Double-rate dynamic control method based on sample hold under random attack

Abstract

The invention discloses a dual-rate dynamic control method based on sample hold under random attack in the field of network security control, which comprises the following steps of: 1, constructing a discrete time model of a dual-rate dynamic system according to the principle that the update rate of a sensor in a multi-rate control system is slower than that of a controller; step 2, giving a DoS attack model based on a signal interference plus noise ratio (SINR); 3, firstly constructing an output compensator and an input compensator to dynamically compensate for loss of a data packet, then estimating the state of the double-rate system under the attack, and designing a safety controller; 4, through a stochastic analysis method and a Lyapunov stability analysis theory, the stochastic stability of the control system is ensured under certain standard conditions; according to the invention, the security of data transmission of the dual-rate system under the denial of service attack is ensured, and the control performance of the system is enhanced at the same time.

Description

Technical Field

[0001] The invention belongs to the technical field of network security control, and in particular relates to a dual-rate dynamic control method based on sampling and holding under random attacks. Background Art

[0002] With the rapid development of the Internet of Things, Industrial Internet, and intelligent manufacturing, network security issues have gradually expanded from information systems to physical systems, especially in industrial control systems and critical infrastructure (such as power systems, transportation systems, etc.), where security issues are more complex. Once these systems are attacked, they will not only cause economic losses, but may also threaten public safety. Therefore, how to ensure the stability of the control system while improving its immunity to network attacks has become the focus of current research.

[0003] Denial of service attack is a common network attack method. Its harm to control systems is mainly manifested in problems such as causing system communication interruption, increased control delay, increased system instability, and resource exhaustion. Attackers occupy network bandwidth through a large amount of false traffic, causing normal communication interruption or delay between sensors and controllers, affecting the real-time performance and control accuracy of the system. In addition, DoS attacks may cause system resources to overload, causing system crashes or loss of control, especially in critical infrastructure and industrial control systems, which may cause serious economic losses and security risks. At present, research on resisting DoS attacks mainly focuses on improving defense capabilities through intelligent intrusion detection and optimizing network resource management. However, when the attack breaks out, the robustness and resilience of the system in responding to the attack determine the system's anti-attack ability. In particular, when it comes to dual-rate dynamic control systems, low-frequency attacks often cause high-frequency packet loss and control failure. There is currently a lack of relevant knowledge on how to enhance the system's ability to resist attacks. In view of this, the present invention proposes a control method based on sampling and holding for network security of dual-rate dynamic systems, which can effectively improve the anti-attack ability and robustness of such systems. Summary of the invention

[0004] In view of the deficiencies in the prior art, the present invention provides a dual-rate dynamic control method based on sampling and holding under random attacks, which solves the problem of poor control effect of the existing dual-rate dynamic system under random bilateral denial of service attacks and enhances the stability of the system.

[0005] To achieve the above object, the present invention adopts the following technical solution: a dual-rate dynamic control method based on sampling and holding under random attack, comprising the following steps:

[0006] Step 1, system model construction: Based on the principle that the update rate of the sensor in the multi-rate control system is slower than the update rate of the controller, a dual-rate dynamic system discrete time model is constructed;

[0007] Step 2, random attack model construction: a denial of service (DoS) attack model based on signal interference plus noise ratio (SINR) is given;

[0008] Step 3, state estimation and security control: First, construct output and input compensators to dynamically compensate for packet loss, then estimate the state of the dual-rate system under attack and design a security controller;

[0009] Step 4, stability analysis: Through the random analysis method and Lyapunov stability analysis theory, the random stability of the control system is guaranteed under certain standard conditions.

[0010] As a further improvement of the technical solution of the present invention, the discrete time model of the dual-rate system in step 1 is specifically:

[0011]

[0012] Among them, x(·) is the system state vector, u(·) is the control input, y(·) is the system output, and y a (·) is the sensor sampling output, A, B and C are known constant matrices of appropriate dimensions, T is the system controller fast update period, MT is the sensor slow sampling period, M is a positive integer, and k and p are the number of running steps in the large and small periods, respectively.

[0013] As a further improvement of the technical solution of the present invention, in order to facilitate subsequent analysis, kMT=T k , Substituting into the discrete time model of the dual-rate system, we obtain:

[0014]

[0015] Among them, T k = kMT,

[0016] As a further improvement of the technical solution of the present invention, step 2 is specifically as follows: for the dual-rate dynamic system, information transmission mainly relies on a wireless shared additive white Gaussian noise (AWGN) channel to describe the signal-to-noise ratio (SNR) of the sensor-controller (SC) and controller-actuator (CA) channels, specifically:

[0017]

[0018] in, are the energy of the sensor and controller sending data packets, are the AWGN energies of SC and CA channels, respectively;

[0019] The bit error rate (SER) is an indicator to measure the communication quality of the wireless channel. The relationship between SER and channel SNR is established as follows:

[0020]

[0021] Where Q(x) is the Gaussian Q function, ξ>0 is the network parameter, and r is the intermediate variable of integration;

[0022] When considering the impact of a dual-channel DoS attack on different channels of a dual-rate dynamic system, SINR is used instead of SNR:

[0023]

[0024] in, are the interference energies of DoS attacks on SC and CA channels respectively. At this time, we get:

[0025]

[0026] in, are the network parameters of SC and CA channels respectively;

[0027] Considering that both the SC and CA bilateral channels of the dual-rate dynamic system are affected by DoS attacks, random loss of data packets occurs when transmitting on the channel. Signal detectors φ(·), θ(·) and v(·) are set up at the sensor sending end, controller receiving end and actuator receiving end respectively, and their specific definitions are as follows:

[0028]

[0029] Assuming that θ(·) and v(·) both obey Bernoulli distribution, we have:

[0030]

[0031] in, represents the probability of successful transmission of the output signal, Indicates the probability of successful transmission of the control signal;

[0032] At this time, the dynamic performance of the dual-rate dynamic system is the following composite form:

[0033]

[0034] in,

[0035]

[0036] where μ(·)∈{0,1}, is the probability of successful transmission of sensor data packets under the combined influence of dual rate and attack, is the system status under DoS attack, It is the system output under DoS attack.

[0037] As a further improvement of the technical solution of the present invention, step 3 is specifically as follows:

[0038] Construct the following output compensator:

[0039]

[0040] in, To compensate the output;

[0041] Construct the following input compensator:

[0042]

[0043] in, To compensate for the input;

[0044] Construct the following state estimator:

[0045]

[0046] in, is the estimated state of the system, is the estimated output of the system, L is the observer gain;

[0047] Build the following security controller:

[0048]

[0049] Where K is the controller gain.

[0050] As a further improvement of the technical solution of the present invention, step 4 is specifically as follows:

[0051] First, define the estimation error as According to the safety controller, input compensator and state estimator, the closed-loop function of the control system is given as follows:

[0052]

[0053] The error system of the control system is as follows:

[0054]

[0055] Then, based on the random analysis theory and Lyapunov stability theory, the asymptotic stability of the control system was established under certain standard conditions, so that the system can still maintain safe and stable operation under random attacks. Specifically:

[0056] If there are parameters α1, α2, α3, α4, ε1 and matrices P1, P2, P3, P4 and P3>0, P4>0, matrices Y1 and R1 satisfy the following linear matrix inequality:

[0057]

[0058] Then the closed-loop system and the error system are both stochastically stable, and the controller gain and observer gain can be expressed by K = Y1P1 and L = P4 respectively. -1 R1 is obtained;

[0059] where I is the identity matrix of appropriate dimensions,

[0060]

[0061]

[0062] Compared with the prior art, the present invention has the following beneficial effects:

[0063] (1) The present invention adopts a discrete-time dual-rate control system model. Compared with most existing control methods based on continuous-time design, this method is easier to implement in a computer control system.

[0064] (2) The present invention selects the SINR attack model. Compared with the existing model, this model can reflect the randomness and degree of damage of the attack signal on different channels (SC, CA).

[0065] (3) The present invention comprehensively considers the problems of slow sensor sampling rate and denial of service attack for the first time, and proposes a unified model based on Bernoulli random distribution, which facilitates the design of subsequent control schemes.

[0066] (4) A control method based on sampling and holding is proposed, which can effectively alleviate the packet loss and control failure caused by slow sampling and denial of service attacks, and enhance the system's ability to resist attacks and robustness. BRIEF DESCRIPTION OF THE DRAWINGS

[0067] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the provided drawings without paying creative work.

[0068] Figure 1 This is a control block diagram of the system of the present invention.

[0069] Figure 2 This is a flow chart of the control method of the present invention. DETAILED DESCRIPTION

[0070] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0071] like Figure 1-2 A dual-rate dynamic control method based on sampling and holding under random attack is shown, comprising the following steps:

[0072] Step 1) System model construction:

[0073] Considering the principle that the update rate of the sensor in the multi-rate control system is slower than that of the controller, a discrete-time model of the dual-rate dynamic system is constructed, which is as follows:

[0074]

[0075] Among them, x(·) is the system state vector, u(·) is the control input, y(·) is the system output, and y a (·) is the sensor sampling output, A, B and C are known constant matrices of appropriate dimensions, T is the fast update period of the system controller, MT is the slow sampling period of the sensor, M is a positive integer, and k and p are the number of running steps in the large and small periods, respectively.

[0076] To facilitate subsequent analysis, the above formula can be rewritten as:

[0077]

[0078] Among them, T k = kMT,

[0079] Step 2) Random attack model construction:

[0080] A denial of service (DoS) attack model based on signal to interference plus noise ratio (SINR) is given. For the above dual-rate system, information transmission mainly relies on the wireless shared additive white Gaussian noise (AWGN) channel. Therefore, the signal-to-noise ratio (SNR) of the sensor-controller (SC) and controller-actuator (CA) channels can be described as:

[0081]

[0082] in, are the energy of the sensor and controller sending data packets, are the AWGN energies of the SC and CA channels respectively; the bit error rate (SER) is an indicator to measure the communication quality of the wireless channel. The relationship between SER and channel SNR is established as follows:

[0083]

[0084] Where Q(x) is the Gaussian Q function, ξ>0 is the network parameter, and r is the integral intermediate variable. When considering the impact of dual-channel DoS attacks on different channels of a dual-rate dynamic system, SINR is used instead of SNR:

[0085]

[0086] in, are the interference energies of DoS attacks on SC and CA channels respectively. At this time, we get:

[0087]

[0088] in, are the network parameters of SC and CA channels respectively.

[0089] Considering that both the SC and CA bilateral channels of the dual-rate dynamic system are affected by DoS attacks, random loss of data packets occurs when they are transmitted on the channel. Based on this, signal detectors φ(·), θ(·), and v(·) are set up at the sensor transmitter, controller receiver, and actuator receiver, respectively. The specific definitions are as follows:

[0090]

[0091] Assuming that θ(·) and v(·) both obey Bernoulli distribution, we have:

[0092]

[0093] in, represents the probability of successful transmission of the output signal, Represents the probability of successful transmission of the control signal.

[0094] At this time, the dynamics of the dual-rate system is expressed in the following composite form:

[0095]

[0096] in,

[0097]

[0098] where μ(·)∈[0,1], is the probability of successful transmission of sensor data packets under the combined influence of dual rate and attack, is the system status under DoS attack, It is the system output under DoS attack.

[0099] Step 3) State estimation and safety control:

[0100] First, output and input compensators are constructed to dynamically compensate for packet loss. Then, the state of the dual-rate system under attack is estimated and a secure controller is designed.

[0101] Construct the following output compensator:

[0102]

[0103] in, For compensation output.

[0104] Construct the following input compensator:

[0105]

[0106] in, For compensation input.

[0107] Construct the following state estimator:

[0108]

[0109] in, is the estimated state of the system, is the estimated output of the system, and L is the observer gain.

[0110] Build the following security controller:

[0111]

[0112] Where K is the controller gain.

[0113] Step 4) Stability analysis:

[0114] First, define the estimation error as First, based on the above safety controller, input compensator and state estimator, the closed-loop function of the control system is given as follows:

[0115]

[0116] The error system of the control system is as follows:

[0117]

[0118] Then, based on the random analysis theory and Lyapunov stability theory, the asymptotic stability of the control system was established under certain standard conditions, so that the system can still maintain safe and stable operation under random attacks. Specifically:

[0119] Theorem 1: If there exist parameters α1, α2, α3, α4, ε1 and matrices P1, P2, P3, P4 and P3>0, P4>0, matrices Y1 and R1 satisfy the following linear matrix inequality:

[0120]

[0121] Then both the closed-loop system and the error system are stochastically stable, and the controller gain and observer gain can be expressed by K = Y1P1 and L = P4 respectively. -1 R1 is obtained.

[0122] where I is the identity matrix of appropriate dimensions,

[0123]

[0124]

[0125] Lemma 1: For any initial state x0, if the system satisfies:

[0126]

[0127] Then the system is stochastically stable.

[0128] Proof: Define the following Lyapunov function:

[0129]

[0130] The expectation is:

[0131]

[0132] in,

[0133]

[0134] To facilitate analysis, we define As a new augmented state variable, we get:

[0135]

[0136] in,

[0137]

[0138] Define G1 = diag{P1,I,I,P1}, G2 = diag{I,P2,I,I}, Π1 = diag{G1,I,I,I,I,I}, Π2 = diag{G2,I,I,I}. Multiply the third linear matrix inequality in Theorem 1 by Π1 on the left and Π1 on the right, and use Shur's complement theorem to obtain:

[0139]

[0140] By multiplying the second linear matrix inequality in Theorem 1 on the left and on the right by Π2, using Shur's complement theorem we can obtain:

[0141]

[0142] Combining the above formula, we can get Therefore, combined with Lemma 1, we can see that the system is randomly stable. Proof completed.

[0143] The invention is not limited to the above-mentioned embodiments. On the basis of the technical solution disclosed in the present invention, technicians in this field can make some substitutions and deformations to some technical features therein according to the disclosed technical content without creative labor, and these substitutions and deformations are all within the protection scope of the present invention.

Claims

1. A dual-rate dynamic control method based on sampling and holding under random attack, characterized in that: The following steps are involved: Step 1, system model construction: Based on the principle that the update rate of the sensor in the multi-rate control system is slower than the update rate of the controller, a dual-rate dynamic system discrete time model is constructed; Step 2, random attack model construction: a denial of service (DoS) attack model based on signal interference plus noise ratio (SINR) is given; Step 3, state estimation and security control: First, construct output and input compensators to dynamically compensate for packet loss, then estimate the state of the dual-rate system under attack and design a security controller; Step 4, stability analysis: Through the random analysis method and Lyapunov stability analysis theory, the random stability of the control system is guaranteed under certain standard conditions.

2. According to the dual-rate dynamic control method based on sampling and holding under random attack according to claim 1, it is characterized in that: The dual-rate system discrete time model is specifically: Among them, x(·) is the system state vector, u(·) is the control input, y(·) is the system output, and y a (·) is the sensor sampling output, A, B and C are known constant matrices of appropriate dimensions, T is the system controller fast update period, MT is the sensor slow sampling period, M is a positive integer, and k and p are the number of running steps in the large and small periods, respectively.

3. According to the dual-rate dynamic control method based on sampling and holding under random attack according to claim 2, it is characterized in that: kMT=T k , Substituting into the discrete time model of the dual-rate system, we obtain:

4. According to the dual-rate dynamic control method based on sampling and holding under random attack according to claim 3, it is characterized in that: Step 2 is as follows: For the dual-rate dynamic system, information transmission mainly relies on the wireless shared additive white Gaussian noise (AWGN) channel, describing the signal-to-noise ratio (SNR) of the sensor-controller (SC) and controller-actuator (CA) channels, specifically: in, are the energy of the sensor and controller sending data packets, are the AWGN energies of SC and CA channels, respectively; The bit error rate (SER) is an indicator to measure the communication quality of the wireless channel. The relationship between SER and channel SNR is established as follows: Where Q(x) is the Gaussian Q function, ξ>0 is the network parameter, and r is the intermediate variable of integration; When considering the impact of a dual-channel DoS attack on different channels of a dual-rate dynamic system, SINR is used instead of SNR: in, are the interference energies of DoS attacks on SC and CA channels respectively. At this time, we get: in, are the network parameters of SC and CA channels respectively; Considering that both the SC and CA bilateral channels of the dual-rate dynamic system are affected by DoS attacks, random loss of data packets occurs when transmitting on the channel. Signal detectors φ(·), θ(·) and v(·) are set up at the sensor sending end, controller receiving end and actuator receiving end respectively, and their specific definitions are as follows: Assuming that θ(·) and v(·) both obey Bernoulli distribution, we have: in, represents the probability of successful transmission of the output signal, Indicates the probability of successful transmission of the control signal; At this time, the dynamic performance of the dual-rate dynamic system is the following composite form: in, where μ(·)∈{0,1}, is the probability of successful transmission of sensor data packets under the combined influence of dual rate and attack, is the system status under DoS attack, It is the system output under DoS attack.

5. According to the dual-rate dynamic control method based on sampling and holding under random attack according to claim 4, it is characterized in that: Step 3 is as follows: Construct the following output compensator: in, To compensate the output; Construct the following input compensator: in, For compensation input; Construct the following state estimator: in, is the estimated state of the system, is the estimated output of the system, L is the observer gain; Build the following security controller: Where K is the controller gain.

6. The dual-rate dynamic control method based on sampling and holding under random attack according to claim 5 is characterized in that: Step 4 is as follows: First, define the estimation error as According to the safety controller, input compensator and state estimator, the closed-loop function of the control system is given as follows: The error system of the control system is as follows: Then, based on the random analysis theory and Lyapunov stability theory, the asymptotic stability of the control system was established under certain standard conditions, so that the system can still maintain safe and stable operation under random attacks. Specifically: If there are parameters α1, α2, α3, α4, ε1 and matrices P1, P2, P3, P4 and P3>0, P4>0, matrices Y1 and R1 satisfy the following linear matrix inequality: Then the closed-loop system and the error system are both stochastically stable, and the controller gain and observer gain can be expressed by K = Y1P1 and to seek; where I is the identity matrix of appropriate dimensions,

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