CN115718427B - Non-fragile network prediction control method for security - Google Patents
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Abstract
The invention discloses a security non-fragile networking prediction control method, which comprises the following steps: step one, establishing a networked control system model under communication delay; step two, designing a matched observer structure; constructing a predictive controller structure based on uniform quantization and false data attack; step four, obtaining a judging basis for guaranteeing the stability of the input-state under the meaning of the mean square of the networked control system; step five, solving the gain parameters of the observer and the gain parameters of the predictive controller; and step six, substituting the obtained observer gain matrix and the predicted controller gain matrix into the observer in the step two and the predicted controller in the step three respectively. The method solves the problems of inaccurate data transmission, low control system and even unstable system caused by the fact that the existing control method can not compensate a networked system with transmission delay and random network attack at the same time after the signal is required to be quantized.
Description
Technical Field
The invention belongs to the field of networked system control, relates to a control method of a networked system under discrete time, and in particular relates to a security non-fragile networked predictive control method.
Background
The advantages of low energy consumption, convenient maintenance, quick transmission and the like of the networked system lead the networked system to be widely applied to the fields of military, traffic, aerospace and the like, and are focuses of attention for the study of control problems of the networked system.
Delay in signal transmission is an unavoidable phenomenon in a networked system, and in order to reduce occupied network bandwidth, the signal often needs to be quantized during transmission, meanwhile, signal transmission through a network brings convenience to an attacker, and the networked system may be attacked by false data injection, so it is very significant to design a control method capable of simultaneously coping with these negative effects.
The existing control method can not process signal quantization transmission and possibly influence the system by false data injection attack under the condition of actively compensating transmission delay, and the robustness of the controller is poor, so that the control performance is reduced, and even the system state can not be controlled to be stable.
Disclosure of Invention
The invention aims to provide a security non-fragile networked prediction control method, which solves the problems that the existing control method cannot compensate a networked system with transmission delay and random network attack after signal quantization, so that data transmission is inaccurate, a control system is low and even the system is unstable.
The invention aims at realizing the following technical scheme:
a security non-fragile networking prediction control method comprises the following steps:
step one, establishing a networked control system model under communication delay;
step two, designing a matched observer structure according to the networking control system model established in the step one;
thirdly, constructing a predictive controller structure based on uniform quantization and false data attack according to the observer designed in the second step;
step four, obtaining a judging basis for guaranteeing the stability of the input-state under the meaning of the mean square of the networked control system;
step five, solving the gain parameters of the observer and the gain parameters of the predictive controller;
and step six, substituting the obtained observer gain matrix and the obtained predictive controller gain matrix into the observer in the step two and the predictive controller in the step three respectively, so as to ensure the input-state stability of the networked control system in the mean square sense.
Compared with the prior art, the invention has the following advantages:
1. the invention provides a safe non-fragile networked prediction control method under the uniform quantization phenomenon aiming at a networked control system with transmission delay and false data injection attack, and considers the influence of signal quantization and false data injection attack on the prediction control performance.
2. The invention provides a design method of the gain parameters of the observer and the gain parameters of the non-fragile predictive controller in the form of linear matrix inequality by means of the Leidepro stability theorem, provides a method for the design of the observer and the controller of the control system, and can ensure the input-state stability of the system in the mean square sense.
3. The invention realizes good control effect, and in the experiment of the invention, even if the probability of occurrence of false data injection attack is 50%, the stability of the system can be ensured.
Drawings
FIG. 1 is a flow chart of the secure non-fragile networked predictive control method of the present invention.
FIG. 2 is a state trace diagram of a lower open loop system, where "-is the system state η 1 The track of (m),
is the system state eta 2 Track of (m), "-" is system state η 3 Track of (m), eta 1 (m) is the first component of the system state at time m, η 2 (m) is the second component of the system state at time m, η 3 (m) is the third component of the system state at time m.
FIG. 3 is a diagram of a closed loop system state trace with uncompensated propagation delay, where "-is the system state η 1 The track of (m),
is the system state eta 2 The locus of (m), "-" isSystem state eta 3 Track of (m), eta 1 (m) is the first component of the system state at time m, η 2 (m) is the second component of the system state at time m, η 3 (m) is the third component of the system state at time m.
FIG. 4 is under the situation
A closed loop system state track diagram obtained by a non-fragile predictive control method, wherein' is the system state eta 1 Track of (m), ->
Is the system state eta 2 Track of (m), "-" is system state η 3 Track of (m), eta 1 (m) is the first component of the system state at time m, η 2 (m) is the second component of the system state at time m, η 3 (m) is the third component of the system state at time m.
FIG. 5 is under the situation
Control input trace map obtained by non-fragile predictive control method, wherein "-is control input u 1 Track of (m), "-" is control input u 2 Track of (m), u 1 (m) is the first component of the control input at time m, u 2 (m) is the second component of the control input at time m.
FIG. 6 is a diagram of case two
A closed loop system state track diagram obtained by a non-fragile predictive control method, wherein' is the system state eta 1 Track of (m), ->
Is the system state eta 2 Track of (m), "-" is system state η 3 Track of (m), eta 1 (m)To be the first component of the system state at m time, η 2 (m) is the second component of the system state at time m, η 3 (m) is the third component of the system state at time m.
FIG. 7 is a diagram of case two
Control input trace map obtained by non-fragile predictive control method, wherein "-is control input u 1 Track of (m), "-" is control input u 2 Track of (m), u 1 (m) is the first component of the control input at time m, u 2 (m) is the second component of the control input at time m.
Detailed Description
The following description of the present invention is provided with reference to the accompanying drawings, but is not limited to the following description, and any modifications or equivalent substitutions of the present invention should be included in the scope of the present invention without departing from the spirit and scope of the present invention.
The invention provides a security non-fragile networking prediction control method, as shown in figure 1, which comprises the following steps:
step one, establishing a networked control system model under communication delay.
In this step, the networked control system model is:
η(m+1)＝Aη(m)+Bu(m) (1)
ξ(m)＝Cη(m) (2)
where η (m+1) and η (m) are represented as state information at m+1 time and m time, u (m) is a control input at m time, ζ (m) is measurement output information obtained at m time, A, B and C are a state transition matrix, a control input matrix and a measurement output matrix, respectively, and B is a matrix of rank-full.
And step two, designing a matched observer structure according to the networked control system model established in the step one.
In this step, the specific structure of the observer is:
in the formula ,
one-step prediction value representing the state at m time versus m+1 time,/for>
A one-step predictor representing the state at time m-1 for time m, u (m) representing the control input at time m, L being the observer gain parameter to be determined.
And thirdly, constructing a predictive controller structure based on uniform quantization and false data attack according to the observer designed in the second step. The method comprises the following specific steps:
designing a prediction formula based on the networked control system model in the first step and the observer in the second step:
where j represents the step size of the prediction process, and j has a value of 2,3, …, delta,
predicted value representing the state at m-delta versus m+j-delta, ++>
The predicted value for the state at m+j-delta-1 at m-delta time, u (m+j-delta-1) represents the control input value at m+j-delta-1, and delta represents the transmission delay generated in the network transmission.
The uniform quantizer form is:
in the formula ,
representing state vector +.>
The value quantized by the uniform quantizer is used for the quantization,
representation->
I has a value of 1,2, … v, wherein v is a state vector
Dimension of->
Is the predicted value of the state vector at m time to m+1 time, T represents the maximum value of the energy of the quantizer, -T is the minimum value of the energy of the quantizer, alpha is the number of quantization intervals, T β Between cells representing the beta-th quantization, beta being the number between the quantized cells, ++>
Representing a downward rounding function, i.e., a maximum integer having a value no greater than "·".
The quantized predicted values after attack are:
wherein ,
representing state predictors after quantization and attack effects,/->
Representing the state predicted value obtained by measuring the output predicted value at m time at m-delta time and passing through a uniform quantizer,
and lambda (m) is a random variable conforming to Bernoulli distribution and is used for indicating whether false data injection attack phenomenon occurs at the moment m, and χ (m) is a false value of the fact that the attacker signal acts in the control system.
The predictive controller structure based on uniform quantization and false data attack is:
where K represents the controller gain parameter to be determined, D and E represent the left and right coefficient matrices, respectively, in the controller gain perturbation, and the time-varying matrix F (m) represents the uncertainty in the gain perturbation at time m.
And step four, obtaining a judging basis for guaranteeing the stability of the input-state under the meaning of the mean square of the networked control system.
In the step, the input-state stability judgment basis of the networked control system in the mean square sense under the quantization and false data attack is as follows:
in the formula ,
representing a mathematical expectation value of lambda (m), A δ-1 For the product of delta-1 matrices A, 0 means that the elements are all 0 matrices, the superscript T means transpose, P 1 For the first positive definite matrix to be determined, P 2 For the second positive definite matrix to be determined, Q 1 For the third positive definite matrix to be determined, Q 2 For the fourth positive definite matrix to be determined, R is the first matrix to be solved, W is the second matrix to be solved, mu is to be solvedPositive scalar parameters.
In this step, the lyapunov stability theorem is utilized when the stability criterion is obtained.
And fifthly, solving the gain parameters of the observer and the gain parameters of the predictive controller.
In this step, the observer gain parameter and the predictive controller gain parameter are calculated as follows:
wherein the orthogonal matrix V is the right matrix of singular value decomposition of matrix B, satisfying
The orthogonal matrix U is the left matrix of the singular value decomposition of matrix B, Θ=diag { γ 1 ,γ 2 ,…,γ n The matrix is composed of non-zero singular values of matrix B, diag { gamma } 1 ,γ 2 ,…,γ n Represented by gamma 1 ,γ 2 ,…,γ n Is a diagonal matrix formed by diagonal elements, gamma 1 ,γ 2 ,…,γ n For the non-zero singular values of matrix B, n represents the rank of matrix B, P 11 Is P 1 The transformed matrix number one satisfies +.>
P 12 Is P 1 The transformed matrix number two, superscript T and-1, represent the transpose and inverse, respectively.
In this step, singular value decomposition of the matrix is used in solving the predictive controller gain parameters.
And step six, substituting the gain matrix of the observer and the gain matrix of the predictive controller which are obtained in the step five into the observer in the step two and the predictive controller in the step three respectively, so as to ensure the input-state stability of the networked control system in the mean square sense.
In this step, the observer gain matrix and the predictive controller gain matrix are respectively substituted into the specific forms of the observer and the predictive controller obtained in the observer in the second step and the predictive controller in the third step, respectively, and are as follows:
the state value of the system is observed through the prediction model (4), the state information is predicted through the prediction model (11), and the signal is transmitted through the uniform quantizer (5), so that the prediction controller (12) can still ensure that the networked control system (1) is stable in input-state in the mean square sense even if false data is injected and attacked.
Examples:
in this embodiment, taking a networked system with transmission delay and network attack as an example, the following simulation is performed by adopting the method of the present invention:
the parameters of the state transition matrix, the control input matrix and the measurement matrix of the networked system with the transmission delay and the network attack are respectively as follows:
other parameters and initial values are: the network transmission delay is delta=4, and the parameters in the gain perturbation term in the controller are
F＝0.1sint，E＝[0.1 0 0.1]The upper limit of the uniform quantizer is T=40, the quantization number alpha=160, and the attack injection signal is χ (m) = [ 0.1.0.2-0.2] T The initial value of the state vector is η (0) = [ 10-10] T Initial observer valueIs->
The initial value of the controller is u (0) = [0 0 ]] T 。
Case 1:
namely, the probability of the system receiving false information of an attacker is 0.5, and in the situation, gain parameters of an observer and a predictive controller are respectively obtained as follows: />
Case 2:
namely, the probability of the system receiving false information of an attacker is 0.1, and in the situation, gain parameters of an observer and a predictive controller are respectively obtained as follows:
the control effect is as follows: as can be seen from fig. 2,3, 4, 5, 6, and 7, the open loop system is unstable, and if the transmission time lag is compensated, the closed loop system is still unstable, and the inventive non-fragile predictive controller design method can effectively cope with the influence of quantization error and false data injection attack on the system and stabilize the control system for the networked control system with transmission delay, quantization, and network attack.
Claims (3)
1. The non-fragile networking prediction control method for the security is characterized by comprising the following steps of:
step one, establishing a networked control system model under communication delay;
step two, designing a matched observer structure according to the networking control system model established in the step one;
thirdly, constructing a predictive controller structure based on uniform quantization and false data attack according to the observer designed in the second step, wherein:
the predictive controller structure based on uniform quantization and false data attack is as follows:
where u (m) represents the control input at time m, K represents the controller gain parameter to be determined, D and E represent the left and right coefficient matrices, respectively, in the controller gain perturbation, the time-varying matrix F (m) represents the uncertainty in the gain perturbation at time m,
representing state predictors after quantization and attack effects, delta representing transmission delays generated in network transmissions;
the said
The method comprises the following steps:
wherein ,
representing the state prediction value obtained by uniformly quantizing the measured output prediction value at m-delta time to m time,/I>
A random variable which is compliant with the Bernoulli distribution and is used for representing whether false data injection attack phenomenon occurs at the moment m, and χ (m) represents a false value of the attacker signal actually acting in a control system;
the said
The form is as follows:
in the formula ,
representing state vector +.>
Quantized value by uniform quantizer, +.>
Representation->
I has a value of 1,2, … v, wherein v is a state vector +.>
Is used for the number of dimensions of (c),
is the predicted value of the state vector at m time to m+1 time, T represents the maximum value of the energy of the quantizer, -T is the minimum value of the energy of the quantizer, alpha is the number of quantization intervals, T β Between cells representing the beta-th quantization, beta being the number between the quantized cells, ++>
Representing a downward rounding function, i.e., a maximum integer having a value not greater than ";
step four, obtaining a judging basis for guaranteeing the stability of the input-state under the meaning of the mean square of the networked control system, wherein:
the input-state stability judging basis of the networked control system in the mean square sense under the quantization and false data attack is as follows:
in the formula ,
represents a mathematical expectation of lambda (m) representing whether a false data injection attack phenomenon occurs at the moment m, A δ-1 For the product of delta-1 matrices A, 0 means that the elements are all 0 matrices, the superscript T means transpose, P 1 For the first positive definite matrix to be determined, P 2 For the second positive definite matrix to be determined, Q 1 For the third positive definite matrix to be determined, Q 2 For the fourth positive definite matrix to be determined, R is the first matrix to be solved, W is the second matrix to be solved, μ is the positive scalar parameter to be solved, A, B and C are the state transition matrix, the control input matrix and the measurement output matrix, respectively, and B is the matrix of column full rank;
fifthly, solving an observer gain parameter and a predictive controller gain parameter according to the following method:
wherein the orthogonal matrix V is the right matrix of singular value decomposition of matrix B, satisfying
The orthogonal matrix U is the left matrix of the singular value decomposition of matrix B, Θ=diag { γ 1 ,γ 2 ,...,γ n The matrix is composed of non-zero singular values of matrix B, diag { gamma } 1 ,γ 2 ,...,γ n Represented by gamma 1 ,γ 2 ,…,γ n Is a diagonal matrix formed by diagonal elements, gamma 1 ,γ 2 ,…,γ n For the non-zero singular values of matrix B, n represents the rank of matrix B, P 11 Is P 1 The first matrix obtained by transformation satisfies
P 12 Is P 1 The transformed matrix II is marked with superscripts T and-1 respectively representing transposition and inverse;
and step six, substituting the obtained observer gain matrix and the obtained predictive controller gain matrix into the observer in the step two and the predictive controller in the step three respectively, so as to ensure the input-state stability of the networked control system in the mean square sense.
2. The method for secure non-fragile network predictive control according to claim 1, wherein in the first step, the network control system model is:
η(m+1)＝Aη(m)+Bu(m)
ξ(m)＝Cη(m)
where η (m+1) and η (m) are represented as state information at m+1 time and m time, u (m) is a control input at m time, ζ (m) is measurement output information obtained at m time, A, B and C are a state transition matrix, a control input matrix and a measurement output matrix, respectively, and B is a matrix of rank-full.
3. The method for secure non-fragile network predictive control according to claim 1, wherein in the second step, the specific structure of the observer is:
in the formula ,
one-step prediction value representing the state at m time versus m+1 time,/for>
A one-step predictor representing the state at time m-1 for time m, ζ (m) representing the measured output information obtained at time m, u (m) representing the control input at time m, L being the observer gain parameter to be determined, A, B and C being the state transition matrix, the control input matrix and the measured output matrix, respectively, and B being the matrix of rank-full. />
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