CN111538239A - Multi-agent navigation following consistency control system and method - Google Patents

Multi-agent navigation following consistency control system and method Download PDF

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CN111538239A
CN111538239A CN202010233200.7A CN202010233200A CN111538239A CN 111538239 A CN111538239 A CN 111538239A CN 202010233200 A CN202010233200 A CN 202010233200A CN 111538239 A CN111538239 A CN 111538239A
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CN111538239B (en
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颜开红
傅涛
穆秀峰
胡燕
王力
聂征
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Bozhi Safety Technology Co ltd
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Abstract

A multi-agent navigation following consistency control system and a method apply a half Markov jump system aiming at the tampering of data transmitted among multi-agents by attackers, and provide a consistency fuzzy control strategy based on an event trigger mechanism, so that the navigator and the follower can reach consistency in mean square sense, and provide an event trigger mechanism, thereby reducing unnecessary communication, avoiding false triggering of redundant data, improving the data packet sending rate when the system is disturbed, and enabling a controller to obtain more information about the agents, thereby improving the control performance of the system.

Description

Multi-agent navigation following consistency control system and method
Technical Field
The invention relates to the technical field of control of consistency of multiple intelligent agents, in particular to a control system and a control method of consistency of multi-intelligent-agent navigation following, and particularly relates to a control system and a control method of consistency of multi-intelligent-agent navigation following when the multi-intelligent-agent navigation following is subjected to network attack.
Background
In the last two decades, research on the cooperative consistency of multi-agent systems has received the attention of many scholars. In the process of actual production and application, because the state equation of the system often has certain randomness, the system can not be generally described by a linear time-invariant motion equation, and the hopping transition probability of the system among different modes can be described by using a half-Markov chain, so that the industrial system with randomness of the state equation can be accurately described.
Disclosure of Invention
In order to solve the problems, the invention provides a control system and a control method for multi-agent navigation following consistency, which effectively avoid the defect that the multi-agent system in the prior art is subjected to malicious attack so that the execution of the system consistency is damaged.
In order to overcome the defects in the prior art, the invention provides a solution of a control system and a method for multi-agent navigation following consistency, which comprises the following steps:
a method of a multi-agent navigation following consistency control system, comprising:
step 1: establishing a navigation following multi-agent system based on a T-S fuzzy model;
step 2: the state transition rate of the continuous time semi-Markov process { s (t) > 0} in the state space meets the set condition;
and step 3: describing network attack signals suffered by a jth intelligent agent when the jth intelligent agent transmits data to an ith intelligent agent, wherein j and i are positive integers;
and 4, step 4: designing an event trigger mechanism;
and 5: and designing a consistency control strategy based on the T-S fuzzy model.
The establishing of the piloting following multi-agent based on the T-S fuzzy modelThe system comprises: describing the nonlinear multi-agent system by using a T-S fuzzy model with r fuzzy rules; the fuzzy rule is as follows: IF theta1(t) is Wi1，and θ2(t)is Wi2，and…，and θq(t) is Wiq，THEN
Figure BDA0002430063280000021
Wherein r and q are positive integers, t represents time,
Figure BDA0002430063280000026
an equation of state representing the follower agent, i 1, 2, N, i representing the number of follower agents, N representing the number of follower agents,
Figure BDA0002430063280000027
equation of state, x, representing the navigator agenti(t)∈Rn，x0(t)∈RnState quantities, u, representing followers and leaders, respectivelyi(t) represents a system control input, Wig(g ═ 1, 2, …, q) denotes a fuzzy set, θ1(t)，θ2(t)，…，θq(t) represents a precondition variable,
Figure BDA0002430063280000022
satisfy hm(θ(t))≥0，m＝1，2，3，…，
Figure BDA0002430063280000023
Representing a normalized membership function, Am，BmIndicating that the equation has a matrix of coefficients of appropriate dimensions.
The setting conditions of the step 2 are as follows:
Figure BDA0002430063280000024
wherein the content of the first and second substances,
Figure BDA0002430063280000025
indicating that when c ≠ d, the mode c jumps to the mode d at time t + Δ, and when c ≠ d,
Figure BDA0002430063280000031
the network attack signal of step 3 is described as follows:
yji(t)＝xj(t)+γjiqj(t)
wherein, γjiWhen 1 indicates that an attack signal is injected into the transmission channel, γjiWhen 0, it means that there is no attack signal, and the attack signal function qj(t) satisfies the following formula:
||qj(t)||2≤||Gjxj(t)||2
wherein G isjRepresenting a matrix of known constants.
The event trigger mechanism of step 4 is as follows:
Figure BDA0002430063280000032
wherein the content of the first and second substances,1，2is a positive scalar quantity, phi > 0 is a weight matrix;
definition of
Figure BDA0002430063280000033
Then the following equation is shown:
Figure BDA0002430063280000034
Figure BDA00024300632800000315
Figure BDA0002430063280000035
Figure BDA0002430063280000036
where Δ h is ρ lh, ρ ∈ [0, 1 ═ h [ ]]，
Figure BDA0002430063280000037
Respectively representing the data transmission time and the current sampling time of the ith agent, obviously,
Figure BDA0002430063280000038
is that
Figure BDA00024300632800000314
And
Figure BDA00024300632800000310
any value in between.
The consistency control strategy of step 5 is shown as follows:
Figure BDA00024300632800000311
wherein the content of the first and second substances,
Figure BDA00024300632800000312
satisfies gn(θ(t))≥0，n＝1，2，3，…，
Figure BDA00024300632800000313
The multi-agent navigation following consistency control system comprises a processor, wherein an establishing module, a setting module, a describing module, a designing module and a control module run on the processor;
the establishing module is used for establishing a T-S fuzzy model-based pilot following multi-agent system
The setting module is used for enabling the state transition rate of the continuous time semi-Markov process { s (t) > 0} in the state space to meet the setting condition;
the description module is used for describing a network attack signal suffered by a jth intelligent agent when the jth intelligent agent transmits data to an ith intelligent agent, wherein j and i are positive integers;
the design module is used for designing an event trigger mechanism;
the control module is used for designing a consistency control strategy based on the T-S fuzzy model.
The invention has the beneficial effects that:
the invention considers the condition that malicious attack signals are injected when data are transmitted among the intelligent agents, adopts a half Markov chain to describe random topology switching caused by a complex network based on a T-S fuzzy model, improves the performance of the system, reduces the conservatism, provides a new event triggering mechanism, can avoid false triggering of redundant data while reducing unnecessary communication, improves the sending rate of data packets when the system is disturbed, and ensures that a controller obtains more information about the intelligent agents, thereby improving the control performance of the system and ensuring that the multi-intelligent agent system can be consistent.
Drawings
FIG. 1 illustrates the architecture of a cyber attack between agents of the present invention;
FIG. 2 illustrates three switching topologies of the present invention;
FIG. 3 shows the error response one between pilot followers of the present invention;
FIG. 4 shows the error response between pilot followers of the present invention two;
fig. 5 shows a network attack signal of the present invention.
Detailed Description
The invention aims to provide a consistency fuzzy control strategy based on an event trigger mechanism aiming at the tampering of data transmitted among a plurality of intelligent agents by an attacker by applying a half Markov jump system, so that a pilot and a follower can be consistent in the mean square sense, and the event trigger mechanism is provided, thereby reducing unnecessary communication, avoiding the false triggering of redundant data, improving the sending rate of data packets when the system is disturbed, and enabling a controller to obtain more information about the intelligent agents, thereby improving the control performance of the system.
The invention will be further described with reference to the following figures and examples.
1-5, a method for a multi-agent piloting a control system for consistency, comprising:
step 1: establishing a navigation following multi-agent system based on a T-S fuzzy model;
step 2: considering that the state transition rate of the continuous time semi-Markov process { s (t) ≧ 0} in the state space meets the set condition;
and step 3: describing network attack signals suffered by a jth intelligent agent when the jth intelligent agent transmits data to an ith intelligent agent, wherein j and i are positive integers;
and 4, step 4: an event trigger mechanism is designed, so that the network load is reduced, and the probability of false triggering of redundant data is reduced;
and 5: and designing a consistency control strategy based on the T-S fuzzy model.
The method for establishing the piloting following multi-agent system based on the T-S fuzzy model comprises the following steps: describing the nonlinear multi-agent system by using a T-S fuzzy model with r fuzzy rules; the fuzzy rule is as follows: IF theta1(t) is Wi1，and θ2(t)is Wi2，and…，and θq(t) is Wiq，THEN
Figure BDA0002430063280000051
Wherein r and q are positive integers, t represents time,
Figure BDA0002430063280000052
an equation of state representing the follower agent, i 1, 2, N, i representing the number of follower agents, N representing the number of follower agents,
Figure BDA0002430063280000053
equation of state, x, representing the navigator agenti(t)∈Rn，x0(t)∈RnState quantities, u, representing followers and leaders, respectivelyi(t) represents a system control input, Wig(g ═ 1, 2, …, q) denotes a fuzzy set, θ1(t)，θ2(t)，…，θq(t) represents a precondition variable,
Figure BDA0002430063280000061
satisfy hm(θ(t))≥0，m＝1，2，3，…，
Figure BDA0002430063280000062
Representing a normalized membership function, Am，BmIndicating that the equation has a matrix of coefficients of appropriate dimensions.
The setting conditions of the step 2 are as follows:
Figure BDA0002430063280000063
wherein the content of the first and second substances,
Figure BDA0002430063280000064
indicating that when c ≠ d, the mode c jumps to the mode d at time t + Δ, and when c ≠ d,
Figure BDA00024300632800000613
the network attack signal of step 3 is described as follows:
yji(t)＝xj(t)+γjiqj(t)
wherein, γjiWhen 1 indicates that an attack signal is injected into the transmission channel, γjiWhen 0, it means that there is no attack signal, and the attack signal function qj(t) satisfies the following formula:
||qj(t)||2≤||Gjxj(t)||2
wherein G isjRepresenting a matrix of known constants.
The event trigger mechanism of step 4 is as follows:
Figure BDA0002430063280000065
wherein the content of the first and second substances,1，2is a positive scalar quantity, phi > 0 is a weight matrix;
definition of
Figure BDA0002430063280000066
Then the following equation is shown:
Figure BDA0002430063280000067
Figure BDA00024300632800000614
Figure BDA0002430063280000068
Figure BDA0002430063280000069
where Δ h is ρ lh, ρ ∈ [0, 1 ═ h [ ]]，
Figure BDA00024300632800000610
Respectively representing the data transmission time and the current sampling time of the ith agent, obviously,
Figure BDA00024300632800000611
is that
Figure BDA00024300632800000612
And
Figure BDA0002430063280000071
any value in between.
The consistency control strategy of step 5 is shown as follows:
Figure BDA0002430063280000072
wherein the content of the first and second substances,
Figure BDA0002430063280000073
satisfies gn(θ(t))≥0，n＝1，2，3，…，
Figure BDA0002430063280000074
The multi-agent navigation following consistency control system comprises a processor, wherein an establishing module, a setting module, a describing module, a designing module and a control module run on the processor;
the establishing module is used for establishing a T-S fuzzy model-based pilot following multi-agent system
The setting module is used for enabling the state transition rate of the continuous time semi-Markov process { s (t) > 0} in the state space to meet the setting condition;
the description module is used for describing a network attack signal suffered by a jth intelligent agent when the jth intelligent agent transmits data to an ith intelligent agent, wherein j and i are positive integers;
the design module is used for designing an event trigger mechanism so as to reduce network burden and reduce the probability of false triggering of redundant data;
the control module is used for designing a consistency control strategy based on the T-S fuzzy model.
In specific implementation, the design principle of the method is as follows:
1. system modeling, comprising:
considering a power grid example, regarding a microgrid as a multi-agent system, wherein each distributed power generation system is an agent, the secondary voltage control of the microgrid can be resolved into a consistency tracking problem, that is, all distributed power generation systems attempt to synchronize terminal voltage amplitude values thereof with a preset reference value, and based on a T-S fuzzy model, a half Markov chain is adopted to describe a system state equation as shown in the following formula (1): describing the nonlinear multi-agent system by using a T-S fuzzy model with r fuzzy rules; the fuzzy rule is as follows: IF theta1(t) is Wi1，and θ2(t) is Wi2，and…，andθq(t) is Wiq，THEN
Figure BDA0002430063280000081
Wherein r and q are positive integers, t represents time,
Figure BDA0002430063280000088
an equation of state representing the follower agent, i 1, 2, N, i representing the number of follower agents, N representing the number of follower agents,
Figure BDA0002430063280000089
equation of state, x, representing the navigator agenti(t)∈Rn，x0(t)∈RnState quantities, u, representing followers and leaders, respectivelyi(t) represents a system control input, Wig(g ═ 1, 2, …, q) denotes a fuzzy set, θ1(t)，θ2(t)，…，θq(t) represents a precondition variable,
Figure BDA0002430063280000082
satisfy hm(θ(t))≥0，m＝1，2，3，…，
Figure BDA0002430063280000083
Representing a normalized membership function, Am，BmIndicating that the equation has a matrix of coefficients of appropriate dimensions.
Considering continuous time semi-Markov process { s (t), t ≧ 0} in state space, in finite state space
Figure BDA0002430063280000086
Taking the value, wherein the state transition rate of the value meets the formula (2):
Figure BDA0002430063280000084
wherein the content of the first and second substances,
Figure BDA0002430063280000085
indicating that the mode c jumps to time t + Δ when c ≠ dAnd the mode d, when c ═ d,
Figure BDA0002430063280000087
as shown in fig. 1, injecting a cyber attack signal between agents is shown in equation (3):
yji(t)＝xj(t)+γjiqj(t) (3)
wherein, γjiWhen 1 indicates that an attack signal is injected into the transmission channel, γjiWhen 0, it means that there is no attack signal, and the attack signal function qj(t) satisfies the condition of formula (4):
||qj(t)||2≤||Gjxj(t)||2(4)
wherein G isjRepresenting a matrix of known constants.
An event trigger mechanism is designed, network burden is reduced, the probability of false triggering of redundant data is reduced, and the multi-agent system can be ensured to be consistent:
first, the state of the ith agent is defined as shown in equation (5):
Figure BDA0002430063280000091
where Δ h is ρ lh, ρ ∈ [0, 1 ═ h [ ]]，
Figure BDA0002430063280000092
Respectively representing the data transmission time and the current sampling time of the ith agent, obviously,
Figure BDA0002430063280000093
is that
Figure BDA0002430063280000094
And
Figure BDA0002430063280000095
any value in between;
the event trigger conditions are as follows:
Figure BDA0002430063280000096
wherein the content of the first and second substances,1，2is a positive scalar quantity of phicMore than 0 is a weight matrix;
note 1.1 when σiWhen 0, the event trigger condition changes to the conventional form:
Figure BDA0002430063280000097
in the present invention, the error
Figure BDA0002430063280000098
Is the current sample packet and
Figure BDA0002430063280000099
the difference between the two can greatly avoid the error sending of the data packet caused by the self state jitter of the intelligent agent; the event triggering mechanism provided by the invention is sensitive to state fluctuation, and the data sending rate is improved when the system is disturbed, so that the controller can obtain more information of the intelligent agent, and the control performance of the system is improved;
definition of
Figure BDA00024300632800000910
Then the following equation is shown:
Figure BDA00024300632800000911
Figure BDA00024300632800000915
Figure BDA00024300632800000912
Figure BDA00024300632800000913
the next packet transmission time of the ith agent is expressed as shown in equation (8):
Figure BDA00024300632800000914
wherein the content of the first and second substances,
Figure BDA00024300632800001011
a consistency control strategy based on the T-S fuzzy model is given as shown in the following formula (9):
Figure BDA0002430063280000103
wherein the content of the first and second substances,
Figure BDA0002430063280000104
satisfies gn(θ(t))≥0，n＝1，2，3，…，
Figure BDA0002430063280000105
Note 1.2 that the inclusion of mismatched membership functions in the system gives an additional condition gn-knhn≥0(0＜kn1) to solve this problem.
The complete fuzzy controller is expressed by the following equation (10):
Figure BDA0002430063280000106
for the sake of brevity, h is usedm，gnRespectively represent hm(θ(t))，gn(θ(t))。
In conjunction with equation (1) and equation (10), the T-S fuzzy model based navigation following multi-agent system can be rewritten as shown in equation (11):
Figure BDA0002430063280000107
by using kronecker product, the T-S fuzzy model based pilot following multi-agent system can be expressed as shown in equation (12):
Figure BDA0002430063280000108
wherein the content of the first and second substances,
Figure BDA0002430063280000109
Hc＝Lc+Dc，
Figure BDA00024300632800001010
Figure BDA0002430063280000118
to simplify the analysis, equation (13) is defined:
Figure BDA0002430063280000112
wherein the content of the first and second substances,
Figure BDA0002430063280000113
Figure BDA0002430063280000114
2. carrying out stability verification:
some definitions and lemmas are given first:
definition under semi-Markov switching topology for any initial condition
Figure BDA0002430063280000119
xi(0) If the following criteria hold, then the multi-agent system (1) implements the collar using a consistency control strategy (9) based on the T-S fuzzy modelAnd (4) flight following consistency.
limt→∞E||xi(t)-x0(t)||＝0，i＝1，2，…，N， (14)
Theorem 1 for scalar τ (t) ∈ [0, h]The matrix R ═ RT> 0, as shown in equation (15):
Figure BDA0002430063280000115
wherein the content of the first and second substances,
Figure BDA0002430063280000116
lemma 2 holds for an arbitrary scalar μ and a symmetric matrix R > 0 as follows inequality (16):
-XR-1X≤-2μX+μ2R (16)
theorem 1 for a given scalar h > 0, κm，knIf there is a matrix
Figure BDA0002430063280000117
Q > 0, U > 0, R > 0 and matrix Z of appropriate dimensionsm，Zn(m, n ═ 1, 2, …, r) such that the following inequality holds, then the multi-agent system achieves navigation following consistency in the mean square sense, as shown in equation (17):
Figure BDA0002430063280000121
wherein the content of the first and second substances,
Figure BDA0002430063280000122
Figure BDA0002430063280000123
Figure BDA0002430063280000124
Figure BDA0002430063280000125
Figure BDA0002430063280000126
Figure BDA0002430063280000127
Figure BDA0002430063280000128
Figure BDA0002430063280000129
Λ＝diag{∈1，…，∈N}，＝diag{σ1，…，σN}。
and (3) proving that: construction of Lyapunov functional shown in formula (18)
Figure BDA00024300632800001210
Wherein the content of the first and second substances,
Figure BDA00024300632800001211
Figure BDA00024300632800001212
Figure BDA00024300632800001213
defining a weak infinitesimal operator, as shown in equation (19):
Figure BDA00024300632800001214
wherein the content of the first and second substances,
Figure BDA0002430063280000131
Figure BDA0002430063280000132
Figure BDA0002430063280000133
according to the theorem 1, the formula (20) can be shown:
Figure BDA0002430063280000134
wherein, W1＝[I 0 -I 0 0 0]，W2＝[I 0 -I -2I 0 0]。
The event triggering mechanism in equation (6) is rewritten as follows:
Figure BDA0002430063280000135
then as shown in equation (22):
Figure BDA0002430063280000136
as shown in formula (23) obtained by combining formula (19) to formula (22),
Figure BDA0002430063280000137
wherein the content of the first and second substances,
Figure BDA0002430063280000138
to solve the problem of unmatched membership function, the following processing is carried out, and a relaxation matrix is introduced
Figure BDA0002430063280000139
Equation (24) is obtained:
Figure BDA00024300632800001310
then there is equation (25):
Figure BDA00024300632800001311
according to theorem 1, the following inequality (26) is obtained:
Figure BDA0002430063280000141
for a sufficiently small scalar v > 0, equation (27) can be derived:
Figure BDA0002430063280000142
by using the Dynkins formula, equation (28) can be derived:
Figure BDA0002430063280000143
similarly, formula (29) is obtained:
Figure BDA0002430063280000144
in addition, in
Figure BDA00024300632800001413
When there is
Figure BDA0002430063280000145
This is true. According to
Figure BDA00024300632800001412
Is provided with
Figure BDA0002430063280000146
The equation (30) can be obtained:
Figure BDA0002430063280000147
namely, as shown in formula (31):
Figure BDA0002430063280000148
that is, it is
Figure BDA0002430063280000149
Therefore, the multi-agent system can realize navigation following consistency in the mean square sense.
3. Designing a controller:
theorem 2 for a given scalar h > 0, κm，kn，μ1＞0，μ2> 0, if a matrix is present
Figure BDA00024300632800001410
And a matrix of appropriate dimensions
Figure BDA00024300632800001411
So that the following inequality holds, then the multi-agent system realizes the navigation following consistency in the mean square sense as shown in formula (32):
Figure BDA0002430063280000151
wherein the content of the first and second substances,
Figure BDA0002430063280000152
Figure BDA0002430063280000153
Figure BDA0002430063280000154
Figure BDA0002430063280000155
Figure BDA0002430063280000156
Figure BDA0002430063280000157
Figure BDA0002430063280000158
Figure BDA0002430063280000159
Figure BDA00024300632800001510
Figure BDA00024300632800001511
Figure BDA00024300632800001512
and (3) proving that: definition of
Figure BDA00024300632800001516
Controller gain megaly
Figure BDA00024300632800001514
Definition of
Figure BDA00024300632800001515
Then, left-multiplying phi and right-multiplying phi for Chinese (17) in theorem 1TFor the non-linear terms, according to theorem 2, equation (33) can be derived:
Figure BDA0002430063280000161
therefore, the formula (32) is a sufficient condition for ensuring that the formula (17) is satisfied, and the confirmation is completed.
4. Performing example simulation:
the coefficient matrix of the distributed power generation system model is given as follows:
Figure BDA0002430063280000162
setting the sampling period h to 0.1, and triggering the parameters by the event
∈1＝0.01，∈2＝0.05，∈3＝0.01，∈4＝0.015，σ1＝0.07，σ2＝0.013，σ3＝0.02，σ40.01, the initial state of the agent is
x0(t)＝[5-4.5]T，x1(t)＝[3.98-1.6]T，x2(t)＝[5.24.6]T，x3(t)＝[-3.32.7]T，x4(t)＝[2.4-2.8]T。
From FIG. 2, the corresponding pull matrix L can be seencAnd a pilot adjacency matrix DcAre respectively as
Figure BDA0002430063280000163
Figure BDA0002430063280000164
The coefficient matrix of the attack signal is
Figure BDA0002430063280000165
The network attack signal is shown in fig. 5.
The established distributed power generation system has three modes, the transition probability of the system is time-varying, and the probability matrix is as follows:
Figure BDA0002430063280000166
using matlab to solve feedback control gain of fuzzy controller
Figure BDA0002430063280000167
And the weight matrix phi of the event trigger mechanismc
Switching topology a:
Figure BDA0002430063280000171
switching topology b:
Figure BDA0002430063280000172
switching topology c:
Figure BDA0002430063280000173
fig. 3 and 4 show the tracking error between the navigator and the follower, and it can be seen that the error is reduced to 0 in a short time by using the control strategy proposed by the present invention, and it also illustrates that the multi-agent consistency is achieved.
The multi-agent navigation following consistency control system comprises a processor, wherein an establishing module, a setting module, a describing module, a designing module and a control module run on the processor;
the establishing module is used for establishing a T-S fuzzy model-based pilot following multi-agent system
The setting module is used for enabling the state transition rate of the continuous time semi-Markov process { s (t) > 0} in the state space to meet the setting condition;
the description module is used for describing a network attack signal suffered by a jth intelligent agent when the jth intelligent agent transmits data to an ith intelligent agent, wherein j and i are positive integers;
the design module is used for designing an event trigger mechanism;
the control module is used for designing a consistency control strategy based on the T-S fuzzy model.
The present invention has been described in an illustrative manner by the embodiments, and it should be understood by those skilled in the art that the present disclosure is not limited to the embodiments described above, but is capable of various changes, modifications and substitutions without departing from the scope of the present invention.

Claims (7)

1. A multi-agent navigation following consistency control system, comprising:
step 1: establishing a navigation following multi-agent system based on a T-S fuzzy model;
step 2: the state transition rate of the continuous time semi-Markov process { s (t) > 0} in the state space meets the set condition;
and step 3: describing network attack signals suffered by a jth intelligent agent when the jth intelligent agent transmits data to an ith intelligent agent, wherein j and i are positive integers;
and 4, step 4: designing an event trigger mechanism;
and 5: and designing a consistency control strategy based on the T-S fuzzy model.
2. The multi-agent pilot-following-consistency control system according to claim 1, wherein the establishing a T-S fuzzy model-based pilot-following multi-agent system comprises: describing the nonlinear multi-agent system by using a T-S fuzzy model with r fuzzy rules; the fuzzy rule is as follows: IF theta1(t)is Wi1，and θ2(t)is Wi2，and...，andθq(t)is Wiq，THEN
Figure FDA0002430063270000011
Wherein r and q are positive integers, t represents time,
Figure FDA0002430063270000012
an equation of state representing the follower agent, i 1, 2, N, i representing the number of the follower agent, N representing the follower agentThe number of the agents is such that,
Figure FDA0002430063270000013
equation of state, x, representing the navigator agenti(t)∈Rn，x0(t)∈RnState quantities, u, representing followers and leaders, respectivelyi(t) represents a system control input, Wig(g ═ 1, 2, …, q) denotes a fuzzy set, θ1(t)，θ2(t)，…，θq(t) represents a precondition variable,
Figure FDA0002430063270000014
satisfy hm(θ(t))≥0，m＝1，2，3，…，
Figure FDA0002430063270000015
Figure FDA0002430063270000016
Representing a normalized membership function, Am，BmIndicating that the equation has a matrix of coefficients of appropriate dimensions.
3. The multi-agent piloting follow-consistency control system as claimed in claim 1, wherein the setting conditions of step 2 are as follows:
Figure FDA0002430063270000021
wherein, the delta is more than 0,
Figure FDA0002430063270000022
πcd≦ 0 indicates that when c ≠ d, time t the mode c jumps to the mode d at time t + Δ, when c ≠ d,
Figure FDA0002430063270000023
4. the multi-agent pilot following consistency control system according to claim 1, wherein the cyber attack signal of step 3 is described by the following equation:
yji(t)＝xj(t)+γjiqj(t)
wherein, yji(t) represents the signal, x, acquired by agent i from neighbor node jj(t) represents the state quantity of agent j, γjiWhen 1 indicates that an attack signal is injected into the transmission channel, γjiWhen 0, it means that there is no attack signal, and the attack signal function qj(t) satisfies the following formula:
||qj(t)||2≤||Gjxj(t)||2
wherein G isjRepresenting a matrix of known constants.
5. The multi-agent piloting follow-up control system as claimed in claim 1, wherein the event trigger mechanism of step 4 is as follows:
Figure FDA0002430063270000024
wherein the content of the first and second substances,1，2is a positive scalar quantity, phi > 0 is a weight matrix;
definition of
Figure FDA0002430063270000025
Then the following equation is shown:
Figure FDA0002430063270000026
Figure FDA0002430063270000027
Figure FDA0002430063270000028
Figure FDA0002430063270000029
where Δ h is ρ lh, ρ ∈ [0, 1 ═ h [ ]]，
Figure FDA00024300632700000210
Figure FDA00024300632700000211
Respectively representing the data transmission time and the current sampling time of the ith agent, obviously,
Figure FDA00024300632700000212
is that
Figure FDA00024300632700000213
And
Figure FDA0002430063270000031
any value in between.
6. The multi-agent piloting follow-up control system of claim 1, wherein the consistency control strategy of step 5 is represented by the following equation:
Figure FDA0002430063270000032
wherein the content of the first and second substances,
Figure FDA0002430063270000033
satisfies gn(θ(t))≥0，n＝1，2，3，…，
Figure FDA0002430063270000034
7. A multi-agent navigation following consistency control system is characterized by comprising a processor, wherein an establishing module, a setting module, a description module, a design module and a control module run on the processor;
the establishing module is used for establishing a T-S fuzzy model-based pilot following multi-agent system
The setting module is used for enabling the state transition rate of the continuous time semi-Markov process { s (t) > 0} in the state space to meet the setting condition;
the description module is used for describing a network attack signal suffered by a jth intelligent agent when the jth intelligent agent transmits data to an ith intelligent agent, wherein j and i are positive integers;
the design module is used for designing an event trigger mechanism;
the control module is used for designing a consistency control strategy based on the T-S fuzzy model.
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