An event-triggered iterative learning consensus control method for multi-agent systems under FDI attacks

Abstract

The present invention discloses an event-triggered iterative learning consistency control method for a multi-agent system under FDI attack, which belongs to the field of intelligent control. The technical scheme proposed by the present invention is as follows: an autoregressive model of the output sequence is established, and the model parameters are trained and predicted in the first m iterations; after m iterations, an attack detection and compensation mechanism is added; based on the topological structure information, the consistency error ε is obtained by the state transfer iterative dynamic linearization technology. k,j (t+1) and the multi-lag input vector u k,j (t); design parameter estimator and iterative learning control law; establish event trigger mechanism model in order to reduce network communication resources. The present invention discloses an event triggered iterative learning consistency control method for a multi-agent system under FDI attack, which adds corresponding compensation schemes to the system after the attack to reduce the impact of the attack and ensure good control performance of the system.

Description

Technical Field

[0001] The present invention belongs to the field of intelligent control technology, and more specifically, relates to an event-triggered iterative learning consistency control method for a multi-agent system under FDI attack. Background Art

[0002] At present, the problem of multi-agent consistency control has received extensive attention in practical applications. A multi-agent system is a network cluster composed of multiple intelligent individuals with communication, sensing, execution capabilities, and independent decision-making. Compared with a single agent, a multi-agent system can achieve effective interaction, collaboration, and competition in various complex environments through the synergy between multiple agents.

[0003] Existing technologies mainly focus on the consistency control performance of the system in the time direction, and cannot guarantee complete tracking within a limited time. Therefore, studying the complete tracking problem of multi-agent systems in the iteration direction also has significant practical application value. At the same time, the network openness of multi-agent systems makes them vulnerable to malicious attacks. Among them, the false data injection (FDI) attack, which is one of the main forms of attack, destroys the integrity of the data by injecting false data into the channel, thereby causing system instability. Unlike traditional noise interference, the false data injection attack can act on multiple links such as the output channel and network transmission channel of the multi-agent system, and is highly deceptive. Therefore, taking the false data injection attack as a typical factor for research can overcome a series of similar external interferences at the same time.

[0004] On the other hand, network congestion and resource constraints are also a key issue in the study of consistency control of multi-agent systems. Event-triggered control has a good effect in saving communication and computing resources and can reduce unnecessary waste of communication resources. Therefore, for multi-agent systems under false data injection attacks, how to design a set of safe and effective attack detection and compensation control schemes so that the system can still achieve the established goals after suffering a network attack is of great significance to improving the reliability and security of multi-agent systems. Summary of the invention

[0005] The present invention discloses an event-triggered iterative learning consistency control method for a multi-agent system under FDI attack. The technical problem to be solved is to compensate for the impact of FDI attack, reduce the number of control input updates, reduce the use of system resources, and ensure the consistency of the multi-agent system. The method disclosed in the present invention patent does not rely on any form of system model information, and is a control scheme design method based only on data.

[0006] The purpose of the present invention is achieved through the following technical solutions:

[0007] The present invention discloses an event-triggered iterative learning consistency control method for a multi-agent system under FDI attack, the method comprising the following steps:

[0008] S1. Establish an output prediction model for a multi-agent system;

[0009] S2, after m iterations, establish FDI attack detection and compensation mechanism;

[0010] S3. Based on the topological structure information, a linear parameterized model of the agent consistency error is constructed;

[0011] S4, construct a distributed iterative learning controller for multi-agent systems;

[0012] S5. Construct event triggering conditions for multi-agent systems;

[0013] S6. Construct the overall control scheme of the system;

[0014] Furthermore, the output prediction model of the multi-agent system described in step 1 is:

[0015] Step 1.1: Use the output values ​​of the previous time in the same batch to build an autoregressive model and obtain the output of the system at time t+1 in the absence of an attack:

[0016]

[0017] in,

[0018] k represents the number of iterations;

[0019] j∈{1,2,...,N} represents the number of the agent;

[0020] t∈{0,1,…,T} represents discrete time, T is a positive integer;

[0021] s=1,…,n p , represents the coefficient of the s-th output value of agent j at the k-th iteration forward, n p is the appropriate order;

[0022] y k,j (t)∈R represents the system output of the jth agent at time t in the kth iteration;

[0023] represents the predicted output of the jth agent at the kth iteration t+1;

[0024]

[0025] Step 1.2: Design parameter update law for unknown parameters θ in (1)k,j (t) To estimate:

[0026]

[0027] Among them, δ represents a positive weight coefficient; ||·|| represents the vector bi-norm operator; represents the agent j's response to θ at time t k,j (t); α∈(0,1] is the step size factor, which makes Algorithm (2) more general.

[0028] Furthermore, the FDI attack detection and compensation mechanism described in step 2 is:

[0029] Step 2.1: Output based on prediction Design an injection attack detection solution:

[0030]

[0031] in, It represents the measured output data after the attack, h k,j (t+1) represents the injected false data; Indicates the false injection data h k,j (t+1) estimate; if Indicates that the agent has been attacked; attack threshold Usually obtained through experiments or expert experience.

[0032] Step 2.2, design output compensation scheme:

[0033]

[0034] in, Represents the compensation output of the j-th agent at the k-th iteration t+1.

[0035] Furthermore, the linear parameterized model of the consistency error of the multi-agent system based on the topological structure information described in step 3 is:

[0036] Step 3.1: Construct the consistency error ε between agent j and its adjacent agents k,j (t+1) is:

[0037]

[0038] in,

[0039] y k,j (t+1) represents the system output at time t+1;

[0040] y d(t+1) represents the expected output at time t+1, i.e., the output of the virtual leader;

[0041] N j represents the set of all neighboring agents of the jth agent;

[0042] a j,i The adjacency matrix A constructed for the topological structure of the multi-agent system is (a j,i )∈R N×N elements, and a j,j =0; a j,i =1 means that agents j and i are adjacent agents, otherwise, a j,i =0;

[0043] a j,0 represents the communication status between agent j and virtual leader 0; a j,0 =1 means that the agent can directly receive information from leader 0, otherwise, a j,0 =0;

[0044] Step 3.2: Design the ideal nonlinear dynamic relationship between consistency error and input variables:

[0045] ε k,j (t+1)=f j (ε k,j (t),…,ε k,j (tn ε ),u k,j (t),…,u k,j (tn u )) (6)

[0046] Among them, u k,j (t)∈R represents the system input; f j (·) represents the nonlinear function of agent j; n ε and n u Respectively represent the system consistency error and the order of output, which are two unknown positive integers;

[0047] Assume that the initial state ε of all iterations is k,j (0) The same, that is: And the nonlinear function f j (·) satisfies the global Lipschitz condition, that is,

[0048] f j (x j,1 ,u j,1 )-f j (x j,2 ,u j,2 )|≤L x |x j,1 -xj,2 |+L u |u j,1 -u j,2

[0049] Among them, 0<L x <∞ and 0<L u <∞ are two Lipschitz constants;

[0050] Furthermore, combined with the state transfer iterative dynamic linearization method, the consistency error ε is obtained k,j (t+1) and the multi-lag input vector u k,j (t) is a linear parameterized model:

[0051]

[0052] And for all times t, represents the equivalent linearization parameter vector, u k,j (t)=[u k,j (0),…,u k,j (t)] T ∈R t+1 , Δ represents the difference operator, that is, Δu k,j (t) = u k,j (t)-u k-1,j (t), Δε k,j (t+1)=ε k,j (t+1)-ε k-1,j (t+1); unless otherwise specified, Δ hereafter means the difference operator.

[0053] Furthermore, the distributed iterative learning controller of the multi-agent system in step 4 is:

[0054] Step 4.1: Design parameter update law for unknown parameters in linear data model (7) Make an estimate:

[0055]

[0056] Among them, ε k,j (t+1) represents the consistency error at time t+1; u k-1,j (t)=[u k-1,j (0),…,u k-1,j (t)] T ∈R t+1 represents a multi-lag input vector; Represents the unknown linearization parameters ; η represents the step size factor, and satisfies 0<η<2; μ represents a positive weight coefficient; ||·|| represents the vector bi-norm operator;

[0057] Step 4.2: Design the reset algorithm of the parameter update law:

[0058] if or

[0059] in, yes The initial value of ν is a small positive number. The reset algorithm (9) makes the parameter update law (8) have stronger tracking ability.

[0060] Step 4.3: Design the iterative learning control law as:

[0061]

[0062] in, yes The tth element of ; λ>0 is the weight factor; 0<ρ≤1 is the step factor.

[0063] Furthermore, the event triggering condition of the multi-agent system in step 5 is:

[0064] Establish the following event trigger mechanism:

[0065] q k,j (t+1)=|m k,j (t+1)|-κ|ε k,j (t+1)| (11)

[0066] in,

[0067] ε k,j (t+1) represents the consistency error at time t+1;

[0068] Indicates the trigger error,

[0069] β and κ∈(0,1) are adjustable coefficients and event trigger thresholds;

[0070] Indicates the trigger error of the input part;

[0071] Indicates that the most recent event at time t triggers an iteration The input value at time ;

[0072] Indicates that the most recent event at time t+1 triggered an iteration The consistency error value when ;

[0073] The choice of triggering iteration depends on in represents the lth triggering iteration of agent j, represents the event-triggered iteration set of the j-th agent;

[0074] Furthermore, the overall control scheme of the multi-agent system in step 6 is:

[0075]

[0076] if or

[0077] in,

[0078] represents the consistency error after compensation;

[0079] The definitions of other symbols remain the same as those in the previous steps.

[0080] The characteristics and beneficial effects of the present invention are:

[0081] 1. The data-driven attack detection and compensation method proposed in the present invention can predict the output at the next moment when there is no attack by using only output information to further detect the attack. It is a data-based prediction method that can effectively resist various external interferences including false data injection attacks and various environmental factors with similar characteristics.

[0082] 2. The present invention can achieve perfect tracking in the iteration direction for the multi-agent system, while effectively reducing the communication and computing consumption of the system. The design and analysis of the controller are also completed under a data-driven framework, in which no model information of the system is used, and only the measured input and output data are used.

[0083] After reading the specific embodiments of the present invention in conjunction with the accompanying drawings, other features and advantages of the present invention will become more clear. BRIEF DESCRIPTION OF THE DRAWINGS

[0084] Figure 1 This is a flow chart of an event-triggered iterative learning consistency control method for a multi-agent system under FDI attack proposed by the present invention;

[0085] Figure 2 This is a principle block diagram of an event-triggered iterative learning consistency control method for a multi-agent system under FDI attack proposed by the present invention;

[0086] Figure 3 is the communication topology diagram between intelligent agents;

[0087] Figure 4Energy diagram for injecting attacks into the channel between Agent 3 and Agent 2;

[0088] Figure 5 Tracking performance graph output by the agent at different iterations;

[0089] Figure 6 It is a convergence performance diagram of the event-triggered iterative learning optimization method proposed in the present invention;

[0090] Figure 7 This is a triggering actual diagram of the event-triggered iterative learning optimization method proposed in the present invention. DETAILED DESCRIPTION

[0091] In order to better illustrate the purpose and advantages of the present invention, the invention is further described in detail below in conjunction with embodiments and corresponding drawings.

[0092] See also Figure 1 , Figure 2 As shown, the present embodiment discloses a set point updating method for model-free adaptive control, comprising the following steps:

[0093] S1. Establish an output prediction model for a multi-agent system;

[0094] S2, after m iterations, establish FDI attack detection and compensation mechanism;

[0095] S3. Based on the topological structure information, a linear parameterized model of the agent consistency error is constructed;

[0096] S4, construct a distributed iterative learning controller for multi-agent systems;

[0097] S5. Construct event triggering conditions for multi-agent systems;

[0098] S6. Build an overall control solution for the system.

[0099] In the first m iterations, we first establish the output prediction model of the multi-agent system and adjust the parameters θ of the model. k,j (t) training; after completing m iterations, the model is applied to the actual system that may be attacked; based on the output prediction of the model, attack detection and compensation mechanisms are combined to mitigate the impact of the attack; then, this method is integrated into the control system to achieve the established control objectives; the following is a detailed design process:

[0100] Consider a discrete-time multi-agent system where y k,j (t)∈R represents the system output, u k,j(t)∈R represents the system input; k represents the number of iterations, j∈{1,2,...,N} represents the number of the agent, t∈{0,1,...,T} represents the discrete time, and T is a positive integer;

[0101] The output values ​​of the previous time in the same batch are used to construct an autoregressive model to obtain the output of the system at time t+1 in the absence of an attack:

[0102]

[0103] in,

[0104] s=1,…,n p , represents the coefficient of the s-th output value of agent j at the k-th iteration forward, n p is the appropriate order;

[0105] represents the predicted output of the jth agent at the kth iteration t+1;

[0106]

[0107] Design parameter update law for unknown coefficients θ in the prediction output model k,j (t) is estimated, considering the following criterion function:

[0108]

[0109] Among them, δ represents a positive weight coefficient; |·| represents the absolute value operator; ||·|| represents the vector bi-norm operator;

[0110] Through the optimization method, the parameter estimation algorithm is obtained from the criterion function (a2):

[0111]

[0112] in, represents the agent j's response to θ at time t k,j (t); α∈(0,1] is the step size factor, which makes algorithm (a3) ​​more general.

[0113] With the development of wireless network technology, signal transmission has gradually gotten rid of its dependence on wired communication. Multi-agent systems achieve complex interactive tasks through network communication. However, the openness of the system also exposes it to the risk of attack. The following will discuss the design of attack detection and compensation.

[0114] When the multi-agent system is attacked by injection, the output of the jth agent is expressed as: in It represents the measured output data after the attack, h k,j (t+1) represents the injected false data.

[0115] According to the prediction output Design an injection attack detection solution:

[0116]

[0117] in, Indicates the false injection data h k,j (t+1) estimate; if Indicates that the agent has been attacked; attack threshold It is usually determined through experimentation or expert experience.

[0118] Further, consider the following compensation scheme for the output:

[0119]

[0120] in, Represents the compensation output of the j-th agent at the k-th iteration t+1.

[0121] After achieving detection and compensation, these mechanisms are further integrated into the control system for designing parameter estimation algorithms and control laws.

[0122] Define the matrix A = (a j,i )∈R N×N is the adjacency matrix of the multi-agent system topology, where a j,i is an element of the matrix, and a j,j = 0; if agents j and i are adjacent agents, then a j,i =1; otherwise a j,i = 0; Based on the topological structure information, the consistency error ε between agent j and its neighboring agents k,j (t+1) is:

[0123]

[0124] in,

[0125] y d (t+1) represents the expected output at time t+1, i.e., the output of the virtual leader;

[0126] N j represents the set of all neighboring agents of the jth agent;

[0127] a j,0 represents the communication status between agent j and virtual leader 0; a j,0=1 means that the agent can directly receive information from leader 0, otherwise, a j,0 =0;

[0128] Theoretically, the consistency error ε of the jth agent at time t+1 is k,j The consistency error ε between (t+1) and the previous time k,j (t),…,ε k,j (tn ε ) and control input u k,j (t),…,u k,j (tn u ) has a certain inevitable relationship; therefore, the consistency error ε at the previous moment k,j (t),…,ε k,j (tn ε ) and control input u k,j (t),…,u k,j (tn u ) as the independent variable, and design the nonlinear dynamic relationship between the ideal consistency error and the input variable:

[0129] ε k,j (t+1)=f j (ε k,j (t),…,ε k,j (tn ε ),u k,j (t),…,u k,j (tn u )) (a7)

[0130] in,

[0131] f j () represents the nonlinear function of agent j;

[0132] n ε and n u Respectively represent the system consistency error and the order of output, which are two unknown positive integers;

[0133] The above nonlinear dynamic association relationship (a7) needs to meet the following assumptions:

[0134] Assumption 1: The initial state ε of all iterations k,j (0) The same, that is:

[0135] Assumption 2: Nonlinear function f j (·) satisfies the global Lipschitz condition, that is,

[0136] |f j (ε j,1 ,u j,1)-f j (ε j,2 ,u j,2 )|≤L ε |ε j,1 -ε j,2 |+L u |u j,1 -u j,2 |

[0137] Among them, 0<L ε <∞ and 0<L u <∞ are two Lipschitz constants;

[0138] The consistency error ε is obtained by the state transfer iterative dynamic linearization method. k,j (t+1) and the multi-lag input vector u k,j (t) is a linear parameterized model:

[0139]

[0140] And for all times t, represents the equivalent linearization parameter vector, u k,j (t)=[u k,j (0),…,u k,j (t)] T ∈R t+1 , Δ represents the difference operator, that is, Δu k,j (t) = u k,j (t)-u k-1,j (t), Δε k,j (t+1)=ε k,j (t+1)-ε k-1,j (t+1); unless otherwise specified, Δ hereafter means the difference operator.

[0141] Furthermore, the parameter update law is designed to update the unknown parameters in the linear data model. To make an estimate, consider the following criterion function:

[0142]

[0143] Among them, μ represents a positive weight coefficient;

[0144] By using the optimization method, the unknown parameters are obtained from the criterion function (a9) The estimation law is:

[0145]

[0146] in,

[0147] Represents the unknown linearization parameters estimates;

[0148] η represents the step size factor and satisfies 0<η<2;

[0149] Reset algorithm for designing parameter update law:

[0150] if or

[0151] in, yes The initial value of ν is a small positive number. The reset algorithm (a11) makes the parameter update law (a10) have stronger tracking ability.

[0152] Based on the consistency error ε k-1,j (t+1), construct the iterative learning control law as:

[0153]

[0154] in, yes The tth element of ; λ>0 is the weight factor; 0<ρ≤1 is the step factor.

[0155] In order to reduce unnecessary transmission and save network communication resources, the following event trigger mechanism is established:

[0156] q k,j (t+1)=|m k,j (t+1)|-κ|ε k,j (t+1)| (a13)

[0157] in,

[0158] Indicates the trigger error,

[0159] β and κ∈(0,1) are adjustable coefficients and event trigger thresholds;

[0160] Indicates the trigger error of the input part;

[0161] Indicates that the most recent event at time t triggers iteration k l j The input value at time ;

[0162] Indicates that the most recent event at time t+1 triggered iteration k l j The consistency error value when ;

[0163] The choice of triggering iteration depends on in represents the lth triggering iteration of agent j, represents the event-triggered iteration set of the j-th agent;

[0164] Combining the attack compensation, parameter estimation algorithm, control law and event triggering mechanism designed above, the FDI attack detection and event-triggered iterative learning consistency control method of the multi-agent system is summarized as follows:

[0165]

[0166] if or

[0167] in, represents the consistency error after compensation; the definitions of other symbols remain unchanged with those in the previous steps.

[0168] Considering that the multi-agent system satisfies assumptions 1-2 and the controller parameters are adjusted within the allowable range, the proposed FDI attack detection and event-triggered iterative learning consistency control method can ensure that: the estimated value of the time-varying parameter is bounded; the consistency error ε k,j (t+1) is bounded; thus the tracking error of the system e k,j (t+1) is also bounded.

[0169] In order to verify the correctness of the method of the present invention, the following simulations were performed on the method of the present invention:

[0170] like Figure 3 As shown in Figure 2, consider a heterogeneous multi-agent system with four follower agents. The dynamic model is as follows:

[0171]

[0172] The expected trajectory is:

[0173] y d (t)=2sin(t / 75)+cos(t / 20),t∈[0,200] (a15)

[0174] The energy function of the injection attack is:

[0175] h k,j (t) = o k (t)(1+0.5sin(2tπ / 1000))(a16)

[0176] Among them, k(t) = 3rand, such as Figure 4 The attacks are shown as a function of time and iterations, with all channels being attacked with probability 0.4.

[0177] The controller parameters are set as λ=0.025, μ=2, η=0.6, ρ=0.032, δ=0.008, ν=10 -5 , α=0.05, β=1, m=10, n p =3, κ=0.03, u 1,j (t)=[0,…,0] T , ε k,j (0) = 0, y k,j (0)=0,j=1,2,3,4;Apply the proposed FDI attack detection and event-triggered iterative learning consistency control method, Figure 5 is the tracking performance of the agent output at different iterations; the convergence of the tracking error is as follows Figure 6 As shown, the vertical axis represents the average tracking error (ATE), which is defined as Figure 7 To trigger the live graph, the vertical axis represents the number of updates of the control input. Figure 5-Figure 7 It can be seen that when the model information is unknown and only the input / output data can be obtained, the proposed FDI attack detection and event-triggered iterative learning consistency control method can obtain good control performance, reduce the impact of the attack, and reduce the number of control input updates.

[0178] The specific description above further illustrates the purpose, technical solutions and beneficial effects of the invention in detail. It should be understood that the embodiments are only used to explain the invention and are not used to limit the scope of protection of the invention. Any modifications, equivalent replacements, improvements, etc. under the same principles and concepts as the invention should be included in the scope of protection of the invention.

Claims

1. An event-triggered iterative learning consistency control method for a multi-agent system under FDI attack, characterized in that: The following steps are involved: Step S1: In the first m iterations, use the output values ​​of the previous time in the same batch to build an autoregressive model, obtain the output of the system at time t+1 without attack, and design the parameter update law to update the unknown parameters θ of the output k,j (t) Estimation is performed to establish an output prediction model for the multi-agent system; Step S2: after m iterations, establish an FDI attack detection and compensation mechanism, and use the output information of the output prediction model to predict the output at the next moment when there is no attack to further detect the attack; Step S21: Output of the output prediction model Design an injection attack detection solution: in, It represents the measured output data after the attack, h k,j (t+1) represents the injected false data; Indicates the false injection data h k,j (t+1) estimate; let the attack threshold be if Indicates that the agent has been attacked; Step S22: design output compensation scheme: in, represents the compensation output of the j-th agent at the k-th iteration t+1; Step S3: Based on the topological structure information, construct the consistency error ε between agent j and its adjacent agents k,j (t+1), and design the ideal nonlinear dynamic relationship between the consistency error and the input variable, and obtain the consistency error ε through the state transfer iterative dynamic linearization method k,j (t+1) and the multi-lag input vector u k,j The linear parameterized model between (t): And for all times t, represents the equivalent linearization parameter vector, u k,j (t)=[u k,j (0),…,u k,j (t)] T ∈R t+1 , △ represents the difference operator, that is, △u k,j (t) = u k,j (t)-u k-1,j (t), ∆ε k,j (t+1)=ε k,j (t+1)-ε k-1,j (t+1); Step S4: Design parameter update law for the parameters in the linear parameterized model (7) Make an estimate And based on the consistency error ε k-1,j (t+1), design a distributed iterative learning controller for multi-agent systems; Step S5, constructing the event triggering condition of the multi-agent system by coordinating the relationship between the trigger error and the consistency error; Step S6: Determine the overall control scheme of the multi-agent system by combining the FDI attack detection and compensation mechanism, the distributed iterative learning controller and the event triggering conditions.

2. The event-triggered iterative learning consistency control method for a multi-agent system under FDI attack according to claim 1, characterized in that: The output prediction model of the multi-agent system established in step S1 is: in, k represents the number of iterations; j∈{1,2,...,N} represents the number of the agent; t∈{0,1,...,T} represents discrete time, T is a positive integer; represents the predicted output of the jth agent at the kth iteration t+1; n p is a positive integer; y k,j (t)∈R represents the system output of the jth agent at time t in the kth iteration; δ represents a positive weight coefficient; represents the two-norm operator of a vector; represents the agent j's response to θ at time t k,j (t) estimate; represents the coefficient of the output value of agent j at the sth moment before the kth iteration, α∈(0,1] is the step size factor.

3. The event-triggered iterative learning consistency control method for a multi-agent system under FDI attack according to claim 1, characterized in that: In step S3: Consistency error ε k,j (t+1) is expressed as: in, y k,j (t+1) represents the system output at time t+1; y d (t+1) represents the expected output at time t+1; N j represents the set of all neighboring agents of the jth agent; a j,i The adjacency matrix A constructed for the topological structure of the multi-agent system is (a j,i )∈R N×N elements, and a j,j =0; a j,i =1 means that agents j and i are adjacent agents, otherwise, a j,i =0; a j,0 represents the communication status between agent j and virtual leader 0; a j,0 =1 means that the agent can directly receive information from leader 0, otherwise, a j,0 =0; The nonlinear dynamic relationship between the consistency error and the input variable is expressed as: ε k,j (t+1)=f j (ε k,j (t),…,ε k,j (t-n ε ),u k,j (t),…,u k,j (t-n u ))(6) Among them, u k,j (t)∈R represents the system input; f j (·) represents the nonlinear function of agent j; n ε and n u Respectively represent the system consistency error and the order of output, which are two unknown positive integers; Assume that the initial state ε of all iterations is k,j (0) is the same, that is: ε k+1,j (0) = ε k,j (0), And the nonlinear function f j (·) satisfies the global Lipschitz condition, that is, Among them, 0 <L ε <∞ and 0 <L u <∞ are two Lipschitz constants.

4. The event-triggered iterative learning consistency control method for a multi-agent system under FDI attack according to claim 1, characterized in that: The step S4 mainly includes the following steps: Step S41: unknown parameters The estimate of is expressed as: in, ε k,j (t+1) represents the consistency error at time t+1; u k-1,j (t)=[u k-1,j (0),…,u k-1,j (t)] T ∈R t+1 represents a multi-lag input vector; η represents the step size factor and satisfies 0<η<2; μ represents a positive weight coefficient; ||·|| represents the vector bi-norm operator; Step S42: Reset algorithm of design parameter update law: in, yes The initial value of ; ν is a very small positive number; Step S43: the designed distributed iterative learning controller is: in, yes The tth element of ; λ>0 is the weight factor; 0<ρ≤1 is the step factor.

5. The event-triggered iterative learning consistency control method for a multi-agent system under FDI attack according to claim 1, characterized in that: The event triggering condition of step S5 is: q k,j (t+1)=|m k,j (t+1)|-κ|ε k,j (t+1)| (11) in, ε k,j (t+1) represents the consistency error at time t+1; Indicates the trigger error, β and κ∈(0,1) are adjustable coefficients and event triggering thresholds; Indicates the trigger error of the input part; Indicates that the most recent event at time t triggers an iteration The input value at time ; Indicates that the most recent event at time t+1 triggered an iteration The consistency error value when ; The choice of triggering iteration depends on in represents the lth triggering iteration of agent j, represents the event-triggered iteration set of the j-th agent.

6. The event-triggered iterative learning consistency control method for a multi-agent system under FDI attack according to claim 1, characterized in that: The overall control scheme constructed in step S6 is: if or in, Represents the consistency error after compensation.

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