-exclusive inclusions. For example, a system, product or device comprising a series of components or units is not limited to the listed components or units, but may optionally also include components or units that are not listed, or may optionally also include other components or units that are inherent to these products or devices. In the description of the present application, the meaning of "plurality" is at least two, such as two, three, etc., unless otherwise clearly and specifically defined.

[0062] References herein to "embodiments" mean that a particular feature, structure, or characteristic described in connection with the embodiments may be included in at least one embodiment of the present application. The appearance of this phrase in various places in the specification does not necessarily refer to the same embodiment, nor does it constitute an independent or alternative embodiment that is mutually exclusive of other embodiments. It is understood, both explicitly and implicitly, by those skilled in the art that the embodiments described herein may be combined with other embodiments.

[0063] Multi-agent systems (MAS) have broad applications in areas such as autonomous vehicle platooning, distributed sensor networks, intelligent robot collaboration, and drone swarm control. Consistency is a core issue in MAS research. Traditional approaches, often based on continuous control strategies, require agents to continuously exchange state information, resulting in high communication overhead and wasted resources. To reduce the communication burden, existing technologies have proposed intermittent communication mechanisms and event-triggered control (ETC) strategies. Intermittent communication reduces communication frequency by pre-setting active and idle periods, while ETC dynamically determines communication timing by setting trigger conditions, further optimizing resource utilization.

[0064] While significant progress has been made in addressing the consistency issues of MAS under DoS attacks, existing approaches still have limitations. Specifically, the integration of intermittent communication mechanisms with DETC is understudied, and their potential synergistic effects in optimizing communication efficiency and enhancing system security have not been fully explored. Furthermore, current research focuses on simple attack scenarios or static communication strategies, lacking a comprehensive approach to addressing DoS attacks in complex network environments. Therefore, developing a strategy that combines dynamic event-triggered communication with intermittent communication mechanisms to effectively mitigate DoS attacks and improve the stability and operational efficiency of MAS has important theoretical and practical value.

[0065] However, the existing technology has the following problems:

[0066] Intermittent communication mechanisms lack dynamism: Existing intermittent communication mechanisms mostly use fixed-time scheduling, which cannot adjust the active and idle periods in real time according to the system status, resulting in inefficient resource utilization.

[0067] Static nature of event triggering strategies: Traditional static event triggering (SETC) mechanisms are difficult to adapt to complex dynamic environments. The triggering conditions are fixed, which can easily cause unnecessary communication or response delays.

[0068] Insufficient security protection: Existing research has limited defense capabilities against denial of service (DoS) attacks, especially in scenarios where intermittent communication is combined with dynamic event triggering. The lack of comprehensive security solutions leads to insufficient system stability under attacks.

[0069] Zeno behavior risk: Some event triggering mechanisms may fail due to unlimited triggering (Zeno behavior), affecting the feasibility of the system.

[0070] In this embodiment, and denote n-dimensional vector space and m×m real matrix space respectively. For a given matrix D, the symbols D>0, D–1, D T ,λ(D) and ||D|| respectively represent the positive definite matrix, the inverse of the matrix, the transpose, the eigenvalue and the matrix 2-norm. min(·) and λ max (·) represents the minimum eigenvalue and the maximum eigenvalue, respectively. represents the Kronecker product.

[0071] The communication network of a MAS composed of N agents can be described by an undirected graph G(V,E,A), where V = {V1,...,V N} represents the set of agents, E = {(i,j)|i,j∈V} represents the set of communication edges, A = [a ij ]∈R N×N is the adjacency matrix. Introduce the leader node v0 and establish directed edges from it to some multi-agent nodes. A directed graph containing N+1 nodes The adjacency matrix of is defined as follows: ii = 0; if {i, j}∈{v0, V}, then aij=1; otherwise aij=0. In addition, the Lap matrix is ​​introduced Its element l ij Defined as: when i≠j, l ij =–a ij ; When i=j,

[0072] Therefore, there is an urgent need for a control method that combines dynamic intermittent communication with event triggering to solve the above problems and improve the communication efficiency, security and stability of MAS.

[0073] Therefore, an embodiment of the present invention provides a method for dynamic event-triggered consistency control of a multi-agent system, wherein the multi-agent system includes multiple agents, wherein the multiple agents include a leader and the rest are followers, and the method includes:

[0074] S100. Setting a dual threshold line based on the Lyapunov function divides the system state function into an activation period region, a holding period region, and an idle period region, and switches the controller operating mode in different period regions; wherein the controller input corresponding to the activation period region is non-zero, the controller input corresponding to the idle period region is zero, and the controller corresponding to the holding period region maintains the control input of the previous moment unchanged, and the control input is forced to zero during a DoS attack; wherein the system state function represents the consistency error between the follower and the leader, and the degree of global consistency of the multi-agent system;

[0075] S200 : Determine a trigger condition based on the error term and the auxiliary variable, and determine whether to perform communication according to the trigger condition during the activation period.

[0076] Specifically, consider a MAS consisting of N followers and one leader. In this framework, the leader is labeled as node 0, and the followers are labeled as nodes i=1,...,N. The system's dynamic equations are described as:

[0077]

[0078] in, represents the state vector of the i-th agent, represents the state vector of the leader, is the control input, is a known system matrix.

[0079] In this embodiment, it is assumed that 1. in the initial state or when not under attack, the topology map Has a directed spanning tree.

[0080] Assumption 2. The matrix pair (A,B) is stable.

[0081] In the case of continuous communication, let s0 represent the initial time, Indicates the time when the attack occurs. Due to the limited attack resources, the attack will occur at s k terminated when Therefore, the attack period can be expressed as The non-attack period is When a DoS attack occurs, the communication links between MASs will be destroyed and the communication connection of the attacked agents will be interrupted. Once the attack ends, the communication network will return to normal. In normal state, the adjacency matrix of the communication network is Its form is There is a root node, the leader node, which does not obtain any information from other agents. The corresponding Laplace matrix is ​​denoted as Its structure is as follows:

[0082]

[0083] Where D = [a 10 ,...,a N0 ] T .matrix is asymmetric, but the submatrix It is symmetrical.

[0084] Based on the above embodiment, in step S100, setting a dual threshold line based on the Lyapunov function specifically includes:

[0085] In each safe communication interval, two straight lines that decay over time are generated according to the initial state and attenuation parameter of the system state function, namely the first threshold line and the second threshold line. The attenuation parameter of the first threshold line is smaller than the attenuation parameter of the second threshold line, and the initial proportional coefficient of the first threshold line is larger than the initial proportional coefficient of the second threshold line.

[0086] Specifically, in the time interval [s0,s m ], the attack duration is S a Expressed as:

[0087]

[0088] in, and s j They represent the starting point and ending point of the j-th attack respectively. For any given initial conditions, if i=1,2,...,N, we have:

[0089]

[0090] It can be determined that the MAS has reached consistency.

[0091] By comparing the size relationship between the system state function and the first threshold line and the second threshold line, the communication interval is divided into three areas:

[0092] When the system state function is greater than or equal to the first threshold line, it is the activation period area

[0093] When the system state function is less than the second threshold line, it is the idle period area

[0094] When the system state function is between the second threshold line and the first threshold line, it is the holding period area, which maintains the area of ​​the control input at the previous moment

[0095] The kth secure communication area [s k-1 , s k ] is the time from the end of the k-1th DoS attack to the start of the kth DoS attack;

[0096] The first threshold line is:

[0097]

[0098] The second threshold line is:

[0099]

[0100] In the above formula, a1 is the initial proportional coefficient of the first threshold line, a2 is the initial proportional coefficient of the second threshold line, and they satisfy 1>a1>a2>0; t represents the current time, Ω1 represents the first threshold line, and Ω2 represents the second threshold line; W represents the system state function; α1 is the decay rate of the first threshold line, α2 is the decay rate of the second threshold line, and α2≥α1>0.

[0101] Specifically, this embodiment provides a Lyapunov-based intermittent communication method for observing the system state by setting two threshold lines. In the activation period, the controller input corresponding to the activation period is non-zero, the controller input corresponding to the space period is zero, and the controller input corresponding to the holding period remains unchanged. Specifically,

[0102]

[0103] The intervals in the control scheme are:

[0104]

[0105] In the above, u i (t) represents the controller input at time t, represents the gain matrix; t_ represents the previous moment, u i (t_) represents the controller input at time t; W(t) represents the system state function at time t; subscript i represents the index of the current agent, subscript j represents the index of the neighboring agent, i = 1, 2, ..., N, j = 1, 2, ..., N; subscript 0 represents the leader agent; is the state of agent i at the time of the most recent event triggering, The state of agent j at the time of the most recent event triggering, x0(t) is the real-time state of the leader at time t; d i represents the connection weight between agent i and the leader. represents the set of positive real numbers.

[0106] Let d i =a i0 ,and in, Indicates the time when the sth trigger event occurs on agent i.

[0107] Step S300: Construct a Lyapunov function including the system state function and auxiliary variables, determine the derivative of the Lyapunov function in the safe communication interval and the DoS attack interval, and obtain the ratio constraint of the attack duration to the total time through inequality transformation and parameter setting.

[0108] In this embodiment, a dynamic event triggering strategy is also proposed, and its framework is as follows: Figure 2As shown in , the error term is introduced and δ i (t) = x i (t)-x0(t), represent measurement error and consistency error respectively.

[0109] Based on the real-time state x(t) of agent i at time t and the state at the most recent time trigger The deviation of determines the measurement error:

[0110]

[0111] Determine the consistency error based on the current state x(t) of agent i and the real-time state x0(t) of the leader at time t:

[0112] δ i (t) = x i (t)-x0(t)

[0113] Determine the trigger conditions:

[0114]

[0115] In the above formula, is the k+1th event triggering time of agent i, inf represents the minimum time to meet the departure conditions; f i represents the trigger weight coefficient of agent i; r1>0, r2>0, is the weight coefficient of the error term; η i (t) is an auxiliary variable. Auxiliary variable η i (t) satisfies the initial value condition η i (t)>0;

[0116]

[0117] In the above formula, 1>ω i ≥0, m i is the attenuation coefficient of the auxiliary variable, ω i is the error feedback coefficient.

[0118] For the predetermined m i 、ω i and f i , it can be proved that the relevant variables meet the following conditions:

[0119] i=1,2,...,N

[0120] In the safe communication interval [s k-1 , s k ], set a specified positive definite function W(t), assuming that its derivative during the control scheme activation period satisfies the inequality Where λ is a constant and satisfies λ>α1, and Then there is time Make the interval For any t on , we have:

[0121]

[0122] Since 1>a1>0, at time s k–1 , W(t) must be located at According to the inequality Available

[0123] Defining a function When F(t)>0, we can get Therefore, there is a moment Make Touching the threshold line at this point Afterwards, W(t) enters the region and The situation of moment is similar, there is moment So that W(t) touches the threshold line a2W(s k–1 )e–α2(t–sk–1). Afterwards, W(t) enters the region At this time, the system enters the idle period. i (t) becomes 0, W(t) is no longer constrained. The moment can be found At this time, W(t) reaches the threshold line Then the system re-enters the activation period. By repeating the above analysis, we can see that if Large enough, W(t) will be The moment touches the threshold line a2W(s k–1 )e –α2(t-sk-1) In summary, in the interval Internal, from time From, W(t)≤a1W(s k–1 )e –α1(t-sk-1) So far, Lemma 1 is proved.

[0124] inequality is a necessary and sufficient condition to ensure that there is a time Make

[0125] like Figure 3As shown in the figure, the intermittent communication principle exploits the current system state. The function W(t) oscillates around two threshold lines and remains below the first threshold line after a certain point. Furthermore, these two threshold lines jointly influence the determination of active and idle periods. By narrowing the gap between the function values ​​of the two threshold lines, more frequent switching between active and idle periods can be achieved. However, the length of the idle period is limited.

[0126] In this embodiment, a sufficient condition is proposed to ensure system consistency by triggering a control strategy through dynamic events.

[0127] Theorem 1, under the condition that Assumption 2 holds, the following matrix inequality can be established:

[0128]

[0129] Where M is a matrix, and M>0, is a non-negative constant, and the control gain is K=-B T M is given. Let:

[0130]

[0131] If A is satisfied T M+MA-QI n <0 and <2, then in a MAS system that receives a QoS attack, to achieve security consistency, the attack duration should meet the following requirements:

[0132]

[0133] Among them, α1<Q * , and Q>0.

[0134] Construct a Lyapunov function as:

[0135]

[0136] In the safe communication interval [s k-1 , s k ], according to formula q i (t), we can get:

[0137]

[0138] definition Similar definitions are made for δ(t) and e(t). The above can be repeatedly defined as:

[0139]

[0140] Given the equation:

[0141]

[0142] You can get:

[0143]

[0144] The derivative of the function V(t) with respect to time t is:

[0145]

[0146] Combining the above content, the following inequality can be derived:

[0147]

[0148] According to Theorem 1, we can get:

[0149]

[0150] set up in, and is a positive constant, so we can derive:

[0151]

[0152] because is a symmetric matrix, we can get:

[0153]

[0154] Based on Young's inequality, we can draw the following conclusions:

[0155]

[0156] Substituting equations (11) and (12) into equation (10), we can obtain:

[0157]

[0158] After arranging the above content, we can get:

[0159]

[0160] in,

[0161]

[0162] Where r1 and r2 are greater than 0, and from equations (5) and (13) we can get:

[0163]

[0164] Considering formula (4), we have:

[0165]

[0166] in,

[0167]

[0168] ρ1>α1, in the interval [s k-1 , s k ], there is a moment For all have:

[0169]

[0170] In the interval [s k-1 , s k ], for DoS attacks, the communication topology is destroyed, at this time, ui(t)=0, and Therefore, we can get The corresponding Lyapunov function is:

[0171]

[0172] According to formula (15), it can be deduced that:

[0173]

[0174] Combining equations (14) and (16), we can obtain:

[0175]

[0176] Combining equations (17) and (18), we can obtain:

[0177]

[0178] Continuing to simplify formula (9), we can obtain:

[0179]

[0180] Because Q * >0, and 0<a1<1, which means lim t→∞ W(t) = 0 and lim t→∞ ‖δ(t)‖=0.

[0181] When an infinite sequence of events occurs within a bounded time interval, resulting in continuous communication, the behavior is called Zeno behavior. One of the main challenges in implementing DETC strategies is to eliminate Zeno behavior. Therefore, it is necessary to prove that the proposed DETC scheme can prevent this phenomenon from occurring.

[0182] Theorem 2. Under the conditions of Theorem 1, the event-triggered control of MASS with DoS attack and intermittent communication does not exhibit Zeno behavior:

[0183]

[0184] in, Based on the above, we can deduce that:

[0185]

[0186] According to formula (4), we can conclude that:

[0187]

[0188] Based on the above analysis, we can get in:

[0189]

[0190] This result shows that the time interval between every two consecutive triggering moments has a strictly positive lower bound Δ.

[0191] This shows that the time interval between any two triggering moments is always positive. The proposed consistency control strategy successfully eliminates Zeno behavior under DoS attacks with intermittent communication. This completes the proof.

[0192] Compared with the SETC protocol, the internal variable η in the DETC protocol proposed in this embodiment is i (t) can ensure a larger trigger interval. The proof of Theorem 2 can also be achieved by contradiction: suppose that agent i exhibits Zeno behavior, that is, the agent triggers infinitely many times in a finite time. Then Converges. Substituting this conclusion into the previous formula, we can get: Its i (t)>0, so It must diverge, thus eliminating the possibility of Zeno behavior.

[0193] Suppose there is a group of seven robots in a multi-robot system, and its communication network is attacked by DoS in an intermittent communication framework. In this framework, node x0 is the leader and the rest of the nodes are followers. The dynamics of each robot in the system satisfies equation (1). Let:

[0194]

[0195]

[0196] Communication topology diagram Figure 4 As shown in , the initial state of the robot is:

[0197]

[0198] according to Figure 4 From the topological diagram in the figure, we can calculate μ = 0.1277. In addition, let θ = 0.2, which satisfies θ < 2μ. and Satisfies the matrix equation (6). Let γ = 557, α = 0.0018, then we get r1 = 5527.1098 and r2 = 0.002551. Set mi = 2, ωi = 0.18, fi = 0.58, and the initial state of the auxiliary variable ηi is ηi(0) = 5×10 4 , where i = 1 to 6. The calculation results show that ρ1=0.56926. Since ρ1>α1, and α2>α1>0, 1>a1>a2, we take a1=0.46, a2=0.34, α1=0.56, α2=0.57. Internally, based on Ω1=a1W(s1)e –α1(t–s1) and Ω2=a2W(s1)e –α2(t–s1) , Figure 2 The figure shows the changes of Ω1, Ω2 and W(t) from 7.5 to 9.75 seconds. It can be seen that after 8.235 seconds, W(t)≤a1W(s1)e –α1(t–s1) .

[0199] make satisfy make In this example, the attack duration is S a = 3.75 seconds, and t–s0 = 12 seconds, so the attack length ratio satisfies

[0200] Based on the above parameters, Figure 5 The state changes of the robot in each dimension can be observed in Figure 6 The error function and threshold function of agents 1 to 6 are shown in Figure 1. i1 (t)–x i3 (t) Achieves security consistency over time.

[0201] In this embodiment, the superiority of the proposed dynamic event-triggered consensus control method based on intermittent communication is verified by comparing it with the method in [Y. Zhang, Z.-G. Wu, and P. Shi, “Resilient event- / self-triggering leader-following consensus control of multiagent systems against DoS attacks,” IEEE Transactions on Industrial Informatics, vol. 19, no. 4, pp. 5925–5934, 2022. Figure 4 The communication network topology is shown in Figure 2. Other relevant parameter settings are the same as those in Example 1, and the initial value of the auxiliary variable ηi(0) is set to 5×105. Both methods achieve consistency. Figure 7 The triggering moment of the proposed method is shown in this paper. Figure 8 The triggering time of the method [Y. Zhang, Z.-G. Wu, and P. Shi, “Resilient event- / self-triggering leader-following consensus control of multiagent systems against DoS attacks,” IEEE Transactions on Industrial Informatics, vol. 19, no. 4, pp. 5925–5934, 2022] is shown. Combined with the comparison results in Table 1, it can be concluded that the proposed method effectively reduces the consumption of computing and communication resources.

[0202] Table 1 Comparative analysis of trigger times under different control methods

[0203]

[0204] In a second aspect, an embodiment of the present invention provides a dynamic event-triggered consistency control system for a multi-agent system, the multi-agent system comprising a plurality of agents, wherein the plurality of agents include a leader and the remaining agents are followers, the system comprising:

[0205] The intermittent communication control module sets a dual threshold line based on the Lyapunov function, divides the system state function into an activation period region, a holding period region, and an idle period region, and switches the controller operating mode in different period regions. The controller input corresponding to the activation period region is non-zero, the controller input corresponding to the idle period region is zero, and the controller input corresponding to the holding period region remains unchanged. During a DoS attack, the control input is forced to zero. The system state function represents the consistency error between the follower and the leader, and the degree of global consistency of the multi-agent system.

[0206] The dynamic event trigger control module determines the trigger condition based on the error term and the auxiliary variable, and determines whether to communicate during the activation period based on the trigger condition.

[0207] Based on the same concept, the embodiment of the present invention also provides a schematic diagram of an entity structure, such as Figure 9 As shown, the server may include: a processor 410, a communication interface 420, a memory 430, and a communication bus 440, wherein the processor 410, the communication interface 420, and the memory 430 communicate with each other via the communication bus 440. The processor 410 may call the logic instructions in the memory 430 to execute the steps of the dynamic event-triggered consistency control method for a multi-agent system as described in the above embodiments.

[0208] In addition, the logic instructions in the above-mentioned memory 430 can be implemented in the form of a software functional unit and can be stored in a computer-readable storage medium when sold or used as an independent product. Based on this understanding, the technical solution of the present invention, or the part that contributes to the prior art, or the part of the technical solution, can be embodied in the form of a software product. The computer software product is stored in a storage medium and includes several instructions for enabling a computer device (which can be a personal computer, a server, or a network device, etc.) to perform all or part of the steps of the method described in each embodiment of the present invention. The aforementioned storage medium includes: various media that can store program codes, such as a USB flash drive, a mobile hard disk, a read-only memory (ROM), a random access memory (RAM), a magnetic disk or an optical disk.

[0209] Based on the same concept, an embodiment of the present invention also provides a non-transitory computer-readable storage medium, which stores a computer program. The computer program includes at least one segment of code, which can be executed by a main control device to control the main control device to implement the steps of the dynamic event-triggered consistency control method of the multi-agent system as described in the above embodiments.

[0210] Based on the same technical concept, an embodiment of the present application also provides a computer program, which, when executed by a main control device, is used to implement the above method embodiment.

[0211] The program may be stored in whole or in part on a storage medium packaged with the processor, or may be stored in whole or in part on a memory not packaged with the processor.

[0212] Based on the same technical concept, the embodiment of the present application further provides a processor, which is used to implement the above method embodiment. The above processor can be a chip.

[0213] The various embodiments of the present invention can be combined arbitrarily to achieve different technical effects.

[0214] In the above embodiments, all or part of the embodiments can be implemented by software, hardware, firmware, or any combination thereof. When implemented using software, all or part of the embodiments can be implemented in the form of a computer program product. The computer program product includes one or more computer instructions. When the computer program instructions are loaded and executed on a computer, the process or function described in this application is generated in whole or in part. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The computer instructions can be stored in a computer-readable storage medium or transmitted from one computer-readable storage medium to another computer-readable storage medium. For example, the computer instructions can be transmitted from one website, computer, server, or data center to another website, computer, server, or data center via wired (e.g., coaxial cable, optical fiber, digital subscriber line) or wireless (e.g., infrared, wireless, microwave, etc.) means. The computer-readable storage medium can be any available medium that can be accessed by a computer or a data storage device such as a server or data center that includes one or more available media. The available medium can be a magnetic medium (e.g., a floppy disk, a hard disk, a tape), an optical medium (e.g., a DVD), or a semiconductor medium (e.g., a solid-state drive).

[0215] Those skilled in the art will appreciate that all or part of the process steps in the above-described method embodiments can be implemented by a computer program instructing the relevant hardware. The program can be stored in a computer-readable storage medium, and when executed, the program can include the process steps in the above-described method embodiments. The aforementioned storage medium includes various media capable of storing program code, such as ROM or random access memory (RAM), magnetic disks, or optical disks.

[0216] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the various embodiments of the present invention.

Claims

1. A method for dynamic event-triggered consistency control of a multi-agent system, wherein the multi-agent system comprises a plurality of agents, wherein the plurality of agents include a leader and the rest are followers, characterized in that: The method comprises: S100. Setting a dual threshold line based on the Lyapunov function divides the system state function into an activation period region, a holding period region, and an idle period region, and switches the controller operating mode in different period regions; wherein the controller input corresponding to the activation period region is non-zero, the controller input corresponding to the idle period region is zero, and the controller corresponding to the holding period region maintains the control input of the previous moment unchanged, and the control input is forced to zero during a DoS attack; wherein the system state function represents the consistency error between the follower and the leader, and the degree of global consistency of the multi-agent system; S200 : Determine a trigger condition based on the error term and the auxiliary variable, and determine whether to perform communication according to the trigger condition during the activation period.

2. The dynamic event-triggered consistency control method for a multi-agent system according to claim 1, characterized in that: In step S100, setting a dual threshold line based on the Lyapunov function specifically includes: In each safe communication interval, two straight lines that decay over time are generated according to the initial state and attenuation parameter of the system state function, namely the first threshold line and the second threshold line. The attenuation parameter of the first threshold line is smaller than the attenuation parameter of the second threshold line, and the initial proportional coefficient of the first threshold line is larger than the initial proportional coefficient of the second threshold line.

3. The dynamic event-triggered consistency control method for a multi-agent system according to claim 2, characterized in that: The kth secure communication area [s k-1 , s k ] is the time from the end of the k-1th DoS attack to the start of the kth DoS attack; The first threshold line is: The second threshold line is: In the above formula, a1 is the initial proportional coefficient of the first threshold line, a2 is the initial proportional coefficient of the second threshold line, and they satisfy 1>a1>a2>0; t represents the current time, Ω1 represents the first threshold line, and Ω2 represents the second threshold line; W represents the system state function; α1 is the decay rate of the first threshold line, α2 is the decay rate of the second threshold line, and α2≥α1>0.

4. The dynamic event-triggered consistency control method for a multi-agent system according to claim 2, characterized in that: In S100, dividing the system state function into an activation period, a holding period, and an idle period includes: By comparing the size relationship between the system state function and the first threshold line and the second threshold line, the communication interval is divided into three areas: When the system state function is greater than or equal to the first threshold line, it is the activation period area When the system state function is less than the second threshold line, it is the idle period area When the system state function is between the second threshold line and the first threshold line, it is the holding period area, which maintains the area of ​​the control input at the previous moment 5. The dynamic event-triggered consistency control method for a multi-agent system according to claim 4, characterized in that: In step S100, the controller input corresponding to the activation period area is non-zero, the controller input corresponding to the space period area is zero, and the controller input corresponding to the holding period area remains unchanged. Specifically, In the above, u i (t) represents the controller input at time t, represents the gain matrix; t_ represents the previous moment, u i (t_) represents the controller input at time t; W(t) represents the system state function at time t; subscript i represents the index of the current agent, subscript j represents the index of the neighboring agent, i = 1, 2, ..., N, j = 1, 2, ..., N; subscript 0 represents the leader agent; is the state of agent i at the time of the most recent event triggering, The state of agent j at the time of the most recent event triggering, x0(t) is the real-time state of the leader at time t; d i represents the connection weight between agent i and the leader.

6. The dynamic event-triggered consistency control method for a multi-agent system according to claim 5, characterized in that: The step S200 includes: Based on the real-time state x(t) of agent i at time t and the state at the most recent time trigger The deviation of determines the measurement error: Determine the consistency error based on the current state x(t) of agent i and the real-time state x0(t) of the leader at time t: δ i (t)=x i (t)-x0(t) Determine the trigger conditions: In the above formula, is the k+1th event triggering time of agent i, inf represents the minimum time to meet the departure conditions; f i represents the trigger weight coefficient of agent i; r1>0, r2>0, is the weight coefficient of the error term; η i (t) is an auxiliary variable; auxiliary variable η i (t) satisfies the initial value condition η i (t)>0; In the above formula, 1>ω i ≥0, m i is the attenuation coefficient of the auxiliary variable, ω i is the error feedback coefficient.

7. The dynamic event-triggered consistency control method for a multi-agent system according to claim 1, characterized in that: Also includes: Step S300: Construct a Lyapunov function including the system state function and auxiliary variables, determine the derivative of the Lyapunov function in the safe communication interval and the DoS attack interval, and obtain the ratio constraint of the attack duration to the total time through inequality transformation and parameter setting.

8. A dynamic event-triggered consistency control system for a multi-agent system, wherein the multi-agent system comprises a plurality of agents, wherein the plurality of agents include a leader and the rest are followers, characterized in that: The system comprises: The intermittent communication control module sets a dual threshold line based on the Lyapunov function, divides the system state function into an activation period region, a holding period region, and an idle period region, and switches the controller operating mode in different period regions. The controller input corresponding to the activation period region is non-zero, the controller input corresponding to the idle period region is zero, and the controller input corresponding to the holding period region remains unchanged. During a DoS attack, the control input is forced to zero. The system state function represents the consistency error between the follower and the leader, and the degree of global consistency of the multi-agent system. The dynamic event trigger control module determines the trigger condition based on the error term and the auxiliary variable, and determines whether to communicate during the activation period based on the trigger condition.

9. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein: When the processor executes the program, the steps of the dynamic event-triggered consistency control method for a multi-agent system as described in any one of claims 1 to 7 are implemented.

10. A non-transitory computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the dynamic event-triggered consistency control method for a multi-agent system as described in any one of claims 1 to 7 are implemented.

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