CN115225380B - State estimation method of networked control system - Google Patents

State estimation method of networked control system Download PDF

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CN115225380B
CN115225380B CN202210850124.3A CN202210850124A CN115225380B CN 115225380 B CN115225380 B CN 115225380B CN 202210850124 A CN202210850124 A CN 202210850124A CN 115225380 B CN115225380 B CN 115225380B
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CN115225380A (en
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缪克雷
陈友荣
庄煜博
张旭东
金丹
吕晓雯
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Zhejiang Shuren University
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L63/00—Network architectures or network communication protocols for network security
    • H04L63/14—Network architectures or network communication protocols for network security for detecting or protecting against malicious traffic
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    • H04L63/1466—Active attacks involving interception, injection, modification, spoofing of data unit addresses, e.g. hijacking, packet injection or TCP sequence number attacks
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    • H03H17/0248—Filters characterised by a particular frequency response or filtering method
    • H03H17/0255—Filters based on statistics
    • H03H17/0257—KALMAN filters
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Abstract

The application discloses a state estimation method of a networked control system, which belongs to the technical field of network security, and comprises the following steps: establishing a state estimation model of a discrete time nonlinear networked control system under FDI attack; setting initial values of all parameters of the state estimation model at initial moments; inputting k moment state filtering value at k+1 momentAnd filtering the error covariance matrix P (k|k) to generate a Sigma point set having 2m+1 points; calculating a one-step predicted value and a one-step prediction filtering covariance matrix of the moment state according to the Sigma point set; calculating a Kalman filtering value at the moment k+1 and a filtering covariance matrix; calculating a new card party check value at the moment k, and evaluating the accuracy of the state estimation model according to the new card party check value; calculating a Kalman filtering value and a filtering covariance matrix at the moment according to the innovation chi-square test value; and judging the value of k, if k is less than N, setting k=k+1, returning, wherein N is the last moment, and if not, exiting, and ending the flow.

Description

State estimation method of networked control system
Technical Field
The application belongs to the technical field of information security, and particularly relates to a state estimation method of a networked control system.
Background
The networked control system has the advantages of less system wiring, increased flexibility, plug and play of equipment and the like, and is widely applied to various fields such as intelligent manufacturing, power systems, smart cities, factory automation and the like. The network facilitates the traditional control system and simultaneously makes it face safety protection challenges. False data injection (False Date Injected, FDI) attacks are one of the main attacks in networked control systems, which can affect system performance by tampering with control input or measurement output signals and are difficult to discover. Furthermore, FDI attacks are considered to some extent the most dangerous and complex attacks, in particular state estimation of the system.
The problem of state estimation has been one of the hot problems in the control and signal processing fields, and the problem of state estimation of a networked control system is also increasingly emphasized by various fields. At present, state estimation methods of a network control system under FDI attack by students are mainly divided into two types: one is a state estimation method based on stability, and the other is a state estimation method based on variance. The former generally derives the gain of the estimator by solving a linear matrix inequality. The latter achieves optimal state estimation by minimizing the variance of the estimation error, which typically requires knowledge of the prior information of the attack signal. Such as Wang Z et al, study the filtering problem of discrete-time linear stochastic networked control systems under spoofing attacks. Firstly, giving a sufficient condition for ensuring the effectiveness of a filtering algorithm, converting a solving problem of the sufficient condition into a solving problem of a linear matrix inequality, and calculating a gain matrix of the filter. The concept can also be used for designing a filtering method of a discrete time random time lag nonlinear networked control system, and the system is considered to be subjected to sensor saturation constraint and sensor spoofing attack. Yang W et al designed a distributed state estimation strategy by minimizing the covariance of the estimation error for a linear stationary system under FDI attack. Lin H et al also studied the problem of linear networked control system state estimation subject to DoS and FDI attacks, proposed a generalized pseudo Bayesian state estimation algorithm, and demonstrated the limitations of mean square estimation error between approximate and optimal estimates. Kazemi Z et al, aiming at the problem of state estimation of a continuous time linear power system under FDI attack, considers that the process noise and the measurement noise of the system are Gaussian white noise, and proposes a hybrid state estimation method based on an unknown input observer and a Kalman filtering method, namely a combination of a stability-based method and a variance-based method. Most of the research results are directed to linear networked control systems, and most of the networked control systems are nonlinear systems in nature, so that the related research of state estimation of the nonlinear networked control systems under the FDI attack is less. One common method for estimating the state of a networked control system based on variance is Kalman filtering, but the traditional Kalman filtering is not suitable for estimating the state of a nonlinear system. The improved Kalman filtering method can be used for state estimation of a nonlinear system, such as extended Kalman filtering obtained by direct linearization and UKF (Unscented Kalman Filter, unscented Kalman filtering) using Sigma point sets to approximate state mean variance. Standard extended kalman filtering and standard unscented kalman filtering require that the noise statistics of the system be known accurately, while the noise statistics of the networked control system under FDI attack becomes unknown, and the state estimation of the networked control system under FDI attack by these methods may obtain divergent results.
In summary, since the networked control system under the FDI attack mostly shows a nonlinear form and the noise statistics characteristics of the system are unknown, most of the current methods for estimating the state of the networked control system under the FDI attack are applicable to the linear system, and the methods for the networked control system for the nonlinear system require that the noise statistics characteristics of the system are precisely known. These methods all have difficulty in accurately realizing the state estimation of the nonlinear networked control system under the FDI attack.
Disclosure of Invention
The embodiment of the application aims to provide a state estimation method of a networked control system, which can solve the technical problems that in the prior art, noise signals of a nonlinear system are difficult to be accurate, and further state estimation of the nonlinear networked control system under FDI attack is difficult to be realized.
In order to solve the technical problems, the application is realized as follows:
the embodiment of the application provides a state estimation method of a networked control system, which comprises the following steps:
s101: establishing a state estimation model of a discrete time nonlinear networked control system under FDI attack;
s102: setting initial values of all parameters of the state estimation model at initial moments;
s103: inputting k moment state filtering value at k+1 momentAnd filtering the error covariance matrix P (k|k), generating a Sigma point set with 2m+1 points, where m is the dimension of the system state;
s104: calculating a one-step predicted value and a one-step prediction filtering covariance matrix of the moment state according to the Sigma point set;
s105: calculating a Kalman filtering value at the moment k+1 and a filtering covariance matrix;
s106: calculating a new card party check value at the moment k, and evaluating the accuracy of the state estimation model according to the new card party check value;
s107: calculating a Kalman filtering value and a filtering covariance matrix at the moment according to the innovation chi-square test value;
and S108, judging the value of k, if k is less than N, setting k=k+1, returning to S103, wherein N is the last moment, and if not, exiting, and ending the flow.
In the embodiment of the application, the process noise of the FDI attack signal and the system is described as total Gaussian white noise with an unknown covariance matrix, and then the covariance matrix of the total Gaussian noise is estimated based on a chi-square test method, and finally, the state estimation is performed by a self-adaptive UKF method. The method can accurately control the noise signal of the nonlinear system, further realize the state estimation of the nonlinear networked control system under the FDI attack, and improve the estimation precision.
Drawings
Fig. 1 is a flow chart of a state estimation method of a networked control system according to an embodiment of the present application.
The achievement of the object, functional features and advantages of the present invention will be further described with reference to the embodiments, referring to the accompanying drawings.
Detailed Description
For the purpose of making the objects, technical solutions and advantages of the present invention more apparent, the technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present application, and it is apparent that the described embodiments are some embodiments of the present application, but not all embodiments. All other embodiments, which can be made by one of ordinary skill in the art based on the embodiments herein without making any inventive effort, are intended to be within the scope of the present application.
The method for estimating the state of the networked control system according to the embodiment of the present application is described in detail below with reference to the accompanying drawings through specific embodiments and application scenarios thereof.
Example 1
Referring to fig. 1, a flow chart of a state estimation method of a networked control system according to an embodiment of the present application is shown.
The state estimation method of the networked control system provided by the embodiment of the application comprises the following steps:
s101: a state estimation model of the discrete time nonlinear networked control system under FDI (False Date Injected, false data injection) attack is built.
S102: and setting initial values of all parameters of the state estimation model at initial time.
S103: inputting k moment state filtering value at k+1 momentAnd filtering the error covariance matrix P (k|k), generating a Sigma point set with 2m+1 points, where m is the dimension of the system state;
s104: and calculating a one-step predicted value and a one-step prediction filtering covariance matrix of the moment state according to the Sigma point set.
S105: and calculating a Kalman filtering value and a filtering covariance matrix at the time k+1.
S106: and calculating an innovation card square test value at the moment k, and evaluating the accuracy of the state estimation model according to the innovation card square test value.
S107: and calculating a Kalman filtering value and a filtering covariance matrix at the moment according to the innovation chi-square test value.
And S108, judging the value of k, if k is less than N, setting k=k+1, returning to S103, wherein N is the last moment, and if not, exiting, and ending the flow.
In one possible implementation manner, the S101 specifically includes:
s1011: an initial model of a discrete time nonlinear networked control system is established, wherein the expression form of the initial model is formula 1,
wherein x is k ∈R m For the state vector of the k-moment system, R is the real number domain, B is the control gain matrix with proper dimension, y k ∈R n For the measurement vector of the time system, n is the dimension of the measurement vector of the system, u k ∈R m Is the control input of the system at time k, g (x k ) Is a nonlinear state transfer function, o (x k ) As a nonlinear measurement function. System process noise omega k Zero mean Gaussian white noise, omega k Covariance matrix of Q k ∈R m×m System measurement noise v k Is zero-mean Gaussian white noise, v k Is of the covariance matrix L k ∈R n×n ；
S1012: introducing an FDI attack signal alpha into the initial model in consideration of the FDI attack of the networked control system k At this time, the expression form of the state estimation model may be adjusted to formula 2,
wherein alpha is k For FDI attack signal, alpha k Obeying a gaussian distribution with a mean value of zero;
s1013: redefining system process noise, adjusting the expression form of the state estimation model to formula 3,
wherein the process noiseZero mean Gaussian white noise, covariance matrix +.>
In one possible implementation manner, the S102 is specifically:
setting k=1, and setting a mean value expected by filtering of the state estimation model when k=1And a filtered error expected covariance matrix P (0|0),
wherein x (0) is a system state vector at an initial time, E ()' is a mathematical desired function () T Is a transpose operation.
In one possible implementation manner, the step S103 is specifically:
let l=0, repeat 2m+1 times the following operations:
if l=0, we get
If l is not less than 1 and not more than m, obtain
If m+1 is less than or equal to l is less than or equal to 2m, the method obtains
Wherein,representing square root matrix->Is the first column of (2); />The state filtering value at the moment k; x is x l (k|k) is represented by x 0 (k|k) is the first Sigma point of the centrosymmetric distribution; m is the dimension of the system state; parameter λ=α 2 (m+κ) -m; the parameter alpha is a scaling factor, which is typically set to 1e -4 Alpha is more than or equal to 1; the parameter κ is a scaling parameter, and the parameter κ=2.
In one possible implementation manner, the step S104 specifically includes:
s1041: let l=0, repeat 2m+1 times the following operations: x is x l (k+1|k)＝g(x l (k|k))；l＝l+1；
Wherein x is l (k+ 1|k) is a k+1 time predicted value generated by the nonlinear state transfer function of the first Sigma point at the k time;
s1042: 2m+1 x l (k+ 1|k) to obtain the following k-time state filter valuesA predicted value of the filtered value at time k+1;
wherein,is->Is a one-step predictor of (a);
s1043: calculating a one-step prediction filtering covariance matrix P (k+ 1|k) of the k moment through a formula 7;
in one possible implementation manner, the step S105 specifically includes:
s1051: let l=0, repeat 2m+1 times the following operations: y is l (k+1|k)＝o(x l (k+ 1|k)), l=l+1, wherein y is l (k+ 1|k) is x l (k+ 1|k) measuring Sigma points generated by a nonlinear measurement function;
s1052: 2m+1 y are used by equation 8 l (k+ 1|k), l=0, 1, …,2m, one-step prediction of the measurement:
wherein,measuring a one-step predictive value of y (k+1) for the time instant;
s1053: the measurement covariance matrix is calculated by equation 9:
wherein P is zz (k+ 1|k) is a measurement covariance matrix;
s1054: the innovation covariance matrix is calculated by equation 10:
P ee (k+1)＝P zz (k+1|k)+R k equation 10
Wherein P is ee (k+1) an innovation covariance matrix required for solving the Kalman gain matrix;
s1055: the measurement cross covariance matrix is calculated by equation 11:
wherein P is xz (k+ 1|k) is a measurement cross covariance matrix;
s1056: the kalman gain matrix is calculated by equation (12):
wherein K (k+1) is a Kalman gain matrix at the moment of k+1;
s1057: the Kalman filter value at time k+1 is calculated by equation 13, and the filter covariance matrix is calculated by equation 14, which is as follows:
P(k+1|k+1)＝P(k+1|k)-K(k+1)P ee (k+1)K(k+1) T equation 14
Wherein,for the Kalman filter value at time k+1, P (k+1|k+1) is the filter error covariance matrix at time k+1.
In one possible implementation manner, the step S106 specifically includes:
s1061: record new informationIs P ee (k) If gamma (k) is p-dimensional random zero-mean Gaussian noise, then (gamma (k)) is given that the covariance matrix of gamma (k) is V (k) T (V(k)) -1 Gamma (k) is a chi-square random variable with a degree of freedom of p, and therefore, the following equation 15 can be obtained:
wherein,representing the value equivalent to the check value of the new chi-square at the moment of k, q k Can be used for evaluating the accuracy of the system model;
s1062: calculated according to equation 16Estimate of +.>
Wherein q is min Confidence lower bound for chi-square distribution, q max Confidence upper bound for chi-square distribution, q min And q max Is determined by a chi-square test critical value table; when q k ＜q min In the time-course of which the first and second contact surfaces,is a constant Q min At the moment, the statistical characteristics of the networked control system model and the system noise are accurate, and the system is not attacked by FDI; when q min ≤q k ≤q max q k ＞q max When (I)>Is a linear function related to chi-square test values; and when q k ＞q max When (I)>Take the maximum value and take the constant Q max The uncertainty of the networked control system model reaches the maximum value.
In one possible implementation manner, the step S107 is specifically:
q in the formula 7 k Replaced byRepeating S103 to obtain Kalman filtering value and filtering covariance matrix, and adding ++>Replace back Q k 。
In the embodiment of the application, the process noise of the FDI attack signal and the system is described as total Gaussian white noise with an unknown covariance matrix, and then the covariance matrix of the total Gaussian noise is estimated based on a chi-square test method, and finally, the state estimation is performed by a self-adaptive UKF method. The method can accurately control the noise signal of the nonlinear system, further realize the state estimation of the nonlinear networked control system under the FDI attack, and improve the estimation precision.
The foregoing is merely exemplary of the present invention and is not intended to limit the present invention. Various modifications and variations of the present invention will be apparent to those skilled in the art. Any modification, equivalent replacement, improvement, etc. which come within the spirit and principles of the invention are to be included in the scope of the claims of the present invention.

Claims (2)

1. A method for estimating a state of a networked control system, comprising:
s101: establishing a state estimation model of a discrete time nonlinear networked control system under FDI attack;
s102: setting initial values of all parameters of the state estimation model at initial moments;
s103: inputting k moment state filtering value at k+1 momentAnd filtering the error covariance matrix P (k|k), generating a Sigma point set with 2m+1 points, where m is the dimension of the system state;
s104: calculating a one-step predicted value and a one-step prediction filtering covariance matrix of the moment state according to the Sigma point set;
s105: calculating a Kalman filtering value at the moment k+1 and a filtering covariance matrix;
s106: calculating a new card party check value at the moment k, and evaluating the accuracy of the state estimation model according to the new card party check value;
s107: calculating a Kalman filtering value and a filtering covariance matrix at the moment according to the innovation chi-square test value;
s108, judging a k value, if k is less than N, setting k=k+1, returning to S103, wherein N is the last moment, otherwise, exiting, and ending the flow;
wherein, the S101 specifically includes:
s1011: an initial model of a discrete time nonlinear networked control system is established, wherein the expression form of the initial model is formula 1,
wherein x is k ∈R m For the state vector of the k-moment system, R is the real number domain, B is the control gain matrix with proper dimension, y k ∈R n For the measurement vector of the time system, n is the dimension of the measurement vector of the system, u k ∈R m Is the control input of the system at time k, g (x k ) Is a nonlinear state transfer function, o (x k ) As a nonlinear measurement function, system process noise omega k Zero mean Gaussian white noise, omega k Covariance matrix of Q k ∈R m×m System measurement noise v k Is zero-mean Gaussian white noise, v k Is of the covariance matrix L k ∈R n×n ；
S1012: introducing an FDI attack signal alpha into the initial model in consideration of the FDI attack of the networked control system k At this time, the expression form of the state estimation model may be adjusted to formula 2,
wherein alpha is k For FDI attack signal, alpha k Obeying a gaussian distribution with a mean value of zero;
s1013: redefining system process noise, adjusting the expression form of the state estimation model to formula 3,
wherein the process noiseZero mean Gaussian white noise, covariance matrix +.>
Wherein, the step S103 specifically includes:
let l=0, repeat 2m+1 times the following operations:
if l=0, we get
If l is not less than 1 and not more than m, obtain
If m+1 is less than or equal to l is less than or equal to 2m, the method obtains
Wherein,representing square root matrix->Is the first column of (2); />The state filtering value at the moment k; x is x l (k|k) is represented by x 0 (k|k) is the first Sigma point of the centrosymmetric distribution; m is the dimension of the system state; parameter λ=α 2 (m+κ) -m; the parameter alpha is a scaling factor, which is typically set to 1e -4 Alpha is more than or equal to 1; parameter k is a scaling parameter, parameter k=2;
wherein, the step S104 specifically includes:
s1041: let l=0, repeat 2m+1 times the following operations: x is x l (k+1|k)＝g(x l (k|k))；l＝l+1；
Wherein x is l (k+ 1|k) is a k+1 time predicted value generated by the nonlinear state transfer function of the first Sigma point at the k time;
s1042: 2m+1 x l (k+ 1|k) to obtain the following k-time state filter valuesA predicted value of the filtered value at time k+1;
wherein,is->Is a one-step predictor of (a);
s1043: calculating a one-step prediction filtering covariance matrix P (k+ 1|k) of the k moment through a formula 7;
wherein, the step S105 specifically includes:
s1051: let l=0, repeat 2m+1 times the following operations: y is l (k+1|k)＝o(x l (k+ 1|k)), l=l+1, wherein y is l (k+ 1|k) is x l (k+ 1|k) measuring Sigma points generated by a nonlinear measurement function;
s1052: 2m+1 y are used by equation 8 l (k+ 1|k), l=0, 1, …,2m, one-step prediction of the measurement:
wherein,measuring a one-step predictive value of y (k+1) for the time instant;
s1053: the measurement covariance matrix is calculated by equation 9:
wherein P is zz (k+ 1|k) is a measurement covariance matrix;
s1054: the innovation covariance matrix is calculated by equation 10:
P ee (k+1)＝P zz (k+1|k)+R k equation 10
Wherein P is ee (k+1) an innovation covariance matrix required for solving the Kalman gain matrix;
s1055: the measurement cross covariance matrix is calculated by equation 11:
wherein P is xz (k+ 1|k) is a measurement cross covariance matrix;
s1056: the kalman gain matrix is calculated by equation 12:
wherein K (k+1) is a Kalman gain matrix at the moment of k+1;
s1057: the Kalman filter value at time k+1 is calculated by equation 13, and the filter covariance matrix is calculated by equation 14, which is as follows:
P(k+1|k+1)＝P(k+1|k)-K(k+1)P ee (k+1)K(k+1) T equation 14
Wherein,the Kalman filtering value at the moment k+1, and the P (k+1|k+1) is a filtering error covariance matrix at the moment k+1;
wherein, the step S106 specifically includes:
s1061: record new informationIs P ee (k) The following equation 15 is obtained:
wherein,the representation is equivalent to q k For k moment of new chi-square test value, q k Can be used for evaluating the accuracy of a system model；
S1062: calculated according to equation 16Estimate of +.>
Wherein q is mi n is the confidence lower bound of chi-square distribution, q max Confidence upper bound for chi-square distribution, q min And q max Is determined by a chi-square test critical value table; when q k ＜q min In the time-course of which the first and second contact surfaces,is a constant Q min At the moment, the statistical characteristics of the networked control system model and the system noise are accurate, and the system is not attacked by FDI; when q min ≤q k ≤q max When (I)>Is a linear function related to chi-square test values; and when q k ＞q max When (I)>Take the maximum value and take the constant Q max The uncertainty of the networked control system model reaches the maximum value;
wherein, the step S107 specifically includes:
q in the formula 7 k Replaced byRepeating S103 to obtain Kalman filtering value and filtering covariance matrix, and adding ++>Replace back Q k 。
2. The state estimation method according to claim 1, wherein S102 is specifically:
setting k=1, and setting a mean value expected by filtering of the state estimation model when k=1And a filtered error expected covariance matrix P (0|0),
wherein x (0) is a system state vector at an initial time, E ()' is a mathematical desired function () T Is a transpose operation.
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CN113992350A (en) * 2021-09-24 2022-01-28 杭州意能电力技术有限公司 Smart grid false data injection attack detection system based on deep learning

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