CN110708284A - A Gradient Descent-Based Attack Estimation Method for Networked Motion Control Systems - Google Patents

Abstract

A networked motion control system attack estimation method based on gradient descent algorithm, first consider the situation of sensor attack in the system, determine its state space equation and discretize it; construct the output equation of τ sensor measurement values; finally, based on the gradient The descent algorithm constructs the observer to converge the estimation error to within a predetermined minimum energy bound. The invention adopts the event-driven technology, which can save computing resources and improve the computing performance of the system. The observer design based on the gradient descent algorithm has higher attack estimation accuracy, and the estimation performance can be improved by adjusting specific parameters.

Description

A Gradient Descent-Based Attack Estimation Method for Networked Motion Control Systems

technical field

The invention belongs to the technical field of network security, and specifically provides an attack estimation method for a networked motion control system based on a gradient descent algorithm, which can identify the attack, evaluate the security situation of the system, and ensure its safe operation.

Background technique

Networked motion control system refers to a kind of network control system in which the information transmission processing process and the dynamic evolution process of the object interact with each other and are tightly coupled. However, it is precisely because of the high coupling between information transmission processing and system dynamics that such systems are vulnerable to information attacks. 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 a very important role in the motion control system.

Currently, methods for real-time identification of attacks rely on the design of observers, including robust observers, sliding-mode observers, and unknown input observers such as intermediate observers. The sliding mode observer requires the system to satisfy the observer matching conditions, and also needs information such as the upper bound of the known attack signal. However, any effective information about the attack cannot be obtained in practical engineering. The robust observer does not have the restriction of observer matching conditions, but the upper bound of the estimation error is unknown, so the accuracy of the estimation cannot be guaranteed. The intermediate observer gives a theoretical bound, but the upper bound is large and only has theoretical significance. It cannot converge the estimation error of the attack signal to a predetermined range, so it is difficult to apply in practice.

SUMMARY OF THE INVENTION

Based on the above problems, the present invention provides a method for estimating an attack of a networked motion control system based on a gradient descent algorithm. Specifically, the output signal containing the sparse sensor attack is reconstructed, and the state and attack of the system are estimated at the same time. Make sure that the estimation error converges within a predetermined minimum energy bound.

The present invention provides the following technical solutions for solving the above-mentioned technical problems:

An attack estimation method for a networked motion control system based on a gradient descent algorithm, comprising the following steps:

Step 1), establish the state space equation of the networked motion control system and discretize it:

Considering the presence of sensor attacks in the system, the state space equation is discretized, as shown in equation (1):

A is the state matrix of the system, B is the input matrix, C is the output matrix, x is the system state quantity, u is the system input, y is the system output, and a is the sensor attack;

Step 2), select τ sensor measurement values to construct the output equation, the process is as follows:

2.1) Collect τ∈N measurement values, and construct the output equation of the i-th sensor as shown in equation (2):

in,

2.2) Since U(t) is known, formula (2) is simplified as shown in formula (3):

Y _i (t)=O _i x(t-τ+1)+E _i (t) ⑶

in,

将输出方程简化为如式(4)所示：2.3) Definition

Simplify the output equation as shown in equation (4):

Q＝[O I]，I为单位矩阵；in,

Q=[OI], I is the identity matrix;

Step 3), construct an observer based on the event-driven gradient descent algorithm, and the process is as follows:

3.1) Construct the Lyapunov energy function as shown in equation (5), and calculate the estimated energy

为系统状态量和传感器攻击z的估计值，||·||₂表示·的二范数；in,

is the estimated value of the system state quantity and sensor attack z, ||·|| ₂ represents the second norm of ·;

3.2) Construct the projection operator as shown in formula (6):

Π(z)＝Π(x,E)＝(x,Π'(E)) ⑹

Among them, Π'(E) means E=(E ₁ , E ₂ ,...,E _p ) In ^T , find the sum of the squares of the elements in E _i , and set the s (s<p) E _i with the smaller sum of squares Set to zero to ensure sparsity of sensor attack estimates;

3.3) Construct the observer based on the gradient descent algorithm as shown in equation (7):

为系统状态量以及传感器攻击z的估计值，η为步长；Among them, the superscript "T" represents the transpose of the matrix,

is the estimated value of the system state quantity and sensor attack z, and η is the step size;

3.4) Initialization definition k=1,

α为人为设定的正实数，且

v∈[0,1]为人为设定值，则由式(7)进行迭代运算且直到为止，令k＝k+1，进入b)；反之，直接进入b)；a) if

α is an artificial positive real number, and

v∈[0,1] is an artificial set value, then the iterative operation is performed by formula (7) and until so far, let k=k+1, enter b); otherwise, enter b) directly;

重置

返回a)；反之，则获得t-τ时刻系统状态和t时刻传感器攻击的估计值

b) if

reset

Return a); otherwise, obtain the estimated value of the system state at time t-τ and the sensor attack at time t

The present invention is a networked motion control system attack estimation method based on gradient descent algorithm. By reconstructing the output signal containing sensor attack, an event-driven gradient descent algorithm is used to construct an observer to estimate the system state and sensor attack.

The beneficial effects of the invention are as follows: by adopting the event-driven technology, computing resources can be saved, and the computing performance of the system can be improved; the observer design based on the gradient descent algorithm has higher accuracy of the attack estimation effect, and the estimation performance can be improved by adjusting specific parameters; The identification accuracy of this method can meet the requirements of practical applications, and the required related parameters can be measured by low-cost sensors.

Description of drawings

Figure 1 is the estimated effect of the system state x ₁ ;

Figure 2 is the estimated effect of the system state x ₂ ;

Figure 3 is the estimated effect of the first sensor attack a ₁ ;

Figure 4 is the estimated effect of the _second sensor attack a2;

Figure 5 is the estimated effect of the _third sensor attack a3.

Detailed ways

In order to make the objectives, technical solutions and advantages of the present invention clearer, the technical solutions of the present invention are further described below with reference to the accompanying drawings and practical experience.

Referring to Figures 1 to 5, a method for estimating the attack of a networked motion control system based on a gradient descent algorithm, firstly model the motion control system, consider the existence of sensor attacks in the system, determine its state space equation and discretize it; Construct the output equation containing the sensor attack; construct the observer based on the gradient descent algorithm to estimate the sensor attack and the system state.

An attack estimation method for a networked motion control system based on a gradient descent algorithm, comprising the following steps:

1) Establish and discretize the state space equation of the networked motion control system;

2) Construct the output equation containing the sensor attack;

3) Construct an observer based on the gradient descent algorithm.

Further, in the step 1), the state space equation of the networked motion control system is established and discretized, as shown in formula (1):

输入矩阵

输出矩阵x表示系统状态量，u为系统输入，y为系统输出，传感器攻击

Among them, the state matrix

input matrix

output matrix x represents system state quantity, u is system input, y is system output, sensor attack

Step 2), select τ=2 sensor measurement values to construct the output equation, the process is as follows:

2.1) Collect τ=2 measurement values, and construct the output equation of the i-th sensor as shown in formula (2):

t≥2；in,

t≥2;

2.2) Since U(t) is known, formula (2) is simplified as shown in formula (3):

Y _i (t)=O _i x(t-1)+E _i (t) ⑶

in,

2.3) Definition Simplify the output equation as shown in equation (4):

in,

Step 3) Construct an observer based on an event-driven gradient descent algorithm. The process is as follows:

3.1) Construct the Lyapunov energy function as shown in equation (5), and calculate the estimated energy

为系统状态量和传感器攻击z的估计值，||·||₂表示·的二范数；in,

is the estimated value of the system state quantity and sensor attack z, ||·|| ₂ represents the second norm of ·;

3.2) Construct the projection operator as shown in formula (6):

Π(z)＝Π(x,E)＝(x,Π'(E)) ⑹

Among them, Π'(E) means E=(E ₁ , E ₂ ,...,E _p ) In ^T , find the sum of squares of the elements in E _i , and set s=1 E _i with the smaller sum of squares to zero, Ensuring sparsity of sensor attack estimates;

3.3) Construct the observer based on the gradient descent algorithm as shown in equation (7):

为系统状态量以及传感器攻击z的估计值，步长η＝0.00001；Among them, the superscript "T" represents the transpose of the matrix,

is the estimated value of system state quantity and sensor attack z, step size η=0.00001;

3.4) Initialization definition k=1, m=0,

且

则由式(7)进行迭代运算且

直到

为止，令

k＝k+1，进入b)；反之，直接进入b)；a) Take α=0.0005, v=0.8, if

and

Then the iterative operation is performed by formula (7) and

until

so far, let

k=k+1, enter b); otherwise, enter b) directly;

重置m＝0,

返回a)；反之，则获得t-τ时刻系统状态和t时刻传感器攻击的估计值

b) if

reset m=0,

Return a); otherwise, obtain the estimated value of the system state at time t-τ and the sensor attack at time t

It can be seen from the experimental results that the present invention can converge the estimation error to a predetermined minimum energy boundary, and can meet the requirements of precision and real-time performance in practical applications. The relevant parameters required by the present invention can be adjusted according to actual conditions and measured by low-cost sensors.

The embodiments of the present invention have been described and described in detail above with reference to the accompanying drawings, but are not limited to the above-mentioned modes. Various changes and improvements can also be made within the scope of knowledge possessed by those skilled in the art, as long as they are based on the concept of the present 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:

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,

2.2) since U (t) is known, the formula (2) is simplified to the formula (3):

Y_i(t)＝O_ix(t-τ+1)+E_i(t) ⑶

wherein,

2.3) definition of

Simplifying the output equation toAs shown in formula (4):

wherein,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

Wherein,

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,…,E_p)^TIn (1), obtain E_iThe sum of squares of the middle elements, s (s < p) E elements with smaller sum of squares_iZero 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,

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,

a) if it isAlpha is an artificially set positive real number, and

v∈[0,1]if the value is an artificial set value, iterative operation is performed by the formula (7) andup to

To that end

Entering b); otherwise, directly entering b);

b) if it is

The reset m is set to 0 and,

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

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