Performance evaluation method for bandwidth limitation network control system under hybrid attack
By modeling denial-of-service attacks and spoofing attacks and designing a two-degree-of-freedom controller, the performance evaluation problem of bandwidth-limited network control systems under various network attacks was solved, achieving improved system performance and stability assurance.
Patent Information
- Application Number
- CN202510817895.6
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-06-18
- Publication Date
- 2025-11-18
AI Technical Summary
Existing technologies fail to fully consider the impact of various network attacks on bandwidth-limited network control systems, resulting in severe impacts on system performance and stability.
A Bernoulli stochastic process is used to model denial-of-service attacks and spoofing attacks, and a mathematical model of a bandwidth-limited network control system under hybrid attacks is established. A two-degree-of-freedom controller is designed using the frequency domain H2 optimal control method, and the optimal tracking performance expression of the system is derived using tools such as coprime decomposition and Youla parameterization.
While ensuring system stability, this study greatly improves the tracking performance of bandwidth-limited network control systems under hybrid attacks, reveals the intrinsic relationship between network attacks and bandwidth limitations on system performance, and provides a more profound performance evaluation method.
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Figure CN120979962A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of network control systems, and more particularly to a performance evaluation method for a bandwidth-limited network control system under hybrid attacks. Background Technology
[0002] With the introduction of networks, network control systems primarily transmit information through communication networks. However, during communication, they are highly susceptible to various network attacks and channel bandwidth limitations. The existence of network attacks can severely impact the performance and even stability of the control system. Therefore, performance evaluation methods for bandwidth-constrained network control systems under hybrid attack conditions are necessary. Existing technology discloses a model to study the optimal tracking performance of a finite-bandwidth feedback control system with colored noise in a fading channel. For the steady-state of the feedback control system, an equivalent average channel model is established by preserving the influence of the first and second moments of the multiplicative channel output. Using coprime decomposition, all-pass decomposition, and Youla parameterization methods, and by designing two compensators, the exact expression of the dynamic programmable controller is derived. Although this system considers bandwidth limitations and fading channel constraints, with the rapid development of the Internet, the impact of network attacks still exists in actual network communication channels. Therefore, the network constraints considered in this model are not comprehensive enough.
[0003] Another model provides a preliminary analysis of denial-of-service (DoS) attacks described by Bernoulli processes on power-constrained networked control systems in additive white noise communication channels. It models the DoS attack as a Bernoulli stochastic process, where the attack can occur at either the transmitter or receiver of the communication channel. Furthermore, it limits the research object to a first-order controlled object model, deriving the impact of the DoS attack on the system at both ends. While this model considers DoS attacks, more complex networked control systems may face multiple network attacks, which this model does not account for. Summary of the Invention
[0004] To address the issue that systems are highly susceptible to various network attacks and channel bandwidth limitations during communication, and that network attacks can severely impact the performance and even stability of control systems, this invention provides a performance evaluation method for bandwidth-limited network control systems under hybrid attack conditions, mainly comprising:
[0005] S1: Using Bernoulli stochastic processes to model denial-of-service attacks and spoofing attacks, a mathematical model of a bandwidth-limited network control system under hybrid attacks is obtained;
[0006] S2: Substitute the mathematical model into the tracking error signal to obtain the tracking error signal of the bandwidth-limited network control system under hybrid attack;
[0007] S3: Based on the tracking error signal and tracking error performance index of the bandwidth-limited network control system, the limit expression for the tracking error performance of the bandwidth-limited network control system under hybrid attacks is obtained.
[0008] A computer device includes a memory, a processor, and a computer program stored in the memory, wherein the processor executes the computer program to implement the steps of the above-described method.
[0009] A computer-readable storage medium storing a computer program that, when executed by a processor, implements the steps of the above method.
[0010] A computer program product includes a computer program or instructions that, when executed by a processor, implement the steps of the above-described method.
[0011] The beneficial effects of the technical solution provided by this invention are as follows: This invention utilizes Bernoulli stochastic processes to model denial-of-service attacks and spoofing attacks, transforming them into a frequency domain model to obtain a mathematical model of a bandwidth-constrained networked control system under mixed attacks. Assuming the feedback channel noise is additive white Gaussian noise, and considering the influence of bandwidth, two optimal controllers with two degrees of freedom are designed using tools such as coprime decomposition and Youla parameterization. This significantly improves the tracking performance of the bandwidth-constrained networked control system under mixed attacks while ensuring system stability. Through the frequency domain H2 optimal control method, the lower bound of the tracking performance of the bandwidth-constrained networked control system under mixed attacks is obtained, revealing a more profound intrinsic relationship between network control system performance, network attacks, and bandwidth constraints. This invention derives the model using tools such as all-pass decomposition, partial fraction decomposition, double Bezout equations, H2 space decomposition techniques, and Youla parameterization of the controllers, obtaining the optimal tracking performance of the system and quantitatively revealing the system's inherent characteristics and the impact of network attacks on the control system performance. Attached Figure Description
[0012] The present invention will be further described below with reference to the accompanying drawings and embodiments. In the accompanying drawings:
[0013] Figure 1 This is a flowchart of a performance evaluation method for a bandwidth-limited network control system under hybrid attacks, as described in an embodiment of the present invention.
[0014] Figure 2 This is a schematic diagram of the system model in the embodiment of the present invention; (a) is a bandwidth-limited network control system model under hybrid attack, and (b) is a simplified model of the feedback channel affected by hybrid attack.
[0015] Figure 3 This is a schematic diagram illustrating the performance limits under different bandwidth constraints in embodiments of the present invention;
[0016] Figure 4 This is a schematic diagram illustrating the tracking performance under different network attacks in embodiments of the present invention. Detailed Implementation
[0017] To provide a clearer understanding of the technical features, objectives, and effects of the present invention, specific embodiments of the present invention will now be described in detail with reference to the accompanying drawings.
[0018] Example 1
[0019] Please refer to Figure 1 , Figure 1 This is a flowchart of a performance evaluation method for a bandwidth-limited network control system under hybrid attacks, as described in an embodiment of the present invention. The method is based on a two-degree-of-freedom controller and specifically includes:
[0020] S1: Using Bernoulli stochastic processes to model denial-of-service attacks and spoofing attacks, we obtain the following... Figure 2 The mathematical model of the bandwidth-limited network control system shown in (a) is as follows:
[0021] u=K1r+K2y a
[0022] y = Gu
[0023] Where y a =(1-a)F[(1-β)y+βh] k ]+n, u is the control input signal, K1 and K2 represent the two controllers of the two-degree-of-freedom controller, and r is the reference input signal, which is a step signal. k = 0, 1, 2, ... corresponds to different sampling times, v is the vector form of the reference input signal, and y a The feedback channel output is represented by y, the system output by G, and the controlled object by G. F represents the bandwidth transfer function, n is the additive white Gaussian noise in the feedback channel, and parameters a and β represent the probabilities of a denial-of-service attack and a spoofing attack simulated using Bernoulli random variables, respectively. The probability of no denial-of-service attack is (1-a), and the probability of no spoofing attack is (1-β). h k This is to inject signals into the networked control system in the event of a deception attack. Figure 2 (b) in the model is a simplified model of the feedback channel affected by the hybrid attack in (a), where the denial-of-service attack and the spoofing attack are independent of each other.
[0024] h k The transfer function of the system output y is denoted as achievable
[0025] S2: Based on the tracking error signal e = ry and the tracking error performance index Where K(z) represents the discrete form of controllers K1 and K2, This represents the set of all controllers that stabilize the system. Let be the variance of the tracking error signal e. Substituting the model formula into the formula for the tracking error signal, we get: Where S=1+(1-α)β-(1-α)(1-2β)FGK2.
[0026] From the definition of power spectral density and Parseval's theorem, we can obtain
[0027]
[0028] in This represents the variance of the reference input r. This represents the variance of additive white Gaussian noise n.
[0029] S3: Coprime decomposition based on system diagram The Youla parameterization of a two-degree-of-freedom controller:
[0030]
[0031] Among them, N,M, It is composed of the transfer function matrix The decomposed matrix, where N and Includes all zeros of the controlled object G, M and Includes all poles of the controlled object G, and N, M, It is the set of all stable, regular rational transfer functions (matrices).
[0032] For N, M, There is a double Bezout equation in Q and R are parameter matrices obtained independently and through free design for different controllers. Therefore, we can obtain:
[0033]
[0034] The tracking performance limit can then be written as:
[0035]
[0036] To facilitate the calculation of the expression for the above optimal performance, we define:
[0037]
[0038] From this we can obtain
[0039] First calculate Because the controlled object G is right-invertible, and If N is a scalar, then N can be decomposed into N = LFN. m , where N m The minimum phase portion includes all minimum phase zeros of the controlled object, and L is the all-pass factor, which includes all non-minimum phase zeros s of the controlled object. i (i = 1, 2, ..., N) S It has a minimum phase decomposition form:
[0040]
[0041] Where L(z) is the discrete form of L, η i Is the non-minimum phase zero point s i The direction vector of , and ||η i || = 1, and matrix U i Satisfying Relationships For s i Conjugate complex numbers, and η i and U i The conjugate transpose of .
[0042] Then you can get for:
[0043]
[0044] Define a non-minimum phase zero s i Related all-pass factor Therefore:
[0045]
[0046] And because in and These are two mutually orthogonal subspaces in a Hilbert space. Based on space decomposition techniques, we have:
[0047]
[0048] Because N m If it is right-hand reversible, then it can be made possible by selecting a suitable controller.
[0049]
[0050] We can determine that the optimal controller is: Q = (1-α)(1-2β)N M Ψ, then
[0051] Calculations show that:
[0052]
[0053] Among them, s k-1 For the (k-1)th non-minimum phase zero of the controlled object, s i For non-minimum phase zero, s j For different from s i Another non-minimum phase zero point.
[0054] According to Cauchy's integral theorem: Substituting into the above formula, we can obtain:
[0055]
[0056] Next calculation Decomposition by all-pass N = LFN m We can obtain:
[0057]
[0058] Total Decomposition Where M m It is the minimum phase factor, which includes all the stable poles of the controlled object. The all-pass factor contains all unstable poles p of the controlled object. i i = 1, 2, ..., N p , It can be broken down into:
[0059]
[0060] in, For unstable poles p i , and With matrix Satisfying Relationships Then we can get:
[0061]
[0062] for Partial fractional factorization:
[0063]
[0064] in B j for The j-th decomposition, B j (p i ) to p i Substitute B j The result after that, For B j (p i The reverse of ) and
[0065]
[0066] make It can be obtained
[0067]
[0068] because Based on spatial decomposition techniques, we can obtain:
[0069]
[0070] It can be calculated that Similarly, you can choose appropriate parameters. Make in Then we can obtain:
[0071]
[0072] From the double Bezout equation, we can obtain and but So
[0073] Substituting, we get:
[0074]
[0075] Calculations show that:
[0076]
[0077] The performance limit expression for the tracking error of the system is:
[0078]
[0079] in, For unstable poles p i , and s i s represents the non-minimum phase zero. j Indicates something different from s i Another non-minimum phase zero, s k-1 For the (k-1)th non-minimum phase zero of the controlled object, For s i Conjugate complex numbers, For s j Conjugate complex numbers, i,j=1,2,…,N S N S Represents the number of non-minimum phase zeros, L is the all-pass factor, and p i Denotes unstable poles, i,j=1,2,...,N p N p Indicates the number of unstable poles. B j (p i ) to p i Substitute B j The result after that, For B j (p i The reverse of ) For unstable poles p j directional vector, express The conjugate transpose of E i H E represents i The conjugate transpose of L H (p i ) represents the conjugate transpose of L, F H (p i ) represents the conjugate transpose of F, L -1 (p i ) is the inverse of L, F -1 (p i ) represents the inverse of F, Q i H Q represents i The conjugate transpose of Ψ(s) k-1 ) represents the all-pass factor of the (k-1)th non-minimum phase zero.
[0080] Experimental data and conclusions:
[0081] Consider a discrete single-input single-output controlled object, whose transfer function matrix model is:
[0082]
[0083] The controlled object is right-invertible, containing a non-minimum phase zero (z=2) and an unstable pole (z=p). A Butterworth low-pass filter is used to model the finite bandwidth F. And set the reference input and feedback channel noise to 1. Select Then there is Based on the controlled object model, we can obtain... The performance limit expression can then be written as:
[0084]
[0085] By setting the probability of a denial-of-service attack to α = 0.3 and the probability of a spoofing attack to β = 0.3, the performance limits under different bandwidth constraints can be obtained, such as... Figure 3 As shown in the figure. The results indicate that as the bandwidth increases, the tracking performance limit of the system decreases, meaning that the system performance improves with increasing bandwidth. Furthermore, when the unstable poles of the controlled object are sufficiently close to the non-minimum phase zeros, the tracking performance of the system deteriorates sharply; this phenomenon should be avoided in daily production and life. When f=5, the tracking performance under different network attacks can be obtained as follows: Figure 4 As shown in the figure, it can be seen that as the probability of hybrid attacks increases, the tracking performance, i.e., the system performance, becomes worse and worse.
[0086] Example 2
[0087] A computer device includes a memory, a processor, and a computer program stored in the memory, wherein the processor executes the computer program to implement the steps of the above-described method.
[0088] Example 3
[0089] A computer-readable storage medium storing a computer program that, when executed by a processor, implements the steps of the above method.
[0090] Example 4
[0091] A computer program product includes a computer program or instructions that, when executed by a processor, implement the steps of the above-described method.
[0092] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.
Claims
1. A method for performance evaluation of a bandwidth-limited network control system under mixed attacks, characterized in that, The method comprises the following steps based on a two-degree-of-freedom controller implementation: S1: modeling denial-of-service attacks and spoofing attacks by using Bernoulli random processes to obtain a mathematical model of a bandwidth-limited network control system under hybrid attacks; S2: substituting the mathematical model into a tracking error signal to obtain a tracking error signal of the bandwidth-limited network control system under hybrid attacks; S3: obtaining a tracking error performance limit expression of the bandwidth-limited network control system under hybrid attacks according to the tracking error signal of the bandwidth-limited network control system and a tracking error performance index.
2. The method of claim 1, wherein the bandwidth-limited network control system is a hybrid attack. In S1, the mathematical model is: u = K1r + K2y a y = Gu where y a = (1-a) F[(1-β)y+βh k ]+n, u is the control input signal, K1 and K2 represent two controllers of the two-degree-of-freedom controller respectively, r is the reference input signal, v is the vector form of the reference input signal, y a represents the feedback channel output; y is the system output, G is the controlled object; F represents the transfer function of the bandwidth, n is the additive white Gaussian noise in the feedback channel, a and β represent the occurrence probability of denial-of-service attacks and deception attacks simulated by Bernoulli random variables respectively, (1-a) represents the probability when the denial-of-service attack does not occur, (1-β) represents the probability when the deception service attack does not occur, and h k is the signal injected into the networked control system when the deception attack occurs.
3. The method of claim 2, wherein the bandwidth-limited network control system is a hybrid attack. In S2, according to the tracking error signal e = r - y, after substituting the mathematical model, the tracking error signal of the bandwidth-limited network control system is obtained Wherein, S = 1 + (1 - a) b - (1 - a) (1 - 2b) FGK2.
4. The method of claim 3, wherein the bandwidth-limited network control system is a hybrid attack. Tracking error performance index K(z) denotes the discrete form of the controllers K1 and K2, J denotes the set of all controllers that stabilize the system, is the variance of the tracking error signal e.
5. The method of claim 4, wherein the bandwidth-limited network control system is a hybrid attack. According to the definition of the power spectral density and the Parseval theorem, the following is obtained: wherein, denotes the variance of the reference input r, denotes the variance of the additive white Gaussian noise n.
6. The method of claim 5, wherein the bandwidth-limited network control system is a hybrid attack. Youla parameterization form of the two-degree-of-freedom controller: where Q and R are parameter matrices corresponding to different controllers and are independent of each other and obtained through free design, N, M, is a matrix decomposed from a transfer function matrix , N and contain all the zeros of the controlled object G, M and contain all the poles of the controlled object G, and is a set composed of all stable and regular rational transfer functions.
7. The method of claim 6, wherein the bandwidth-limited network control system is a hybrid attack. In S3, the tracking error performance limit expression of the bandwidth-limited network control system under hybrid attacks is: wherein is the direction vector of the unstable pole p i , and s i denotes a non-minimum phase zero, s j denotes another non-minimum phase zero different from s i , s k-1 is the k-1th non-minimum phase zero of the controlled object, is the conjugate complex of s i , is the conjugate complex of s j , i,j = 1,2,...,N S , N S denotes the number of non-minimum phase zeros, L is the all-pass factor, p i denotes an unstable pole, i,j = 1,2,...,N p , N p denotes the number of unstable poles, B j (p i ) is the result of bringing p i into B j , is the inverse of B j (p i ), is the direction vector of the unstable pole p j , denotes the conjugate transpose of , E i H denotes the conjugate transpose of E i , L H (p i ) denotes the conjugate transpose of L, F H (p i ) denotes the conjugate transpose of F, L -1 (p i ) is the inverse of L, F -1 (p i ) denotes the inverse of F, Q i H denotes the conjugate transpose of Q i , Ψ(s k-1 ) denotes the all-pass factor of the k-1th non-minimum phase zero.
8. A computer apparatus comprising a memory, a processor, and a computer program stored on the memory, wherein the computer program, when executed by the processor, causes the processor to perform the method of any one of claims 1 to 7. The processor executes a computer program to implement the steps of the performance evaluation method of the bandwidth-limited network control system under hybrid attacks according to any one of claims 1-7.
9. A computer-readable storage medium, characterized in that, The computer program is stored in the memory, and when the program is executed by the processor, the steps of the performance evaluation method of the bandwidth-limited network control system under hybrid attacks according to any one of claims 1-7 are implemented.
10. A computer program product, characterised in that, The computer program or instructions are included, and when the program or instructions are executed by the processor, the steps of the performance evaluation method of the bandwidth-limited network control system under hybrid attacks according to any one of claims 1-7 are implemented.