Networked control system security control method with dual-channel false data injection attack

Abstract

The invention relates to the field of safety control of a networked control system with communication constraints, in particular to a sampling controller design method based on state feedback of a networked control system. Comprising the following steps: constructing a random integral quadratic constraint operator on the basis of a networked control system based on an uncertain disturbance model to quantify uncertainty caused by sampling interval and false data injection attack and data packet loss; model transformation is carried out, and corresponding index stability conditions are given for a closed-loop system; analyzing the H-infinity performance index of the closed-loop system by using a random integral quadratic constraint operator and a KYP lemma; a two-stage heuristic solving iterative algorithm based on the state feedback controller is designed; the reliability and feasibility of the controller are verified through numerical simulation. The challenge brought by combination of false data injection attack and data packet loss is specifically solved.

Description

Technical Field

[0001] The present invention relates to the field of networked control system control, and specifically to a security control method for a networked control system with dual-channel false data injection attacks. Background Art

[0002] With the continuous improvement of system performance requirements, networked control systems are increasingly widely used in modern industrial and automation fields, and their importance has become more prominent. Networked control systems connect sensors, controllers, and actuators through a network, enabling efficient transmission and processing of information, thereby effectively reducing the impact of interference on passengers or system operation. However, due to signal transmission delays, limitations of sampling data periods, and the complexity of the network environment, the control effect of networked control systems is often affected to a certain extent, thereby reducing the stability and control performance of the system.

[0003] Networked control systems have significant advantages such as easy maintenance, simple installation, high flexibility, and strong scalability. These characteristics have enabled them to be widely used in many fields and attracted increasing attention. However, the openness of communication networks also exposes networked control systems to many potential risks, among which the most typical is malicious network attacks. In recent years, the forms and means of network attacks have become increasingly diverse, and the research focus has gradually shifted from traditional attack types to more concealed and destructive deception attacks. Deception attack is an attack method that misleads system decisions by injecting false information or tampering with data into the system. According to whether the attacker understands the dynamic model of the system, deception attacks can be divided into two types: false data injection attacks and data replay attacks. False data injection attack refers to the attacker injecting false data into the system to interfere with the normal operation of the system, while data replay attack refers to the attacker intercepting and resending legitimate data to achieve the attack purpose. It is worth noting that the attacker may cause significant damage to the system while evading detection through a carefully planned attack strategy, and may even lead to serious security consequences.

[0004] In actual physical systems, cyberattacks and packet losses often occur simultaneously, and this complex situation poses greater challenges to the stability and reliability of the system. However, many previous studies have mainly focused on single-channel packet loss or single types of cyberattacks, and relatively few studies have been conducted on the combination of multi-channel packet loss and cyberattacks. In response to this problem, many scholars have conducted in-depth research and exploration. For example, some research has proposed a distributed filter that can keep the filtering error system mean-square finite-time bounded under random attacks, thereby improving the robustness of the system. There is also research that has designed a Kalman filter-based FDI attack, which can cleverly avoid the monitoring of the attack detector, thus providing new ideas for the study of attack detection and defense mechanisms. However, in practical engineering applications, the sampling interval is usually random and may be disturbed by noise due to unnecessary physical constraints or network environment uncertainties. In other words, the sampling interval is affected by noise and fluctuates around the preferred sampling data interval according to a certain probability distribution. This randomness and uncertainty bring greater complexity to the analysis and design of the system.

[0005] To address these challenges, stochastic analysis techniques have been widely applied to design probability-related controllers for complex dynamic networks affected by noisy sampling intervals and packet losses. By introducing stochastic analysis methods, the uncertainties and randomness of the system can be more accurately described, thus providing theoretical support for the design of controllers with strong robustness and excellent performance. In recent years, with the increasing requirements for the security and reliability of networked control systems, researchers have begun to pay more attention to how to comprehensively consider the influence of various factors in complex network environments and design advanced control strategies that can effectively address problems such as cyberattacks and packet losses. These studies not only help improve the performance and security of networked control systems but also provide important references for the theoretical development and technical applications in related fields.

[0006] With the continuous development of computer and digital controller technologies, various mature research methods have emerged in the field of sampled-data control. For example, the small-gain type integral quadratic constraint is used to describe the characteristics of operators, and then the stability of sampled-data systems with time-delay signals is analyzed. In addition, there are input-delay methods, loop-based functional methods, switched-system methods, and stochastic-system methods, etc. These methods are of great significance for the performance analysis of networked control systems. Among them, the integral quadratic constraint method has attracted much attention due to its low computational complexity. A dynamic integral quadratic constraint method has been proposed for model predictive control strategies that jointly predict error-bound systems and nominal models. However, although the definition of stochastic integral quadratic constraint has been introduced in the continuous-time case, the related research in the discrete-time case still needs to be improved. To address the deficiencies in existing research, this study focuses on the control problems in networked control systems, especially the challenges brought about by the combination of false data injection attacks and packet losses. At the same time, the complexity introduced by the noise sampling data interval is also considered. By establishing a unified feedback interconnection model with an exponential decay rate, a new estimation method for the upper bound of the expected value of random variables is derived for the random characteristics of the noise sampling data interval and packet losses. On this basis, an operator that satisfies the definition of stochastic integral quadratic constraint is proposed, which combines the upper bound of the false data injection attack signal with the performance index, and an exponential stability condition with an exponential decay rate is given. Finally, a controller that can ensure the exponential stability of networked control systems is designed, and a corresponding controller algorithm is proposed, which has high prospects in practical applications. Summary of the Invention

[0007] To solve the above problems, the present invention discloses a security control method for a networked control system with dual-channel false data injection attacks.

[0008] The specific solution is as follows:

[0009] A security control method for a networked control system with dual-channel false data injection attacks, comprising the following steps:

[0010] Step 1, establish a mathematical model of a networked control system with uncertain disturbances;

[0011] Step 2, give the construction process of the equivalent feedback interconnection of the closed-loop networked control system;

[0012] Step 3, give the stability theorem of the networked control system;

[0013] Step 4, give an iterative algorithm for solving the state feedback controller.

[0014] Further, the specific process of Step 1 is to consider the following state-space model of the networked control system:

[0015]

[0016] where \(x(t)\) is the system state, is the derivative of the system state, \(u(t)\) is the system input, \(w(t)\) is the system uncertain disturbance, and \(A\), \(B\), and \(F_1\) represent the system matrix, input matrix, and disturbance matrix respectively; considering that the system is simultaneously subject to false data injection attacks and packet losses; the sampling interval \(l\) j is affected by noise and satisfies

[0017] l j =t j+1 -t j =l + δ j ,

[0018] where \(l>0\) represents the nominal sampling interval, \(t\) j represents the sampling time, and δ j represents the random noise sampling interval that follows a certain probability distribution; represents the sampling data sequence, and represent the maximum and minimum sampling intervals respectively, and the sampling interval is the sampling sequence in which the controller successfully receives the data packet, where in \([s\) k , s k+1 ), the number of consecutive packet losses is denoted as ε k ∈N, and the upper limit is

[0019] In the sensor - controller channel, considering the false data injection attack, the signal received by the controller is can be expressed as

[0020]

[0021] where \(\eta(s\) k ) is a discrete random variable that follows a Bernoulli distribution and satisfies and \(\mu\in[0,1)\), \(\varphi(s\) k ) is the malicious signal injected by the attacker during the data packet transmission process that satisfies \(\|\varphi(s\) k )\|\) 2 ≤\(\|H_1x(s\) k ))\|\) 2 , where the constant matrix \(H_1\) is the prior matrix.

[0022] Considering the packet loss and false data injection attack in the controller - actuator (C - A) channel, the control input \(u(t)\) based on the zero - order hold property can be expressed as

[0023]

[0024] where θ(s k ) follows a Bernoulli distribution and satisfies and φ(s k ) is the malicious signal injected during the data packet transmission process, satisfying ||θ(s k )|| 2 ≤ ||Q1x(s k ))|| 2 , where the constant matrix Q1 is the prior matrix;

[0025] Discretize the system (3) into the following stochastic discrete-time system

[0026]

[0027] where,

[0028] Furthermore, the specific process of step two is to substitute equation (1) into equation (4), and the following closed-loop system can be obtained:

[0029]

[0030] where

[0031]

[0032] Θ k = Θ1(s k ) + Θ2(s k ) + Θ3(s k ) + Θ4(s k ),

[0033]

[0034] Furthermore, the specific process of step three is to consider designing a state feedback controller. State feedback does not require measuring all system state variables, requires fewer sensors, and has lower costs. The state feedback design obtained by comparison is simpler, easier to implement, and can provide better robustness. In addition, the state can achieve better networked control by adjusting the output of the system, thereby improving the stability and comfort of the aircraft.

[0035] Regarding the stability of the networked control system, there are the following steps:

[0036] 1. According to the packet loss rate α, packet loss may randomly occur during the data transmission process from the sensor to the controller. Therefore, there is

[0037]

[0038] Among them, is the maximum number of lost packets;

[0039] Let and The exponential decay rate ρ ∈ (0, 1) and the closed-loop system equivalent to system (6) can be established as

[0040]

[0041] Among them, ρ ∈ (0, 1) is the exponential decay rate; Δ = diag{Δ 11 , Δ 12 , Δ 13 , Δ 14 , Δ 15},

[0042] Δ 11 = diag{Δ1, Δ1, Δ2, Δ3, Δ1Δ2, Δ1Δ3, Δ2Δ3},

[0043] Δ 12 = diag{Δ1Δ2Δ3, Δ3Δ4, Δ1Δ3Δ4, Δ2Δ3Δ4},

[0044] Δ 13 = diag{Δ1Δ2Δ3Δ4, Δ3Δ5, Δ1Δ3Δ5, Δ2Δ3Δ5},

[0045] Δ 14 = diag{Δ1Δ2Δ3Δ5, Δ3Δ4Δ5, Δ1Δ3Δ4Δ5},

[0046] Δ 15 = diag{Δ2Δ3Δ4Δ5, Δ1Δ2Δ3Δ4Δ5},

[0047] Δ3 = θ k Δ4 = η k ,

[0048] In addition, system (7) is also an uncertainty model of a control output where By analyzing the operator with random characteristics the specific expression of the linear time-invariant bounded self-adjoint multiplier is given.

[0049] II. In order to analyze the performance index γ of the networked control system, the stochastic discrete-time system (8) is exponentially stable when w k = 0, and its exponential convergence rate is ρ; when wk When it is not equal to 0, there exists H ∞ with performance γ > 0 such that where the operator satisfies the stochastic discrete-time integral quadratic constraint defined by a linear time-invariant bounded self-adjoint multiplier

[0050] Π = diag{Π1, Π2}, (8)

[0051] By introducing the H ∞ index to construct the multiplier Π that satisfies the definition of the stochastic discrete-time integral quadratic constraint;

[0052] For the prior constants γ, J1 and J2, the linear networked control system is exponentially stable and has an exponential decay rate if the spectral radius of is less than 1 and there exists a positive definite matrix G such that

[0053]

[0054] where

[0055]

[0056] III. For the networked control system, a state feedback controller is designed and a two-stage solution algorithm is given. The designed controller stabilizes the system and meets the finite frequency domain requirements. For the given Φ, ψ and Π, the state space of the networked control system can be realized. When there exist a scalar ξ > 0, a matrix K and a matrix Q, the existence of a controller for the networked control system to be stable and further meet the finite frequency domain index is satisfied and

[0057]

[0058] the networked control system is stable.

[0059] where

[0060]

[0061] From this, the state feedback control gain matrix can be obtained Using the generalized KYP lemma and the heuristic two-step method, the above inequality holds, and the finally obtained can be used as the desired state feedback control gain matrix.

[0062] Further, the specific process of Step 4 is as follows: A heuristic algorithm for synthesizing a state feedback controller is studied based on the KYP lemma. The controller solution algorithm adopts a two-stage idea. In the first step, an initial controller is obtained, and a feasible solution is used as the initial value. In the second step, an output feedback controller is solved to give the optimal solution of the designed iterative algorithm; an iterative algorithm for solving the controller is given:

[0063] 1: Preset the maximum sampling data interval The minimum sampling data interval and the scalar ξ, a1, i = 0;

[0064] 2: Let Solve the LMI (9) to obtain the initial controller gain matrix

[0065] 3: If

[0066] 4: Then let t = -1, i = i + 1;

[0067] 5: Otherwise let t = 1;

[0068] 7: End;

[0069] 8: If t < 0, (ε k -(ε k -0.001)) / ε k ≥ δ do;

[0070] 9: Let q = q + 1,

[0071] 10: Solve the LMI (9) to obtain the gain matrix Repeat 3 - 8 until t > 0

[0072] 11: End.

[0073] The beneficial effects of the present invention are as follows: By constructing a stochastic integral quadratic constraint operator, the uncertainties caused by sampled data, false data injection attacks, and packet losses are quantified. A "two-stage heuristic" solution iterative algorithm based on a state feedback controller is designed to effectively handle complex problems in networked control systems. This method overcomes the difficulty of solving the operator norm of a stochastic property, gives a closer upper bound of the operator, and ensures the stability of the system through the exponential stability theorem. Its state feedback controller is simple in design, low in cost, and can achieve optimal control performance by minimizing the performance index, enhancing the anti-interference ability of the system. In addition, the reliability and feasibility of the controller are verified through numerical simulation, which has high theoretical innovation and practical application prospects, providing an effective solution for the security control of networked control systems. Description of the Drawings

[0074] Figure 1 The state response of the system under different control inputs.

[0075] Figure 2 The probabilities of false data injection attacks and packet losses occurring in different channels.

[0076] Figure 3 The sampling interval of the networked control system.

[0077] Figure 4 The flowchart of the method of the present invention. Detailed implementation manners

[0078] The following describes the detailed implementation manners of the present invention with reference to the accompanying drawings, so that those skilled in the art can better understand the present invention. It should be noted that in the following description, when the detailed descriptions of known functions and designs may obscure the main content of the present invention, these descriptions will be omitted here.

[0079] As Figure 4 shown, the present invention discloses and studies the H ∞ control problem under the background of a networked control system, and specifically solves the challenges brought about by the combination of false data injection attacks and packet losses. The steps of the present invention are as follows: Step 1: Construct a stochastic integral quadratic constraint operator on the basis of a networked control system based on an uncertain disturbance model to quantify the uncertainty caused by sampled data and false data injection attacks and packet losses; Step 2: Perform a model transformation and give corresponding exponential stability conditions for the closed-loop system; Step 3: Analyze the H ∞ performance index of the closed-loop system by using the stochastic integral quadratic constraint operator and the generalized KYP lemma; Step 4: Design a "two-stage heuristic" solution iterative algorithm based on a state feedback controller.

[0080] The specific steps give a method for designing an H ∞ controller for a networked control system, including the following aspects:

[0081] Step 1, establish a mathematical model of a networked control system with uncertain disturbances;

[0082] Step 2, give the construction process of the equivalent feedback interconnection of the closed-loop networked control system;

[0083] Step 3, give the stability theorem of the networked control system;

[0084] Step 4, give an iterative algorithm for solving the state feedback controller.

[0085] In this embodiment, the specific process of Step 1 is to consider the following networked control system:

[0086]

[0087] where \(x(t)\) is the system state, is the derivative of the system state, \(u(t)\) is the system input, \(w(t)\) is the system uncertain disturbance, and \(A\), \(B\), and \(F_1\) represent the system matrix, input matrix, and disturbance matrix respectively; it is considered that the system is simultaneously subject to false data injection attacks and packet losses; the sampling interval \(l\) j is affected by noise and satisfies

[0088] l j =t j+1 -t j =l + δ j ,

[0089] where \(l>0\) represents the nominal sampling interval, \(t\) j represents the sampling time, and δ j represents the random noise sampling interval that follows a certain probability distribution; represents the sampling data sequence, and represent the maximum and minimum sampling intervals respectively, and the sampling interval is the sampling sequence in which the controller successfully receives the packet, where and \(t_0 = s_0 = 0\); in \([s\) k , s k+1 )), the number of consecutive packet losses is denoted as ε k ∈N, and the upper limit is

[0090] In the sensor - controller channel, considering false data injection attacks, the signal received by the controller is can be expressed as

[0091]

[0092] where \(\eta(s\) k ) is a discrete random variable that follows a Bernoulli distribution and satisfies and \(\mu\in[0,1)\), \(\varphi(s\) k ) is the malicious signal injected by the attacker during the packet transmission process that satisfies \(\|\varphi(s\) k )\|\) 2 ≤\(\|H_1x(s\) k ))\|\) 2 , where the constant matrix \(H_1\) is a priori matrix.

[0093] Considering packet losses and false data injection attacks in the controller - actuator (C - A) channel, the control input \(u(t)\) based on the zero - order hold property can be expressed as

[0094]

[0095] where θ(s k ) is a random variable representing the packet loss situation occurring in the controller-actuator channel; it follows a Bernoulli distribution and satisfies and φ(s k ) is the malicious signal injected during the data packet transmission process, satisfying ||θ(s k )|| 2 ≤||Q1x(s k ))|| 2 , where the constant matrix Q1 is a prior matrix;

[0096] Discretize (3) into the following stochastic discrete-time system

[0097]

[0098] where,

[0099] In this embodiment, the specific process of step two is to substitute equation (1) into equation (4), and the following closed-loop system can be obtained:

[0100]

[0101] where

[0102]

[0103] Θ k = Θ1(s k ) + Θ2(s k ) + Θ3(s k ) + Θ4(s k ),

[0104]

[0105] In this embodiment, the specific process of step three is to consider designing a state feedback controller. State feedback does not require measuring all system state variables, requires fewer sensors, and has lower costs. The state feedback design obtained through comparison is simpler, easier to implement, and can provide better robustness. In addition, the state can achieve better networked control by adjusting the output of the system, thereby improving the stability and comfort of the aircraft.

[0106] Regarding the stability of the networked control system, there are the following steps:

[0107] 1. According to the packet loss rate α, packet loss may randomly occur during the data transmission process from the sensor to the controller. Therefore, there is

[0108]

[0109] wherein, is the maximum number of lost packets;

[0110] Let and the exponential decay rate ρ ∈ (0, 1), an equivalent closed-loop system to system (6) can be established as

[0111]

[0112] wherein, ρ ∈ (0, 1) is the exponential decay rate;

[0113] Δ = diag{Δ 11 , Δ 12 , Δ 13 , Δ 14 , Δ 15},

[0114] Δ 11 = diag{Δ1, Δ1, Δ2, Δ3, Δ1Δ2, Δ1Δ3, Δ2Δ3},

[0115] Δ 12 = diag{Δ1Δ2Δ3, Δ3Δ4, Δ1Δ3Δ4, Δ2Δ3Δ4},

[0116] Δ 13 = diag{Δ1Δ2Δ3Δ4, Δ3Δ5, Δ1Δ3Δ5, Δ2Δ3Δ5},

[0117] Δ 14 = diag{Δ1Δ2Δ3Δ5, Δ3Δ4Δ5, Δ1Δ3Δ4Δ5},

[0118] Δ 15 = diag{Δ2Δ3Δ4Δ5, Δ1Δ2Δ3Δ4Δ5},

[0119] Δ3 = θ k , Δ4 = η k ,

[0120] In addition, system (7) is also an uncertainty model of a control output wherein By analyzing the operator with random characteristics the specific expression of the linear time-invariant bounded self-adjoint multiplier is given.

[0121] II. To analyze the performance index γ of the networked control system, for the feedback interconnection structure (8) that is exponentially stable when w(t) = 0, the operator satisfies the stochastic discrete-time integral quadratic constraint defined by the linear time-invariant bounded self-adjoint multiplier

[0122] Π = diag{Π1, Π2}, (8)

[0123] By introducing the H ∞ index to construct the multiplier Π that satisfies the definition of the stochastic discrete-time integral quadratic constraint.

[0124] With the help of the stochastic discrete-time integral quadratic constraint theory, an exponential stability theorem of the networked control system including the upper bound of the false data injection attack signal is given. On this basis, an H ∞ controller is designed to make the networked control system exponentially stable under the given control performance index γ.

[0125] For the prior constants γ, J1, and J2, the linear networked control system is exponentially stable and has an exponential decay rate if the spectral radius of is less than 1 and there exists a positive definite matrix G such that

[0126]

[0127] where

[0128]

[0129] III. For the networked control system, a state feedback controller is designed, and a two-stage solution algorithm is given. The designed controller stabilizes the system and meets the finite frequency domain requirements. For the given Φ, ψ, and Π, the state space of the networked control system can be realized. When there exist a scalar ξ > 0, a matrix K, and a matrix Q, the existence of a controller that further stabilizes the networked control system and meets the finite frequency domain index is satisfied and

[0130]

[0131] where

[0132]

[0133] From this, the state feedback control gain matrix can be obtained Using the KYP lemma and the heuristic two-step method, the above inequality holds, and the finally obtained can be used as the desired state feedback control gain matrix.

[0134] In this embodiment, the specific process of step four is as follows: a heuristic algorithm for synthesizing a state feedback controller is studied based on the KYP lemma. The controller solving algorithm adopts a two-stage idea. In the first step, an initial controller is obtained, and there is a feasible solution as the initial value. In the second step, an output feedback controller is solved to give the optimal solution of the designed iterative algorithm; an iterative algorithm for solving the controller is given:

[0135] 1: Preset the maximum sampling data interval The minimum sampling data interval and the scalar ξ, a1, i = 0;

[0136] 2: Let Solve the LMI(9) to obtain the initial controller gain matrix

[0137] 3: If

[0138] 4: Then let t = -1, i = i + 1;

[0139] 5: Otherwise let t = 1;

[0140] 7: End;

[0141] 8: If t < 0, (ε k -(ε k -0.001)) / ε k ≥ δ do;

[0142] 9: Let q = q + 1,

[0143] 10: Solve the LMI(9) to obtain the gain matrix Repeat 3 - 8 until t > 0

[0144] 11: End.

[0145] Through numerical simulation comparison, using the proposed state feedback controller solving algorithm, the control gain matrix of the state feedback control is solved by MATLAB as

[0146] K = [0.1960 0.1768 0.2153].

[0147] By observing the control gain matrix obtained by the algorithm solution, the numerical values of the control effect and the performance index γ on the H ∞ controller are obtained, which shows the effectiveness of the proposed controller method. Comparing with the literature (H ∞The state-feedback controller proposed in (controller design for networked systems with two-channel packet dropouts and FDI attacks) is

[0148] K = [-0.3310 -2.5974 -2.3615 -1.0517].

[0149] The simulation results are as Figures 1-3 shown. Figure 1 shown that the increase in the exponential decay rate improves the stability performance of the system while increasing the requirements for the controller. Under different exponential decay rates, Figure 2 it describes whether packet loss and false data injection attacks will occur in the two channels. The noise sampling interval in the flight control system is as Figure 3 shown.

[0150] The above results show that the advantages of the proposed H ∞ control gain in the networked control system are as follows: This controller can effectively handle the uncertainties brought by noise sampling data based on stochastic integral quadratic constraints and false data injection attacks, increase the state-feedback gain, suppress the influence of external disturbances on the system, and enhance the anti-interference ability of the system. State feedback achieves optimal control performance by minimizing the H ∞ performance index. To sum up, H ∞ state-feedback control has the advantages of robustness, improved control performance, simplified design, etc., and can improve the robustness and control performance of the system.

[0151] The present invention studies the H ∞ control problem under the background of networked control systems, and specifically solves the challenges brought by the combination of false data injection attacks and packet loss. A stochastic integral quadratic constraint operator is constructed on the basis of a networked control system with an uncertain disturbance model to quantify the uncertainties caused by sampling data and false data injection attacks and packet loss. Model transformation is carried out, and corresponding exponential stability conditions are given for the closed-loop system. The H ∞ performance index of this closed-loop system is analyzed using the stochastic integral quadratic constraint operator and the generalized KYP lemma. A "two-stage heuristic" solution iteration algorithm based on a state-feedback controller is designed. Finally, the reliability and feasibility of this controller are verified through numerical simulations.

[0152] The above is only a preferred and feasible embodiment of the present invention, and it does not limit the scope of rights of the present invention. Any equivalent structural changes made by using the content of the specification and drawings of the present invention are included in the scope of rights of the present invention.

Claims

1. A security control method for a networked control system with a two-channel false data injection attack, characterized in that, including the following steps Step 1, establish a mathematical model of a networked control system with uncertain disturbances Step 2, give the construction process of the equivalent feedback interconnection of the closed-loop networked control system Step 3, give the stability theorem of the networked control system Step 4, give an iterative algorithm for solving the state feedback controller 2. The security control method for a networked control system with a dual-channel false data injection attack according to claim 1, characterized in that, The specific process of Step 1 is as follows. Consider the following state-space model of the networked control system where \(x(t)\) is the system state, is the derivative of the system state, \(u(t)\) is the system input, \(w(t)\) is the system uncertain disturbance, and \(A\), \(B\), and \(F_1\) represent the system matrix, input matrix, and disturbance matrix, respectively. It is considered that the system is simultaneously subject to false data injection attacks and packet losses. The sampling interval \(l\) j is affected by noise and satisfies l j = t j+1 -t j = l + δ j , where l > 0 represents the nominal sampling interval, t j represents the sampling time, and δ j represents the sampling interval of the random noise that follows a certain probability distribution; represents the sampling data sequence, and represent the maximum and minimum sampling intervals respectively, and the sampling interval is the sampling sequence for the controller to successfully receive data packets, where and t0 = s0 = 0; the number of consecutive packet losses is represented by ε k ∈N, with the upper limit being In the sensor-controller communication channel, considering false data injection attacks, the signal received by the controller is Denoted as where η(s k ) is a discrete random variable, following a Bernoulli distribution, satisfying and φ(s k ) is the malicious signal injected during the data packet transmission process, satisfying ||φ(s k )|| 2 ≤||H1x(s k ))|| 2 , and the constant matrix H1 is a prior matrix; Considering packet loss and false data injection attacks in the controller-actuator channel, the control input u(t) based on the properties of the zero-order hold is expressed as where θ(s k ) follows a Bernoulli distribution and satisfies and φ(s k ) is the malicious signal injected during the data packet transmission process, satisfying ||θ(s k )|| 2 ≤||Q1x(s k ))|| 2 , and the constant matrix Q1 is the prior matrix; Discretize Equation (3) into the following stochastic discrete-time system Among them, 3. The security control method for a networked control system with a dual-channel false data injection attack according to claim 2, characterized in that, The specific process of Step 2 is as follows. The networked control system is expressed as the following closed-loop networked control system where Θ k = Θ1(s k ) + Θ2(s k ) + Θ3(s k ) + Θ4(s k ), 4. The security control method for a networked control system with dual-channel false data injection attack according to claim 3, characterized in that The specific process of Step 3 is as follows. According to the packet loss rate α, packet loss will randomly occur during the transmission from the sensor to the controller. Therefore, we obtain where α is the packet loss rate, is the maximum number of lost packets; Let and establish a closed-loop system equivalent to the exponential decay rate ρ ∈ (0, 1) and Equation (6) where ρ ∈ (0, 1) is the exponential decay rate; Δ = diag{Δ 11 , Δ 12 , Δ 13 , Δ 14 , Δ 15}, Δ 11 = diag{Δ1, Δ1, Δ2, Δ3, Δ1Δ2, Δ1Δ3, Δ2Δ3}, Δ 12 = diag{Δ1Δ2Δ3, Δ3Δ4, Δ1Δ3Δ4, Δ2Δ3Δ4}, Δ 13 = diag{Δ1Δ2Δ3Δ4,Δ3Δ5,Δ1Δ3Δ5,Δ2Δ3Δ5}, Δ 14 = diag{Δ1Δ2Δ3Δ5, Δ3Δ4Δ5, Δ1Δ3Δ4Δ5}, Δ 15 = diag{Δ2Δ3Δ4Δ5, Δ1Δ2Δ3Δ4Δ5}, In addition, the system (7) is an uncertainty model that controls the output wherein Analysis shows that the stochastic discrete-time system (8) is exponentially stable. When w k = 0, its exponential convergence rate is ρ; when w k ≠0, there exists H ∞ such that the performance γ > 0 satisfies where the operator satisfies the stochastic discrete-time integral quadratic constraint defined by a linear time-invariant bounded self-adjoint multiplier Π = diag{Π1, Π2}, (8) By introducing the H ∞ index to construct a multiplier Π that satisfies the definition of the stochastic discrete-time integral quadratic constraint; For the prior constants γ, J1, and J2, the linear networked control system is exponentially stable and has an exponential decay rate if has a spectral radius less than 1 and there exists a positive definite matrix G such that where If there exist scalars ξ > 0, matrices K and Q such that the networked control system is stable where 5. The security control method for a networked control system with a dual-channel false data injection attack according to claim 4, characterized in that The specific process of Step 4 is as follows. Based on the KYP lemma, a heuristic algorithm for synthesizing a state feedback controller is studied. The controller solution algorithm adopts a two-stage idea. In the first step, an initial controller is obtained, and a feasible solution is used as the initial value. In the second step, an output feedback controller is solved to give the optimal solution of the designed iterative algorithm. Give the iterative algorithm for solving the controller 1: Preset maximum sampling data interval Minimum sampling data interval and scalars ξ, a1, i = 0; 2: Let Solve the LMI (9) to obtain the initial controller gain matrix 3: If 4: Then let t = -1, i = i + 1 5: Otherwise let t = 1 7: End 8: If t < 0, (ε k -(ε k - 0.001)) / ε k ≥ δdo; 9: Let q = q + 1, 10: Solve the LMI (9) to obtain the gain matrix Repeat steps 3 - 8 until t > 0 11: End

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