CN110579963A - Networked motion control system state estimation method based on adaptive state observer - Google Patents
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Abstract
A networked motion control system state estimation method based on an adaptive state observer comprises the following steps: modeling a motion control system and determining a transfer function of the motion control system; converting the system transfer function into a state space model; switching the gain of the constructed state observer back and forth through a switching function after the system is attacked by switching; thereby accurately estimating the system state. The method of the invention considers the phenomenon that the networked motion control system generates switching attack, and the invention is not limited to the example, and the state estimation effect can meet the requirements of the precision and the real-time performance of the practical application.
Description
Technical Field
The invention belongs to the technical field of network security, and particularly provides a state estimation method of a networked motion control system based on an adaptive state observer, which can accurately estimate a state.
Background
with the continuous development of science and technology, the strategy of depth fusion of two types is continuously promoted, and the industrial application becomes more and more complex and huge. The networked industrial control system is used as an important infrastructure of national life-cycle industries such as energy, manufacturing, military industry and the like, and faces more and more risks, various attacks not only can cause data leakage and loss, but also can cause environmental disasters and casualties of people, directly influence economic development and social stability, and cause great damage to national safety.
In view of the importance of networked industrial control systems, researchers have employed various techniques to ensure stable operation of the systems from different directions. In the case of a system attack, many studies attempt to identify the attack and then find a coping strategy. From the perspective of system identification principle, compared with the traditional state estimation problem, the attack identification algorithm requires the system to satisfy more strict unknown input observability conditions, and thus is more difficult to implement in practical engineering. Therefore, researchers are more concerned about how to accurately estimate the state in an attack situation.
Many research efforts have proposed some important methods for system state estimation under certain types of attacks, such as spoofing attacks (FDI) or denial of service attacks (DOS). In recent years, the problem of system state estimation in the case of FDI attacks has been extensively studied. For a discrete time linear system, some research works attempt to convert a state estimation problem into a static batch processing optimization problem, solve the problem through a self-defined gradient descent algorithm, and partially research estimates the state by designing an attack elastic state observer; for continuous-time linear systems, researchers have attempted to reconstruct the state of the system in a multi-model system using an observable Gramian and Luenberger observer. However, an attacker may switch attack targets at any time, i.e. may attack different sensors at different times, whereas existing methods generally still use all sensor data under a switching attack, and using contaminated sensor data tends to cause rapid degradation of state estimation performance.
Disclosure of Invention
In order to overcome the defects of the existing method, the invention provides a state estimation method of a networked motion control system based on a self-adaptive state observer.
the technical scheme adopted by the invention for solving the technical problems is as follows:
a networked motion control system state estimation method based on an adaptive state observer comprises the following steps:
1) Determining a networked motion control system transfer function;
The transfer function of the networked motion control system is shown as the formula (1):
wherein G(s) is a transfer function of the networked motion control system, s is a parameter of the transfer function, K, Tsis a system parameter;
2) establishing a state equation and an output equation of a networked motion control system, wherein the process is as follows:
2.1) converting the transfer function of the networked motion control system into a state space equation as shown in the formula (2):
x(t)＝Ax(t)+Bu(t) (2)
wherein, A is a state matrix of the system, B is an input matrix, x (t) represents a state quantity of the system, t is a time variable, and u (t) is system input;
2.2) the output equation of the networked motion control system is shown in formula (3):
y(t)＝Cx(t)+a(t) (3)
wherein y (t) represents system output quantity, x (t) represents system state quantity, C represents output matrix, a (t) represents attack signal;
3) Constructing an observer, and carrying out the following process;
3.1) calculating the switching matrix R of the switching functionξas shown in formula (4);
Rξ＝diag{r1(ξ)，…，ri(ξ)} (4)
when i ∈ SξTime, ri(xi) 0, otherwise1, i-1, 2, …, l, l representing the number of sensors, SξRepresenting the ξ -th attack model,s represents the number of attacked sensors;
3.2) based on various parameters, designing the self-adaptive state observer as shown in the formula (5):
Wherein the content of the first and second substances,An estimate of the system state quantity x is represented,Representing the estimated value of the output y, A representing the state transition matrix, u being the system input, B representing the input matrix, Lξrepresenting the gain, R, of the state observer to be designedξRepresenting a switching matrix of the switching function, and C representing an output matrix;
4) and solving the gain of the adaptive observer, wherein the process is as follows:
4.1) constructing a matrix, as shown in formula (6):
Wherein the content of the first and second substances, is the actual attack pattern of the attack, Alpha > 0 is observerdesign parameters, A denotes a state transition matrix, B denotes an input matrix, C denotes an output matrix, Rξrepresenting a switching matrix of the switching function;
4.2) if a positive real number η is present, the matrix P is positively determinedξand U, matrix NξSuch that the matrix inequality G < 0, P is obtainedξh, design adaptive observer gain Lξas shown in formula (7):
Lξ＝Pξ -1H (7)
where the superscript "-1" represents the inverse of the matrix, so that an accurate estimation of the state x is achieved by the adaptive observer (5).
the working principle of the invention is as follows: the method comprises the steps of firstly modeling a networked motion control system to obtain a state space model of the networked motion control system, and switching the gain of a constructed adaptive state observer back and forth through a switching function after the system is attacked, so that the state of the system is accurately estimated.
the invention has the beneficial effects that: solving observer gain L by matrix inequalityξand an adaptive state observer is constructed to realize accurate estimation of the state, and compared with the prior art, the method has the following practicability: under the condition that the system is attacked, the attack does not need to be identified, and the gain of the constructed adaptive observer is switched back and forth through a switch function, so that the state is accurately estimated.
Drawings
FIG. 1 is a schematic diagram of a networked motion control platform architecture;
FIG. 2 is a state estimation diagram for an original system;
Fig. 3 is a diagram of state estimation after an attack is injected into the sensor.
Detailed Description
In order to make the technical features, purposes and advantages of the present invention clearer and clearer, the technical scheme of the present invention is further described below with reference to the accompanying drawings and practical experiments.
referring to fig. 1-3, a networked motion control system state estimation method based on an adaptive state observer firstly models a motion control system and determines a transfer function of the motion control system; converting the system transfer function into a state space model; switching the gain of the constructed adaptive state observer back and forth through a switching function after the system is attacked; and finally, accurately estimating the state by a state observer.
the invention relates to a networked motion control system state estimation method based on a self-adaptive state observer, which comprises the following steps of:
1) determining a networked motion control system transfer function;
2) Establishing a state equation and an output equation of a networked motion control system;
3) constructing an observer;
4) and designing and solving the gain of the intermediate observer through a matrix inequality.
further, in step 1), determining a transfer function of the networked motion control system, wherein the process is as follows:
The transfer function of the networked motion control system is shown as the formula (1):
Wherein G(s) is a transfer function of the networked motion control system, s is a parameter of the transfer function, K, Tsas a system parameter, K is 0.08373, Ts＝0.02433。
Further, in the step 2), a state equation and an output equation of the networked motion control system are established, and the process is as follows:
2.1) converting the transfer function of the networked motion control system into a state space equation as shown in the formula (2):
x(t)＝Ax(t)+Bu(t) (2)
Wherein x represents the system state quantity, t is the time variable, the state transition matrixThe system inputs u (t) ═ kx (t), and selects parameter k ═ 14.669823.5635]input matrix B ═ 03.4414]TThe state curve is asAs shown in fig. 2.
2.2) the output equation of the networked motion control system is shown in formula (3):
y(t)＝Cx(t)+a(t) (3)
wherein y (t) represents system output quantity, x (t) represents system state quantity, C represents output matrix, a (t) represents attack signal, and the attack signal is designed as
3) constructing an observer, and carrying out the following process;
3.1) calculating the switching matrix R of the switching functionξAs shown in formula (4);
Rξ＝diag{r1(ξ)，…，ri(ξ)} (4)
when i ∈ Sξtime, ri(xi) ═ 0, otherwise 1, i ═ 1, 2, …, l, l represent the number of sensors, Sξrepresenting the ξ -th attack model,s represents the number of attacked sensors, and in practical experiments, the sensors are divided into two types: speed sensor and position sensor, so l 2, s 1, R1＝diag{1，1}，R2＝diag{0，1}，R3＝diag{1，0}。
3.2) based on various parameters, designing the self-adaptive state observer as shown in the formula (5):
Wherein the content of the first and second substances,an estimate of the system state quantity x is represented,representing the estimated value of the output y, A representing the state transition matrix, u being the system input, B representing the input matrix, LξIndicating a need to designgain of the state observer, Rξrepresenting switching matrices, output matrices of switching functions
4) The gain of the adaptive observer is designed and solved through a matrix inequality, and the process is as follows:
4.1) constructing a matrix, as shown in formula (6):
Wherein the content of the first and second substances, Is the actual attack pattern of the attack,Observer design parameter α is 0.5, a denotes a state transition matrix, B denotes an input matrix, C denotes an output matrix, RξRepresenting a switching matrix of the switching function;
4.2) if a positive real number η is present, the matrix P is positively determinedξAnd U, matrix NξSuch that the matrix inequality G < 0, P is obtainedξh, design adaptive observer gain LξAs shown in formula (7):
Lξ＝Pξ -1H (7)
Wherein the superscript "-1" represents the inverse of the matrix, and is found thus, the adaptive observer (5) can accurately estimate the state x, and the state estimation under the attack is obtained as shown in fig. 3.
The invention provides a method based on self-adaptationthe state estimation method of networked motion control system based on state observer solves observer gain L through matrix inequalityξcompared with the prior art, the method has the following practicability: the attack does not need to be identified, and the gain of the constructed adaptive observer can be switched back and forth through a switching function, so that the state can be accurately estimated.
the technical solution of the present invention is described in detail above with reference to the accompanying drawings but is not limited thereto, and various changes and modifications can be made within the knowledge of those skilled in the art based on the concept of the present invention.
Claims (1)
1. a networked motion control system state estimation method based on an adaptive state observer is characterized by comprising the following steps:
step 1), determining a transfer function of a networked motion control system:
determining a transfer function of the networked motion control system as shown in formula (1):
wherein G(s) is a transfer function of the networked motion control system, s is a parameter of the transfer function, K, Tsis a system parameter;
in step 2), establishing a state equation and an output equation of the networked motion control system, comprising the following steps:
2.1) converting the transfer function of the networked motion control system into a state space equation as shown in the formula (2):
x(t)＝Ax(t)+Bu(t) (2)
Wherein, A is a state matrix of the system, B is an input matrix, x (t) represents a state quantity of the system, t is a time variable, and u (t) is system input;
2.2) the output equation of the networked motion control system is shown as the formula (3):
y(t)＝Cx(t)+a(t) (3)
Wherein y (t) represents system output quantity, x (t) represents system state quantity, C represents output matrix, a (t) represents attack signal;
In the step 3), an observer is constructed, and the process is as follows;
3.1) calculating the switching matrix R of the switching functionξas shown in formula (4):
Rξ＝diag{r1(ξ)，…，ri(ξ)} (2)
When i ∈ SξTime, ri(xi) ═ 0, otherwise 1, i ═ 1, 2, …, l, l represent the number of sensors, SξRepresenting the ξ -th attack model,s represents the number of attacked sensors;
3.2) based on various parameters, designing the self-adaptive state observer as shown in the formula (5):
wherein the content of the first and second substances,An estimate of the system state quantity x is represented,Representing the estimated value of the output y, A representing the state transition matrix, u being the system input, B representing the input matrix, LξRepresenting the gain, R, of the state observer to be designedξRepresenting a switching matrix of the switching function, and C representing an output matrix;
in the step 4), the gain of the state observer is designed and solved through a matrix inequality, and the process is as follows:
4.1) constructing a matrix, as shown in formula (6):
Wherein the content of the first and second substances, Is the actual attack pattern of the attack,alpha > 0 is an observer design parameter, A represents a state transition matrix, B represents an input matrix, C represents an output matrix, Rξrepresenting a switching matrix of the switching function;
4.2) if a positive real number η is present, the matrix P is positively determinedξand U, matrix Nξsuch that the matrix inequality G < 0, P is obtainedξH, design adaptive observer gain LξAs shown in formula (7):
Lξ＝Pξ -1H (5)
where the superscript "-1" represents the inverse of the matrix, so that an accurate estimation of the state x is achieved by the intermediate observer (5).
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Application publication date: 20191217 |