CN110850817B - Safety estimation method of networked industrial control system - Google Patents

Safety estimation method of networked industrial control system Download PDF

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CN110850817B
CN110850817B CN201910994731.5A CN201910994731A CN110850817B CN 110850817 B CN110850817 B CN 110850817B CN 201910994731 A CN201910994731 A CN 201910994731A CN 110850817 B CN110850817 B CN 110850817B
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estimator
estimation
matrix
industrial control
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CN110850817A (en
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陈云
孟雪阳
陈张平
赵晓东
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Hangzhou Dianzi University
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Hangzhou Dianzi University
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    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B19/00—Programme-control systems
    • G05B19/02—Programme-control systems electric
    • G05B19/418—Total factory control, i.e. centrally controlling a plurality of machines, e.g. direct or distributed numerical control [DNC], flexible manufacturing systems [FMS], integrated manufacturing systems [IMS], computer integrated manufacturing [CIM]
    • G05B19/41885—Total factory control, i.e. centrally controlling a plurality of machines, e.g. direct or distributed numerical control [DNC], flexible manufacturing systems [FMS], integrated manufacturing systems [IMS], computer integrated manufacturing [CIM] characterised by modeling, simulation of the manufacturing system
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02P—CLIMATE CHANGE MITIGATION TECHNOLOGIES IN THE PRODUCTION OR PROCESSING OF GOODS
    • Y02P90/00—Enabling technologies with a potential contribution to greenhouse gas [GHG] emissions mitigation
    • Y02P90/02—Total factory control, e.g. smart factories, flexible manufacturing systems [FMS] or integrated manufacturing systems [IMS]

Abstract

The invention discloses a safety estimation method of a networked industrial control system. The existing method can only monitor the system state at fixed time and fixed point, and is difficult to accurately reflect the real-time running state of the system. The method comprises the steps of firstly establishing a model of state estimation of the networked industrial control system, then establishing an error system model of safety estimation, and finally solving an estimator gain matrix. The method adopts a complex network estimation method based on an event trigger strategy, considers the influence of network attack on a system, designs a recursive state estimator by an extended Kalman filtering method, and determines a gain matrix of the state estimator by solving two Riccath differential equations. Based on the event trigger strategy, the network burden and energy consumption caused by a large amount of information transmission are reduced, the constructed estimator can realize timely and accurate estimation of the system state under the condition of suffering network attack, and a timely and effective method is provided for safety estimation, monitoring and control of a networked industrial control system.

Description

Safety estimation method of networked industrial control system
Technical Field
The invention belongs to the technical field of automatic control, and relates to a safety estimation method of a networked industrial control system, which considers the network attack possibly suffered by an important industrial control system and can be used for the safe operation and estimation of a modern large-scale networked industrial control system.
Background
The structure of the modern industrial control system is more and more complex, and gradually develops towards networking direction, so that the combination of a computer network and a control network is promoted, the industrial control field is widened, and meanwhile, a great challenge is brought to the safe operation of the industrial control system. For example, viruses and trojans attack industrial control systems on the global scale frequently, the scope of influence, economic loss and duration of the attacks are far from those of common network security events, so that the attacks not only cause huge economic loss, but also bring serious threats to national security.
Although the industrial control system usually includes a monitoring device, the application of the industrial control system is often limited, and the system state can only be monitored at regular time and fixed point, so that the real-time state of the system is difficult to accurately reflect, and particularly, timely and effective early warning cannot be performed when an emergency occurs. Therefore, for a complex networked industrial control system suffering from network attack, an effective new method for safety estimation is urgently needed to be provided, so that the important industrial control system is ensured to be safely and effectively monitored.
Disclosure of Invention
The invention aims to provide a safety estimation method of an industrial control system based on a complex network, aiming at the problem that the state estimation of the networked industrial control system in China is difficult to be carried out timely and accurately under the network attack.
Distributed Control Systems (DCS) are widely used in modern industrial processes, which usually employ a hierarchical structure, each level consisting of several subsystems. It is necessary for different subsystems to achieve several specified limited goals. One subsystem of the DCS is selected as a node, and different subsystems of the DCS form a typical complex network structure. Each part in the DCS system is connected by a communication network, so that information flows between adjacent subsystems, and a coupling relationship exists between nodes, which is expressed as an external coupling characteristic of a complex network. For a certain node, the main control parameters comprise temperature, pressure, concentration, flow and flow rate, and there may be coupling relations between different parameters, such as flow and flow rate, and the coupling relations between the five different parameters form the internal coupling of the complex network.
In order to save network resources and reduce the burden of a network communication channel, the invention adopts a complex network security estimation method based on an event trigger strategy, considers the influence of network attack possibly suffered on the state of an industrial control system, designs a recursive state estimator by using an extended Kalman filtering method, determines a gain matrix of the state estimator by solving two Riccati (Riccati) differential equations, and provides a timely and effective method for the security estimation and operation of the networked industrial control system under the network attack.
The method comprises the following specific steps:
step (1), establishing a spatial model for state estimation of a networked industrial control system;
establishing a dynamic equation of the state of the networked industrial control system based on the complex network model:
Figure GDA0002637992030000021
wherein the content of the first and second substances,
Figure GDA0002637992030000022
the state vector of the node i at the moment k is represented, k is 0,1,2 …, i belongs to N, and N represents the number of nodes forming the complex network;
Figure GDA0002637992030000023
respectively representing the temperature, pressure, concentration, flow and flow rate of the controlled quantity,
Figure GDA0002637992030000024
represents n0The column vector of the dimension, superscript T represents the transposition of the matrix;
Figure GDA0002637992030000025
represents the measured output value of node i at time k,
Figure GDA0002637992030000026
temperature, concentration and flow rate of the output quantity are respectively expressed;
＝diag{γ1,γ2,γ3,γ4,γ5denotes the internal coupling matrix of the complex network model, diag {. cndot } denotes the diagonal matrix, γl≧ 0(l ═ 1,2,3,4,5) is a known constant representing the internal coupling coefficient of node i;
Figure GDA0002637992030000027
an external coupling matrix representing a complex network model with matrix dimensions of NxN, constants
Figure GDA0002637992030000028
Representing the connection condition between nodes i, j, and the content of i, j belongs to N: when in use
Figure GDA0002637992030000029
When, it represents that the nodes i, j are communicated; when in use
Figure GDA00026379920300000210
When the node I is not communicated with the node j, the node I is not communicated with the node j;
wi,k∈R1representing the process noise at node i at time k, with variance Qi,kI.e. E { wi,k}＝0,
Figure GDA00026379920300000211
vi,k∈R1Representing the measurement noise of node i at time k, with variance Ri,kI.e. E { v }i,k}＝0,
Figure GDA00026379920300000212
E {. is the mathematically expected symbol;
Ai,k∈R5×5、Bi,k∈R5×1、Ci,k∈R3×5and Di,k∈R3×1Are all known matrices, symbols
Figure GDA00026379920300000213
Represents n1×n2A real matrix of dimensions.
If the node i suffers from a network attack at time k, a set of random variables d satisfying Bernoulli distribution is usedi,kTo describe, di,kSatisfies the following conditions:
Figure GDA00026379920300000214
wherein
Figure GDA00026379920300000215
Prob {. for a known scalar represents the probability of a random event.
Measurement output after being affected by spoofing attack
Figure GDA00026379920300000216
Therein, ζi,k＝-yi,k+μi,kSpoof signal, y, representing an attacker inputi,kIs the measured output value, mu, of node ii,kIs a signal with limited energy, and the k is more than or equal to 0 for any k, so as to meet the requirement
Figure GDA0002637992030000031
Wherein
Figure GDA0002637992030000032
Is a known scalar.
Using an event-triggered communication protocol:
Figure GDA0002637992030000033
wherein
Figure GDA0002637992030000034
Is a positive scalar quantity;
Figure GDA0002637992030000035
is about measuring the output
Figure GDA0002637992030000036
Sum positive scalar quantity
Figure GDA0002637992030000037
I.e. the condition triggered by the event;
Figure GDA0002637992030000038
indicating node i at trigger time stThe transmitted measurement output value, t ═ 0,1,2.
According to an event-triggered communication protocol, only if
Figure GDA0002637992030000039
When the trigger condition is met, the measurement data is transmitted; otherwise, not transmitting the measurement data;
data for eventual transmission to an estimator
Figure GDA00026379920300000310
Step (2), establishing an error system model of safety estimation;
(2-1) constructing a safety estimator:
based on an extended Kalman filtering method, establishing an estimator model:
Figure GDA00026379920300000311
wherein
Figure GDA00026379920300000312
Represents a state vector xi,kA step of prediction value at the moment k;
Figure GDA00026379920300000314
represents a state vector xi,k+1An estimate at time k + 1; ki,k+1∈R5×3Is the estimator gain matrix to be solved.
(2-2) establishing an estimation error system:
defining prediction error of node i
Figure GDA00026379920300000315
And estimation error
Figure GDA00026379920300000316
Establishing an estimation error system model:
Figure GDA00026379920300000317
step (3), solving a gain matrix of the safety estimator;
(3-1) solving the covariance of the prediction error Pi,k+1|k：
Figure GDA00026379920300000318
Obtaining a prediction error covariance Pi,k+1|kOne upper bound of (c):
Figure GDA0002637992030000041
wherein
Figure GDA0002637992030000042
(3-2) solving the estimation error covariance Pi,k+1|k+1：
Figure GDA0002637992030000043
Wherein the content of the first and second substances,
Figure GDA0002637992030000044
Figure GDA0002637992030000045
Figure GDA0002637992030000046
Figure GDA0002637992030000047
Figure GDA0002637992030000048
Figure GDA0002637992030000049
Figure GDA00026379920300000410
obtaining an estimation error covariance Pi,k+1|k+1One upper bound of (c):
Figure GDA00026379920300000411
wherein the content of the first and second substances,
Figure GDA0002637992030000052
h(h 1.., 6) is 6 arbitrary positive scalars within the interval (0,1), the superscript-1 representing the matrix or the inverse of the scalar; scalar ξi,k+1E {0,1}, and xi when the event trigger condition at the moment k is meti,k+10; conversely xii,k+1＝1。
(3-3) solving an estimator gain matrix:
the following two ricatty difference equations are solved:
Figure GDA0002637992030000053
Figure GDA0002637992030000054
wherein the content of the first and second substances,
Figure GDA0002637992030000055
and
Figure GDA0002637992030000056
are two solutions of the system of equations and the initial values satisfy
Figure GDA0002637992030000057
I.e. the estimated error covariance Pi,k+1|k+1An upper bound of; to pair
Figure GDA0002637992030000058
Calculating a partial derivative:
Figure GDA0002637992030000059
order to
Figure GDA00026379920300000510
To obtain
Figure GDA00026379920300000511
Ki,k+1Namely a gain matrix of the networked industrial control system safety estimator.
The method of the invention is a complex network estimation method based on the event trigger strategy, which can save network resources and reduce the burden of network communication channels. Considering the influence of network attacks on the system, a recursive state estimator is designed through an extended Kalman filtering method, and a gain matrix of the state estimator is determined by solving two Riccati (Riccati) difference equations.
The estimator constructed by the invention can realize timely and accurate estimation of the system state under the condition of network attack, and ensures the safety monitoring and control of the system, so the estimator is called as a safety estimator and can provide a timely and effective method for the safety estimation, monitoring and control of a networked industrial control system.
Detailed Description
A safety estimation method of a networked industrial control system comprises the following specific steps:
step (1), establishing a spatial model for state estimation of a networked industrial control system;
establishing a dynamic equation of the state of the networked industrial control system based on the complex network model:
Figure GDA0002637992030000061
wherein the content of the first and second substances,
Figure GDA0002637992030000062
the state vector of the node i at the moment k is represented, k is 0,1,2 …, i belongs to N, and N represents the number of nodes forming the complex network;
Figure GDA0002637992030000063
respectively representing the temperature, pressure, concentration, flow and flow rate of the controlled quantity,
Figure GDA0002637992030000064
represents n0The column vector of the dimension, superscript T represents the transposition of the matrix;
Figure GDA0002637992030000065
represents the measured output value of node i at time k,
Figure GDA0002637992030000066
temperature, concentration and flow rate of the output quantity are respectively expressed;
＝diag{γ1,γ2,γ3,γ4,γ5denotes the internal coupling matrix of the complex network model, diag {. cndot } denotes the diagonal matrix, γl≧ 0(l ═ 1,2,3,4,5) is a known constant representing the internal coupling coefficient of node i;
Figure GDA0002637992030000067
an external coupling matrix representing a complex network model with matrix dimensions of NxN, constants
Figure GDA0002637992030000068
Representing the connection condition between nodes i, j, and the content of i, j belongs to N: when in use
Figure GDA0002637992030000069
When, it represents that the nodes i, j are communicated; when in use
Figure GDA00026379920300000610
When the node I is not communicated with the node j, the node I is not communicated with the node j;
wi,k∈R1representing the process noise at node i at time k, with variance Qi,kI.e. E { wi,k}＝0,
Figure GDA00026379920300000611
vi,k∈R1Representing the measurement noise of node i at time k, with variance Ri,kI.e. E { v }i,k}＝0,
Figure GDA00026379920300000612
E {. is the mathematically expected symbol;
Ai,k∈R5×5、Bi,k∈R5×1、Ci,k∈R3×5and Di,k∈R3×1Are all known matrices, symbols
Figure GDA00026379920300000613
Represents n1×n2A real matrix of dimensions.
If the node i suffers from a network attack at time k, a set of random variables d satisfying Bernoulli distribution is usedi,kTo describe, di,kSatisfies the following conditions:
Figure GDA00026379920300000614
wherein
Figure GDA00026379920300000615
Prob {. for a known scalar represents the probability of a random event.
Measurement output after being affected by spoofing attack
Figure GDA0002637992030000071
Therein, ζi,k＝-yi,k+μi,kSpoof signal, y, representing an attacker inputi,kIs the measured output value, mu, of node ii,kIs a signal with limited energy, and the k is more than or equal to 0 for any k, so as to meet the requirement
Figure GDA0002637992030000072
Wherein
Figure GDA0002637992030000073
Is a known scalar.
Using an event-triggered communication protocol:
Figure GDA0002637992030000074
wherein
Figure GDA0002637992030000075
Is a positive scalar quantity;
Figure GDA0002637992030000076
is about measuring the output
Figure GDA0002637992030000077
Sum positive scalar quantity
Figure GDA0002637992030000078
I.e. the condition triggered by the event;
Figure GDA0002637992030000079
indicating node i at trigger time stTransmitted byThe output value is measured, t ═ 0,1,2.
According to an event-triggered communication protocol, only if
Figure GDA00026379920300000710
When the trigger condition is met, the measurement data is transmitted; otherwise, not transmitting the measurement data;
data for eventual transmission to an estimator
Figure GDA00026379920300000711
Step (2), establishing an error system model of safety estimation;
(2-1) constructing a safety estimator:
based on an extended Kalman filtering method, establishing an estimator model:
Figure GDA00026379920300000712
wherein
Figure GDA00026379920300000713
Represents a state vector xi,kA step of prediction value at the moment k;
Figure GDA00026379920300000714
represents a state vector xi,k+1An estimate at time k + 1; ki,k+1∈R5×3Is the estimator gain matrix to be solved.
(2-2) establishing an estimation error system:
defining prediction error of node i
Figure GDA00026379920300000715
And estimation error
Figure GDA00026379920300000716
Establishing an estimation error system model:
Figure GDA00026379920300000717
step (3), solving a gain matrix of the safety estimator;
(3-1) solving the covariance of the prediction error Pi,k+1|k：
Figure GDA0002637992030000081
Obtaining a prediction error covariance Pi,k+1|kOne upper bound of (c):
Figure GDA0002637992030000082
wherein
Figure GDA0002637992030000083
(3-2) solving the estimation error covariance Pi,k+1|k+1：
Figure GDA0002637992030000084
Wherein the content of the first and second substances,
Figure GDA0002637992030000085
Figure GDA0002637992030000086
Figure GDA0002637992030000087
Figure GDA0002637992030000088
Figure GDA0002637992030000089
Figure GDA00026379920300000810
Figure GDA00026379920300000811
obtaining an estimation error covariance Pi,k+1|k+1One upper bound of (c):
Figure GDA0002637992030000091
wherein the content of the first and second substances,
Figure GDA0002637992030000093
h(h 1.., 6) is 6 arbitrary positive scalars within the interval (0,1), the superscript-1 representing the matrix or the inverse of the scalar; scalar ξi,k+1E {0,1}, and xi when the event trigger condition at the moment k is meti,k+10; conversely xii,k+1＝1。
(3-3) solving an estimator gain matrix:
the following two ricatty difference equations are solved:
Figure GDA0002637992030000094
Figure GDA0002637992030000095
wherein the content of the first and second substances,
Figure GDA0002637992030000096
and
Figure GDA0002637992030000097
are two solutions of the system of equations and the initial values satisfy
Figure GDA0002637992030000098
I.e. the estimated error covariance Pi,k+1|k+1An upper bound of; to pair
Figure GDA0002637992030000099
Calculating a partial derivative:
Figure GDA00026379920300000910
order to
Figure GDA00026379920300000911
To obtain
Figure GDA00026379920300000912
Ki,k+1Namely the gain matrix of the networked industrial control system safety estimator solved by the invention.

Claims (1)

1. A safety estimation method of a networked industrial control system is characterized by comprising the following specific steps:
step (1), establishing a spatial model for state estimation of a networked industrial control system;
establishing a dynamic equation of the state of the networked industrial control system based on the complex network model:
Figure FDA0002637992020000011
wherein the content of the first and second substances,
Figure FDA0002637992020000012
representing a state vector of a node i at the moment k, wherein k is 0,1,2, i belongs to N, and N represents the number of nodes forming the complex network;
Figure FDA0002637992020000013
respectively representing the temperature, pressure, concentration, flow and flow rate of the controlled quantity,
Figure FDA0002637992020000014
represents n0The column vector of the dimension, superscript T represents the transposition of the matrix;
Figure FDA0002637992020000015
represents the measured output value of node i at time k,
Figure FDA0002637992020000016
temperature, concentration and flow rate of the output quantity are respectively expressed; biag { γ ═1,γ2,γ3,γ4,γ5Denotes the internal coupling matrix of the complex network model, diag {. cndot } denotes the diagonal matrix, γl≧ 0(l ═ 1,2,3,4,5) is a known constant representing the internal coupling coefficient of node i;
Figure FDA0002637992020000017
an external coupling matrix representing a complex network model with matrix dimensions of NxN, constants
Figure FDA0002637992020000018
Representing the connection condition between nodes i, j, and the content of i, j belongs to N: when in use
Figure FDA0002637992020000019
When, it represents that the nodes i, j are communicated; when in use
Figure FDA00026379920200000110
When the node I is not communicated with the node j, the node I is not communicated with the node j;
wi,k∈R1representing the process noise at node i at time k, with variance Qi,kI.e. E { wi,k}＝0,
Figure FDA00026379920200000111
vi,k∈R1Representing the measurement noise of node i at time k, with variance Ri,kI.e. E { v }i,k}＝0,
Figure FDA00026379920200000112
E {. is the mathematically expected symbol;
Ai,k∈R5×5、Bi,k∈R5×1、Ci,k∈R3×5and Di,k∈R3×1Are all known matrices, symbols
Figure FDA00026379920200000113
Represents n1×n2A real matrix of dimensions;
if the node i suffers from a network attack at time k, a set of random variables d satisfying Bernoulli distribution is usedi,kTo describe, di,kSatisfies the following conditions:
Figure FDA00026379920200000114
wherein
Figure FDA00026379920200000115
Prob {. for a known scalar represents the probability of a random event;
measurement output after being affected by spoofing attack
Figure FDA00026379920200000116
Therein, ζi,k＝-yi,k+μi,kSpoof signal, y, representing an attacker inputi,kIs the measured output value, mu, of node ii,kIs a signal with limited energy, and the k is more than or equal to 0 for any k, so as to meet the requirement
Figure FDA0002637992020000021
Wherein
Figure FDA0002637992020000022
Is a known scalar;
using an event-triggered communication protocol:
Figure FDA0002637992020000023
wherein
Figure FDA0002637992020000024
Is a positive scalar quantity;
Figure FDA0002637992020000025
is about the measurement output after being affected by the spoofing attack
Figure FDA0002637992020000026
Sum positive scalar quantity
Figure FDA0002637992020000027
I.e. the condition triggered by the event;
Figure FDA0002637992020000028
indicating node i at trigger time stA transmitted measurement output value, t ═ 0,1, 2.;
according to an event-triggered communication protocol, only if
Figure FDA0002637992020000029
When the trigger condition is met, the measurement data is transmitted; otherwise, not transmitting the measurement data;
data for eventual transmission to an estimator
Figure FDA00026379920200000210
k∈{st,st+1,...,st+1-1}；
Step (2), establishing an error system model of safety estimation;
(2-1) constructing a safety estimator:
based on an extended Kalman filtering method, establishing an estimator model:
Figure FDA00026379920200000211
wherein
Figure FDA00026379920200000212
Represents a state vector xi,kA step of prediction value at the moment k;
Figure FDA00026379920200000213
represents a state vector xi,k+1An estimate at time k + 1; ki,k+1∈R5×3Is estimator gain matrix to be solved;
(2-2) establishing an estimation error system:
defining prediction error of node i
Figure FDA00026379920200000214
And estimation error
Figure FDA00026379920200000215
Establishing an estimation error system model:
Figure FDA00026379920200000216
step (3), solving a gain matrix of the safety estimator;
(3-1) solving the covariance of the prediction error Pi,k+1|k：
Figure FDA0002637992020000031
Obtaining a prediction error covariance Pi,k+1|kOne upper bound of (c):
Figure FDA0002637992020000032
wherein
Figure FDA0002637992020000033
(3-2) solving the estimation error covariance Pi,k+1|k+1：
Figure FDA0002637992020000034
Wherein the content of the first and second substances,
Figure FDA0002637992020000035
Figure FDA0002637992020000036
Figure FDA0002637992020000037
Figure FDA0002637992020000038
Figure FDA0002637992020000039
Figure FDA00026379920200000310
Figure FDA00026379920200000311
obtaining an estimation error covariance Pi,k+1|k+1One upper bound of (c):
Figure FDA0002637992020000041
wherein the content of the first and second substances,
Figure FDA0002637992020000042
his any positive scalar in the interval (0,1), h is 1,2, …,6, superscript-1 denotes the matrix or the inverse of the scalar; scalar ξi,k+1E {0,1}, and xi when the event trigger condition at the moment k is meti,k+10; conversely xii,k+1＝1；
(3-3) solving an estimator gain matrix:
the following two ricatty difference equations are solved:
Figure FDA0002637992020000043
Figure FDA0002637992020000044
wherein the content of the first and second substances,
Figure FDA0002637992020000045
and
Figure FDA0002637992020000046
are two solutions of the system of equations and the initial values satisfy
Figure FDA0002637992020000047
Figure FDA0002637992020000048
I.e. the estimated error covariance Pi,k+1|k+1An upper bound of; to pair
Figure FDA0002637992020000049
Calculating a partial derivative:
Figure FDA00026379920200000410
order to
Figure FDA00026379920200000411
To obtain
Figure FDA00026379920200000412
Ki,k+1Namely a gain matrix of the networked industrial control system safety estimator.
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