CN110647033A - Networked motion control system attack identification method based on class-Longberger observer - Google Patents

Networked motion control system attack identification method based on class-Longberger observer Download PDF

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CN110647033A
CN110647033A CN201910821302.8A CN201910821302A CN110647033A CN 110647033 A CN110647033 A CN 110647033A CN 201910821302 A CN201910821302 A CN 201910821302A CN 110647033 A CN110647033 A CN 110647033A
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朱俊威
王琪
张文安
俞立
董辉
徐建明
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Zhejiang University of Technology ZJUT
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Abstract

A networked motion control system attack identification method based on a quasi-Luenberger observer comprises the steps of firstly modeling a networked motion control system, considering the condition of sensor attack in the system, determining a state space equation of the system and discretizing the state space equation; selecting tau sensor measurement values, and constructing an output equation; and finally, constructing a quasi-Luenberger observer to estimate the system state and the sensor attack. The invention adopts the event-driven technology, can save the computing resource and improve the computing performance of the system. By constructing the Lyapunov energy function, the error is converged into a minimum energy boundary, and the attack identification effect precision is higher.

Description

Networked motion control system attack identification method based on class-Longberger observer
Technical Field
The invention belongs to the technical field of network security, and particularly provides a networked motion control system attack identification method based on a quasi-Luenberger observer, which can identify the attack, evaluate the security situation of a system and guarantee the safe operation of the system.
Background
With the high-speed development of network information technology, the use of networks to replace the traditional motion control architecture becomes a necessary trend, and the networked motion control system becomes a hotspot in the current motion control field. The information space and the physical space of the networked motion control system are highly fused and mutually influenced, and because the modern networked motion control system has lower security level, the network attack starting from the information space can directly damage the normal operation of the physical system. Therefore, whether the attack signal can be accurately identified plays an important role in the motion control system.
The real-time online identification of the attack depends on the design of an observer, and the existing attack identification methods mainly include an attack identification method based on unknown input observers such as a robust observer, a sliding mode observer, an intermediate observer and the like. The sliding mode observer needs prior knowledge such as known upper bound of an attack signal and the like, and needs a system to meet the matching condition of the observer, however, any information of an attacker cannot be obtained in actual engineering. Although the robust observer has no observer matching condition, an accurate estimation error upper bound cannot be obtained, and the estimation accuracy cannot be ensured in the actual application process. The intermediate observer gives a theoretical upper bound, but the upper bound is large and only has theoretical significance, and the estimation error of the attack signal cannot be limited within a preset range, so that the intermediate observer is difficult to apply to practice.
Disclosure of Invention
Based on the problems, the invention provides a network motion control system attack identification method based on a similar Luenberger observer, and particularly, the method is used for reconstructing an output signal containing sparsity sensor attack, estimating the state and the attack of a system at the same time, and ensuring that the estimation error of the system is converged into a very small energy range.
The invention provides the following technical scheme for solving the technical problems:
a networked motion control system attack identification method based on a quasi-Luenberger observer comprises the following steps:
step 1), establishing a state space equation of a networked motion control system and discretizing:
considering the situation that sensor attack and noise exist in the system, the state space equation is discretized, and the equation (1) is shown as the following formula:
Figure BDA0002187509850000021
wherein, A is a state matrix of the system, B is an input matrix, C is an output matrix, x represents a state quantity of the system, u is a system input, y is a system output, and a represents a sensor attack;
step 2), selecting tau sensor measurement values to construct an output equation, wherein the process is as follows:
2.1) acquiring tau epsilon N measurement values, and constructing an output equation of the ith sensor as shown in the formula (2):
Figure BDA0002187509850000022
wherein the content of the first and second substances,
Figure BDA0002187509850000024
2.2) since U (t) is known, the formula (2) is simplified to the formula (3):
Yi(t)＝Oix(t-τ+1)+Ei(t) ⑶
wherein the content of the first and second substances,
Figure BDA0002187509850000025
2.3) definition of
Figure BDA0002187509850000026
The output equation is simplified as shown in equation (4):
Figure BDA0002187509850000027
wherein the content of the first and second substances,
Figure BDA0002187509850000028
Q＝[O I]i is an identity matrix;
step 3), constructing a quasi-Luenberger observer, and carrying out the following process:
3.1) augmenting the system, using y (t) as new input quantity, and enabling
Figure BDA0002187509850000031
Obtaining an augmented state space equation as shown in formula (5):
wherein the content of the first and second substances,
Figure BDA0002187509850000033
Figure BDA0002187509850000034
bifor natural basis vectors, the superscript "T" represents the transpose of the matrix,
Figure BDA0002187509850000035
as an estimate of the system state quantity and sensor attack z,
Figure BDA0002187509850000036
pre-estimated values of system state quantity and sensor attack z;
3.2) constructing a Lyapunov energy function, as shown in the formula (6):
Figure BDA0002187509850000037
wherein the content of the first and second substances,
Figure BDA0002187509850000038
is an estimated value of the system state quantity and the sensor attack z, | ·| non-calculation2A two-norm representing a;
3.3) constructing a projection operator as shown in formula (7):
Π(z)＝Π(x,E)＝(x,Π'(E)) ⑺
wherein pi' (E) represents E ═ E (E)1,E2,…,Ep)TIn (1), obtain EiThe sum of squares of the middle elements, s (s < p) E elements with smaller sum of squaresiZero setting is carried out, and the sparsity of sensor attack estimation is ensured;
3.4) constructing a Lorberg-like observer as shown in formula (8):
Figure BDA0002187509850000039
wherein, L ═ QTSigma, sigma is a positive definite matrix;
3.5) initialization definition based on equation (5)
Figure BDA00021875098500000310
m＝0,
a) If it isAnd is
Figure BDA0002187509850000042
v∈[0,1]The artificial set value is obtained by performing iterative operation according to the formula (8) until the artificial set value is obtained
Figure BDA0002187509850000043
To that end
Figure BDA0002187509850000044
Entering b); otherwise, directly entering b);
b) if it is
Figure BDA0002187509850000045
Reset
Figure BDA0002187509850000046
Returning to a); otherwise, obtaining the system state at the t-T moment and the estimation value of the sensor attack at the t moment
Figure BDA0002187509850000047
According to the network motion control system attack identification method based on the class-Luenberger observer, an event-driven class-Luenberger observer is constructed by reconstructing output signals containing sensor attacks, and system states and the sensor attacks are estimated.
The invention has the beneficial effects that: by adopting the event-driven technology, the computing resources can be saved, and the computing performance of the system is improved; through the design of a Lorberg observer, a Lyapunov energy function is constructed, so that the error is converged into a minimum energy boundary, and the attack identification effect precision is higher; the identification precision of the method can meet the requirements of practical application, and the required related parameters can be measured by a low-cost sensor.
Drawings
FIG. 1 is a system state x1The estimated effect of (2);
FIG. 2 is a system state x2The estimated effect of (2);
FIG. 3 is an attack a on the first sensor1The estimated effect of (2);
FIG. 4 shows an attack a on a second sensor2The estimated effect of (2);
FIG. 5 shows an attack a on a third sensor3The effect of the estimation of (2).
Detailed Description
In order to make the purpose, technical solution and advantages of the present invention more clear, the technical solution of the present invention is further described below with reference to the accompanying drawings and practical experience.
Referring to fig. 1-5, a networked motion control system attack identification method based on a quasi-lunberg observer firstly models a motion control system, considers the sensor attack in the system, determines a state space equation of the system and discretizes the equation; constructing an output equation containing sensor attack; a quasi-Luenberger observer is constructed to estimate the sensor attack and the system state.
A networked motion control system attack identification method based on a quasi-Luenberger observer comprises the following steps:
1) establishing a state space equation of a networked motion control system and discretizing;
2) constructing an output equation containing sensor attack;
3) and constructing a quasi-Luenberger observer.
Further, in the step 1), a state space equation of the networked motion control system is established and discretized, as shown in formula (1):
Figure BDA0002187509850000051
wherein the state matrix
Figure BDA0002187509850000052
Input matrix
Figure BDA0002187509850000053
Output matrixx represents the system state quantity, u is the system input, y is the system output, and the sensor attacks
Figure BDA0002187509850000055
Step 2), selecting tau-2 sensor measurement values to construct an output equation, wherein the process is as follows:
2.1) acquiring tau which is 2 measured values, and constructing an output equation of the ith sensor as shown in formula (2):
Figure BDA0002187509850000056
wherein the content of the first and second substances,
Figure BDA0002187509850000057
Figure BDA0002187509850000058
Figure BDA0002187509850000059
t≥2；
2.2) since U (t) is known, the formula (2) is simplified to the formula (3):
Yi(t)＝Oix(t-1)+Ei(t) ⑶
wherein the content of the first and second substances,
2.3) definition of
Figure BDA0002187509850000062
The output equation is simplified as shown in equation (4):
Figure BDA0002187509850000063
wherein the content of the first and second substances,
Figure BDA0002187509850000064
step 3), constructing a quasi-Luenberger observer, and carrying out the following process:
3.1) augmenting the system, using y (t) as new input quantity, and enabling
Figure BDA0002187509850000065
Obtaining an augmented state space equation as shown in formula (5):
Figure BDA0002187509850000066
wherein the content of the first and second substances,
Figure BDA0002187509850000071
Figure BDA0002187509850000073
as an estimate of the system state quantity and sensor attack z,
Figure BDA0002187509850000074
pre-estimated values of system state quantity and sensor attack z;
3.2) constructing a Lyapunov energy function, as shown in the formula (6):
Figure BDA0002187509850000075
wherein the content of the first and second substances,
Figure BDA0002187509850000076
is an estimated value of the system state quantity and the sensor attack z, | ·| non-calculation2A two-norm representing a;
3.3) constructing a projection operator as shown in formula (7):
Π(z)＝Π(x,E)＝(x,Π'(E)) ⑺
wherein pi' (E) represents E ═ E (E)1,E2,…,Ep)TIn (1), obtain EiThe sum of squares of the elements in the formula (I), and s, which is the smaller of the sum of squares, is 1EiZero setting is carried out, and the sparsity of sensor attack estimation is ensured;
3.4) constructing a Lorberg-like observer as shown in formula (8):
Figure BDA0002187509850000077
wherein the content of the first and second substances,
Figure BDA0002187509850000078
3.5) initialization definition based on equation (5)
Figure BDA0002187509850000079
m＝0,
Figure BDA00021875098500000710
a) If v is 0.8
Figure BDA00021875098500000711
And is
Figure BDA00021875098500000712
Then the iterative operation is performed by equation (8) until
Figure BDA00021875098500000713
To that end
Figure BDA00021875098500000714
Entering b); otherwise, directly entering b);
b) if it is
Figure BDA0002187509850000081
The reset m is set to 0 and,
Figure BDA0002187509850000082
returning to a); otherwise, obtaining the system state at the t-T moment and the estimation value of the sensor attack at the t moment
Figure BDA0002187509850000083
The experimental results show that the attack can be accurately estimated in real time, and the system state before tau moments is estimated. The operation result can meet the requirements of precision and real-time performance of practical application, and required relevant parameters can be measured by using a low-cost sensor.
The embodiments of the present invention have been described and illustrated in detail above with reference to the accompanying drawings, but are not limited thereto. Many variations and modifications are possible which remain within the knowledge of a person skilled in the art, given the concept underlying the invention.

Claims (1)

1. A networked motion control system attack identification method based on a Loenberger-like observer is characterized by comprising the following steps:
step 1), establishing a state space equation of a networked motion control system and discretizing:
considering the situation that sensor attack and noise exist in the system, the state space equation is discretized, and the equation (1) is shown as the following formula:
Figure FDA0002187509840000011
wherein, A is a state matrix of the system, B is an input matrix, C is an output matrix, x represents a state quantity of the system, u is a system input, y is a system output, and a represents a sensor attack;
step 2), selecting tau sensor measurement values to construct an output equation, wherein the process is as follows:
2.1) acquiring tau epsilon N measurement values, and constructing an output equation of the ith sensor as shown in the formula (2):
wherein the content of the first and second substances,
2.2) since U (t) is known, the formula (2) is simplified to the formula (3):
Yi(t)＝Oix(t-τ+1)+Ei(t) ⑶
wherein the content of the first and second substances,
Figure FDA0002187509840000015
2.3) definition of
Figure FDA0002187509840000016
The output equation is simplified as shown in equation (4):
Figure FDA0002187509840000021
wherein the content of the first and second substances,
Figure FDA0002187509840000022
Q＝[O I]i is an identity matrix;
step 3), constructing a quasi-Luenberger observer, and carrying out the following process:
3.1) augmenting the system, using y (t) as new input quantity, and enabling
Figure FDA0002187509840000023
Obtaining an augmented state space equation as shown in formula (5):
wherein the content of the first and second substances,
Figure FDA0002187509840000025
Figure FDA0002187509840000026
bifor natural basis vectors, the superscript "T" represents the transpose of the matrix,
Figure FDA0002187509840000027
as an estimate of the system state quantity and sensor attack z,
Figure FDA0002187509840000028
pre-estimated values of system state quantity and sensor attack z;
3.2) constructing a Lyapunov energy function, as shown in the formula (6):
wherein the content of the first and second substances,
Figure FDA00021875098400000210
is an estimated value of the system state quantity and the sensor attack z, | ·| non-calculation2A two-norm representing a;
3.3) constructing a projection operator as shown in formula (7):
Π(z)＝Π(x,E)＝(x,Π'(E)) ⑺
wherein pi' (E) represents E ═ E (E)1,E2,…,Ep)TIn (1), obtain EiThe sum of squares of the middle elements, s (s < p) E elements with smaller sum of squaresiZero setting is carried out, and the sparsity of sensor attack estimation is ensured;
3.4) constructing a Lorberg-like observer as shown in formula (8):
Figure FDA0002187509840000031
wherein, L ═ QTSigma, sigma is a positive definite matrix;
3.5) initialization definition based on equation (5)
Figure FDA0002187509840000032
a) If it is
Figure FDA0002187509840000033
And is
Figure FDA0002187509840000034
v∈[0,1]The artificial set value is obtained by performing iterative operation according to the formula (8) until the artificial set value is obtained
Figure FDA0002187509840000035
To that end
Figure FDA0002187509840000036
Entering b); otherwise, directly entering b);
b) if it is
Figure FDA0002187509840000037
Reset
Figure FDA0002187509840000038
Returning to a); otherwise, obtaining the system state at the t-T moment and the estimation value of the sensor attack at the t moment
Figure FDA0002187509840000039
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CN111258223A (en) * 2020-03-12 2020-06-09 电子科技大学 Sliding mode-based switching networked control system safety control method
CN112596387A (en) * 2020-12-14 2021-04-02 电子科技大学 Networked system security control method based on extended observer
CN113489673A (en) * 2021-05-25 2021-10-08 浙江工业大学 Networked motion control system attack estimation method based on projection intermediate observer
CN113595974A (en) * 2021-06-11 2021-11-02 山东师范大学 Security control method and system for attacked discrete random distribution control system

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Cited By (6)

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Publication number Priority date Publication date Assignee Title
CN111258223A (en) * 2020-03-12 2020-06-09 电子科技大学 Sliding mode-based switching networked control system safety control method
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