Asynchronous processing method for resisting zero dynamic attack in non-uniform sampling control system

Abstract

The invention relates to the field of network control system security, in particular to an asynchronous processing method for resisting zero dynamic attacks in a non-uniform sampling control system. Comprising the following steps: comparing and analyzing an attacked system and an unattacked system, and establishing a dynamic relation model between an output signal difference value and an attack signal; based on the relation between the zero-dynamic attack signal and the system state space, a zero-dynamic attack signal design strategy which is kept invisible at the non-uniform sampling moment is given; active introduction of a time difference into a controller of the sampling control system is considered, and a dynamic relation between a corresponding attack signal and an output difference value is reconstructed; active introduction of a time difference into a controller of a sampling control system is considered, and a dynamic relation between an output signal difference value containing the time difference and an attack signal is reconstructed; the existence of the time difference is determined by constructing a system containing the time difference and combining with a zero dynamic attack definition; on the basis of the given time difference, the condition for detecting the zero dynamic attack in the non-uniform sampling control system is determined, so that the system is protected; the method is used for enhancing the detection capability and defense effect of the non-uniform sampling control system on the zero dynamic attack.

Description

Technical Field

[0001] The invention relates to the field of network control system security, and in particular to an asynchronous processing method for resisting zero dynamic attacks in non-uniform sampling control systems. Background Art

[0002] In recent years, with the rapid development of communication technology, physical systems and network systems have been deeply connected through the network. This networked system structure not only greatly promotes the transmission of effective information between physical devices, but also improves the efficiency of system control and the flexibility of operation. Therefore, it has been applied in many industrial fields, such as collaborative control between group robots, smart grids, network traffic, etc. However, with the improvement of the degree of networking, the risk of malicious attacks has also increased significantly, and the system is facing increasingly severe security threats. Among them, denial of service attacks and stealth attacks are two common types of attacks. Unlike denial of service attacks that can interrupt communication and hinder information exchange, stealth attacks can successfully evade detection mechanisms while destroying the performance of the system, and thus have become one of the focuses of current system security research.

[0003] As a type of stealth attack, the design of zero-dynamic attack relies on the zero-point characteristics of the system. By hiding in the zero space represented by the control system state space, it destroys the system performance and successfully avoids the detection of the detector. Among them, when the system zero point is the minimum phase, the attack signal can be regarded as a bounded disturbance, and the impact on the system performance is limited. However, if the zero point of the system is non-minimum phase, the attack signal is unbounded, causing serious damage to the system. Therefore, this attack is a great threat in security-sensitive fields such as industrial control systems, unmanned driving systems, and critical infrastructure. In particular, for sampled control systems, even if the continuous-time system is the minimum phase, when the sampling period is too small and the relative degree is greater than 2, the corresponding discrete-time system after discretization will produce non-minimum phase zero points. Zero-dynamic attacks designed based on this zero point will also damage the performance of the system.

[0004] In order to meet the above challenges, researchers have proposed a variety of detection and protection methods for zero dynamic attacks in recent years. For example, multi-rate sampling, in which the sampling device rate is a multiple of the holding rate, is used to protect the system by eliminating the sampling zero points generated by sampling. A generalized retainer is used to transfer the unstable zero points generated by sampling to a safe area, thereby achieving security defense of the system. However, these methods still have certain limitations when dealing with non-uniform sampling systems. This is because the sampling time of non-uniform sampling is random, and it is impossible to achieve a holding rate of the retainer that is a multiple of the sampling rate. Summary of the invention

[0005] In order to solve the security problem of non-uniform sampling control systems under zero dynamic attacks, the present invention proposes an asynchronous processing method for countering zero dynamic attacks in non-uniform sampling control systems, thereby enhancing the detection capability and defense effect of non-uniform sampling control systems against zero dynamic attacks and improving the security of the system.

[0006] The present invention provides an asynchronous processing method for resisting zero dynamic attack in a non-uniform sampling control system, which is characterized by comprising the following steps:

[0007] Step 1, establish a discrete time model of the non-uniform sampling control system damaged under attack;

[0008] Step 2, by comparing and analyzing the non-uniform sampling control system that has been attacked and the non-uniform sampling control system that has not been attacked, a dynamic relationship model between the output signal difference and the attack signal is established;

[0009] Step 3, based on the state space relationship between the zero dynamic attack signal and the discrete time model of the non-uniform sampling control system, a zero dynamic attack signal design algorithm that remains invisible at the non-uniform sampling moment is given;

[0010] Step 4, consider an asynchronous sampling and holding method that actively introduces time difference in the controller of the non-uniform sampling control system, and reconstruct the dynamic relationship model between the output signal difference including the time difference and the attack signal;

[0011] Step 5: Analyze the invisibility of zero dynamic attack in non-uniform sampling control system using asynchronous sample-and-hold method.

[0012] Furthermore, in step 1, consider the following continuous-time system

[0013]

[0014] in, Represent the state, input signal and output signal of system (1), A c , B c , C are the state matrices of system (1). The sampling sequence of the output signal measured by system (1) is Satisfies 0=t0<t1<t2<…<t k <… and The sampling period is h k =t k+1 -t k , whose lower and upper bounds are h and Right now The sampled data control input signal can be described as F is the sampling control gain.

[0015] Therefore, the corresponding discrete-time system after discretization is

[0016]

[0017] in, They represent the unattacked state, input signal and output signal at the sampling time respectively.

[0018] When the system (2) is attacked by a network attack signal g(t k ), the zero-order holder receives the damaged signal u(t k )+g(t k ). Therefore, the discrete time model of the non-uniform sampling control system under attack is obtained

[0019]

[0020] Furthermore, in step 2

[0021] Combining system (2) and system (3), the difference between the output signal and the attack signal g(t k ) can be described as:

[0022]

[0023] in, u(t k )=Fy(t k ) represent the state, input signal and output signal difference caused by the attack respectively.

[0024] Furthermore, in step 3, the zero dynamic attack design algorithm for the non-uniform sampling control system is

[0025] a. Solve the interval zero point: solve the matrix The point z that loses rank k , get the interval zero point z of each sampling interval k , where I n×n is the n-dimensional identity matrix, For n y Line n u A zero matrix of columns.

[0026] b. Solve for the zero dynamic attack signal g(t0) at time t0: For (A0, B0, C), solve If the non-zero parameters x′(t0) and g(t0) are , then g(t0) is the zero dynamic attack signal at time t0.

[0027] c. Solve for t k The zero dynamic attack signal g(t k ): x(tk )=z k-1 x(t k-1 ), where x(t1) = z0x′(t0). Choose a suitable interval zero point z k , then by solving You can get t k The zero dynamic attack signal g(t k ), then we get a zero dynamic attack sequence

[0028] d. Injection attack: The attack signal g(t k ) at the sampling instant t k Injection non-uniform sampling control system (2).

[0029] Further, in step 4, the discrete time model of the non-uniform sampling control system using the asynchronous sampling and holding method can be described as:

[0030]

[0031] in, τ k is the time difference introduced into the controller.

[0032] Furthermore, by injecting the designed zero dynamic attack signal into system (5), the corresponding system can be obtained as follows:

[0033]

[0034] Combining systems (5) and (6), the dynamic relationship between the output signal difference and the attack signal under the asynchronous sampling and holding method can be obtained:

[0035]

[0036] in,

[0037] Furthermore, in step 5, define the set The set describes the signal [x Τ (t k ) Τ (t k )] Τ Does not belong to the null space of the system matrix The time difference of Ω is clear. k It is not an empty set. There must be a time difference added to the controller that makes the designed attack signal no longer meet the definition of zero dynamic attack.

[0038] For a sampling control system using an asynchronous sample-and-hold method, there must be a Τ (t k) Τ (t k )] Τ Not Time difference make sure

[0039] The asynchronous processing method for counteracting zero dynamic attacks in non-uniform sampling control systems provided by the present invention is based on the potential safety hazards of destructive zero dynamic attacks brought to the system by non-uniform sampling control, attack algorithm design analysis, and corresponding detection countermeasure strategy issues; through model transformation, the system model is converted into a dynamic model between the sampling output difference and the attack signal; based on the definition of zero dynamic attack and the time-varying characteristics of non-uniform sampling, a zero dynamic attack design algorithm in non-uniform sampling control systems is given; finally, based on the fact that the sampling control system has both discrete time characteristics and continuous time characteristics, an asynchronous sampling and holding method is proposed. In summary, the present invention has the following beneficial effects:

[0040] 1. The present invention provides a zero dynamic attack design strategy for a non-uniform sampling control system by analyzing and expanding the general definition of zero dynamic attack to ensure the concealment of zero dynamic attack at the sampling moment;

[0041] 2. The present invention proposes an asynchronous sample-and-hold countermeasure, which can effectively realize attack detection by introducing a time difference to change the hold interval of the zero-dynamic attack. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] Figure 1 is a flow chart of the method of the present invention;

[0043] Figure 2 Comparison of signals maintained by the system holder of the present invention before and after asynchronous sampling-holding and countermeasure and attack destruction;

[0044] Figure 3 A holding signal in interval I for zero dynamic attack designed for the automatic voltage transformer regulator system of the present invention;

[0045] Figure 4 It is the detection signal of the automatic voltage transformer regulator system of the present invention under the designed zero dynamic attack;

[0046] Figure 5 The state of the automatic voltage transformer regulator system of the present invention before and after being destroyed by the designed attack signal;

[0047] Figure 6 A holding signal in interval II for zero dynamic attack designed for the automatic voltage transformer regulator system of the present invention;

[0048] Figure 7A detection signal of the automatic voltage transformer regulator system subjected to zero dynamic attack damage of the present invention using an asynchronous sampling and holding method;

[0049] Figure 8 The detection signals of the automatic transformer regulator system subjected to zero dynamic attack damage of the present invention using the proposed asynchronous sampling and holding method are compared with the detection signals of the Naghnaeian method. DETAILED DESCRIPTION

[0050] The present invention will be further described below in conjunction with the accompanying drawings and specific embodiments. It should be understood that the following specific embodiments are only used for the present invention and are not used to limit the scope of the present invention.

[0051] The present invention provides an asynchronous processing method for counteracting zero dynamic attack in non-uniform sampling control system, such as Figure 1 As shown, it mainly includes: step 1, establishing a discrete time model of a non-uniform sampling control system damaged under attack; step 2, establishing a dynamic relationship model between the output signal difference and the attack signal by comparing and analyzing the non-uniform sampling control system under attack and the non-uniform sampling control system that is not attacked; step 3, based on the state space relationship between the zero dynamic attack signal and the discrete time model of the non-uniform sampling control system, a zero dynamic attack signal design algorithm that remains invisible at the non-uniform sampling moment is given; step 4, considering an asynchronous sampling and holding method that actively introduces a time difference in the controller of the non-uniform sampling control system, a dynamic relationship model between the output signal difference containing the time difference and the attack signal is reconstructed; step 5, analyzing the invisibility of zero dynamic attack in a non-uniform sampling control system that adopts an asynchronous sampling and holding method. The specific implementation process of the present invention is described in detail below.

[0052] Step 1: Consider the following continuous-time system

[0053]

[0054] in, Represent the state, input signal and output signal of system (1), A c , B c , C are the state matrices of system (1). The sampling sequence of the output signal measured by system (1) is Satisfies 0=t0<t1<t2<…<t k <… and The sampling period is h k =t k+1 -t k , whose lower and upper bounds are h and Right now The sampled data control input signal can be described as F is the sampling control gain.

[0055] Therefore, the discrete time model of the non-uniform sampling control system is

[0056]

[0057] in, They represent the unattacked state, input signal and output signal at the sampling time respectively.

[0058] For the attacker, they know the system (1) (A c ,B c ,C). More importantly, if the sampling data device comes with a Trojan installed by the attacker, then the sampling sequence T can be sent to a remote attacker. When the network on the controller-holder channel of system (2) is attacked, the zero-order holder receives the corrupted signal u(t k )+g(t k ), g(t k ) is the network attack signal. Therefore, the discrete time model of the non-uniform sampling control system under attack is:

[0059]

[0060] Step 2: Combine the unattacked system (2) and the attacked system (3), and the difference in output signal y(t k ) and the attack signal g(t k ) can be described as:

[0061]

[0062] in, They represent the state and output signal difference caused by the attack respectively.

[0063] Step 3: Definition based on zero dynamic attack:

[0064] Consider a discrete-time system with an attack signal g(k) and a zero z0:

[0065] x(k+1)=A d x(k)+B d g(k),

[0066] y(k)=C d x(k).

[0067] If and only if there exist non-zero vectors g0 and x0 satisfying

[0068]

[0069] Among them, I n×n is the n-dimensional identity matrix, For ny Line n u The zero matrix of the column and z0 is the zero point of system (2), then the attack signal is a zero dynamic attack signal, and results in the system state and measurement output being

[0070]

[0071] in, and They represent the state and measurement output of the system when there is no attack.

[0072] According to the definition of zero dynamic attack and the characteristics of non-uniform sampling control system, the zero dynamic attack design strategy is proposed. k According to each sampling interval [t k ,t k+1 ) After injecting the designed zero-dynamic attack sequence into the system, consider the following steps

[0073] When k = 0, the initial state x(t0) of system (4) is zero. If there are non-zero vectors x′(t0) and g(t0) satisfying the following equation

[0074]

[0075] Then we can get the zero dynamic attack at time t0 as g(t0).

[0076] when When the system (4) is in the sampling interval [t k ,t k+1 ) is the initial state x(t k )≠0. Applying the definition of zero dynamic attack, if there exists a non-zero vector g(t k )satisfy

[0077]

[0078] Then we can get k The attack signal at time is g(t k ).

[0079] According to the definition of zero dynamic attack, the attacker should consider the control gain F when designing zero dynamic for system (4). By transformation, the zero dynamic attack design problem of system (4) is transformed into the attack design problem of the system without considering the control gain. This system is described as

[0080]

[0081] Therefore, the zero dynamic attack design algorithm for non-uniform sampling control systems is

[0082] a. Solve the interval zero point: solve the matrix The point z that loses rank k , get the interval zero point z of each sampling interval k .

[0083] b. Solve for the zero dynamic attack signal g(t0) at time t0: For (A0, B0, C), solve

[0084] If the non-zero parameters x′(t0) and g(t0) are , then g(t0) is the zero dynamic attack signal at time t0.

[0085] c. Solve for t k The zero dynamic attack signal g(t k ): x(t k )=z k-1 x(t k-1 ), where x(t1) = z0x′(t0). Choose a suitable interval zero point z k , then by solving You can get t k The zero dynamic attack signal g(t k ), then we get a zero dynamic attack sequence

[0086] d. Injection attack: The attack signal g(t k ) at the sampling instant t k Inject into the system.

[0087] Step 3: The discrete time model of the non-uniform sampling control system using the asynchronous sample-and-hold method is:

[0088]

[0089] in, τ k is the time difference introduced into the controller.

[0090] In addition, due to the time difference τ k It is only introduced in the controller-holder channel, so the time series obtained by the attacker under asynchronous sample-hold is still T. Therefore, the attacker still has k Inject the attack signal g(t k ). Specifically, in the sampling interval [t k ,t k+1 ), the keeper receives and holds the time t k The zero dynamic attack signal g(t k ), until the input signal is at time t k +τ kThe signal is transmitted to the keeper. The keeper keeps the signal as follows Figure 2 The holding process of the attack signal and input signal with zero dynamic attack in the healthy system and the damaged system before and after the asynchronous sampling and holding method is adopted is shown.

[0091] Furthermore, by injecting the designed zero dynamic attack signal into the sampling asynchronous sample-and-hold system, the corresponding system can be obtained as:

[0092]

[0093] Step 4: Combining systems (8) and (9), the dynamic relationship between the output signal difference and the attack signal under asynchronous sampling and holding can be obtained:

[0094]

[0095] in,

[0096] Step 5: Define the collection The set describes the signal [x Τ (t k ) Τ (t k )] Τ Does not belong to the null space of the system matrix This means that there is at least one time interval that causes the zero-dynamic attack to fail to be invisible. k It is not an empty set. There must be a time difference added to the controller that makes the designed attack signal no longer meet the definition of zero dynamic attack.

[0097] For satisfaction Time difference If y(t k )=Cx(t k )=0 So. Assume there is satisfy Therefore, we can get x(t k+1 )=z k x(t k )+Δx(t k+1 ),in and Therefore, at the sampling time t k The measured output is

[0098] y(t k+1 )=Cx(t k+1 )=C(z k x(t k )+Δx(t k+1))=CΔx(t k+1 ).

[0099] because So

[0100]

[0101] Because the matrix and CB c is the full column rank, so is also the full column rank. Therefore, Available

[0102] if and So therefore,

[0103] It can be seen that the zero dynamics designed according to step 2 can be detected by the asynchronous processing method.

[0104] The asynchronous processing of this design effectively handles the system security issues brought by sampling, provides effective detection countermeasures against zero-dynamic attacks, and realizes the security control of the system.

[0105] In order to verify the validity of the proposed theoretical results, an automatic voltage regulator system was selected for relevant simulation experiments:

[0106] Consider a model of an automatic voltage regulation system described by the transfer function, The parameters of the system are described as τ A =0.1,K A =10,K E =1,τ E =0.4,K G =1,τ G =1,K R =1,τ R = 0.05. Obviously, this continuous time does have unstable zeros.

[0107] When an attacker destroys the sampling device of the system and obtains the sampling sequence When the dynamic matrix (A k ,B k ,C). Then, according to the attack design algorithm in step 2, the zero point z of the unstable interval is obtained k And each sampling interval [t k ,t k+1 ) corresponding to the zero dynamic attack signal and are recorded in Table 1.

[0108] Table 1 Information about zero dynamic attack and asynchronous sample-and-hold method

[0109]

[0110]

[0111] When the system does not take countermeasures, the zero dynamic attack signal in Table 1 is injected into the sampling instant t k , keep the time interval as interval I, such as Figure 3 The system status and detection signals are shown as Figure 4 and 5 As shown. It can be seen that the performance of the system has changed greatly, but the output signal difference y(t k ) is always zero, which is undetectable by the anomaly detector.

[0112] To solve this security problem, the defender selects the time interval τ in Table 1 k The zero dynamic attack signal in Table 1 is still at the sampling time t k Inject into the system, but due to the time difference, keep the time interval as interval II, such as Figure 6 As shown. Figure 3 and Figure 6 It is easy to see that the time gap τ generated by the asynchronous sampling and holding method k The zero dynamic attack interval is changed. Figure 7 It can be found that at the sampling time t k When , the zero dynamic attack signal no longer remains invisible. Further considering the periodic sampling data control system with a sampling period of h = 0.5s, it can be seen from the figure that the asynchronous sampling and holding method can also realize the attack detection of the periodic sampling system. Figure 8 It can be found that the countermeasure proposed by the present invention takes 3 seconds to detect the zero dynamic attack signal, while the double rate countermeasure in Naghnaeian takes 3.75 seconds. Therefore, the countermeasure proposed by the present invention is more effective.

Claims

1. An asynchronous processing method for counteracting zero dynamic attack in non-uniform sampling control system, characterized in that The following steps are included: Step 1, establish a discrete time model of the non-uniform sampling control system damaged under attack; Step 2, by comparing and analyzing the non-uniform sampling control system that has been attacked and the non-uniform sampling control system that has not been attacked, a dynamic relationship model between the output signal difference and the attack signal is established; Step 3, based on the state space relationship between the zero dynamic attack signal and the discrete time model of the non-uniform sampling control system, a zero dynamic attack signal design algorithm that remains invisible at the non-uniform sampling moment is given; Step 4, consider an asynchronous sampling and holding method that actively introduces time difference in the controller of the non-uniform sampling control system, and reconstruct the dynamic relationship model between the output signal difference including the time difference and the attack signal; Step 5: Analyze the invisibility of zero dynamic attack in non-uniform sampling control system using asynchronous sample-and-hold method.

2. The asynchronous processing method for counteracting zero dynamic attack in non-uniform sampling control system according to claim 1, characterized in that: In step 1, Consider a continuous-time system in, Represent the state, input signal and output signal of system (1), A c , B c , C are the state matrices of system (1) respectively; the sampling sequence of the output signal measured by system (1) is Satisfies 0=t0<t1<t2<…<t k <… and The sampling period is h k =t k+1 -t k , whose lower and upper bounds are h and Right now The sampled data control input signal is described as F is the sampling control gain; Therefore, the discrete-time model of the nonuniform sampling control system is in, Represent the unattacked state, input signal, and output signal at the sampling time, respectively; When the system (2) is attacked by a network attack signal g(t k ), the zero-order holder receives the damaged signal u(t k )+g(t k ); therefore, the corresponding discrete-time system under attack is obtained 3. The asynchronous processing method for counteracting zero dynamic attack in non-uniform sampling control system according to claim 2, characterized in that: In step 2 Combining system (2) and system (3), the difference between the output signal and the attack signal g(t k ) is described as: in, u(t k )=Fy(t k ) represent the state, input signal and output signal difference caused by the attack respectively.

4. The asynchronous processing method for counteracting zero dynamic attack in a non-uniform sampling control system according to claim 3, characterized in that: In step 3, The algorithm for designing a zero-dynamic attack signal that remains invisible at non-uniform sampling times is: a. Solve the interval zero point: solve the matrix The point z that loses rank k , get the interval zero point z of each sampling interval k , where I n×n is the n-dimensional identity matrix, For n y Line n u zero matrix of columns; b. Solve for the zero dynamic attack signal g(t0) at time t0: For (A0, B0, C), solve The non-zero parameters x′(t0) and g(t0) are, then g(t0) is the zero dynamic attack signal at time t0; c. Solve for t k The zero dynamic attack signal g(t k ): x(t k )=z k-1 x(t k-1 ), where x(t1) = z0x′(t0); select an appropriate interval zero point z k , by solving Get k The zero dynamic attack signal g(t k ), then we get a zero dynamic attack sequence d. Injection attack: The attack signal g(t k ) at the sampling instant t k Injection system (2).

5. The asynchronous processing method for counteracting zero dynamic attack in non-uniform sampling control system according to claim 4, characterized in that: In step 4, The discrete time model of the non-uniform sampling control system using the asynchronous sample-and-hold method is: in, τ k is the time difference introduced into the controller; Injecting the designed zero dynamic attack signal into system (5), the corresponding discrete time model of the non-uniform sampling control system under attack is obtained as follows: Combining systems (5) and (6), the dynamic relationship between the output signal difference and the attack signal is obtained: in, 6. The asynchronous processing method for counteracting zero dynamic attack in a non-uniform sampling control system according to claim 5, characterized in that: In step 5, Defining a Collection The set describes the signal [x Τ (t k ) Τ (t k )] Τ Does not belong to the system (7) state space null space The time difference of k It is not an empty set. There must be a time difference added to the controller that makes the designed attack signal no longer meet the definition of zero dynamic attack. For a sampling control system using an asynchronous sample-and-hold method, there must be a Τ (t k ) Τ (t k )] Τ Not Time difference make sure

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