Mobile robot system hidden attack detection method based on finite frequency domain

Abstract

A mobile robot system hidden attack detection method based on a finite frequency domain specifically comprises the following steps: firstly, determining a transfer function of a mobile robot system through a system identification method, and converting the transfer function into a discrete state space equation; meanwhile, sensor attack, external interference and measurement disturbance existing in the system are considered. And then, a generalized KYP lemma is utilized, filter performance indexes are designed in a frequency band division manner, filter parameters of different frequency bands are solved through a linear matrix inequality, and sensor attacks of frequency domain partitions are detected in real time. The method does not need historical data for analysis, can be applied to a linear time-varying system, and can detect the attack of the corresponding frequency band more accurately compared with a traditional full-frequency-domain detection method.

Description

Technical Field

[0001] The present invention belongs to the technical field of network security, and specifically provides a method for detecting covert attacks on a mobile robot system based on a finite frequency domain, which can accurately detect whether an attack occurs and provide guarantee for the safe operation of the mobile robot. Background Art

[0002] With the continuous improvement of robot performance, the application scope of mobile robots is becoming wider and wider. A mobile robot system is a mechatronic system. During the operation process, relevant internal and external environmental information needs to be fed back to the control system. However, due to physical or technical limitations, data between network components of the mobile robot system may be transmitted through the network without appropriate security protection measures. This leads to external attackers being able to invade the system through network protocols, tamper with internal data or inject false data, causing a series of economic losses. Therefore, the detection of attacks on mobile robot systems has become a very important research field.

[0003] Currently, the main attack detection methods include data-driven attack detection methods and attack detection methods based on model residual analysis. First, the data-driven attack detection method is a method for analyzing the frequency domain characteristics of a series of signals, mainly by comparing the changes in the signal spectrum characteristics under normal and abnormal operating conditions of the system to determine whether the system is abnormal. Therefore, this method mainly uses historical data for fine analysis, or requires knowledge of the system structure and some prior knowledge. It is not only not applicable to overly complex interference, but also unable to determine in real time whether an attack has occurred. In order to detect attack signals in real time, researchers have proposed an attack detection method based on model residual analysis. However, the existing attack detection methods based on model residual analysis mainly design observers or filters in the full frequency domain to detect attack signals. It ignores the frequency domain change characteristics of attack signals, easily resulting in the detection performance of the system for attack signals not meeting the requirements or being unable to effectively detect. Summary of the Invention

[0004] In order to overcome the deficiencies of the prior art, the present invention provides a method for detecting covert attacks on a mobile robot system based on a finite frequency domain. Specifically, first, through a system identification method, the transfer function of the mobile robot system is determined and converted into a discrete state space equation. At the same time, sensor attacks, external interference, and measurement disturbances in the system are considered. Then, using the generalized KYP lemma, filter performance indicators are designed in different frequency bands, and filter parameters in different frequency bands are solved through linear matrix inequalities to detect sensor attacks in the frequency domain partition in real time. The experimental results verify the effectiveness of this method. It should be noted that the covert attacks considered in the present invention specifically refer to a type of low-amplitude high-frequency signal similar to noise signals. For such signals, traditional full-frequency domain detection methods are difficult to effectively detect.

[0005] To solve the above technical problems, the present invention provides the following technical solutions:

[0006] A method for detecting stealth attacks on a mobile robot system based on a finite frequency domain, comprising the following steps:

[0007] Step 1), through a system identification method, determine the transfer function of the mobile robot system and convert it into a discrete state-space equation;

[0008] Considering the attacks and disturbances existing in the system, the continuous state-space equation shown in Equation (1) is obtained:

[0009]

[0010] y(t) = Cx(t) + D s f s (t) + D v v(t) (1)

[0011] where x(t) = [x a (t) y a (t) φ(t)] T are respectively the x-axis displacement, y-axis displacement and orientation angle of the mobile robot, y(t) represents the measurement output, is the control input, w(t) ∈ R w and v(t) ∈ R v represent external disturbance and measurement disturbance respectively, represents sensor attack, w, v, f s all belong to the square-integrable vector function space L2[0, +∞), A is a parameter time-varying matrix with appropriate dimensions, and B, B w , C, D s , D v , k are all constant matrices with appropriate dimensions;

[0012] Discretize it, as shown in Equation (2):

[0013] x(k + 1) = Ax(k) + Bu(k) + B w w(k)

[0014] y(k) = Cx(k) + D s f s (k) + D v v(k) (2)

[0015] Step 2), using the generalized KYP lemma, design the filter performance index in frequency bands, and the process is as follows:

[0016] 2.1) Design the filter to have the following structure:

[0017]

[0018] wherein, is the state of the filter, and r(k) ∈ R r is the residual output, A f , B f , C f , D f are the coefficient matrices of the filter to be designed;

[0019] Let From equations (2) and (3), the global augmented attack detection system is obtained as follows:

[0020]

[0021]

[0022] wherein,

[0023] 2.2) Design the performance indicators of the high-frequency attack detection filter as follows:

[0024] Full-band suppression of disturbances:

[0025] Low-frequency band suppression of attacks:

[0026] High-frequency band sensitive to attacks:

[0027] wherein, α1 represents the performance indicator of full-band suppression of disturbances, α2 represents the performance indicator of low-frequency band suppression of attacks, and α3 represents the performance indicator of high-frequency band sensitivity to attacks. For α1 and α2, the smaller their values, the less sensitive the system is to disturbances or low-frequency band attacks; for α3, the larger its value, the more sensitive the system is to high-frequency band attacks;

[0028] Step 3), determine the filter parameters of different frequency bands by solving linear matrix inequalities and perform real-time detection. The process is as follows:

[0029] Integrate equations (5), (6), and (7) to construct the following matrix inequalities:

[0030] Full-band suppression of disturbances:

[0031]

[0032]

[0033] Low-frequency band suppression of attacks:

[0034]

[0035]

[0036]

[0037]

[0038] High frequency band is sensitive to attack:

[0039]

[0040]

[0041]

[0042]

[0043]

[0044]

[0045]

[0046] In the above matrix inequality, P a ,P b ,P c ,Q a ,Q b , D f ,Y,R,N are all matrix variables to be solved, ω l ,ω h ,L 11 ,L 12 , L2, v are all given scalars, and the matrix obtained by combining equations (8), (9), and (10) is D f The parameters of the high-frequency attack detection filter are obtained after conversion through the equation shown below:

[0047] D f =D f , N = VDV T .

[0048] The present invention provides a covert attack detection method for a mobile robot system based on a finite frequency domain. Compared with the existing data-driven attack detection method and the attack detection method based on model residual analysis, the present invention has the following beneficial effects: it does not require historical data for analysis, can be applied to linear time-varying systems, and can more accurately detect attacks in the corresponding frequency band than traditional full-frequency domain detection methods. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] Figure 1 is the structure diagram of the mobile robot system;

[0050] Figure 2 is the detection effect diagram of the stealth attack detection filter. Specific implementation manners

[0051] To make the objectives, technical solutions and advantages of the present invention clearer, the technical solutions of the present invention will be further described below in conjunction with the accompanying drawings and actual experiments.

[0052] The mobile robot system considered in the present invention is as Figure 1 shown. The host obtains the photos taken by the digital camera and obtains the position information of the mobile robot through image processing. At the same time, the control commands generated by the host are sent to the mobile robot via wireless communication.

[0053] Referring to Figure 1 and Figure 2 , a method for detecting stealth attacks on a mobile robot system based on a finite frequency domain. Specifically, first, the transfer function of the mobile robot system is determined through a system identification method and converted into a discrete state space equation. At the same time, sensor attacks, external disturbances, and measurement perturbations in the system are considered. Then, using the generalized KYP lemma, the filter performance index is designed in different frequency bands, and the filter parameters in different frequency bands are solved through linear matrix inequalities to detect the sensor attacks in the frequency domain partition in real time.

[0054] A method for detecting stealth attacks on a mobile robot system based on a finite frequency domain includes the following steps:

[0055] 1) Determine the transfer function of the mobile robot system through a system identification method and convert it into a discrete state space equation;

[0056] 2) Use the generalized KYP lemma to design the filter performance index in different frequency bands;

[0057] 3) Determine the filter parameters in different frequency bands by solving linear matrix inequalities and perform real-time detection.

[0058] In the step 1), the transfer function of the mobile robot system is determined through a system identification method and converted into a discrete state space equation:

[0059] Considering the existence of attacks and disturbances in the system, the continuous state space equation shown in Equation (1) is obtained.

[0060]

[0061] y(t) = Cx(t) + D s fs (t) + D v v(t)(1)

[0062] where \(x(t)=[x a (t)\ y a (t)\ \varphi(t)] T are respectively the x - axis displacement, y - axis displacement and orientation angle of the mobile robot, \(y(t)\) represents the measurement output, is the control input, \(w(t)\in R w and \(v(t)\in R v represent external disturbance and measurement disturbance respectively, represents sensor attack, \(w\), \(v\), \(f s all belong to the square - integrable vector function space \(L_2[0,+\infty)\), \(A\) is a parameter - time - varying matrix with appropriate dimensions, and \(B\), \(B w , C, D s , D v , k are all constant matrices with appropriate dimensions;

[0063] Discretize it as shown in Equation (2):

[0064] \(x(k + 1)=Ax(k)+Bu(k)+B w w(k)

[0065] \(y(k)=Cx(k)+D s f s (k)+D v v(k)(2)

[0066] where,

[0067]

[0068]

[0069] \(u(t)=-Kx(t)\).

[0070] \(w(k)=0.1*\sin(0.3*k)\), \(v(k)=0.1*\cos(0.4*k)\) represent external disturbance and measurement disturbance respectively. \(f s (t)\) is the sensor attack signal, which is set as follows:

[0071]

[0072] In step 2), using the generalized KYP lemma, design the filter performance index in frequency bands. The process is as follows:

[0073] 2.1) Design the filter with the following structure:

[0074]

[0075] Among them, is the state of the filter, and r(k) ∈ R r is the residual output, A f , B f , C f , D f are the coefficient matrices of the filter to be designed.

[0076] Let From equations (2) and (3), the global augmented attack detection system can be obtained as follows:

[0077]

[0078]

[0079] Among them,

[0080] 2.2) Design the performance indicators of the high-frequency attack detection filter as follows:

[0081] Full-band suppression of disturbances:

[0082] Low-frequency band suppression of attacks:

[0083] High-frequency band sensitive to attacks:

[0084] Among them, α1 represents the performance indicator of full-band suppression of disturbances, α2 represents the performance indicator of low-frequency band suppression of attacks, and α3 represents the performance indicator of high-frequency band sensitivity to attacks. For α1 and α2, the smaller their values, the less sensitive the system is to disturbances or low-frequency band attacks; for α3, the larger its value, the more sensitive the system is to high-frequency band attacks. These performance indicators are all solved for their optimal solutions through LMI.

[0085] Furthermore, in step 3), the filter parameters in different frequency bands are determined by solving linear matrix inequalities and real-time detection is carried out as follows:

[0086] Combining equations (5), (6), and (7) to construct the following matrix inequality:

[0087] Full-band suppression of disturbances:

[0088]

[0089]

[0090] Low-frequency band suppression of attacks:

[0091]

[0092]

[0093]

[0094]

[0095] High frequency band is sensitive to attacks:

[0096]

[0097]

[0098]

[0099]

[0100]

[0101]

[0102]

[0103] In the above matrix inequality, P a , P b , P c , Q a , Q b , D f , Y, R, N are all matrix variables to be solved. Given scalars ω l = 0.1, ω h = 0.25, L 11 = [-0.2 2 1.1] T , L 12 = [0.4 0.7 1.8] T , L2 = [-0.1], v = [-1 -0.04 0.8] T . By solving equations (8), (9), and (10) simultaneously, the obtained matrix D f The parameters of the high-frequency attack detection filter are obtained after being transformed by the following equations:

[0104] D f = D f , N = VDV T .

[0105] Since it is a linear time-varying system, only when k = 300, the parameters of the high-frequency attack detection filter obtained are shown as follows:

[0106]

[0107] C f = [74.4189 0.9155 95.6522], D f = [-1.5371 -0.6850 2.0199],

[0108] α1 = 0.3059, α2 = 1.6077, α3 = 1.0954.

[0109] From the experimental results ( Figure 2 ), it can be seen that the present invention accurately detects the covert sensor attacks suffered by the mobile robot system, and can issue an alarm in real time, ensuring the safe operation of the system. The results can meet the requirements of accuracy and real-time performance in practical applications.

[0110] The embodiments of the present invention have been described and stated in detail above in conjunction with the accompanying drawings, but are not limited to the above embodiments. Within the scope of knowledge possessed by those skilled in the art, as long as it is based on the concept of the present invention, various changes and improvements can still be made.

Claims

1. A method for detecting covert attacks in a mobile robot system based on a finite frequency domain, characterized in that, The method includes the following steps: Step 1), determine the transfer function of the mobile robot system through a system identification method and convert it into a discrete state space equation; Considering the attacks and disturbances existing in the system, the continuous state space equation shown in Equation (1) is obtained: y(t) = Cx(t) + D s f s (t) + D v v(t) (1) where \(x(t)=[x a (t)\ y a (t)\ \varphi(t)] T represents the x-axis displacement, y-axis displacement and direction angle of the mobile robot respectively, \(y(t)\) represents the measurement output, is the control input, \(w(t)\in\mathbb{R} w and \(v(t)\in\mathbb{R} v represent the external disturbance and measurement disturbance respectively, represents the sensor attack, \(w\), \(v\), \(f s all belong to the square-integrable vector function space \(L_2[0, +\infty)\), \(A\) is a parameter time-varying matrix with appropriate dimensions, and \(B\), \(B w , \(C\), \(D s , \(D v , \(k\) are all constant matrices with appropriate dimensions; Discretize it, as shown in Equation (2): x(k + 1) = Ax(k) + Bu(k) + B w w(k) y(k) = Cx(k) + D s f s (k) + D v v(k) (2) Step 2), use the generalized KYP lemma to design the filter performance index in different frequency bands, and the process is as follows: 2.1) Design the filter with the following structure: wherein, is the state of the filter, r(k) ∈ R r is the residual output, A f , B f , C f , D f are the coefficient matrices of the filter to be designed; Let From equations (2) and (3), the global augmented attack detection system is as follows: Among them, 2.2) Design the performance index of the high-frequency attack detection filter as follows: Full-bandwidth disturbance suppression: Low-frequency band suppression attack: The high-frequency band is sensitive to attacks: Among them, α1 represents the performance index for suppressing disturbances in the full frequency band, α2 represents the performance index for suppressing attacks in the low frequency band, α3 represents the performance index for being sensitive to attacks in the high frequency band. For α1 and α2, the smaller their values, the less sensitive the system is to disturbances or low-frequency band attacks; for α3, the larger its value, the more sensitive the system is to high-frequency band attacks; Step 3), determine the filter parameters in different frequency bands by solving linear matrix inequalities and perform real-time detection, and the process is as follows: Combining Equations (5), (6), and (7), construct the following matrix inequalities: Full frequency band disturbance suppression: Low frequency band attack suppression: High frequency band sensitive to attacks: In the above matrix inequality, P a , P b , P c , Q a , Q b , D f , Y, R, N are all matrix variables to be solved, ω l , ω h , L 11 , L 12 , L2, v are all given scalars. By combining equations (8), (9), and (10), the obtained matrix D f The parameters of the high-frequency attack detection filter are obtained after being transformed by the equation shown below: D f = D f ,N = VDV T 。

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