CN113741198A - T-S fuzzy system self-adaptive event trigger state estimation method under random network attack - Google Patents
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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
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:
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,representing a normalized membership function;
the system state estimator model is built as follows:
whereinRepresents an estimate of the system state x (t),represents an estimate of the signal to be estimated z (t),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,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 momentExpressed as:
whereinRepresenting the data of the transmission at the current time,which represents the sampling period of the sample,whereinA maximum allowable number representing a continuous packet loss; (ii) a Ω is a positive definite weight matrix; and is provided with
Indicated as the most recently transmitted data,representing the current sample data;is full ofVector of adaptive law, iota>0:
To separate time intervalsIs divided intoδ=tk+1-tk-1; is provided withAnd tau (t) is more than or equal to 0 and less than or equal to tauMThen the true measurement output after the adaptive event triggerThe following were used:
wherein the conditions for adaptive event triggering are:
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:
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;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:
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:
the system state estimation error model is then expressed as:
let xi (t) be [ x ]T(t) eT(t)]TThe system state estimation error model is rewritten as:
wherein,
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 quantityτM,rM,dM,σ,Matrix KjF, when there is a forward scalar κ1,κ2,Matrix omega>0,P1>0,P2>0,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:
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 quantityτM,rM,dM,σ,Matrix F, YjWhen there is a forward scalar κ1,κ2,∈1,∈2,∈3Matrix of P1=diag{P11,P12}>0,P2=diag{P21,P22}>0, m=1,2,3;UiIs a matrix of several dimensions; for any i, j ═ 1,2, …, r, when the following inequality is satisfied:
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:
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.
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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 inventionA graph;
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:
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,representing a normalized membership function;
the system state estimator model is built as follows:
whereinRepresents an estimate of the system state x (t),represents an estimate of the signal to be estimated z (t),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,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 momentExpressed as:
wherein inRepresents the currentThe transmission data of the time of day is,which represents the sampling period of the sample,whereinA maximum allowable number representing a continuous packet loss; (ii) a Ω is a positive definite weight matrix; and is provided with
Indicated as the most recently transmitted data,representing the current sample data;is a vector that satisfies the following adaptive law, iota>0:
To separate time intervalsIs divided intoδ=tk+1-tk-1; is provided withAnd tau (t) is more than or equal to 0 and less than or equal to tauMThen the true measurement output after the adaptive event triggerThe following were used:
wherein the conditions for adaptive event triggering are:
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:
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;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:
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:
the system state estimation error model is then expressed as:
let xi (t) be [ x ]T(t) eT(t)]TThe system state estimation error model is rewritten as:
wherein,
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:
the derivatives are calculated as follows:
wherein,and is The value of (d) indicates whether a DoS attack has occurred. The following two cases will be discussed:
given scalar quantityτM,rM,dM,ρ,Matrix KjF, if there is a forward scalar κ1,κ2,Matrix omega>0,P1>0,P2>0,UiA matrix of appropriate dimensions; for any i, j ═ 1,2, …, r, the inequality is satisfied
The system may be considered to be asymptotically stable.
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 quantityτM,rM,dM,σ,Matrix F, YjWhen there is a forward scalar κ1,κ2,∈1,∈2,∈3Matrix of P1=diag{P11,P12}>0,P2=diag{P21,P22}>0, UiIs a matrix of several dimensions; for any i, j ═ 1,2, …, r, when the following inequality is satisfied:
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:
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
the uncertainty parameter matrix and uncertainty are expressed as:
F=diag{0.5,0.02}
consider the perturbation inputs as:the system initial conditions and state estimates are as follows:
the spoofing attack is expressed as:
Let σ be 0.01,∈1=1,∈2=1,∈3=1,τM=0.01,rM=0.01,dM=0.02, the following matrix parameters were derived using the LMI toolbox of matlab:
and the gain of the state estimator is:
in the simulation experiment, the system estimation error is shown in fig. 2, and the system state x (t) and the error thereofAs shown in FIG. 3, the estimated value of the signal z (t) to be estimatedAs 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 thereofEstimation of the signal z (t) to be estimatedTend 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:
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,representing a normalized membership function;
the system state estimator model is built as follows:
whereinRepresents an estimate of the system state x (t),represents an estimate of the signal to be estimated z (t),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,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 momentExpressed as:
wherein inRepresenting the data of the transmission at the current time,which represents the sampling period of the sample,whereinA maximum allowable number representing a continuous packet loss; Ω is a positive definite weight matrix; and is provided with
Indicated as the most recently transmitted data,representing the current sample data;is a vector that satisfies the following adaptive law, iota > 0:
to separate time intervalsIs divided intoδ=tk+1-tk-1; is provided withAnd tau (t) is more than or equal to 0 and less than or equal to tauMThen the true measurement output after the adaptive event triggerThe following were used:
wherein the conditions for adaptive event triggering are:
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:
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;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:
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:
the system state estimation error model is then expressed as:
let xi (t) be [ x ]T(t) eT(t)]TThe system state estimation error model is rewritten as:
wherein,
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 quantityτM,rM,dM,σ,Matrix KjF, when there is a forward scalar κ1,κ2,Matrix omega > 0, P1>0,P2>0,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:
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 quantityτM,rM,dM,σ,Matrix F, YjWhen there is a forward scalar κ1,κ2,∈1,∈2,∈3Matrix of P1=diag{P11,P12}>0,P2=diag{P21,P22}>0, UiIs a matrix of several dimensions; for any i, j ═ 1, 2.
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:
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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 |
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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 |
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