CN113741198A - T-S fuzzy system self-adaptive event trigger state estimation method under random network attack - Google Patents

T-S fuzzy system self-adaptive event trigger state estimation method under random network attack Download PDF

Info

Publication number
CN113741198A
CN113741198A CN202111085232.8A CN202111085232A CN113741198A CN 113741198 A CN113741198 A CN 113741198A CN 202111085232 A CN202111085232 A CN 202111085232A CN 113741198 A CN113741198 A CN 113741198A
Authority
CN
China
Prior art keywords
attack
matrix
model
estimation error
state estimation
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Withdrawn
Application number
CN202111085232.8A
Other languages
Chinese (zh)
Inventor
曹杰
刘金良
钱妍
申冬琴
马丽娜
罗婕
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Yunjing Business Intelligence Research Institute Nanjing Co ltd
Original Assignee
Yunjing Business Intelligence Research Institute Nanjing Co ltd
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Yunjing Business Intelligence Research Institute Nanjing Co ltd filed Critical Yunjing Business Intelligence Research Institute Nanjing Co ltd
Priority to CN202111085232.8A priority Critical patent/CN113741198A/en
Publication of CN113741198A publication Critical patent/CN113741198A/en
Withdrawn legal-status Critical Current

Links

Images

Classifications

    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
    • G05B13/02—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric
    • G05B13/04—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators
    • G05B13/042—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators in which a parameter or coefficient is automatically adjusted to optimise the performance

Landscapes

  • Engineering & Computer Science (AREA)
  • Health & Medical Sciences (AREA)
  • Artificial Intelligence (AREA)
  • Computer Vision & Pattern Recognition (AREA)
  • Evolutionary Computation (AREA)
  • Medical Informatics (AREA)
  • Software Systems (AREA)
  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Automation & Control Theory (AREA)
  • Data Exchanges In Wide-Area Networks (AREA)

Abstract

The invention discloses a method for estimating self-adaptive event triggering state of a T-S fuzzy system under random network attack, which comprises the steps of firstly establishing a T-S fuzzy system model and a system state estimator model, introducing a self-adaptive event triggering mechanism and obtaining real measurement output after self-adaptive event triggering; then, based on the influence on the transmission data under replay attack, deception attack and DoS attack, a network attack model is established; obtaining a system state estimation error model based on the self-adaptive event triggering mechanism and the network attack model; secondly, acquiring a progressive stability sufficiency condition of a system state estimation error model based on a Lyapunov stability theory, and finally solving a linear matrix inequality to acquire a state estimator gain; the invention adopts a self-adaptive triggering mechanism to improve the resource utilization rate, considers the influence of network attack on the transmission data and can ensure the stability of the designed system.

Description

T-S fuzzy system self-adaptive event trigger state estimation method under random network attack
Technical Field
The invention relates to the technical field of random network control, in particular to a T-S fuzzy system adaptive event trigger state estimation method under random network attack.
Background
With the continuous development of the network society, the importance of network communication resources becomes more and more precious, and how to reasonably and effectively utilize the network resources without losing the transmission performance of the system is a problem worthy of deep research. If the system can operate smoothly, a large amount of unnecessary sampling data enters the network, thereby wasting limited network resources. In the existing event triggering scheme, data is allowed to be sent only when the triggering condition is met, so that the transmission frequency of sampled data is reduced, and network resources are effectively saved.
Meanwhile, with the rapid development of information technology and the widespread use of networks, network security has become one of the pressing problems that everyone must face. People are increasingly under network attacks and network security issues have extended to the corners of the network. One of the important issues is the network security problem, which causes the system performance to be greatly degraded. Generally, network attacks are classified into spoofing attacks, denial of service (DoS) attacks, and replay attacks. DoS attacks can send large amounts of spam or interference information to disrupt the service system. The replay attacker sends the data packet which is received by the target host to achieve the purpose of deceiving the system. Spoofing attacks reduce system performance by pretending to be a trusted party to replace normal data. Therefore, it is also a challenging problem to research the adaptive event-triggered state estimation method under multiple network attacks based on the T-S fuzzy system.
Disclosure of Invention
The purpose of the invention is as follows: aiming at the problems in the background technology, the invention provides a method for estimating the self-adaptive event triggering state of the T-S fuzzy system under random network attack.
The technical scheme is as follows: in order to achieve the purpose, the invention adopts the technical scheme that:
a T-S fuzzy system self-adaptive event trigger state estimation method under random network attack comprises the following steps:
step S1, firstly, establishing a T-S fuzzy system model and a system state estimator model; in particular, the amount of the solvent to be used,
the T-S fuzzy system model is as follows:
Figure BDA0003265388130000021
wherein x (t) e RmRepresents a state variable, y (t) e RmRepresenting the measurement output, z (t) ε RmRepresenting the signal to be estimated, ω (t) representing the external disturbance, Ai,Bi,Ci,LiIs a matrix of constants, and the matrix of constants,
Figure BDA00032653881300000218
representing a normalized membership function;
the system state estimator model is built as follows:
Figure BDA0003265388130000022
wherein
Figure BDA0003265388130000023
Represents an estimate of the system state x (t),
Figure BDA0003265388130000024
represents an estimate of the signal to be estimated z (t),
Figure BDA0003265388130000025
representing the true input of the system state estimator, KjRepresents the expected gain of the system state estimator, Aj,Kj,Cj,LjIs a matrix of constants, and the matrix of constants,
Figure BDA0003265388130000026
representing a normalized membership function;
step S2, introducing a self-adaptive event trigger mechanism;
under the self-adaptive event trigger mechanism, the transmission data of the next transmission moment
Figure BDA0003265388130000027
Expressed as:
Figure BDA0003265388130000028
wherein
Figure BDA0003265388130000029
Representing the data of the transmission at the current time,
Figure BDA00032653881300000210
which represents the sampling period of the sample,
Figure BDA00032653881300000211
wherein
Figure BDA00032653881300000212
A maximum allowable number representing a continuous packet loss; (ii) a Ω is a positive definite weight matrix; and is provided with
Figure BDA00032653881300000213
Figure BDA00032653881300000214
Indicated as the most recently transmitted data,
Figure BDA00032653881300000215
representing the current sample data;
Figure BDA00032653881300000216
is full ofVector of adaptive law, iota>0：
Figure BDA00032653881300000217
To separate time intervals
Figure BDA0003265388130000031
Is divided into
Figure BDA0003265388130000032
δ＝tk+1-tk-1; is provided with
Figure BDA0003265388130000033
And tau (t) is more than or equal to 0 and less than or equal to tauMThen the true measurement output after the adaptive event trigger
Figure BDA0003265388130000034
The following were used:
Figure BDA0003265388130000035
wherein the conditions for adaptive event triggering are:
Figure BDA0003265388130000036
step S3, establishing a network attack model based on the influence of replay attack, deception attack and DoS attack on the transmission data;
step S4, obtaining a system state estimation error model based on the self-adaptive event trigger mechanism and the network attack model;
step S5, acquiring the progressive and stable sufficiency condition of the state estimation error model of the established system;
and step S6, solving the linear matrix inequality to obtain the estimator gain of the state estimation error model of the established system.
Further, the step of building a network attack model in step S3 includes:
step S3.1, replay attack is considered;
the data transmitted under a replay attack is represented as follows:
Figure BDA0003265388130000037
θ (t) represents a bernoulli variable and is used for indicating whether a replay attack occurs or not, wherein θ (t) ═ 1 indicates that the replay attack occurs, and θ (t) ═ 0 indicates that the replay attack does not occur;
Figure BDA0003265388130000038
representing the transmitted data after passing through the adaptive event triggering mechanism; y (t-r (t)) represents the injected past signal r (t) recorded by the attacker at the time t, and represents that the replay data is the data transmitted in the first r (t) seconds.
Step S3.2, considering the deception attack;
the data transmitted under a spoofing attack is represented as follows:
y2(t)＝β(t)f(y(t-d(t))+(1-β(t))y1(t)
β (t) represents a bernoulli variable for indicating whether a spoofing attack occurs, where β (t) ═ 1 indicates that a spoofing attack occurs, and β (t) ═ 0 indicates that a spoofing attack does not occur; f (y (t-d (t))) is a non-linear function representing the impact of a spoofing attack;
s3.3, DoS attack is considered;
the data transmitted under DoS attack is represented as follows:
Figure BDA0003265388130000041
wherein a isnRepresents the start time, l, of the nth entry of the DoS attack into the sleep statenIndicating the end time of the nth sleep state.
Further, the step S4 of obtaining the state estimation error model of the established system specifically includes:
the estimation error is defined as follows:
Figure BDA0003265388130000042
Figure BDA0003265388130000043
the system state estimation error model is then expressed as:
Figure BDA0003265388130000044
let xi (t) be [ x ]T(t) eT(t)]TThe system state estimation error model is rewritten as:
Figure BDA0003265388130000045
wherein the content of the first and second substances,
Figure BDA0003265388130000046
Figure BDA0003265388130000047
H＝[I 0]。
further, in the step S5, a sufficiency condition for gradual stabilization of the system state estimation error model is obtained through the Lyapunov stability theory, and specifically,
given scalar quantity
Figure BDA0003265388130000051
τM,rM,dM,σ,
Figure BDA0003265388130000052
Matrix KjF, when there is a forward scalar κ1,κ2,
Figure BDA00032653881300000519
Matrix omega>0,P1>0,P2>0,
Figure BDA0003265388130000053
m＝1,2,3；UiFor a matrix of several dimensions, for any i, j ═ 1,2, …, r, the following inequality is satisfied, and the system state estimation error model becomes progressively stable:
Figure BDA0003265388130000054
Figure BDA0003265388130000055
Figure BDA0003265388130000056
Figure BDA0003265388130000057
further, in step S6, solving the linear matrix inequality to obtain the estimator gain of the state estimation error model of the established system, specifically,
given scalar quantity
Figure BDA0003265388130000058
τM,rM,dM,σ,
Figure BDA0003265388130000059
Matrix F, YjWhen there is a forward scalar κ1,κ2,
Figure BDA00032653881300000520
∈1,∈2,∈3Matrix of
Figure BDA00032653881300000510
Figure BDA00032653881300000511
P1＝diag{P11,P12}>0,P2＝diag{P21,P22}>0,
Figure BDA00032653881300000512
Figure BDA00032653881300000513
m＝1,2,3；UiIs a matrix of several dimensions; for any i, j ═ 1,2, …, r, when the following inequality is satisfied:
Figure BDA00032653881300000514
Figure BDA00032653881300000515
Figure BDA00032653881300000516
Figure BDA00032653881300000517
the system state estimation error model is asymptotically stable; the expected gains of the estimator for the state estimation error model of the system established at this time are as follows:
Figure BDA00032653881300000518
has the advantages that:
the invention provides a method for estimating a self-adaptive event trigger state of a T-S fuzzy system under random network attack, which aims at designing a state estimator for estimating the system state of the T-S fuzzy system with a self-adaptive trigger mechanism and random network attack. And a self-adaptive triggering mechanism is adopted to improve the resource utilization rate and consider the influence of network attack on the transmission data. By utilizing the Lyapunov stability theory, a sufficient condition capable of ensuring the stability of the designed system is obtained. In addition, the estimator expected gain is obtained by solving a set of linear matrix inequalities.
Drawings
FIG. 1 is a flow chart of the design of a T-S fuzzy system adaptive event-triggered state estimation model provided by the present invention;
FIG. 2 is a diagram illustrating system estimation errors in an embodiment of the present invention;
FIG. 3 shows the system states x (t) and their errors in the embodiment of the present invention
Figure BDA0003265388130000061
A graph;
FIG. 4 is a diagram illustrating the estimated value of the signal z (t) to be estimated according to an embodiment of the present invention
Figure BDA0003265388130000062
Graph is shown.
Detailed Description
The present invention will be further described with reference to the accompanying drawings.
The flow chart of the design of the T-S fuzzy system adaptive event triggered state estimator under random network attack provided by the invention is shown in figure 1. In particular, the amount of the solvent to be used,
step S1, firstly, a T-S fuzzy system model and a system state estimator model are established. In particular, the amount of the solvent to be used,
the T-S fuzzy system model is as follows:
Figure BDA0003265388130000063
wherein x (t) e RmRepresents a state variable, y (t) e RmRepresenting the measurement output, z (t) ε RmRepresenting the signal to be estimated, ω (t) representing the external disturbance, Ai,Bi,Ci,LiIs a matrix of constants, and the matrix of constants,
Figure BDA0003265388130000064
representing a normalized membership function;
the system state estimator model is built as follows:
Figure BDA0003265388130000065
wherein
Figure BDA0003265388130000066
Represents an estimate of the system state x (t),
Figure BDA0003265388130000067
represents an estimate of the signal to be estimated z (t),
Figure BDA0003265388130000071
representing the true input of the system state estimator, KjRepresents the expected gain of the system state estimator, Aj,Kj,Cj,LjIs a matrix of constants, and the matrix of constants,
Figure BDA0003265388130000072
representing a normalized membership function;
and step S2, introducing an adaptive event trigger mechanism.
Under the self-adaptive event trigger mechanism, the transmission data of the next transmission moment
Figure BDA0003265388130000073
Expressed as:
Figure BDA0003265388130000074
wherein in
Figure BDA0003265388130000075
Represents the currentThe transmission data of the time of day is,
Figure BDA0003265388130000076
which represents the sampling period of the sample,
Figure BDA0003265388130000077
wherein
Figure BDA0003265388130000078
A maximum allowable number representing a continuous packet loss; (ii) a Ω is a positive definite weight matrix; and is provided with
Figure BDA0003265388130000079
Figure BDA00032653881300000710
Indicated as the most recently transmitted data,
Figure BDA00032653881300000711
representing the current sample data;
Figure BDA00032653881300000712
is a vector that satisfies the following adaptive law, iota>0：
Figure BDA00032653881300000713
To separate time intervals
Figure BDA00032653881300000714
Is divided into
Figure BDA00032653881300000715
δ＝tk+1-tk-1; is provided with
Figure BDA00032653881300000716
And tau (t) is more than or equal to 0 and less than or equal to tauMThen the true measurement output after the adaptive event trigger
Figure BDA00032653881300000717
The following were used:
Figure BDA00032653881300000718
wherein the conditions for adaptive event triggering are:
Figure BDA00032653881300000719
and step S3, establishing a network attack model based on the influence of replay attack, deception attack and DoS attack on the transmission data. In particular, the amount of the solvent to be used,
step S3.1, replay attack is considered;
the data transmitted under a replay attack is represented as follows:
Figure BDA00032653881300000720
θ (t) represents a bernoulli variable and is used for indicating whether a replay attack occurs or not, wherein θ (t) ═ 1 indicates that the replay attack occurs, and θ (t) ═ 0 indicates that the replay attack does not occur;
Figure BDA00032653881300000721
representing the transmitted data after passing through the adaptive event triggering mechanism; y (t-r (t)) represents the injected past signal recorded by the attacker at the time t, and r (t) represents the replay data as the data transmitted in the first r (t) seconds.
Step S3.2, considering the deception attack;
the data transmitted under a spoofing attack is represented as follows:
y2(t)＝β(t)f(y(t-d(t))+(1-β(t))y1(t)
β (t) represents a bernoulli variable for indicating whether a spoofing attack occurs, where β (t) ═ 1 indicates that a spoofing attack occurs, and β (t) ═ 0 indicates that a spoofing attack does not occur; f (y (t-d (t))) is a non-linear function representing the impact of a spoofing attack;
s3.3, DoS attack is considered;
the data transmitted under DoS attack is represented as follows:
Figure BDA0003265388130000081
wherein a isnRepresents the start time, l, of the nth entry of the DoS attack into the sleep statenIndicating the end time of the nth sleep state.
And step S4, obtaining a system state estimation error model based on the self-adaptive event trigger mechanism and the network attack model. In particular, the amount of the solvent to be used,
the estimation error is defined as follows:
Figure BDA0003265388130000082
Figure BDA0003265388130000083
the system state estimation error model is then expressed as:
Figure BDA0003265388130000084
let xi (t) be [ x ]T(t) eT(t)]TThe system state estimation error model is rewritten as:
Figure BDA0003265388130000091
wherein the content of the first and second substances,
Figure BDA0003265388130000092
Figure BDA0003265388130000093
H＝[I 0]。
and step S5, acquiring the progressive and stable sufficiency condition of the state estimation error model of the established system based on the Lyapunov stability theory.
The Lyapunov function was constructed as follows:
Figure BDA0003265388130000094
Figure BDA0003265388130000095
Figure BDA0003265388130000096
Figure BDA0003265388130000097
the derivatives are calculated as follows:
Figure BDA0003265388130000098
Figure BDA0003265388130000101
wherein the content of the first and second substances,
Figure BDA0003265388130000102
and is
Figure BDA0003265388130000103
Figure BDA0003265388130000104
Figure BDA0003265388130000105
The value of (d) indicates whether a DoS attack has occurred. The following two cases will be discussed:
given scalar quantity
Figure BDA0003265388130000106
τM,rM,dM,ρ,
Figure BDA0003265388130000107
Matrix KjF, if there is a forward scalar κ1,κ2,
Figure BDA00032653881300001020
Matrix omega>0,P1>0,P2>0,
Figure BDA0003265388130000108
UiA matrix of appropriate dimensions; for any i, j ═ 1,2, …, r, the inequality is satisfied
Figure BDA0003265388130000109
Figure BDA00032653881300001010
Figure BDA00032653881300001011
Figure BDA00032653881300001012
The system may be considered to be asymptotically stable.
Wherein
Figure BDA00032653881300001013
The method comprises the following steps:
Figure BDA00032653881300001014
Figure BDA00032653881300001015
Figure BDA00032653881300001016
Figure BDA00032653881300001017
φ4＝g1(-Q11-R11),
Figure BDA00032653881300001018
Figure BDA00032653881300001019
Figure BDA0003265388130000111
φ7＝g1(-Q12-R12),
Figure BDA0003265388130000112
Ψ5＝diag{-Ω,-I}
Figure BDA0003265388130000113
Figure BDA0003265388130000114
Figure BDA0003265388130000115
Γ31＝[01×5 FH 01×4],
Figure BDA0003265388130000116
when in use
Figure BDA0003265388130000117
The method comprises the following steps:
Figure BDA0003265388130000118
Figure BDA0003265388130000119
Figure BDA00032653881300001110
Figure BDA00032653881300001111
Figure BDA00032653881300001112
Figure BDA00032653881300001113
Figure BDA00032653881300001114
Λ31＝[Π4 Π5],Λ33＝diag{-R21,-R22,-R23},
Figure BDA00032653881300001115
Figure BDA0003265388130000121
and step S6, solving the linear matrix inequality to obtain the state estimator gain of the state estimation error model of the established system.
Given scalar quantity
Figure BDA0003265388130000122
τM,rM,dM,σ,
Figure BDA0003265388130000123
Matrix F, YjWhen there is a forward scalar κ1,κ2,
Figure BDA00032653881300001220
∈1,∈2,∈3Matrix of
Figure BDA0003265388130000124
Figure BDA0003265388130000125
P1＝diag{P11,P12}>0,P2＝diag{P21,P22}>0,
Figure BDA0003265388130000126
Figure BDA0003265388130000127
UiIs a matrix of several dimensions; for any i, j ═ 1,2, …, r, when the following inequality is satisfied:
Figure BDA0003265388130000128
Figure BDA0003265388130000129
Figure BDA00032653881300001210
Figure BDA00032653881300001211
the system state estimation error model is asymptotically stable; the expected gain of the state estimator for the state estimation error model of the system established at this time is as follows:
Figure BDA00032653881300001212
wherein
Figure BDA00032653881300001213
The method comprises the following steps:
Figure BDA00032653881300001214
Figure BDA00032653881300001215
Figure BDA00032653881300001216
Figure BDA00032653881300001217
Δ6＝[F 0]
Figure BDA00032653881300001218
Figure BDA00032653881300001219
Figure BDA0003265388130000131
Figure BDA0003265388130000132
Figure BDA0003265388130000133
Figure BDA0003265388130000134
Figure BDA0003265388130000135
Figure BDA0003265388130000136
Figure BDA0003265388130000137
Figure BDA0003265388130000138
Figure BDA0003265388130000139
Figure BDA00032653881300001310
Figure BDA00032653881300001311
the method comprises the following steps:
Figure BDA00032653881300001312
Figure BDA00032653881300001313
Figure BDA00032653881300001314
Figure BDA00032653881300001315
Figure BDA0003265388130000141
Figure BDA0003265388130000142
Figure BDA0003265388130000143
Figure BDA0003265388130000144
Figure BDA0003265388130000145
simulation analysis is performed, a Matlab program is written to solve the linear matrix inequality to solve the estimator gain, a simulation curve is drawn, and the effectiveness of the method is proved by using a simulation example.
The system parameters are set as follows:
A1＝diag{-0.76,-0.76},A2＝diag{-0.6,-1.3},B1＝B2＝[0 1]T
L1＝L2＝[0 1],
Figure BDA0003265388130000146
the uncertainty parameter matrix and uncertainty are expressed as:
F＝diag{0.5,0.02}
consider the perturbation inputs as:
Figure BDA0003265388130000147
the system initial conditions and state estimates are as follows:
Figure BDA0003265388130000148
the spoofing attack is expressed as:
Figure BDA0003265388130000149
sampling period
Figure BDA00032653881300001410
Dos interference signal is κ1＝0.08,κ21.05 and parameters in hybrid networks
Figure BDA00032653881300001411
Figure BDA00032653881300001412
Let σ be 0.01,
Figure BDA00032653881300001417
∈1＝1,∈2＝1,∈3＝1,τM＝0.01,rM＝0.01,dM＝0.02,
Figure BDA00032653881300001413
Figure BDA00032653881300001414
the following matrix parameters were derived using the LMI toolbox of matlab:
Figure BDA00032653881300001415
Figure BDA00032653881300001416
and the gain of the state estimator is:
Figure BDA0003265388130000151
in the simulation experiment, the system estimation error is shown in fig. 2, and the system state x (t) and the error thereof
Figure BDA0003265388130000152
As shown in FIG. 3, the estimated value of the signal z (t) to be estimated
Figure BDA0003265388130000153
As shown in fig. 4. With the help of the Lyapunov stability theory and the LMI technology, sufficient conditions for ensuring the system stability are obtained, and the gain of a state estimator of a state estimation error model of the established system is obtained. Finally, the simulation result verifies the feasibility of the designed method. It is evident from fig. 2-4 that the designed system state estimator performs well, and the system estimation error e (t), the system state x (t) and the error thereof
Figure BDA0003265388130000154
Estimation of the signal z (t) to be estimated
Figure BDA0003265388130000155
Tend to be stable.
The above description is only of the preferred embodiments of the present invention, and it should be noted that: it will be apparent to those skilled in the art that various modifications and adaptations can be made without departing from the principles of the invention and these are intended to be within the scope of the invention.

Claims (5)

1. A T-S fuzzy system self-adaptive event trigger state estimation method under random network attack is characterized by comprising the following steps:
step S1, firstly, establishing a T-S fuzzy system model and a system state estimator model; in particular, the amount of the solvent to be used,
the T-S fuzzy system model is as follows:
Figure FDA0003265388120000011
wherein x (t) e RmRepresents a state variable, y (t) e RmRepresenting the measurement output, z (t) ε RmRepresenting the signal to be estimated, ω (t) representing an external disturbance, obeying ωk∈L2[0，∞)，Ai，Bi，Ci，LiIs a matrix of constants, and the matrix of constants,
Figure FDA00032653881200000113
representing a normalized membership function;
the system state estimator model is built as follows:
Figure FDA0003265388120000012
wherein
Figure FDA0003265388120000013
Represents an estimate of the system state x (t),
Figure FDA0003265388120000014
represents an estimate of the signal to be estimated z (t),
Figure FDA0003265388120000015
representing the true input of the system state estimator, KjRepresents the expected gain of the system state estimator, Aj，Kj，Cj，LjIs a matrix of constants, and the matrix of constants,
Figure FDA0003265388120000016
representing a normalized membership function;
step S2, introducing a self-adaptive event trigger mechanism;
under the self-adaptive event trigger mechanism, the transmission data of the next transmission moment
Figure FDA0003265388120000017
Expressed as:
Figure FDA0003265388120000018
wherein in
Figure FDA0003265388120000019
Representing the data of the transmission at the current time,
Figure FDA00032653881200000110
which represents the sampling period of the sample,
Figure FDA00032653881200000111
wherein
Figure FDA00032653881200000112
A maximum allowable number representing a continuous packet loss; Ω is a positive definite weight matrix; and is provided with
Figure FDA0003265388120000021
Figure FDA0003265388120000022
Indicated as the most recently transmitted data,
Figure FDA0003265388120000023
representing the current sample data;
Figure FDA0003265388120000024
is a vector that satisfies the following adaptive law, iota > 0:
Figure FDA0003265388120000025
to separate time intervals
Figure FDA0003265388120000026
Is divided into
Figure FDA0003265388120000027
δ＝tk+1-tk-1; is provided with
Figure FDA0003265388120000028
And tau (t) is more than or equal to 0 and less than or equal to tauMThen the true measurement output after the adaptive event trigger
Figure FDA0003265388120000029
The following were used:
Figure FDA00032653881200000210
wherein the conditions for adaptive event triggering are:
Figure FDA00032653881200000211
step S3, establishing a network attack model based on the influence of replay attack, deception attack and DoS attack on the transmission data;
step S4, obtaining a system state estimation error model based on the self-adaptive event trigger mechanism and the network attack model;
step S5, acquiring the progressive and stable sufficiency condition of the established system state estimation error model;
and step S6, solving the linear matrix inequality to obtain the state estimator gain of the established system state estimation error model.
2. The method for estimating the adaptive event-triggered state of the T-S fuzzy system under the random network attack as claimed in claim 1, wherein the step of establishing the network attack model in the step S3 comprises:
step S3.1, replay attack is considered;
the data transmitted under a replay attack is represented as follows:
Figure FDA00032653881200000212
θ (t) represents a bernoulli variable and is used for indicating whether a replay attack occurs or not, wherein θ (t) ═ 1 indicates that the replay attack occurs, and θ (t) ═ 0 indicates that the replay attack does not occur;
Figure FDA00032653881200000213
representing the transmitted data after passing through the adaptive event triggering mechanism; y (t-r (t)) represents the injected past signal recorded by the attacker at the time t, and r (t) represents the replay data as the data transmitted in the first r (t) seconds.
Step S3.2, considering the deception attack;
the data transmitted under a spoofing attack is represented as follows:
y2(t)＝β(t)f(y(t-d(t))+(1-β(t))y1(t)
β (t) represents a bernoulli variable for indicating whether a spoofing attack occurs, where β (t) ═ 1 indicates that a spoofing attack occurs, and β (t) ═ 0 indicates that a spoofing attack does not occur; f (y (t-d (t))) is a non-linear function representing the impact of a spoofing attack;
s3.3, DoS attack is considered;
the data transmitted under DoS attack is represented as follows:
Figure FDA0003265388120000031
wherein a isnRepresents the start time, l, of the nth entry of the DoS attack into the sleep statenIndicating the end time of the nth sleep state.
3. The method for estimating the adaptive event-triggered state of the T-S fuzzy system under the random network attack according to claim 2, wherein the obtaining the state estimation error model of the established system in the step S4 specifically includes:
the estimation error is defined as follows:
Figure FDA0003265388120000032
Figure FDA0003265388120000033
the system state estimation error model is then expressed as:
Figure FDA0003265388120000034
let xi (t) be [ x ]T(t) eT(t)]TThe system state estimation error model is rewritten as:
Figure FDA0003265388120000041
wherein the content of the first and second substances,
Figure FDA0003265388120000042
Figure FDA0003265388120000043
H＝[I 0]。
4. the method for estimating the adaptive event-triggered state of the T-S fuzzy system under the random network attack according to claim 3, wherein in the step S5, a sufficiency condition for gradual stabilization of a system state estimation error model is obtained through a Lyapunov stability theory, and specifically,
given scalar quantity
Figure FDA0003265388120000044
τM，rM，dM，σ，
Figure FDA0003265388120000045
Matrix KjF, when there is a forward scalar κ1，κ2，
Figure FDA0003265388120000046
Matrix omega > 0, P1＞0，P2＞0，
Figure FDA0003265388120000047
UiFor a matrix with several dimensions, for any i, j ═ 1,2, r, the following inequality is satisfied, and the system state estimation error model is gradually stable:
Figure FDA0003265388120000048
Figure FDA0003265388120000049
Figure FDA00032653881200000410
Figure FDA00032653881200000411
5. the adaptive event-triggered state estimation method for T-S fuzzy system under random network attack according to claim 4, wherein in step S6, solving the linear matrix inequality to obtain the state estimator gain of the state estimation error model of the established system, specifically,
given scalar quantity
Figure FDA00032653881200000412
τM，rM，dM，σ，
Figure FDA00032653881200000413
Matrix F, YjWhen there is a forward scalar κ1，κ2，
Figure FDA00032653881200000414
∈1，∈2，∈3Matrix of
Figure FDA00032653881200000415
Figure FDA00032653881200000416
P1＝diag{P11，P12}＞0，P2＝diag{P21，P22}＞0，
Figure FDA00032653881200000417
Figure FDA00032653881200000418
UiIs a matrix of several dimensions; for any i, j ═ 1, 2.
Figure FDA0003265388120000051
Figure FDA0003265388120000052
Figure FDA0003265388120000053
Figure FDA0003265388120000054
The system state estimation error model is asymptotically stable; the expected gain of the state estimator for the state estimation error model of the system established at this time is as follows:
Figure FDA0003265388120000055
CN202111085232.8A 2021-09-16 2021-09-16 T-S fuzzy system self-adaptive event trigger state estimation method under random network attack Withdrawn CN113741198A (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN202111085232.8A CN113741198A (en) 2021-09-16 2021-09-16 T-S fuzzy system self-adaptive event trigger state estimation method under random network attack

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN202111085232.8A CN113741198A (en) 2021-09-16 2021-09-16 T-S fuzzy system self-adaptive event trigger state estimation method under random network attack

Publications (1)

Publication Number Publication Date
CN113741198A true CN113741198A (en) 2021-12-03

Family

ID=78739294

Family Applications (1)

Application Number Title Priority Date Filing Date
CN202111085232.8A Withdrawn CN113741198A (en) 2021-09-16 2021-09-16 T-S fuzzy system self-adaptive event trigger state estimation method under random network attack

Country Status (1)

Country Link
CN (1) CN113741198A (en)

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN114355993A (en) * 2021-12-28 2022-04-15 杭州电子科技大学 Sliding mode control method for deception attack reservoir water level system
CN115051872A (en) * 2022-06-30 2022-09-13 苏州科技大学 Attack detection method considering attack signal and unknown disturbance based on interconnected CPS

Cited By (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN114355993A (en) * 2021-12-28 2022-04-15 杭州电子科技大学 Sliding mode control method for deception attack reservoir water level system
CN114355993B (en) * 2021-12-28 2024-03-26 杭州电子科技大学 Sliding mode control method for reservoir water level system under spoofing attack
CN115051872A (en) * 2022-06-30 2022-09-13 苏州科技大学 Attack detection method considering attack signal and unknown disturbance based on interconnected CPS

Similar Documents

Publication Publication Date Title
CN110213115B (en) Security control method of event-driven network control system under multi-network attack
CN113009825B (en) Deception-attacked nonlinear networked system state estimation method
CN113741198A (en) T-S fuzzy system self-adaptive event trigger state estimation method under random network attack
CN113741309B (en) Dual-dynamic event trigger controller model design method based on observer
CN112286051A (en) Neural network quantitative control method based on adaptive event trigger mechanism under complex network attack
CN112865752A (en) Filter design method based on adaptive event trigger mechanism under hybrid network attack
CN113625684B (en) Design method of tracking controller based on event trigger mechanism under hybrid network attack
Yuan et al. Secure filtering for stochastic non‐linear systems under multiple missing measurements and deception attacks
Huang et al. Adaptive control of a class of strict feedback nonlinear systems under replay attacks
Tahoun et al. Secure control design for nonlinear cyber–physical systems under DoS, replay, and deception cyber-attacks with multiple transmission channels
CN113721467B (en) Self-adaptive event triggering-based H under spoofing attack and DoS attack∞Filter design method
CN110850817B (en) Safety estimation method of networked industrial control system
CN114415633B (en) Security tracking control method based on dynamic event triggering mechanism under multi-network attack
CN112866281B (en) Distributed real-time DDoS attack protection system and method
Wang et al. Guaranteed cost control of cyber‐physical systems with packet dropouts under dos jamming attacks
CN107612878A (en) Dynamic window system of selection and wireless network trust management system based on game theory
Li et al. Optimal filter design for cyber‐physical systems under stealthy hybrid attacks
CN114442592A (en) Design method of self-adaptive event trigger controller of networked interconnected system under replay attack and deception attack
CN108847983A (en) Intrusion detection method based on MQTT agreement
Zha et al. Finite‐time adaptive event‐triggered asynchronous state estimation for Markov jump systems with cyber‐attacks
Casetti et al. An analytical framework for the performance evaluation of TCP Reno connections
Khoshnevisan et al. Adaptive rate‐based congestion control with weighted fairness through multi‐loop gradient projection internal model controller
CN115314251B (en) Elastic event trigger control method and device for random jump information physical system
Lucia et al. Covert channels in stochastic cyber‐physical systems
Gong et al. Distributed event‐triggered tracking consensus control for privacy preservation in multi‐agent systems with denial‐of‐service attacks

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
WW01 Invention patent application withdrawn after publication
WW01 Invention patent application withdrawn after publication

Application publication date: 20211203