CN110708284A - Networked motion control system attack estimation method based on gradient descent algorithm - Google Patents

Networked motion control system attack estimation method based on gradient descent algorithm Download PDF

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CN110708284A
CN110708284A CN201910812076.7A CN201910812076A CN110708284A CN 110708284 A CN110708284 A CN 110708284A CN 201910812076 A CN201910812076 A CN 201910812076A CN 110708284 A CN110708284 A CN 110708284A
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attack
formula
sensor
gradient descent
constructing
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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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    • 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
    • H04L63/1408—Network architectures or network communication protocols for network security for detecting or protecting against malicious traffic by monitoring network traffic
    • H04L63/1416—Event detection, e.g. attack signature detection
    • 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
    • H04L63/20—Network architectures or network communication protocols for network security for managing network security; network security policies in general

Abstract

A networked motion control system attack estimation method based on a gradient descent algorithm comprises the steps of firstly, considering the condition that a sensor attack exists in a system, determining a state space equation of the system and discretizing the state space equation; constructing an output equation of the tau sensor measurement values; and finally, constructing an observer based on a gradient descent algorithm, and converging the estimation error to a preset minimum energy boundary. The invention adopts the event-driven technology, can save the computing resource and improve the computing performance of the system. The observer design based on the gradient descent algorithm has higher attack estimation effect precision, and can improve the estimation performance by adjusting specific parameters.

Description

Networked motion control system attack estimation method based on gradient descent algorithm
Technical Field
The invention belongs to the technical field of network security, and particularly provides a networked motion control system attack estimation method based on a gradient descent algorithm, which can identify the attack, evaluate the security situation of a system and guarantee the safe operation of the system.
Background
The networked motion control system refers to a network control system in which an information transmission processing process and an object dynamic evolution process are mutually influenced and closely coupled. However, it is the high coupling of the information transfer process to the dynamics of the system that makes such systems vulnerable to information attacks. In order to ensure that networked motion control systems can operate safely and reliably, they must have the ability to automatically identify attacks. Therefore, whether the attack signal can be accurately identified plays an important role in the motion control system.
At present, a method for identifying attacks in real time depends on the design of an observer, including unknown input observers such as a robust observer, a sliding mode observer and a middle observer. The sliding mode observer needs a system to meet the observer matching condition, and also needs to know information such as an attack signal upper bound, however, any effective information about the attack cannot be obtained in actual engineering. The robust observer has no limit of observer matching conditions, but the upper bound of the estimation error is unknown, so that the estimation accuracy cannot be guaranteed. 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 converged into 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 networked motion control system attack estimation method based on a gradient descent algorithm, and particularly, the method is used for reconstructing an output signal containing sparsity sensor attack, estimating the state and the attack of the system and ensuring that an estimation error is converged within a preset minimum energy boundary.
The invention provides the following technical scheme for solving the technical problems:
a networked motion control system attack estimation method based on a gradient descent algorithm comprises the following steps:
step 1), establishing a state space equation of a networked motion control system and discretizing:
considering the situation that the sensor attack exists in the system, the state space equation is discretized, and the equation (1) is shown as follows:
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 BDA0002185344400000022
wherein the content of the first and second substances,
Figure BDA0002185344400000023
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 BDA0002185344400000025
2.3) definition of
Figure BDA0002185344400000026
The output equation is simplified as shown in equation (4):
Figure BDA0002185344400000027
wherein the content of the first and second substances,
Figure BDA0002185344400000028
Q＝[O I]i is an identity matrix;
step 3), constructing an observer based on an event-driven gradient descent algorithm, wherein the process is as follows:
3.1) constructing a Lyapunov energy function as shown in the formula (5), and calculating the energy of an estimated value
Figure BDA0002185344400000031
Figure BDA0002185344400000032
Wherein the content of the first and second substances,
Figure BDA0002185344400000033
is an estimated value of the system state quantity and the sensor attack z, | ·| non-calculation2A two-norm representing a;
3.2) constructing a projection operator as shown in formula (6):
Π(z)＝Π(x,E)＝(x,Π'(E)) ⑹
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;
3.3) constructing an observer based on a gradient descent algorithm as shown in the formula (7):
wherein the superscript "T" denotes the transpose of the matrix,
Figure BDA0002185344400000035
the estimated values of the system state quantity and the sensor attack z are obtained, and eta is a step length;
3.4) initialization definition k ═ 1,
a) if it is
Figure BDA0002185344400000037
Alpha is an artificially set positive real number, and
Figure BDA0002185344400000038
v∈[0,1]if the value is an artificial set value, iterative operation is performed by the formula (7) andup toTo that endk +1, into b); otherwise, directly entering b);
b) if it is
Figure BDA00021853444000000312
Reset
Figure BDA00021853444000000313
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 BDA00021853444000000314
The invention discloses a networked motion control system attack estimation method based on a gradient descent algorithm.
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; due to the adoption of the design of the observer based on the gradient descent algorithm, the attack estimation effect is higher in precision, and the estimation performance can be improved by adjusting specific parameters; 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 estimation method based on a gradient descent algorithm, firstly modeling a motion control system, considering sensor attacks in the system, determining a state space equation of the system and discretizing the equation; constructing an output equation containing sensor attack; an observer is constructed based on a gradient descent algorithm to estimate the sensor attack and the system state.
A networked motion control system attack estimation method based on a gradient descent algorithm 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) an observer based on a gradient descent algorithm is constructed.
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 BDA0002185344400000041
wherein the state matrix
Figure BDA0002185344400000042
Input matrix
Figure BDA0002185344400000043
Output matrixx represents the system state quantity, u is the system input, y is the system output, and the sensor attacks
Figure BDA0002185344400000051
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 BDA0002185344400000052
wherein the content of the first and second substances,
Figure BDA0002185344400000054
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,
Figure BDA0002185344400000055
2.3) definition ofThe output equation is simplified as shown in equation (4):
Figure BDA0002185344400000057
wherein the content of the first and second substances,
Figure BDA0002185344400000058
step 3) constructing an observer based on an event-driven gradient descent algorithm, wherein the process is as follows:
3.1) constructing a Lyapunov energy function as shown in the formula (5), and calculating the energy of an estimated value
Figure BDA0002185344400000061
Figure BDA0002185344400000062
Wherein the content of the first and second substances,
Figure BDA0002185344400000063
is an estimated value of the system state quantity and the sensor attack z, | ·| non-calculation2A two-norm representing a;
3.2) constructing a projection operator as shown in formula (6):
Π(z)＝Π(x,E)＝(x,Π'(E)) ⑹
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;
3.3) constructing an observer based on a gradient descent algorithm as shown in the formula (7):
Figure BDA0002185344400000064
wherein the superscript "T" denotes the transpose of the matrix,
Figure BDA0002185344400000065
the step length eta is 0.00001 and is an estimated value of the system state quantity and the sensor attack z;
3.4) initialization definition k is 1, m is 0,
a) if α is 0.0005 and v is 0.8, then
Figure BDA0002185344400000067
And is
Figure BDA0002185344400000068
Then the iterative operation is performed by equation (7) and
Figure BDA0002185344400000069
up to
Figure BDA00021853444000000610
To that end
Figure BDA00021853444000000611
k +1, into b); otherwise, directly entering b);
b) if it is
Figure BDA00021853444000000612
The reset m is set to 0 and,
Figure BDA00021853444000000613
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 BDA00021853444000000614
The experimental result shows that the method can converge the estimation error into a preset minimum energy boundary, and can meet the requirements of precision and real-time performance of practical application. The relevant parameters required by the invention can be adjusted according to actual conditions and measured by low-cost sensors.
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 estimation method based on a gradient descent algorithm is characterized in that
The method comprises the following steps:
step 1), establishing a state space equation of a networked motion control system and discretizing:
considering the situation that the sensor attack exists in the system, the state space equation is discretized, and the equation (1) is shown as follows:
Figure RE-FDA0002277024430000011
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 RE-FDA0002277024430000012
wherein the content of the first and second substances,
Figure RE-FDA0002277024430000013
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 RE-FDA0002277024430000015
2.3) definition of
Figure RE-FDA0002277024430000016
Simplifying the output equation toAs shown in formula (4):
wherein the content of the first and second substances,Q＝[O I]i is an identity matrix;
step 3), constructing an observer based on an event-driven gradient descent algorithm, wherein the process is as follows:
3.1) constructing a Lyapunov energy function as shown in the formula (5), and calculating the energy of an estimated value
Figure RE-FDA0002277024430000023
Figure RE-FDA0002277024430000024
Wherein the content of the first and second substances,
Figure RE-FDA0002277024430000025
is an estimated value of the system state quantity and the sensor attack z, | ·| non-calculation2A two-norm representing a;
3.2) constructing a projection operator as shown in formula (6):
Π(z)＝Π(x,E)＝(x,Π'(E)) ⑹
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;
3.3) constructing an observer based on a gradient descent algorithm as shown in the formula (7):
Figure RE-FDA0002277024430000026
wherein the superscript "T" denotes the transpose of the matrix,
Figure RE-FDA0002277024430000027
the estimated values of the system state quantity and the sensor attack z are obtained, and eta is a step length;
3.4) initialization definition k is 1, m is 0,
Figure RE-FDA0002277024430000028
a) if it isAlpha is an artificially set positive real number, and
Figure RE-FDA00022770244300000210
v∈[0,1]if the value is an artificial set value, iterative operation is performed by the formula (7) andup to
Figure RE-FDA00022770244300000212
To that end
Figure RE-FDA00022770244300000213
Entering b); otherwise, directly entering b);
b) if it is
Figure RE-FDA00022770244300000214
The reset m is set to 0 and,
Figure RE-FDA00022770244300000215
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 RE-FDA00022770244300000216
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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
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* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN112596387A (en) * 2020-12-14 2021-04-02 电子科技大学 Networked system security control method based on extended observer
CN113810906A (en) * 2021-02-24 2021-12-17 浙江工业大学 Sensor attack estimation method for networked servo motor
CN113810906B (en) * 2021-02-24 2024-04-16 浙江工业大学 Sensor attack estimation method for networked servo motor
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
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