CN111538239B - Multi-agent navigation following consistency control system and method - Google Patents

Abstract

A multi-agent pilot-following consistency control system and method, aiming at the data transmitted between multi-agents being tampered with by an attacker, a semi-Markov jumping system is applied, and a consistent fuzzy control based on an event-triggered mechanism is proposed The strategy enables the leader and the follower to reach an agreement in the mean square sense, and proposes an event-triggered mechanism, which can reduce unnecessary communication while avoiding the false triggering of redundant data, and increase the data packet rate when the system is disturbed. The sending rate enables the controller to obtain more information about the agent, thereby improving the control performance of the system.

Description

Control system and method for multi-agent pilot-following consistency

technical field

The invention relates to the technical field of multi-agent consistency control, in particular to a multi-agent pilot-following consistency control system and method, and in particular to a multi-agent pilot-following consistency control system and method when subjected to network attacks .

Background technique

In the last two decades, the research on the cooperative consensus of multi-agent systems has attracted the attention of many scholars. There are extensive studies in many engineering application fields. In the actual production application process, because the state equation of the system often has a certain randomness, such systems generally cannot be described by linear time-invariant motion equations, which can be described by semi-Marko Chains describe the transition probability of the system between different modes, so as to accurately describe such industrial systems with random state equations. The consistency problem is one of the most widely studied problems in multi-agent system control. Agent systems, especially systems under the leadership of multi-agents, are often in various complex network environments, and will inevitably suffer malicious attacks, and the execution of system consistency will be destroyed.

SUMMARY OF THE INVENTION

In order to solve the above problems, the present invention provides a multi-agent pilot-following consistency control system and method, which effectively avoids the multi-agent system in the prior art from being maliciously attacked and the execution of system consistency is destroyed. Defects.

In order to overcome the deficiencies in the prior art, the present invention provides a solution of a multi-agent pilot-following consistency control system and method, as follows:

A method for a multi-agent pilot-following-consistent control system, comprising:

Step 1: Establish a pilot-following multi-agent system based on the T-S fuzzy model;

Step 2: Let the state transition rate of the continuous-time semi-Markov process {s(t), t≥0} in the state space satisfy the set condition;

Step 3: Describe the network attack signal suffered by the jth agent when it transmits data to the ith agent, where j and i are both positive integers;

Step 4: Design the event trigger mechanism;

Step 5: Design the consistency control strategy based on T-S fuzzy model.

The establishment of a pilot-following multi-agent system based on the TS fuzzy model includes: using a TS fuzzy model with r fuzzy rules to describe the nonlinear multi-agent system; the fuzzy rules are: IF θ ₁ (t) is W _i1 , and θ ₂ (t) is W _i2 , and…, and θ _q (t) is W _iq , THEN

表示跟随者智能体的状态方程，i＝1，2，...，N，i表示跟随者智能体的编号，N表示跟随者智能体的数量，

表示领航者智能体的状态方程，x_i(t)∈Rⁿ，x₀(t)∈Rⁿ分别表示跟随者和领导者的状态量，u_i(t)表示系统控制输入，W_ig(g＝1，2，…，q)表示模糊集，θ₁(t)，θ₂(t)，…，θ_q(t)表示前提变量，

满足h_m(θ(t))≥0，m＝1，2，3，…，

表示归一化隶属度函数，A_m，B_m表示该方程具有适当维数的系数矩阵。Among them, r, q are positive integers, t represents the time,

represents the state equation of the follower agent, i=1, 2,...,N, i represents the number of the follower agent, N represents the number of follower agents,

represents the state equation of the leader agent, x _i (t)∈R ⁿ , x ₀ (t)∈R ⁿ represent the state quantities of the follower and leader, respectively, _ui (t) represents the system control input, _Wig ( g=1, 2, ..., q) represents the fuzzy set, θ ₁ (t), θ ₂ (t), ..., θ _q (t) represent the premise variables,

Satisfy h _m (θ(t))≥0, m=1, 2, 3,...,

denote the normalized membership function, A _m , B _m denote the coefficient matrix of the equation with appropriate dimensions.

The setting conditions of the step 2 are as follows:

表示当c≠d时，t时刻模态c跳变到t+Δ时刻的模态d，当c＝d时，

in,

It means that when c≠d, mode c at time t jumps to mode d at time t+Δ, when c=d,

The network attack signal in step 3 is described as the following formula:

y _ji (t)=x _j (t)+γ _ji q _j (t)

Among them, when γ _ji = 1, it means that an attack signal is injected into the transmission channel, and when γ _ji = 0, it means that there is no attack signal, and the attack signal function q _j (t) satisfies the following formula:

||q _j (t)|| ₂ ≤||G _j x _j (t)|| ₂

Among them, G _j represents the known constant matrix.

The event triggering mechanism of the step 4 is as follows:

Among them, δ ₁ and δ ₂ are positive scalars, and Φ>0 is a weight matrix;

则如下式所示：definition

Then the formula is as follows:

分别表示第i个智能体的数据发送时刻和当前采样时刻，明显，

是

和

之间的任意值。Among them, Δh=ρlh, ρ∈[0, 1],

respectively represent the data sending time and the current sampling time of the i-th agent, obviously,

Yes

and

any value in between.

The consistency control strategy of the step 5 is shown in the following formula:

满足g_n(θ(t))≥0，n＝1，2，3，…，

in,

Satisfy g _n (θ(t))≥0, n=1, 2, 3,...,

The multi-agent pilot-following-consistency control system includes a processor, and the establishment module, the setting module, the description module, the design module and the control module run on the processor;

The establishment module is used to establish a pilot-following multi-agent system based on the T-S fuzzy model

The setting module is used to make the state transition rate of the continuous-time semi-Markov process {s(t), t≥0} in the state space satisfy the setting condition;

The description module is used to describe the network attack signal suffered by the jth agent when it transmits data to the ith agent, wherein j and i are both positive integers;

The design module is used to design an event trigger mechanism;

The control module is used to design a consistent control strategy based on the T-S fuzzy model.

The beneficial effects of the present invention are:

The invention considers the situation of malicious attack signal injection when transmitting data between multi-agents, based on T-S fuzzy model, adopts semi-Markov chain to describe random topology switching caused by complex network, improves the performance of the system and reduces conservative A new event triggering mechanism is proposed, which can avoid the false triggering of redundant data while reducing unnecessary communication, and improve the data packet sending rate when the system is disturbed, so that the controller can obtain more information about the agent. Thus, the control performance of the system is improved, and the multi-agent system can achieve consistency.

Description of drawings

Fig. 1 shows the network attack structure between agents of the present invention;

Fig. 2 shows three kinds of switching topology structures of the present invention;

Fig. 3 shows the error response one between the pilot followers of the present invention;

Fig. 4 shows the error response 2 between the pilot followers of the present invention;

FIG. 5 shows the network attack signal of the present invention.

Detailed ways

The purpose of the present invention is to propose a consistent fuzzy control strategy based on an event-triggered mechanism by applying a semi-Markov jumping system, so that the leader and the follower can A consensus is reached in the mean square sense, and an event triggering mechanism is proposed, which can avoid the false triggering of redundant data while reducing unnecessary communication, and improve the data packet sending rate when the system is disturbed, so that the controller can obtain more relevant information. The information of the agent can improve the control performance of the system.

The present invention will be further described below with reference to the accompanying drawings and embodiments.

As shown in Figures 1-5, the method for a multi-agent pilot-following consistent control system includes:

Step 1: Establish a pilot-following multi-agent system based on the T-S fuzzy model;

Step 2: Consider that the state transition rate of the continuous-time semi-Markov process {s(t), t≥0} in the state space satisfies the set condition;

Step 3: Describe the network attack signal suffered by the jth agent when it transmits data to the ith agent, where j and i are both positive integers;

Step 4: Design an event trigger mechanism to reduce the network burden and reduce the probability of false triggering of redundant data;

Step 5: Design the consistency control strategy based on T-S fuzzy model.

The establishment of a pilot-following multi-agent system based on the TS fuzzy model includes: using a TS fuzzy model with r fuzzy rules to describe the nonlinear multi-agent system; the fuzzy rules are: IF θ ₁ (t) is W _i1 , and θ ₂ (t) is Wi ₂ , and…, and θ _q (t) is Wi _q , THEN

表示跟随者智能体的状态方程，i＝1，2，...，N，i表示跟随者智能体的编号，N表示跟随者智能体的数量，

表示领航者智能体的状态方程，x_i(t)∈Rⁿ，x₀(t)∈Rⁿ分别表示跟随者和领导者的状态量，u_i(t)表示系统控制输入，W_ig(g＝1，2，…，q)表示模糊集，θ₁(t)，θ₂(t)，…，θ_q(t)表示前提变量，

满足h_m(θ(t))≥0，m＝1，2，3，…，

表示归一化隶属度函数，A_m，B_m表示该方程具有适当维数的系数矩阵。Among them, r, q are positive integers, t represents the time,

represents the state equation of the follower agent, i=1, 2,...,N, i represents the number of the follower agent, N represents the number of follower agents,

represents the state equation of the leader agent, x _i (t)∈R ⁿ , x ₀ (t)∈R ⁿ represent the state quantities of the follower and leader, respectively, _ui (t) represents the system control input, _Wig ( g=1, 2, ..., q) represents the fuzzy set, θ ₁ (t), θ ₂ (t), ..., θ _q (t) represent the premise variables,

Satisfy h _m (θ(t))≥0, m=1, 2, 3,...,

denote the normalized membership function, A _m , B _m denote the coefficient matrix of the equation with appropriate dimensions.

The setting conditions of the step 2 are as follows:

表示当c≠d时，t时刻模态c跳变到t+Δ时刻的模态d，当c＝d时，

in,

It means that when c≠d, mode c at time t jumps to mode d at time t+Δ, when c=d,

The network attack signal in step 3 is described as the following formula:

y _ji (t)=x _j (t)+γ _ji q _j (t)

Among them, when γ _ji = 1, it means that an attack signal is injected into the transmission channel, and when γ _ji = 0, it means that there is no attack signal, and the attack signal function q _j (t) satisfies the following formula:

||q _j (t)|| ₂ ≤||G _j x _j (t)|| ₂

Among them, G _j represents the known constant matrix.

The event triggering mechanism of the step 4 is as follows:

Among them, δ ₁ and δ ₂ are positive scalars, and Φ>0 is a weight matrix;

则如下式所示：definition

Then the formula is as follows:

分别表示第i个智能体的数据发送时刻和当前采样时刻，明显，

是

和

之间的任意值。Among them, Δh=ρlh, ρ∈[0, 1],

respectively represent the data sending time and the current sampling time of the i-th agent, obviously,

Yes

and

any value in between.

The consistency control strategy of the step 5 is shown in the following formula:

满足g_n(θ(t))≥0，n＝1，2，3，…，

in,

Satisfy g _n (θ(t))≥0, n=1, 2, 3,...,

The multi-agent pilot-following consistency control system includes a processor, and the establishment module, the setting module, the description module, the design module and the control module run on the processor;

The establishment module is used to establish a pilot-following multi-agent system based on the T-S fuzzy model

The setting module is used to make the state transition rate of the continuous-time semi-Markov process {s(t), t≥0} in the state space satisfy the setting condition;

The description module is used to describe the network attack signal suffered by the jth agent when it transmits data to the ith agent, wherein j and i are both positive integers;

The design module is used to design an event trigger mechanism, thereby reducing the network burden and reducing the probability of false triggering of redundant data;

The control module is used to design a consistent control strategy based on the T-S fuzzy model.

During specific implementation, the design principle of the method of the present invention is as follows:

1. System modeling, including:

By considering a grid instance, considering the microgrid as a multi-agent system, where each distributed generation system is an agent, the secondary voltage control of the microgrid can be reduced to a consistency tracking problem, that is, all distributed generation systems The power generation system tries to synchronize the terminal voltage amplitude with the preset reference value. Based on the TS fuzzy model, the semi-Markov chain is used to describe the state equation of the system as shown in the following formula (1): TS fuzzy model to describe the nonlinear multi-agent system; the fuzzy rules are: IF θ ₁ (t) is _Wi1 , and θ ₂ (t) is _Wi2 , and..., and θ _q (t) is _Wiq , THEN

表示跟随者智能体的状态方程，i＝1，2，...，N，i表示跟随者智能体的编号，N表示跟随者智能体的数量，

表示领航者智能体的状态方程，x_i(t)∈Rⁿ，x₀(t)∈Rⁿ分别表示跟随者和领导者的状态量，u_i(t)表示系统控制输入，W_ig(g＝1，2，…，q)表示模糊集，θ₁(t)，θ₂(t)，…，θ_q(t)表示前提变量，

满足h_m(θ(t))≥0，m＝1，2，3，…，

表示归一化隶属度函数，A_m，B_m表示该方程具有适当维数的系数矩阵。Among them, r, q are positive integers, t represents the time,

represents the state equation of the follower agent, i=1, 2,...,N, i represents the number of the follower agent, N represents the number of follower agents,

represents the state equation of the leader agent, x _i (t)∈R ⁿ , x ₀ (t)∈R ⁿ represent the state quantities of the follower and leader, respectively, _ui (t) represents the system control input, _Wig ( g=1, 2, ..., q) represents the fuzzy set, θ ₁ (t), θ ₂ (t), ..., θ _q (t) represent the premise variables,

Satisfy h _m (θ(t))≥0, m=1, 2, 3,...,

denote the normalized membership function, A _m , B _m denote the coefficient matrix of the equation with appropriate dimensions.

上取值，其状态转移率满足公式(2)：Consider a continuous-time semi-Markov process {s(t), t ≥ 0} in the state space, in the finite state space

Take the value above, and its state transition rate satisfies formula (2):

表示当c≠d时，t时刻模态c跳变到t+Δ时刻的模态d，当c＝d时，

in,

It means that when c≠d, mode c at time t jumps to mode d at time t+Δ, when c=d,

As shown in Figure 1, injecting network attack signals between agents is shown in formula (3):

y _ji (t)=x _j (t)+γ _ji q _j (t) (3)

Among them, when γ _ji = 1, it means that an attack signal is injected into the transmission channel, and when γ _ji = 0, it means that there is no attack signal, and the attack signal function q _j (t) satisfies the condition of formula (4):

||q _j (t)|| ₂ ≤||G _j x _j (t)|| ₂ (4)

Among them, G _j represents the known constant matrix.

Design an event-triggering mechanism to reduce the network burden and reduce the probability of false triggering of redundant data to ensure that the multi-agent system can achieve consistency:

First define the state of the i-th agent as shown in formula (5):

分别表示第i个智能体的数据发送时刻和当前采样时刻，明显，

是

和

之间的任意值；Among them, Δh=ρlh, ρ∈[0, 1],

respectively represent the data sending time and the current sampling time of the i-th agent, obviously,

Yes

and

any value between;

The event trigger conditions are as follows:

Among them, δ ₁ , δ ₂ are positive scalars, and Φ _c > 0 is the weight matrix;

Note 1.1 When σ _i = 0, the event trigger condition becomes the normal form:

是当前采样数据包和

之间的差值，可以极大的避免由于智能体自身状态抖动引发的数据包误发送；本发明中提出的事件触发机制对状态波动很敏感，当系统受到扰动时数据发送率会提高，使得控制器获得更多智能体的信息，提高了系统的控制性能；In the present invention, the error

is the current sampled packet and

The difference between the two can greatly avoid the mistransmission of data packets caused by the state jitter of the agent itself; the event trigger mechanism proposed in the present invention is very sensitive to state fluctuations, and the data transmission rate will increase when the system is disturbed, so that the The controller obtains more information about the agent, which improves the control performance of the system;

则如下式所示：definition

Then the formula is as follows:

The sending moment of the next data packet of the i-th agent is expressed as formula (8):

in,

The consistency control strategy based on the T-S fuzzy model is given as shown in the following formula (9):

满足g_n(θ(t))≥0，n＝1，2，3，…，

in,

Satisfy g _n (θ(t))≥0, n=1, 2, 3,...,

Note 1.2 Since the system contains mismatched membership functions, an additional condition g _n -k _n h _n ≥ 0 (0<k _n ≤ 1) is given to solve this problem.

The complete fuzzy controller representation is shown in the following formula (10):

For the sake of brevity, h _m and g _n are used to represent h _m (θ(t)) and g _n (θ(t)), respectively.

Combining formula (1) and formula (10), the pilot-following multi-agent system based on the T-S fuzzy model can be rewritten as formula (11):

By using the Kronecker product, the pilot-following multi-agent system based on the T-S fuzzy model can be expressed as formula (12):

in,

H _c =L _c +D _c ,

To simplify the analysis, formula (13) is defined:

in,

2. Proof of stability:

First some definitions and lemmas are given:

x_i(0)，如下标准成立，则多智能体系统(1)使用基于T-S模糊模型的一致性控制策略(9)实现领航跟随一致性。Defined in a semi-Markov switching topology, for any initial condition

x _i (0), if the following criteria are established, the multi-agent system (1) uses the consistency control strategy (9) based on the TS fuzzy model to achieve pilot-following consistency.

lim _t→∞ E||x _i (t)-x ₀ (t)||=0, i=1, 2, ..., N, (14)

Lemma 1 For the scalar τ(t)∈[0,h], the matrix R=R ^T > 0, then it is shown in formula (15):

in,

Lemma 2 For any scalar μ and symmetric matrix R>0, the following inequality (16) holds:

-XR ^-1 X≤-2μX+μ ² R (16)

Q＞0，U＞0，R＞0以及适当维数的矩阵Z_m，Z_n(m，n＝1，2，…，r)使得如下不等式成立，那么多智能体系统在均方意义下实现领航跟随一致性，如公式(17)所示：Theorem 1 For a given scalar h>0, κ _m , k _n , if there is a matrix

Q>0, U>0, R>0, and matrices Z _m , Z _n (m, n=1, 2, . To achieve the pilot-following consistency, as shown in formula (17):

in,

Λ=diag{ _∈1 ,..., _∈N }, Γ ₌ diag{σ1,..., _σN }.

Proof: Construct the Lyapunov functional as shown in Equation (18)

in,

Defining the weak infinitesimal operator, the formula (19) can be obtained:

in,

According to Lemma 1, the formula (20) can be obtained as follows:

Wherein, W ₁ =[I 0 -I 0 0 0], W ₂ =[I 0 -I -2I 0 0].

Rewrite the event trigger mechanism in formula (6) into the following form:

Then as shown in formula (22):

Combining formula (19)-formula (22), the formula (23) can be obtained,

in,

得到公式(24)：In order to solve the situation that the membership function does not match, do the following processing, and introduce the relaxation matrix

Equation (24) is obtained:

Then there is formula (25):

According to Theorem 1, the following inequality (26) can be obtained:

For a sufficiently small scalar v>0, equation (27) can be obtained:

By using the Dynkins formula, formula (28) can be obtained:

Similarly, formula (29) is obtained:

时，有

成立。根据

有

In addition, in

when there is

established. according to

Have

The formula (30) can be obtained:

That is, as shown in formula (31):

因此可知多智能体系统在均方意义下实现领航跟随一致性。that is

Therefore, it can be seen that the multi-agent system achieves the pilot-following consistency in the mean square sense.

3. Carry out controller design:

以及适当维数的矩阵

使得如下不等式成立，那么多智能体系统在均方意义下实现领航跟随一致性如公式(32)所示：Theorem 2 For a given scalar h>0, κ _m , k _n , μ ₁ >0, μ ₂ >0, if there is a matrix

and a matrix of the appropriate dimension

If the following inequality is established, the multi-agent system achieves the pilot-following consistency in the mean square sense, as shown in formula (32):

in,

Proof: Definition

控制器增益兆

Controller Gain Mega

definition

然后对定理1中式(17)左乘Φ右乘Φ^T，针对其中的非线性项，根据引理2，可得公式(33)：

Then multiply Φ on the left by Φ ^T in the formula (17) in Theorem 1, and for the nonlinear term, according to Lemma 2, formula (33) can be obtained:

Therefore, formula (32) is a sufficient condition to guarantee the establishment of formula (17), and the proof is completed.

4. Carry out example simulation:

The coefficient matrix of the distributed generation system model is given as follows:

Set sampling period h=0.1, event trigger parameter

∈ ₁ = 0.01, ∈ ₂ = 0.05, ∈ ₃ = 0.01, ∈ ₄ = 0.015, σ ₁ = 0.07, σ ₂ = 0.013, σ ₃ = 0.02, σ ₄ = 0.01, and the initial state of the agent is

x ₀ (t)=[5-4.5] ^T , x ₁ (t)=[3.98-1.6] ^T , x ₂ (t)=[5.24.6] ^T , x ₃ (t)=[-3.32.7 ] ^T , x ₄ (t)=[2.4-2.8] ^T .

According to Fig. 2, it can be seen that the corresponding pull matrix L _c and the leader adjacency matrix D _c are respectively

网络攻击信号如图5所示。The attack signal coefficient matrix is

The network attack signal is shown in Figure 5.

The established distributed generation system has three modes, and its transition probability is time-varying. The probability matrix is as follows:

以及事件触发机制的权重矩阵Φ_c Using matlab to find the feedback control gain of fuzzy controller

and the weight matrix Φ _c of the event-triggered mechanism

Switch topology a:

Switch topology b:

Switch topology c:

Figures 3 and 4 show the tracking error between the leader and the follower. It can be seen that using the control strategy proposed by the present invention, the error is reduced to 0 in a short time, and it also shows the consistency of the multi-agent achieved.

The multi-agent pilot-following-consistency control system includes a processor, and the establishment module, the setting module, the description module, the design module and the control module run on the processor;

The establishment module is used to establish a pilot-following multi-agent system based on the T-S fuzzy model

The setting module is used to make the state transition rate of the continuous-time semi-Markov process {s(t), t≥0} in the state space satisfy the setting condition;

The description module is used to describe the network attack signal suffered by the jth agent when it transmits data to the ith agent, wherein j and i are both positive integers;

The design module is used to design an event trigger mechanism;

The control module is used to design a consistent control strategy based on the T-S fuzzy model.

The present invention has been described above by way of illustrating the embodiments. Those skilled in the art should understand that the present disclosure is not limited to the above-described embodiments, and various changes can be made without departing from the scope of the present invention. Change and replace.

Claims (5)

1. a control system of multi-agent piloting and following consistency, is characterized in that, comprises: Step 1: Establish a pilot-following multi-agent system based on the T-S fuzzy model; Step 2: Let the state transition rate of the continuous-time semi-Markov process {s(t), t≥0} in the state space satisfy the set condition; Step 3: Describe the network attack signal suffered by the jth agent when it transmits data to the ith agent, where j and i are both positive integers; Step 4: Design the event trigger mechanism, The event triggering mechanism of the step 4 is as follows:

Among them, δ1, δ2 are positive scalars, and Φ>0 is the weight matrix; definition

Then it is shown in the following formula,

Among them, Δh=ρlh, ρ∈[0, 1],

respectively represent the data sending time and the current sampling time of the i-th agent. Obviously,

Yes

and

any value between; Step 5: Design a consistency control strategy based on the T-S fuzzy model, and the consistency control strategy in step 5 is shown in the following formula:

in,

Satisfy

. 2. The multi-agent pilot-following-consistency control system according to claim 1, wherein the establishing the pilot-following multi-agent system based on the TS fuzzy model comprises: using a TS fuzzy with r fuzzy rules model to describe nonlinear multi-agent systems; the fuzzy rules are: IF θ ₁ (t) is _Wi1 , and θ ₂ (t) is _Wi2 , and..., and θ _q (t) is _Wiq , THEN

Among them, r, q are positive integers, t represents the time,

Represents the state equation of the follower agent, i=1, 2,...,N, i represents the number of the follower agent, N represents the number of follower agents, represents the state equation of the leader agent, x _i (t)∈R ⁿ , x ₀ (t)∈R ⁿ represent the state quantities of the follower and leader respectively, u _i (t) represents the system control input,

represents a fuzzy set,

represents the premise variable,

Satisfy

represents the normalized membership function,

Represents a matrix of coefficients of the appropriate dimension for this equation. 3. The multi-agent pilot-following-consistency control system according to claim 1, wherein the setting condition of the step 2 is as follows:

where Δ>0,

, πcd≤0 means that when c≠d, the mode c at time t jumps to the mode d at time t+Δ, when c=d,

. 4. The multi-agent pilot-following-consistency control system according to claim 1, wherein the network attack signal of the step 3 is described as the following formula:

Among them, y _ji (t) represents the signal obtained by the agent i from the neighbor node j, and x _j (t) represents the state quantity of the agent j,

When it means that an attack signal is injected into the transmission channel,

Indicates that there is no attack signal, and the attack signal function q _j (t) satisfies the following formula:

Among them, G _j represents the known constant matrix. 5. A multi-agent pilot-following-consistency control system, characterized in that it comprises a processor, and a building module, a setting module, a description module, a design module and a control module run on the processor; The establishment module is used to establish a pilot-following multi-agent system based on the T-S fuzzy model The setting module is used to make the state transition rate of the continuous-time semi-Markov process {s(t), t≥0} in the state space satisfy the setting condition; The description module is used to describe the network attack signal suffered by the jth agent when it transmits data to the ith agent, wherein j and i are both positive integers; The design module is used to design an event trigger mechanism, and the event trigger mechanism is as follows:

Among them, δ1, δ2 are positive scalars, and Φ>0 is the weight matrix; definition

Then it is shown in the following formula,

Among them, Δh=ρlh, ρ∈[0, 1],

respectively represent the data sending time and the current sampling time of the i-th agent, obviously,

Yes

and

any value between; The control module is used to design a consistency control strategy based on the T-S fuzzy model, and the consistency control strategy is shown in the following formula:

in,

Satisfy

.

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