CN113489673B - Networked motion control system attack estimation method based on projection intermediate observer - Google Patents
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Abstract
A networked motion control system attack estimation method based on a projection intermediate observer comprises the steps of firstly modeling a motion control system, considering sensor attack and actuator attack in the system, determining a state space equation of the motion control system and discretizing the state space equation; constructing an output equation containing sensor attack and actuator attack; estimating system state, sensor attack and actuator attack based on a projection intermediate observer. The method 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 and actuator attack; 3) A projection intermediate observer is constructed. The identification precision of the invention can meet the requirements of practical application, and the required related parameters can be measured by a low-cost sensor.
Description
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 projection intermediate observer, which can stably and accurately reconstruct faults of an actuator and a sensor, so as to evaluate the security situation of a system and guarantee the safe operation of the system.
Background
The networked motion control system refers to a kind of network control system in which the information transmission processing process and the object dynamic evolution process are mutually influenced and tightly coupled. However, it is the high coupling of the information transfer process to the system dynamics 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 a motion control system, the purpose of attack reconstruction is to acquire explicit information such as the shape and size of the attack signal, so far, in order to solve the problem of attack reconstruction, researchers regard the attack signal as a fault or interference and extend the traditional unknown input observers such as an ESO, an SMO and an intermediate estimator to estimate the attack signal on line. The main advantage is that attacks can be designed manually with high rates of change and randomness, which are difficult to identify accurately on the web, and therefore attack reconstruction is a common challenge for unknown input observers.
In recent years, security estimation techniques based on sparsity concepts have been developed rapidly, and many iterative algorithms on sensor attacks have been proposed to guarantee estimation performance. It should be noted that computational complexity is a major obstacle to the application of these iterative algorithms. Although there have been some achievements in improving the sensor attack reconstruction algorithm by modifying the nominal gradient descent method. Experiments show that the time cost caused by the actuator attack is more surprising than that caused by the sensor attack. Meanwhile, the calculation performance and the estimation capability are difficult to be simultaneously ensured. To date, the problem of multi-attack reconstruction has not been well studied.
Disclosure of Invention
Based on the problems, the invention provides a networked motion control system attack estimation method based on a projection intermediate observer, and particularly relates to a method for reconstructing output signals containing sparse sensor attacks, estimating the state and the attacks of a system at the same time, and ensuring that an estimation error is converged within a preset minimum energy range.
The invention provides the following technical scheme for solving the technical problems:
a networked motion control system attack estimation method based on a projection intermediate observer comprises the following steps:
step 1), establishing a state space equation of a networked motion control system and discretizing, wherein the process is as follows:
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 the state matrix of the system, B is the input matrix, C is the output matrix, x (t) represents the state quantity of the system, u (t) is the system input, y (t) is the system output, a s (t) denotes a sensor attack, a u (t) represents an actuator attack, w (t) and e (t) represent bounded process noise and measurement noise, respectively;
step 2), introducing an intermediate variable,
ξ(t)＝a u (t)-ωB T x(t) (2)
omega is a scalar artificially selected, and tau sensor measurement values are selected to construct an output equation by the following process:
2.1 τ ∈ N measured values are collected, and an output equation of the ith sensor is constructed as shown in formula (2):
wherein U (t-1) = (U (t- τ + 1),.., U (t-1)),
ζ(t-1)＝(ξ(t-τ+1),ξ(t-τ+2),...,ξ(t-1))，W(t-1)＝(ω(t-τ+1),ω(t-τ+2),...,ω(t))，G i (t)＝(a si (t-τ+1),a si (t-τ+2),...,a si (t))，E i (t)＝(e i (t-τ+1),e i (t-τ+2),...,e i (t)), wherein, a si And e i Is a s Ith elements of (t) and e (t), coefficient matrix
At the same time
2.2 Define (b) definition of
Simplifying equation (3) yields:
Y(t)＝Qz(t)+MW(t-1)+E(t) (4)
wherein Q = [ O ] i1 F Π I]，z(t)＝(x(t-τ+1),ζ(t-1),G(t))，
Wherein, O (j) ＝O j1 +O j2 ,
M (j) ＝M j1 +M j2 ,j＝1,…,p；
Step 3) constructing a projection intermediate observer, wherein the process is as follows:
3.1 Define P (z (t)) as the closest point to z in the two-norm sense:
3.2 A Lyapunov energy function is constructed as shown in formula (6), and the energy of the estimated value is calculated
Wherein the content of the first and second substances,
the norm of the norm is expressed by | | · | | | |, which is the estimated values of the system state quantity and the sensor attack z (t);
3.3 Constructing a projection intermediate observer, the estimated values of the i +1 th system state quantity and the sensor attack z (t) are
Wherein Q + The Moore-penrose pseudo inverse of Q,
is a matrix in the sense of a two-norm
The most recent point is:
3.4 Initialization defines i =1, k =0,
a) When k is less than or equal to alpha, alpha and v 1 If the real number is artificially set, the iterative operation is performed by the formula (7) and the energy function at the moment is calculated
If i > v is satisfied 1 Then calculate the average value of energy
b) If it is
Let k = k +1, otherwise reset k =0;
c) i = i +1, if the k is still less than or equal to the alpha condition, repeating the steps a) and b) to carry out iterative operation, and if the iteration is finished, calculating:
The invention discloses a networked motion control system attack estimation method based on a projection intermediate observer.
The invention has the beneficial effects that: based on the design of the projection intermediate observer, 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 shows sensor failure a s The estimated effect of (2);
FIG. 2 shows an actuator failure a u The estimated effect of (2);
FIG. 3 is a system state x 1 And x 2 The 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. 1-3, a networked motion control system attack estimation method based on a projection intermediate observer firstly models a motion control system, considers sensor attack and actuator attack in the system, determines a state space equation of the system and discretizes the equation; constructing an output equation containing sensor attack and actuator attack; estimating system state, sensor attack and actuator attack based on a projection intermediate observer.
A networked motion control system attack estimation method based on a projection intermediate 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 and actuator attack;
3) A projection intermediate observer 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):
wherein the state matrix
Input matrix
Output matrix
x(t)＝(x p (t),x v (t)) represents a system state quantity, x p (t)、x v (t) respectively representing the position and speed of the servo motor system, u (t) being system input, y (t) being system output, sensor attack
w (t) and e (t) respectively representThe process noise and the measurement noise of the boundary are random signals, and the boundary is 0.5 ℃;
in the step 2), introducing an intermediate variable,
ξ(t)＝a u (t)-ωB T x(t) (2)
ω is set to 1, and 2 sensor measurements are selected to construct the output equation as follows:
2.1 τ =2 measurements are acquired, and the output equation of the ith sensor is constructed as shown in equation (2):
wherein U (t-1) = U (t-1),
ζ(t-1)＝ξ(t-1),W(t-1)＝(w(t-1),w(t))，G i (t)＝(a si (t-1),a si (t))，E i (t)＝(e i (t-1),e i (t)) wherein a si And e i Is a s Ith elements of (t) and e (t), coefficient matrix
2.2 Since U (t) is known, equation (2) is simplified as shown in equation (3):
Y(t)＝Qz(t)+MW(t-1)+E(t) (4)
wherein Q = [ O ] i1 F Π I]Z (t) = (x (t-1), ζ (t-1), G (t)), p is the Y (t) dimension,
in the step 3), the process of constructing the projection intermediate observer is as follows:
3.1 A Lyapunov energy function is constructed as shown in formula (5), and the energy of the estimated value is calculated
Wherein the content of the first and second substances,
the system state quantity and the estimated value of the sensor attack z are represented by | · | | |, which represents a quadratic norm of the system state quantity and the sensor attack z;
3.2 Construct a projection operator as shown in equation (6):
wherein Q is + The Moore-dependent pseudo inverse of Q,
3.4 Initialization defines i =1, k =0,
a) When k is less than or equal to alpha, alpha =5,v 1 If =3, the iterative operation is performed by the equation (6) and
if i > v is satisfied 1 Then calculate the average value of energy
Entering b);
b) If it is
η 1 =0.05, let k = k +1, otherwise reset k =0;
c) i = i +1, if the condition k is still less than or equal to alpha, repeating the steps a) and b) to carry out iterative operation, and if the iteration is finished, calculating
Obtaining the attack estimation value of the actuator at the t-1 moment and the attack estimation value of the sensor at the t moment
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 projection intermediate observer is characterized by comprising the following steps:
step 1), establishing a state space equation of a networked motion control system and discretizing, wherein the process is as follows:
considering the case of a sensor attack in the system, the state space equation is discretized, as shown in equation (1):
wherein A is the state matrix of the system, B is the input matrix, C is the output matrix, x (t) represents the state quantity of the system, u (t) is the system input, y (t) is the system output, a s (t) denotes a sensor attack, a u (t) represents an actuator attack, w (t) and e (t) represent bounded process noise and measurement noise, respectively;
step 2), introducing an intermediate variable,
ξ(t)＝a u (t)-ωB T x(t) (2)
omega is a scalar artificially selected, and tau sensor measurement values are selected to construct an output equation by the following process:
2.1 τ ∈ N measured values are collected, and an output equation of the ith sensor is constructed as shown in formula (2):
wherein U (t-1) = (U (t- τ + 1),.., U (t-1)),
ζ(t-1)＝(ξ(t-τ+1),ξ(t-τ+2),...,ξ(t-1))，W(t-1)＝(ω(t-τ+1),ω(t-τ+2),...,ω(t))，G i (t)＝(a si (t-τ+1),a si (t-τ+2),...,a si (t))，E i (t)＝(e i (t-τ+1),e i (t-τ+2),...,e i (t)), wherein a si And e i Is a s Ith elements of (t) and e (t), coefficient matrix
At the same time
2.2 Define (c) definition
Simplifying equation (3) yields:
Y(t)＝Qz(t)+MW(t-1)+E(t) (4)
wherein Q = [ O ] i1 F Π I]，z(t)＝(x(t-τ+1),ζ(t-1),G(t))，
Wherein, O (j) ＝O j1 +O j2 ,
M (j) ＝M j1 +M j2 ,j＝1,…,p；
Step 3) constructing a projection intermediate observer, wherein the process is as follows:
3.1 Define P (z (t)) as the closest point to z in the two-norm sense:
3.2 Constructing a Lyapunov energy function as shown in formula (6), and calculating an estimated value energy
Wherein the content of the first and second substances,
the norm of the norm is expressed by | | · | | | |, which is the estimated values of the system state quantity and the sensor attack z (t);
3.3 Constructing a projection intermediate observer, the estimated values of the i +1 th system state quantity and the sensor attack z (t) are
Wherein Q is + The Moore-penrose pseudo inverse of Q,
is a matrix in the sense of a two-norm
The most recent point is:
3.4 Initialization defines i =1, k =0,
a) When k is less than or equal to alpha, alpha and v 1 If the real number is artificially set, the iterative operation is performed by the formula (7) and the energy function at the moment is calculated
If i > v is satisfied 1 Then calculate the average value of energy
Entering b);
b) If it is
Let k = k +1, otherwise reset k =0;
c) i = i +1, if the k is still less than or equal to the alpha condition, repeating the steps a) and b) to carry out iterative operation, and if the iteration is finished, calculating:
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| CN111158343A (en) * | 2020-01-10 | 2020-05-15 | 淮阴工学院 | Asynchronous fault-tolerant control method for switching system with actuator and sensor faults |
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| CN110531616A (en) * | 2019-07-29 | 2019-12-03 | 浙江工业大学 | A kind of network motion control systems under coloured noise attack discrimination method |
| CN110708284A (en) * | 2019-08-30 | 2020-01-17 | 浙江工业大学 | Networked motion control system attack estimation method based on gradient descent algorithm |
| CN110647033A (en) * | 2019-09-02 | 2020-01-03 | 浙江工业大学 | Networked motion control system attack identification method based on class-Longberger observer |
| CN110794811A (en) * | 2019-11-07 | 2020-02-14 | 浙江工业大学 | Safety control method of networked motion control system with quantification |
| CN111158343A (en) * | 2020-01-10 | 2020-05-15 | 淮阴工学院 | Asynchronous fault-tolerant control method for switching system with actuator and sensor faults |
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