State-restricted high-order nonlinear information physical system security control method and device

Abstract

The application discloses a state-restricted high-order nonlinear information physical system security control method and device, and relates to the technical field of information security. The method comprises the following steps: a state-restricted high-order nonlinear information physical system with external disturbance under malicious attack is established to obtain a control-oriented dynamic model; an ideal virtual controller and an adaptive law are designed based on the dynamic model; a fixed-time adaptive fuzzy controller is designed based on the dynamic model, the ideal virtual controller, the adaptive law and Lyapunov stability theorem, so as to realize security control of the information physical system suffering from malicious attack. The application can ensure that the system output accurately tracks the ideal output in a fixed time, and the rest of the system states can also track the ideal virtual control signal, and meanwhile, all the system states satisfy the respective state constraint conditions in the whole control process.

Description

Technical Field

[0001] This invention relates to the field of information security technology, and in particular to a security control method and device for a state-constrained high-order nonlinear cyber-physical system. Background Technology

[0002] With the deep integration of informatization and industrialization, traditional physical control systems can no longer meet the needs of the informatization and networking of next-generation production equipment. Against this backdrop, cyber-physical systems (CPS) have emerged. Through the organic and deep integration of computing, communication, and control technologies, they enable real-time perception, dynamic control, and information services for large-scale engineering systems, possessing characteristics such as reliability, real-time performance, and high efficiency. This has driven the upgrading and leapfrog development of key technologies in fields such as transportation, power, and healthcare. A typical characteristic of CPS is that communication between the control layer and the perception / execution layer requires a data transmission layer. Therefore, malicious attackers can launch diverse and complex cyber-physical cross-domain attacks targeting CPS systems, aiming to probe, intrude into, and hijack information systems, thereby causing serious non-contact damage to physical systems.

[0003] In recent years, scholars both domestically and internationally have proposed a series of approaches to security control of cyber-physical systems (CPS) under malicious attacks from different perspectives. While significant progress has been made, the following shortcomings remain: Most methods only achieve asymptotic or finite-time stability of nonlinear CPS systems under malicious attacks, without considering the state constraints present in the system. There are almost no fixed-time control methods for state-constrained nonlinear CPS systems with external disturbances under malicious attacks. In particular, the simultaneous existence of malicious attacks and external disturbances makes achieving fixed-time stability control of state-constrained CPS systems with external disturbances under malicious attacks extremely difficult. Therefore, it is urgent to design fixed-time control methods for state-constrained nonlinear CPS systems with external disturbances under malicious attacks. Summary of the Invention

[0004] This invention addresses the problem of designing a fixed-time control method for a state-constrained nonlinear cyber-physical system subject to external disturbances under malicious attacks.

[0005] To solve the above-mentioned technical problems, the present invention provides the following technical solution:

[0006] On one hand, this invention provides a security control method for a state-constrained high-order nonlinear cyber-physical system, implemented by an electronic device, comprising:

[0007] S1. Establish a control-oriented dynamic model for a state-constrained high-order nonlinear cyber-physical system with external disturbances under malicious attacks.

[0008] S2. Based on the dynamic model, design an ideal virtual controller and adaptive laws.

[0009] S3. Based on the dynamic model, ideal virtual controller, adaptive law and Lyapunov stability theorem, a fixed-time adaptive fuzzy controller is designed to realize the security control of cyber-physical systems subjected to malicious attacks.

[0010] Alternatively, the dynamic model in S1 is shown in equation (1) below:

[0011]

[0012] Where t represents time, and ξ(t) represents the state vector of the cyber-physical system ξ(t) = [ξ1(t), ξ2(t), ..., ξ n (t)] T ∈R n ξ i (t) represents the state variables of the cyber-physical system. n indicates that the cyber-physical system is an nth-order nonlinear system, φ i (.) and q i (.), i = 1, 2, ..., n, represents a known real continuous nonlinear function with respect to the state variables of the cyber-physical system. q i,0 Denotes the lower bound, q n,1 Let α(t,t) denote the upper bound, y(t) denote the actual output of the cyber-physical system, and α(t,t) denote the upper bound. α ) represents a multiplicative malicious attack signal, α(t,t) α )∈[0,1] and satisfy 0<α min <α(t,t α )≤1, where α min Represents α(t,t) α The lower bound of ), β(t,t) β ) represents an additive malicious attack signal, and satisfies β(t,t) β )≤β max , where β max Represents β(t,t) β The upper bound of ), u(t) represents the control input of the cyber-physical system, d i (t), i = 1, 2, ..., n represents the external disturbances existing in the controlled object. It is a positive number.

[0013] Optionally, the design of the ideal virtual controller and adaptive laws based on the dynamic model in S2 includes:

[0014] Based on the dynamic model, the constraints corresponding to the state of the cyber-physical system, the actual output of the cyber-physical system, the ideal output of the cyber-physical system, the backstepping method, the obstacle Lyapunov function, and the fuzzy logic system, an ideal virtual controller and an adaptive law are designed.

[0015] Optionally, based on the dynamic model, the constraints corresponding to the state of the cyber-physical system, the actual output of the cyber-physical system, the ideal output of the cyber-physical system, the backstepping method, the obstacle Lyapunov function, and the fuzzy logic system, the ideal virtual controller and adaptive rules are designed, including:

[0016] S21. Based on the dynamic model, the constraints corresponding to the state of the cyber-physical system, the actual output of the cyber-physical system, the ideal output of the cyber-physical system, the backstepping method, the obstacle Lyapunov function, and the fuzzy logic system, design an ideal virtual controller.

[0017] S22. Based on the dynamic model, the constraints corresponding to the state of the cyber-physical system, the actual output of the cyber-physical system, the ideal output of the cyber-physical system, the backstepping method, the obstacle Lyapunov function, the fuzzy logic system, and the ideal virtual controller, design an adaptive rule for the weight vector of the fuzzy logic system.

[0018] Alternatively, the ideal virtual controller in S2 is as shown in equation (2) below:

[0019]

[0020]

[0021] in, C B1 (t), C U1 (t) represents the preset constraint on the output tracking error, and ζ1 represents the output tracking error. Unknown parameters The forecast, ∈1(∑1(t)) represents the approximation error, and β1 is a positive design parameter. x 11 >0, x 21 >0, g1(t)>0, r=(2m+d) / (2m+1)>1, m∈N, d>1 is a positive odd integer, e=1 / r>1 / 2.

[0022] Alternatively, the adaptive rule in S2 is shown in equation (4) below:

[0023]

[0024] Where, σ 1i >0, σ 2i Indicates design parameters, Unknown parameters The estimated value is r = (2m + d) / (2m + 1) > 1, where m ∈ N and d > 1 is a positive odd integer. C i For virtual tracking error ζ i The constraint boundary on 2≤i≤n-1, ζ i For virtual tracking error, ∈ i (∑ i (t) represents the approximation error, β i The design parameters are positive.

[0025] Optionally, the fixed-time adaptive fuzzy controller in S3 is as shown in equation (5):

[0026]

[0027] in, C n For virtual tracking error ζ n The constraint boundary on ζ n For virtual tracking error, α min The malicious attack signal α(t,t) represents multiplicative properties. α The lower bound of ) Unknown parameters The forecast, ∈ n (∑ n (t) represents the approximation error. β n For positive design parameters, x 1n >0, x 2n >0, r=(2m+d) / (2m+1)>1, m∈N, d>1 is a positive odd integer, e=1 / r>1 / 2.

[0028] On the other hand, the present invention provides a security control device for a state-constrained high-order nonlinear cyber-physical system. This device is used to implement a security control method for a state-constrained high-order nonlinear cyber-physical system. The device includes:

[0029] The dynamics model building module is used to establish control-oriented dynamics models for state-constrained high-order nonlinear cyber-physical systems with external disturbances under malicious attacks.

[0030] The design module is used to design ideal virtual controllers and adaptive laws based on dynamic models.

[0031] The output module is used to design a fixed-time adaptive fuzzy controller based on dynamic models, ideal virtual controllers, adaptive laws, and Lyapunov stability theorem, so as to realize the secure control of cyber-physical systems subjected to malicious attacks.

[0032] Alternatively, the dynamic model is as shown in equation (1):

[0033]

[0034] Where t represents time, and ξ(t) represents the state vector of the cyber-physical system ξ(t) = [ξ1(t), ξ2(t), ..., ξ n (t)] T ∈R n ξ i (t) represents the state variables of the cyber-physical system. n indicates that the cyber-physical system is an nth-order nonlinear system, φ i (.) and q i (.), i = 1, 2, ..., n, represents a known real continuous nonlinear function with respect to the state variables of the cyber-physical system. q i,0 Denotes the lower bound, q n,1 Let α(t,t) denote the upper bound, y(t) denote the actual output of the cyber-physical system, and α(t,t) denote the upper bound. α ) represents a multiplicative malicious attack signal, α(t,t) α )∈[0,1] and satisfy 0<α min <α(t,t α )≤1, where α min Represents α(t,t) α The lower bound of ), β(t,t) β ) represents an additive malicious attack signal, and satisfies β(t,t) β )≤β max , where β max Represents β(t,t) β The upper bound of ), u(t) represents the control input of the cyber-physical system, d i (t), i = 1, 2, ..., n represents the external disturbances existing in the controlled object. It is a positive number.

[0035] Optionally, the design module is further used for:

[0036] Based on the dynamic model, the constraints corresponding to the state of the cyber-physical system, the actual output of the cyber-physical system, the ideal output of the cyber-physical system, the backstepping method, the obstacle Lyapunov function, and the fuzzy logic system, an ideal virtual controller and an adaptive law are designed.

[0037] Optionally, the design module is further used for:

[0038] S21. Based on the dynamic model, the constraints corresponding to the state of the cyber-physical system, the actual output of the cyber-physical system, the ideal output of the cyber-physical system, the backstepping method, the obstacle Lyapunov function, and the fuzzy logic system, design an ideal virtual controller.

[0039] S22. Based on the dynamic model, the constraints corresponding to the state of the cyber-physical system, the actual output of the cyber-physical system, the ideal output of the cyber-physical system, the backstepping method, the obstacle Lyapunov function, the fuzzy logic system, and the ideal virtual controller, design an adaptive rule for the weight vector of the fuzzy logic system.

[0040] Alternatively, the ideal virtual controller is as shown in equation (2):

[0041]

[0042]

[0043] in, C B1 (t), C U1 (t) represents the preset constraint on the output tracking error, and ζ1 represents the output tracking error. Unknown parameters The forecast, ∈1(∑1(t)) represents the approximation error, and β1 is a positive design parameter. x 11 >0, x 21 >0, g1(t)>0, r=(2m+d) / (2m+1)>1, m∈N, d>1 is a positive odd integer, e=1 / r>1 / 2.

[0044] Alternatively, the adaptive rule is as shown in equation (4):

[0045]

[0046] Where, σ 1i >0, σ 2i Indicates design parameters, Unknown parameters The estimated value is r = (2m + d) / (2m + 1) > 1, where m ∈ N and d > 1 is a positive odd integer. C i For virtual tracking error ζ i The constraint boundary on 2≤i≤n-1, ζ i For virtual tracking error, ∈i (∑ i (t) represents the approximation error, β i The design parameters are positive.

[0047] Alternatively, a fixed-time adaptive fuzzy controller can be used, as shown in equation (5):

[0048]

[0049] in, C n For virtual tracking error ζ n The constraint boundary on ζ n For virtual tracking error, α min The malicious attack signal α(t,t) represents multiplicative properties. α The lower bound of ) Unknown parameters The forecast, ∈ n (∑ n (t) represents the approximation error. β n For positive design parameters, x 1n >0, x 2n >0, r=(2m+d) / (2m+1)>1, m∈N, d>1 is a positive odd integer, e=1 / r>1 / 2.

[0050] On one hand, an electronic device is provided, comprising a processor and a memory, wherein the memory stores at least one instruction, which is loaded and executed by the processor to implement the aforementioned security control method for a state-constrained high-order nonlinear cyber-physical system.

[0051] On the one hand, a computer-readable storage medium is provided, wherein at least one instruction is stored in the storage medium, and the at least one instruction is loaded and executed by a processor to implement the above-described security control method for a state-constrained high-order nonlinear cyber-physical system.

[0052] The beneficial effects of the technical solutions provided by the embodiments of the present invention include at least the following:

[0053] In the above scheme, for state-constrained high-order nonlinear cyber-physical systems with external disturbances under malicious attacks, a cyber-physical system security control method is proposed to ensure that the system output accurately tracks the ideal output within a fixed time, and that the other system states can also track the ideal virtual control signal. At the same time, during the entire control process, all system states satisfy their respective state constraints.

[0054] The cyber-physical system security control method provided in this application is designed for state-constrained high-order nonlinear cyber-physical systems with external disturbances, and therefore can be applied to the security control of nonlinear cyber-physical systems of any order.

[0055] This application incorporates the barrier Lyapunov function method, which ensures the fixed-time stability of the cyber-physical system while guaranteeing that all system states satisfy their respective state constraints throughout the entire control operation. Attached Figure Description

[0056] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0057] Figure 1 This is a schematic diagram of the security control method for state-constrained high-order nonlinear cyber-physical systems provided in an embodiment of the present invention;

[0058] Figure 2 A schematic diagram of the structure of a cyber-physical system provided in an embodiment of the present invention;

[0059] Figure 3 Case 1 provided for the embodiment of the present invention: System output y, reference signal y d Schematic diagrams of B(t) and U(t);

[0060] Figure 4 Case 1 provided for the embodiment of the present invention: Schematic diagram of the trajectory curve result of tracking error ζ1;

[0061] Figure 5 Case 1 provided for the embodiment of the present invention: ξ2, Schematic diagram of -z2 and z2 results;

[0062] Figure 6 Case 1 provided for the embodiment of the present invention: Schematic diagram of the trajectory curve result of the control input u;

[0063] Figure 7 Case 2 provided for the embodiment of the present invention: System output y, reference signal y d Schematic diagram of B(t) and U(t) results;

[0064] Figure 8 This is a block diagram of a state-constrained high-order nonlinear cyber-physical system security control device provided in an embodiment of the present invention;

[0065] Figure 9This is a schematic diagram of the structure of an electronic device provided in an embodiment of the present invention. Detailed Implementation

[0066] To make the technical problems, technical solutions and advantages of the present invention clearer, a detailed description will be given below in conjunction with the accompanying drawings and specific embodiments.

[0067] like Figure 1 As shown, this embodiment of the invention provides a security control method for a state-constrained high-order nonlinear cyber-physical system, which can be implemented by an electronic device. Figure 1 The flowchart shown is for a state-constrained high-order nonlinear cyber-physical system security control method. The processing flow of this method may include the following steps:

[0068] S1. Establish a control-oriented dynamic model for a state-constrained high-order nonlinear cyber-physical system with external disturbances under malicious attacks.

[0069] One feasible implementation method is, for example Figure 2 As shown, the communication method in the cyber-physical system is wireless communication. The controller sends control commands to the actuators via a wireless communication network. The actuators act on the controlled object. External disturbances always exist in the controlled object. Sensors measure the signals in the controlled object and then send them to the controller via the wireless communication network. A malicious attack intends to add a multiplicative attack signal α(t,t) before and after the control command u(t) (i.e., the system control input) sent by the controller to the actuator via the wireless communication network. α ) and additive attack signal β(t,t β This allows them to carry out malicious attacks.

[0070] Alternatively, the dynamic model in S1 is shown in equation (1) below:

[0071]

[0072] Where t represents time, and ξ(t) represents the state vector of the cyber-physical system ξ(t) = [ξ1(t), ξ2(t), ..., ξ n (t)] T ∈R n ξ i (t) represents the state variables of the cyber-physical system. n indicates that the cyber-physical system is an nth-order nonlinear system, φ i (.) and q i (.), i = 1, 2, ..., n, represents a known real continuous nonlinear function with respect to the state variables of the cyber-physical system. qi,0 Denotes the lower bound, q n,1Let α(t,t) denote the upper bound, y(t) denote the actual output of the cyber-physical system, and α(t,t) denote the upper bound. α ) represents a multiplicative malicious attack signal, α(t,t) α )∈[0,1] and satisfy 0<α min <α(t,t α )≤1, where α min Represents α(t,t) α The lower bound of ), β(t,t) β ) represents an additive malicious attack signal, and satisfies β(t,t) β )≤β max , where β max Represents β(t,t) β The upper bound of ), u(t) represents the control input of the cyber-physical system, d i (t), i = 1, 2, ..., n represents the external disturbances existing in the controlled object. It is a positive number.

[0073] S2. Based on the dynamic model, design an ideal virtual controller and adaptive laws.

[0074] Optionally, step S2 above may include the following steps S21-S22:

[0075] S21. Based on the dynamic model, the constraints corresponding to the state of the cyber-physical system, the actual output of the cyber-physical system, the ideal output of the cyber-physical system, the backstepping method, the obstacle Lyapunov function, and the fuzzy logic system, design an ideal virtual controller.

[0076] S22. Based on the dynamic model, the constraints corresponding to the state of the cyber-physical system, the actual output of the cyber-physical system, the ideal output of the cyber-physical system, the backstepping method, the obstacle Lyapunov function, the fuzzy logic system, and the ideal virtual controller, design an adaptive rule for the weight vector of the fuzzy logic system.

[0077] One feasible implementation method is, for example Figure 2 As shown, the malicious attack signal exists on the controller-to-actuator channel. (Targeting...) Figure 2 In a state-constrained cyber-physical system, the system output must satisfy the following constraints:

[0078] B(t)<y(t)<U(t), (2)

[0079] Here, B(t) and U(t) are predefined functions, and their nth derivatives can be obtained with respect to time t. The remaining system states must satisfy the following constraints:

[0080] -z i <ξ i<z i , 2≤i≤n, (3)

[0081] For a given reference signal y d The output tracking error can be defined as:

[0082] ζ1=yy d (4)

[0083] The ideal virtual control signal is represented as Representative by The resulting new function:

[0084]

[0085] Throughout the control process, Used to replace ideal virtual control signals This is called the actual virtual control signal. Then, the virtual tracking error is expressed as... in

[0086] This application will utilize the obstacle Lyapunov function in the controller design process. As can be seen from equation (2), since the constraint on the system output y is asymmetric, this application defines the constraint on ζ1 as follows:

[0087] -C B1 (t)<ζ1(t)<C U1 (t). (6)

[0088] For the sake of simplicity and readability, It can be represented as in Representing C B1 The i-th time derivative of (t). Similarly, It can be represented as in, Representing C U1 The i-th time derivative of (t).

[0089] From equation (3), it can be seen that because the system state ξ i The constraints on ,2≤i≤n are asymmetric. Next, this invention defines ζ. i The constraints on (t) are:

[0090] -C i <ζ i (t)<C i (7)

[0091] Among them, C i Represents the virtual tracking error ζ i The constraint boundary on.

[0092] Next, for simplicity, time t will be ignored. Then, the barrier Lyapunov function will be used in the design of the fixed-time adaptive fuzzy controller. For the tracking error ζ1, this application designs a barrier Lyapunov function of the following form:

[0093]

[0094] To improve the simplicity and readability of this invention, time (t) will be omitted in the following text. Then, V... b1 Taking the derivative of time t, we get:

[0095]

[0096] in,

[0097] Based on virtual tracking error ζ i For 2≤i≤n, this application designs a barrier Lyapunov function of the following form:

[0098]

[0099] For V bi Taking the derivative of time t, we get:

[0100]

[0101] Next, we will provide specific details on how to use the iterative design process of backstepping to obtain adaptive laws and ideal virtual controllers.

[0102] Step 1. According to the system dynamics (4), the dynamics of ζ1 can be expressed as:

[0103]

[0104] Based on the backstepping method, in the current step, this application aims to find the ideal virtual control signal. To ensure that (12) is stable. If It has been found, and then ξ2 needs to be tracked. Furthermore, throughout the entire control operation, ξ2 must be maintained within (-C2, C2). Similarly, It must also satisfy the constraint on ξ2. To solve this problem, this application defines a saturation function as follows:

[0105]

[0106] Where s = c2 < C2, next, according to (5), a hyperbolic tangent function It can be used to approximate c(ξ) * ).Then, It will be used to replace It will be used in real control processes. Clearly, It remains within the range (-C2, C2). Therefore, this application can define... The design process described above will be used in the following design steps:

[0107]

[0108] Where ρ1=q 1,0 f1, and For unknown parameters, This is its estimate. Based on the output constraint (2), the following expression can be obtained:

[0109] C B1 =y d -B,C U1 =Uy d (15)

[0110] Combining equations (9), (12), and (15), we can obtain:

[0111]

[0112] in, Represents an unknown function.

[0113] According to fuzzy logic systems, for a continuous function h(ξ) defined on a compact set Λ, and with arbitrary precision ε > 0, there exists a fuzzy logic system K. T Δ(ξ) satisfies in, K = [κ1(t),κ2(t),…,κ n (t)] T c represents the weight vector of the Gaussian function. j =[c j1 ,c j2 ,…,c jn ] T μ represents the center vector. j =[μ j1 ,μ j2 ,…,μ jn ] T This represents the width of the Gaussian function. Therefore, there exists a fuzzy logic system K1Δ1(∑1) that can be used to approximate an unknown function. For a given The following expression is true:

[0114]

[0115] Where ∈1(∑1) represents the approximation error, and satisfies

[0116] Substituting equation (17) into equation (16), we get:

[0117]

[0118] Through calculation, the following inequality can be obtained:

[0119]

[0120] in,

[0121] Then, substituting equation (19) into equation (18) yields:

[0122]

[0123] To ensure a fixed conversion rate over a given time, an ideal virtual controller is designed as shown below.

[0124]

[0125] in,

[0126]

[0127] in, x 11 >0, x 21 >0, g1>0, r=(2m+d) / (2m+1)>1, m∈N, d>1 is a positive odd integer, e=1 / r>1 / 2. This application can obtain k through the following calculation. 11 and k 21 :

[0128]

[0129] Next, design adaptive rules. for:

[0130]

[0131] Where, σ 11 >0 and σ 21 Indicates design parameters.

[0132] According to the mean value theorem... It can be rewritten as:

[0133]

[0134] in, In addition, by setting Equation (24) can be rewritten as follows:

[0135]

[0136] From equation (26), it can be deduced that there exists a constant f. i >0, satisfies

[0137] Then, according to ρ1=f1q 1,0 According to equation (26), for |η1|≥g1, this application can obtain:

[0138]

[0139] Substituting equations (26) and (27) into (20), we get:

[0140]

[0141] because (28) Can be rewritten as:

[0142]

[0143] Step i: (2≤i≤n-1) According to equation (1), The dynamics can be expressed in the following form:

[0144]

[0145] in,

[0146]

[0147]

[0148] According to the backstep method, the state variables The input to the subsystem (30) is considered as the input, and then this application focuses on finding an ideal virtual control signal to stabilize (30). The subsequent control design focuses on To track the ideal virtual control signal. It should be noted that state ξ i The constraints faced by i = 2, ..., n are constant constraints. Next, this application designs a barrier Lyapunov function of the following form:

[0149]

[0150] Where, ρ i =f i q i,0, and For unknown parameters, This is its estimate. Because |ξ i |<z i , z i The constraint can be set to C i =z i -j i .

[0151] Although an ideal virtual control signal has been designed For state ξ i The constraints may not be met. Therefore, this application designs actual virtual control signals. This ensures that the constraints are met. Next, in the subsequent control design process, actual virtual control signals will be used. replace Taking the first derivative of equation (34), and considering both equations (30) and (11), we get:

[0152]

[0153] in,

[0154] Furthermore, using the sum of squares formula, we can obtain the following inequality:

[0155]

[0156] Then, this application defines function G. i (∑ i )for:

[0157]

[0158] in,

[0159] Accordingly, equation (33) can be rewritten as:

[0160]

[0161] For an unknown function G i (∑ i There exists a fuzzy logic system K. i Δ i (∑ i It can be used to approximate unknown functions. For a given... The following expression is true:

[0162]

[0163] Where, ∈ i (∑ i ) represents the approximation error, and satisfies Then, substituting equation (37) into (36) yields:

[0164]

[0165] Similar to the analysis process of equation (18), this application can obtain inequalities of the following form:

[0166]

[0167] in,

[0168] Then, substituting equation (39) into equation (38) yields:

[0169]

[0170] Next, this application designs an ideal virtual controller in the following form:

[0171]

[0172] in,

[0173]

[0174] in, x 1i and x 2i All are positive design parameters.

[0175] Then, this application designs an adaptive law of the following form.

[0176]

[0177] Where, σ 1i >0, σ 2i Indicates design parameters, Unknown parameters The estimated value is r = (2m + d) / (2m + 1) > 1, where m ∈ N and d > 1 is a positive odd integer. C i (t) represents the virtual tracking error ζ i The constraint boundary on 2≤i≤n-1, ζ i (t) represents the virtual tracking error. ∈ i (∑ i ) represents the approximation error, β i The design parameter is positive. Based on ρ i =f i qi,0 And equation (29), for |η i |≥g i This application yields a formula of the following form:

[0178]

[0179] By combining equations (41) to (44), we can obtain:

[0180]

[0181] S3. Based on the dynamic model, ideal virtual controller, adaptive law and Lyapunov stability theorem, a fixed-time adaptive fuzzy controller is designed to realize the security control of cyber-physical systems subjected to malicious attacks.

[0182] Step n: In the final step, this application designs a fixed-time adaptive fuzzy controller u. Similar to step i, this application defines... and Then, construct the following barrier Lyapunov function:

[0183]

[0184] Where, ρ n =q n,0 , and For unknown parameters, For its prediction. Referring to the process of equations (16) to (23), we can obtain:

[0185]

[0186] Next, the actual fixed-time adaptive fuzzy controller u and the adaptive rule... The design is as follows:

[0187]

[0188] Where, x 1n and x 2n These are design parameters.

[0189]

[0190] Where, σ 1n >0, and σ 2n Represents design parameters. Because ρ n =q n,0 Substituting equations (48) and (49) into equation (47), we obtain:

[0191]

[0192] The Lyapunov function is chosen as follows:

[0193]

[0194] After calculation, the following expression can be obtained:

[0195]

[0196] also,

[0197]

[0198] because This application yields the following inequality:

[0199]

[0200] Next, substituting (54) and (53) into (52) yields:

[0201]

[0202] in,

[0203]

[0204] set up Then, equation (55) can be rewritten as:

[0205]

[0206] Where, l=ψχ 1-r 2 1-r Clearly, equation (57) demonstrates the boundedness of the closed-loop system state. According to equation (57), all transformation errors η... i All will be at a fixed time T η ≤1 / (h(1-e))+1 / (l(r-1)) enters the set {η i |V(η i )≤(ν / l) (1 / r) In particular, η i It is bounded, which means that when time t≥0, the barrier Lyapunov function (C0) is bounded. B1 C U1 ζ1) / [(C U1 -ζ1)(C B1 +ζ1)] and It is bounded. At the same time, it also means that for t≥0, -C B1 (t)<ζ1(t)<C U1 (t) and |ζ i |<C iEstablished. Accordingly, by We can obtain the following inequality:

[0207]

[0208] In summary, when time t≥0, all state constraints are satisfied.

[0209] Furthermore, to better understand the present invention, the security control method for state-restricted cyber-physical systems under malicious attacks provided in the embodiments of the present invention will be described. In this embodiment,

[0210]

[0211] Among them, the malicious attack signal α(t,t) α ) and β(t,t β ) is α(t,t α )=0.4+0.6exp(-0.1t) and β(t,t β )=cos 2 (ξ1)ξ2. Reference signal y d Select y d =0.5cos(t) + sin(0.5t). d1 and d2 are arbitrary possible bounded external perturbations. The time-varying constraints on the system output y are B(t) = 0.5cos(t) + sin(0.5t) - 0.1 - 0.3e -0.6t and U(t)=0.5cos(t)+sin(0.5t)+0.15+0.3e -0.5t The state constraint corresponding to state ξ2 is ξ2∈(-1.5,1.5). Accordingly, this application can obtain C B1 (t) = 0.1 + 0.3e -0.6t and C U1 (t) = 0.15 + 0.3e -0.5t .

[0212] The first step is to develop a control-oriented dynamic model for a state-constrained high-order nonlinear cyber-physical system under malicious attack and external disturbances:

[0213]

[0214] The second step is to design the actual virtual controller and the ideal virtual controller as follows:

[0215]

[0216]

[0217] Where, η1=(C B1 CU1 ζ1 / [(C U1 -ζ1)(C B1 +ζ1)]),

[0218] as well as

[0219]

[0220] in, ζ1=ξ1-y d .

[0221] The adaptive law is designed as follows:

[0222]

[0223] Next, the split points are selected as -4, -3, -2, -1, 0, 1, 2, 3, 4, and the fuzzy set is defined in [-4, 4]. The corresponding fuzzy membership function is defined as δ1(∑1)=exp((∑1-∑ l,1 ) T (∑1-∑ l,1 ) / 8), δ2(Σ2)=exp(-(Σ2-Σ l,2 ) T (∑2-∑ l,2 ) / 8), l=1,2,…,9, ∑1 and ∑2 are defined as ∑ l,1 and ∑ l,2 Represented as follows

[0224] The third step involves designing a fixed-time adaptive fuzzy controller based on the dynamic model, ideal virtual controller, adaptive law, and Lyapunov stability theorem to achieve secure control of cyber-physical systems subjected to malicious attacks.

[0225] Design a fixed-time adaptive fuzzy controller in the following form:

[0226]

[0227] in,

[0228] In this embodiment, the initial values ​​are chosen as [ξ1(0), ξ2(0)]. T =[0.9,-1] T , The specific design parameters are x 11 =x 21 =30, x 12 =x 22 =20, σ 11 =σ21 =σ 12 =σ 22 =0.5, g1=0.1, β1=β2=0.1, r=101 / 99, e=99 / 101.

[0229] The simulation results for the two scenarios are shown in [the table / document / etc.]. Figures 3 to 7 In case 1, the actual virtual control signal f(ξ) i * This is used in the control process. To compare with existing control methods, in case 2, the virtual control signal ξ... i * It is directly used in the control process. The simulation results for case 1 are shown in... Figures 3 to 6 middle, Figure 7 The simulation results for case 2 are shown. Figure 3 This describes the system output y and the reference signal y. d The trajectory curve clearly shows that the proposed safety control method ensures good tracking performance, and the system output y satisfies its corresponding constraints throughout the control process. Figure 4 The tracking error trajectory is shown, and it is clear that the tracking error stabilizes within a fixed time period. Figure 5 The system state ξ2 and the actual virtual control signal are shown. The trajectories of both clearly lie within the interval (-1.5, 1.5) throughout the entire control operation. Figure 6 The trajectory curve of the fixed-time adaptive fuzzy controller u is shown. Figure 7 This demonstrates the situation when an ideal virtual control signal is directly used in the control process. However, Figure 7 This demonstrates that an ideal virtual control signal cannot guarantee a tracking effect similar to that in Case 1, meaning that the control objective cannot be achieved.

[0230] In this embodiment of the invention, a cyber-physical system security control method is proposed for a state-constrained high-order nonlinear cyber-physical system under malicious attack and external disturbance. This method ensures that the system output accurately tracks the ideal output within a fixed time, and that the other system states can also track the ideal virtual control signal. At the same time, during the entire control process, all system states satisfy their respective state constraints.

[0231] The cyber-physical system security control method provided in this application is designed for state-constrained high-order nonlinear cyber-physical systems with external disturbances, and therefore can be applied to the security control of nonlinear cyber-physical systems of any order.

[0232] This application incorporates the barrier Lyapunov function method, which ensures the fixed-time stability of the cyber-physical system while guaranteeing that all system states satisfy their respective state constraints throughout the entire control operation.

[0233] like Figure 8 As shown, this embodiment of the invention provides a state-constrained high-order nonlinear cyber-physical system security control device 800. This device 800 is used to implement a state-constrained high-order nonlinear cyber-physical system security control method. The device 800 includes:

[0234] The dynamics model building module 810 is used to establish a control-oriented dynamics model for a state-constrained high-order nonlinear cyber-physical system with external disturbances under malicious attacks.

[0235] Design module 820 is used to design ideal virtual controllers and adaptive laws based on dynamic models.

[0236] Output module 830 is used to design a fixed-time adaptive fuzzy controller based on dynamic models, ideal virtual controllers, adaptive laws and Lyapunov stability theorem, so as to realize the secure control of cyber-physical systems subjected to malicious attacks.

[0237] Alternatively, the dynamic model is as shown in equation (1):

[0238]

[0239] Where t represents time, and ξ(t) represents the state vector of the cyber-physical system ξ(t) = [ξ1(t), ξ2(t), ..., ξ n (t)] T ∈R n ξ i (t) represents the state variables of the cyber-physical system. n indicates that the cyber-physical system is an nth-order nonlinear system, φ i (.) and q i (.), i = 1, 2, ..., n, represents a known real continuous nonlinear function with respect to the state variables of the cyber-physical system. q i,0 Denotes the lower bound, q n,1 Let α(t,t) denote the upper bound, y(t) denote the actual output of the cyber-physical system, and α(t,t) denote the upper bound. α ) represents a multiplicative malicious attack signal, α(t,t) α )∈[0,1] and satisfy 0<α min <α(t,t α )≤1, where α min Represents α(t,t) α The lower bound of ), β(t,t)β ) represents an additive malicious attack signal, and satisfies β(t,t) β )≤β max , where β max Represents β(t,t) β The upper bound of ), u(t) represents the control input of the cyber-physical system, d i (t), i = 1, 2, ..., n represents the external disturbances existing in the controlled object. It is a positive number.

[0240] Optionally, design module 820 is further used for:

[0241] Based on the dynamic model, the constraints corresponding to the state of the cyber-physical system, the actual output of the cyber-physical system, the ideal output of the cyber-physical system, the backstepping method, the obstacle Lyapunov function, and the fuzzy logic system, an ideal virtual controller and an adaptive law are designed.

[0242] Optionally, design module 820 is further used for:

[0243] S21. Based on the dynamic model, the constraints corresponding to the state of the cyber-physical system, the actual output of the cyber-physical system, the ideal output of the cyber-physical system, the backstepping method, the obstacle Lyapunov function, and the fuzzy logic system, design an ideal virtual controller.

[0244] S22. Based on the dynamic model, the constraints corresponding to the state of the cyber-physical system, the actual output of the cyber-physical system, the ideal output of the cyber-physical system, the backstepping method, the obstacle Lyapunov function, the fuzzy logic system, and the ideal virtual controller, design an adaptive rule for the weight vector of the fuzzy logic system.

[0245] Alternatively, the ideal virtual controller is as shown in equation (2):

[0246]

[0247]

[0248] in, C B1 (t), C U1 (t) represents the preset constraint on the output tracking error, and ζ1 represents the output tracking error. Unknown parameters The forecast, ∈1(∑1(t)) represents the approximation error, and β1 is a positive design parameter. x 11 >0, x 21>0, g1(t)>0, r=(2m+d) / (2m+1)>1, m∈N, d>1 is a positive odd integer, e=1 / r>1 / 2.

[0249] Alternatively, the adaptive rule is as shown in equation (4):

[0250]

[0251] Where, σ 1i >0, σ 2i Indicates design parameters, Unknown parameters The estimated value is r = (2m + d) / (2m + 1) > 1, where m ∈ N and d > 1 is a positive odd integer. C i For virtual tracking error ζ i The constraint boundary on 2≤i≤n-1, ζ i For virtual tracking error, ∈ i (∑ i (t) represents the approximation error, β i The design parameters are positive.

[0252] Alternatively, a fixed-time adaptive fuzzy controller can be used, as shown in equation (5):

[0253]

[0254] in, C n For virtual tracking error ζ n The constraint boundary on ζ n For virtual tracking error, α min The malicious attack signal α(t,t) represents multiplicative properties. α The lower bound of ) Unknown parameters The forecast, ∈ n (∑ n (t) represents the approximation error. β n For positive design parameters, x 1n >0, x 2n >0, r=(2m+d) / (2m+1)>1, m∈N, d>1 is a positive odd integer, e=1 / r>1 / 2.

[0255] In this embodiment of the invention, a cyber-physical system security control method is proposed for a state-constrained high-order nonlinear cyber-physical system under malicious attack and external disturbance. This method ensures that the system output accurately tracks the ideal output within a fixed time, and that the other system states can also track the ideal virtual control signal. At the same time, during the entire control process, all system states satisfy their respective state constraints.

[0256] The cyber-physical system security control method provided in this application is designed for state-constrained high-order nonlinear cyber-physical systems with external disturbances, and therefore can be applied to the security control of nonlinear cyber-physical systems of any order.

[0257] This application incorporates the barrier Lyapunov function method, which ensures the fixed-time stability of the cyber-physical system while guaranteeing that all system states satisfy their respective state constraints throughout the entire control operation.

[0258] Figure 9 This is a schematic diagram of the structure of an electronic device 900 provided in an embodiment of the present invention. The electronic device 900 can vary considerably due to differences in configuration or performance. It may include one or more central processing units (CPUs) 901 and one or more memories 902. The memory 902 stores at least one instruction, which is loaded and executed by the processor 901 to implement the following state-constrained high-order nonlinear cyber-physical system security control method:

[0259] S1. Establish a control-oriented dynamic model for a state-constrained high-order nonlinear cyber-physical system with external disturbances under malicious attacks.

[0260] S2. Based on the dynamic model, design an ideal virtual controller and adaptive laws.

[0261] S3. Based on the dynamic model, ideal virtual controller, adaptive law and Lyapunov stability theorem, a fixed-time adaptive fuzzy controller is designed to realize the security control of cyber-physical systems subjected to malicious attacks.

[0262] In an exemplary embodiment, a computer-readable storage medium is also provided, such as a memory including instructions that can be executed by a processor in a terminal to perform the aforementioned state-constrained high-order nonlinear cyber-physical system security control method. For example, the computer-readable storage medium may be a ROM, random access memory (RAM), CD-ROM, magnetic tape, floppy disk, and optical data storage device, etc.

[0263] Those skilled in the art will understand that all or part of the steps of the above embodiments can be implemented by hardware or by a program instructing related hardware. The program can be stored in a computer-readable storage medium, such as a read-only memory, a disk, or an optical disk.

[0264] 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 security control method for a state-constrained high-order nonlinear cyber-physical system, characterized in that, The method includes: S1. Establish a control-oriented dynamic model for a state-constrained high-order nonlinear cyber-physical system with external disturbances under malicious attacks; S2. Based on the aforementioned dynamic model, design an ideal virtual controller and adaptive laws; S3. Based on the dynamic model, ideal virtual controller, adaptive law and Lyapunov stability theorem, design a fixed-time adaptive fuzzy controller to achieve secure control of cyber-physical systems subjected to malicious attacks. The dynamic model in S1 is shown in equation (1) below: （1） in, Indicates time, Represents the state vector of a cyber-physical system , Represents the state variables of a cyber-physical system. , , Indicates cyber-physical system as Order-order nonlinear systems, and , Represents a known real continuous nonlinear function of the state variables of a cyber-physical system. , , Indicates the lower bound. Indicates the upper bound. This represents the actual output of the cyber-physical system. This indicates a malicious attack signal involving multiplication. And satisfy ,in, represent The lower bound, Indicates an additive malicious attack signal, and satisfies ,in, represent The upper realm, Represents the control input of a cyber-physical system. This indicates an external disturbance present in the controlled object. , It is a positive number; The ideal virtual controller in S2 is shown in equation (2) below: （2） （3） in, , , , As a preset constraint on the output tracking error, To output the tracking error, Unknown parameters The forecast, , Represents the approximation error. Positive design parameters , , , , , , , , A positive odd integer. ; The adaptive rule in S2 is shown in equation (4) below: （4） in, , Indicates design parameters, Unknown parameters The forecast, , , A positive odd integer. , For virtual tracking error On the constraint boundary, For virtual tracking error, , , Represents the approximation error. Positive design parameters; The fixed-time adaptive fuzzy controller in S3 is shown in equation (5) below: （5） in, , For virtual tracking error On the constraint boundary, For virtual tracking error, Malicious attack signals representing multiplication The lower bound, Unknown parameters The forecast, , Represents the approximation error. , Positive design parameters , , , , A positive odd integer. .

2. The method according to claim 1, characterized in that, The design of the ideal virtual controller and adaptive law based on the dynamic model in S2 includes: Based on the aforementioned dynamic model, the constraints corresponding to the state of the cyber-physical system, the actual output of the cyber-physical system, the ideal output of the cyber-physical system, the backstepping method, the obstacle Lyapunov function, and the fuzzy logic system, an ideal virtual controller and an adaptive rule are designed.

3. The method according to claim 2, characterized in that, The design of the ideal virtual controller and adaptive rules based on the dynamic model, the constraints corresponding to the state of the cyber-physical system, the actual output of the cyber-physical system, the ideal output of the cyber-physical system, the backstepping method, the obstacle Lyapunov function, and the fuzzy logic system includes: S21. Based on the dynamic model, the constraints corresponding to the state of the cyber-physical system, the actual output of the cyber-physical system, the ideal output of the cyber-physical system, the backstepping method, the obstacle Lyapunov function, and the fuzzy logic system, design an ideal virtual controller. S22. Based on the dynamic model, the constraints corresponding to the state of the cyber-physical system, the actual output of the cyber-physical system, the ideal output of the cyber-physical system, the backstepping method, the obstacle Lyapunov function, the fuzzy logic system, and the ideal virtual controller, design an adaptive rule for the weight vector of the fuzzy logic system.

4. A state-constrained high-order nonlinear cyber-physical system security control device, the device being used to implement the state-constrained high-order nonlinear cyber-physical system security control method as described in any one of claims 1-3, characterized in that, The device includes: The dynamics model building module is used to establish a control-oriented dynamics model for a state-constrained high-order nonlinear cyber-physical system under malicious attacks and external disturbances. The design module is used to design an ideal virtual controller and adaptive laws based on the dynamic model. The output module is used to design a fixed-time adaptive fuzzy controller based on the dynamic model, ideal virtual controller, adaptive law and Lyapunov stability theorem, so as to realize the security control of cyber-physical systems subjected to malicious attacks.

5. The apparatus according to claim 4, characterized in that, The design module is further used for: Based on the aforementioned dynamic model, the constraints corresponding to the state of the cyber-physical system, the actual output of the cyber-physical system, the ideal output of the cyber-physical system, the backstepping method, the obstacle Lyapunov function, and the fuzzy logic system, an ideal virtual controller and an adaptive rule are designed.

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