CPS adaptive sliding mode control method and device under FDI attack and actuator fault

Abstract

The invention provides a CPS adaptive sliding mode control method and device under FDI attack and actuator fault, and the method comprises the following steps: constructing an information physical system model under FDI attack and actuator fault, introducing a dynamic event triggering communication mechanism into a measurement channel, and considering the system time delay from a sensor to an actuator; constructing a state-fault estimator according to the information physical system model; establishing a discrete sliding mode function according to the established state-fault estimator; based on the discrete sliding mode function, a system equivalent control law and a system sliding mode dynamic state are obtained; constructing an augmented closed-loop system according to the dynamic state of the sliding mode of the system; and constructing a self-adaptive sliding mode controller based on the system equivalent control law, and performing compensation control on the augmented closed-loop system by adopting the self-adaptive sliding mode controller. According to the method, adaptive factors can be adjusted according to different attack occurrence frequencies so as to optimize control performance, and system uncertainty such as FDI attacks and system actuator faults can be effectively handled.

Description

Technical Field

[0001] The present invention belongs to the technical field of cyber - physical system security control, and relates to a cyber - physical system event - triggered adaptive sliding mode control method and device under FDI attacks and actuator failures. Background Technique

[0002] A cyber - physical system (CPS) is a type of system highly integrated by an application control layer, a data transmission layer, and a sensing and execution layer. Due to the high efficiency, coordination, and real - time performance of CPS, it is widely used in fields such as power systems and multi - agent systems. However, due to the openness of the data transmission layer of CPS, both the control channel and the measurement channel are likely to be maliciously threatened by network attacks. Common network attacks include three types: Denial of Service (DoS) attacks, Replay attacks, and False Data Injection (FDI) attacks. For example, the Slammer virus attack incident on the Iranian nuclear power plant; on the other hand, due to the vulnerability of the sensing and execution layer of CPS, CPS is also easily subject to problems such as actuator (sensor) node failures and external disturbances, which in turn affect the stability of the system, such as the major blackout accident of the Brazilian power grid. In addition, due to the large number of heterogeneous nodes in CPS, their computing and storage capabilities are limited, and network attacks will exacerbate the sparsity of transmitted data, making resource scheduling more demanding, thus reducing the control performance of the system. In this context, for the event - triggered security control problem of CPS under network attacks in a complex network environment, it is urgent to further conduct in - depth research.

[0003] Currently, certain progress has been made in both the research on CPS security control under network attacks and the research on CPS fault - tolerant control under actuator failures, while less attention has been paid to the research on CPS security control considering both network attacks and actuator failures. With the maturity of attack means and the increasingly complex network environment, network attacks and actuator failures may simultaneously damage the data transmission layer and the sensing and execution layer, resulting in data loss and damage to the integrity of system information. Therefore, the research on CPS security control under network attacks and actuator (sensor) failures has gradually become a research hotspot in the control field.

[0004] Therefore, how to provide a CPS adaptive sliding mode control method and device that can compensate for the negative impacts of FDI attacks, actuator failures, and external disturbances on the system control performance is an urgent problem to be solved by those skilled in the art. Summary of the Invention

[0005] In view of this, the present invention proposes a CPS adaptive sliding mode control method and device under FDI attacks and actuator faults, aiming to reduce communication pressure while compensating for the negative impacts of FDI attacks, actuator faults, and external disturbances on the system control performance, and effectively improving the system control performance and stability.

[0006] To achieve the above object, the present invention adopts the following technical solutions:

[0007] The present invention discloses a CPS adaptive sliding mode control method under FDI attacks and actuator faults, including the following steps:

[0008] S1. Construct an information - physical system model with FDI attacks and actuator faults, and introduce a dynamic event - triggered communication mechanism into the measurement channel of the information - physical system;

[0009] S2. Based on the information - physical system model, considering the system delay from sensors to actuators, construct a state - fault estimator; and establish a discrete sliding mode function according to the system state estimation value estimated by the constructed state - fault estimator;

[0010] S3. Based on the discrete sliding mode function, obtain the system equivalent control law and the system sliding mode dynamics;

[0011] S4. Construct an augmented closed - loop system according to the system sliding mode dynamics;

[0012] S5. Construct an adaptive sliding mode controller based on the system equivalent control law, and use the adaptive sliding mode controller to perform compensation control on the augmented closed - loop system.

[0013] Preferably, the FDI attack mode in S1 is expressed as:

[0014]

[0015] In the formula, represents the actuator control signal damaged by FDI attacks; a(k) represents the FDI attack signal satisfying the unilateral Lipschitz condition and the quadratic inner - boundary condition; κ represents a positive scalar; represents the channel diagonal matrix with the order equal to the system state dimension, and its diagonal element being 0 indicates that the corresponding channel is not under FDI attacks, and its diagonal element being 1 indicates that the corresponding channel is under FDI attacks; υ(k) represents a Bernoulli random variable;

[0016] The actuator fault f(k) in S1 has a known upper bound.

[0017] Preferably, the information - physical system model in S1 is expressed as:

[0018]

[0019] In the formula, represents the system state vector; represents the actuator control signal damaged by the FDI attack; represents the measurement output; represents the external disturbance, and satisfies the condition ω(k) ∈ L 2 [0, ∞); represents the actuator fault, Δf(k) = f(k + 1) - f(k); g(x(k), k) represents the system nonlinear function, and respectively represent constant matrices.

[0020] Preferably, the dynamic event-triggered communication mechanism in S1 is expressed as:

[0021]

[0022] In the formula, χ(k) is an internal dynamic variable and satisfies:

[0023] χ(0) = χ 0 , χ 0 represents the initial state of χ(k); e y (k) = y(k i +j) - y(k i ), j represents the moment when the next measurement signal is triggered, j ≥ 1, Ω is a weight matrix and Ω > 0, ε ∈ (0, 1), θ ∈ (0, ∞), ρ ∈ (0, 1) are given positive scalars, and satisfy the following relational expressions:

[0024]

[0025] Preferably, S2 includes the following steps:

[0026] S21: Construct a state-fault estimator according to the cyber-physical system model, expressed as:

[0027]

[0028] In the formula, represents the state estimate value at the k + 1 moment; represents the current system state estimate value; represents the current fault estimate value; represents the current measurement output estimate value; represents the current measurement output estimate value considering the sensor-to-actuator delay d(k); Denote the actuator input when under attack; L and M denote the estimated gain matrices; Denote the estimated value of system nonlinearity; A, B, C, and F denote constant matrices;

[0029] S22. Based on the estimated value of the system state Combine the sliding mode gain matrix K to establish a discrete sliding mode function:

[0030]

[0031] Obtain a preset sliding mode surface, denoted as:

[0032]

[0033] In the formula, s(k) = [s 1 (k), s 2 (k), …, s p (k)] T Denote the sliding mode function at the current moment, s(k + 1) denotes the sliding mode surface at the (k + 1)-th moment; b(k) denotes the compensation term, b(0) = 0, G denotes a constant matrix, and GB satisfies the non-singular condition; e y (k) = y(k i ) - y(k i + j), j = 1, 2, …, j * - 1, j* denotes the right bound of the total time delay interval from the sensor to the actuator; e x (k) denotes the difference between the state vector x(k) at the current moment and the state observation value at the current moment, that is

[0034] Preferably, the S3 includes the following steps:

[0035] Construct the equivalent control law of the system Denoted as:

[0036]

[0037] Construct the sliding mode dynamics of the system, denoted as:

[0038]

[0039] In the formula, the matrix W = I - B(GB) -1 G, Denote the estimated value of system nonlinearity, and I denotes the identity matrix.

[0040] Preferably, the augmented closed-loop system in S4 is denoted as:

[0041]

[0042] Among them, are the augmented matrices respectively; ψ(k) = [ω T (k) Δf T (k)] T , Δf(k) = f(k + 1) - f(k), are the augmented vectors respectively, I represents the identity matrix, f(k) represents the actuator fault, represents the difference between the system nonlinearity at the current moment and its estimated value.

[0043] Preferably, the adaptive sliding mode controller constructed based on the system equivalent control law in S5 is expressed as:

[0044]

[0045] In the formula, u(k) represents the adaptive sliding mode controller; represents a positive scalar; represents the adaptive parameter; represents the value of the adaptive parameter variable; and both represent intermediate parameter variables; is the expected value when an attack occurs.

[0046] Preferably, in the process of compensating and controlling the augmented closed-loop system by using the adaptive sliding mode controller, the sufficient condition for the asymptotic stability of the augmented closed-loop system is expressed as:

[0047]

[0048] In the formula, τ 1 = τ + 1, τ 2 = d(k) + 1 - τ , are both scalars, τ = min{τ i |i = 0, 1, 2,..., ∞} is the lower bound of the system time delay, Θ 1 (d(k)) = [μ 1 τ 1 μ 6 - μ 3 τ 2 μ 7 + τ 3 μ 8 - μ 4 - μ 5}], Θ 2 (d(k)) = [μ 2 τ 1 μ6 -μ 2 τ 2 μ 7 +τ 3 μ 8 -μ 3 -μ 4 , Θ 3 =[μ 2 μ 3 μ 5 , Θ 4 =μ 1 -μ 2 , Θ 5 =[μ 2 -μ 3 μ 2 +μ 3 -2μ 6 , Θ 6 =[μ 3 -μ 4 μ 3 +μ 4 -2μ 7 μ 4 -μ 5 μ 4 +μ 5 -2μ 8 , are matrices respectively, Λ 1 =diag{R 1 , 3R 1}, are augmented matrices respectively, is a known matrix,

[0049] R 2 and Ω are positive definite matrices respectively, Ψ and S are arbitrary matrices, γ m , γ n ∈(0, +∞) is a given scalar;

[0050] Solve the inequality of the sufficient condition. When there is a solution for the unknown matrix, the augmented system satisfies asymptotic stability.

[0051] The present invention also provides a CPS adaptive sliding mode control device according to the CPS adaptive sliding mode control method under the FDI attack and actuator fault, including:

[0052] A cyber-physical system model construction module, configured to construct a cyber-physical system model with FDI attack and actuator fault, and introduce a dynamic event-triggered communication mechanism into the cyber-physical system measurement channel;

[0053] The discrete sliding mode surface design module is used to construct a state-fault estimator based on the cyber-physical system model, considering the system delay from the sensor to the actuator; and establish a discrete sliding mode function according to the system state estimation value estimated by the constructed state-fault estimator.

[0054] The augmented system model construction module is used to obtain the system sliding mode dynamics and the system equivalent control law based on the discrete sliding mode function; and construct an augmented closed-loop system according to the system sliding mode dynamics.

[0055] The adaptive sliding mode control module is used to construct an adaptive sliding mode controller based on the system equivalent control law, and use the adaptive sliding mode controller to perform compensation control on the augmented closed-loop system.

[0056] As can be seen from the above technical solutions, compared with the prior art, the beneficial effects of the present invention include:

[0057] The adaptive sliding mode controller designed by the present invention can adjust the adaptive factor in real time to optimize the system control performance for the negative impacts of FDI attacks and actuator faults on the control performance of the cyber-physical system; thus effectively coping with system uncertainties such as FDI attacks, actuator faults, and external disturbances.

[0058] The present invention gives a design method for the adaptive sliding mode control strategy based on the Lyapunov-Krasovskii stability theory, the LMI technique, and the adaptive sliding mode controller based on the equivalent control law, thereby effectively improving the control performance and stability of the cyber-physical system.

[0059] The cyber-physical system studied by the present invention is affected by uncertainties such as FDI attacks, actuator faults, and external disturbances, which is more in line with industrial reality. Brief Description of the Drawings

[0060] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for the description of the embodiments or the prior art. Obviously, the drawings in the following description are only the embodiments of the present invention. For those of ordinary skill in the art, other drawings can be obtained according to the provided drawings without creative efforts.

[0061] Figure 1 It is a schematic flowchart of the cyber-physical system event-triggered adaptive sliding mode control method under FDI attacks and actuator faults provided by the embodiment of the present invention.

[0062] Figure 2 It is a schematic diagram of the network-induced random time delay distribution provided by the embodiment of the present invention.

[0063] Figure 3Schematic diagram of the occurrence time of FDI attack provided by an embodiment of the present invention.

[0064] Figure 4 Schematic diagram of actuator fault and its estimated trajectory provided by an embodiment of the present invention.

[0065] Figure 5 Schematic diagram of the dynamic event trigger time provided by an embodiment of the present invention. Detailed implementation manners

[0066] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0067] Embodiment 1:

[0068] As Figure 1 shown, the first aspect of the embodiment of the present invention provides a CPS adaptive sliding mode control method under FDI attack and actuator fault, and discloses an information - physical system event - triggered adaptive sliding mode control method under FDI attack and actuator fault, including the following steps:

[0069] S1. Construct an information - physical system model under FDI attack and actuator fault, introduce a dynamic event - triggered communication mechanism in the information - physical system measurement channel, and consider the system delay between the sensor and the actuator at the same time;

[0070] S2. Construct a state - fault estimator according to the information - physical system model; and establish a discrete sliding mode function according to the constructed state - fault estimator;

[0071] S3. Based on the ideal sliding mode condition and the discrete sliding mode function, obtain the system equivalent control law and the system sliding mode dynamics;

[0072] S4. Construct an augmented closed - loop system according to the system sliding mode dynamics and the system error dynamics;

[0073] S5. Construct an adaptive sliding mode controller based on the system equivalent control law, and use the adaptive sliding mode controller to perform compensation control on the augmented closed - loop system.

[0074] Next, each of the above steps will be described in detail.

[0075] In one embodiment, in the above step S1, the following specific contents are included:

[0076] The FDI attack mode and actuator fault mode suffered by the information - physical system are expressed as:

[0077]

[0078] Among them, is the control signal damaged by the FDI attack; a(k) is the FDI attack signal; is a diagonal matrix and its order is equal to the dimension of the system state. Its diagonal elements are 0 or 1, indicating whether the channel is under attack. For example, if the system state is three-dimensional and states 1 and 3 are under attack, then For m communication channels, if the diagonal element T corresponding to the i-th channel among them ii is 1, it means that this channel is under the FDI attack; conversely, if the diagonal element T corresponding to the i-th channel ii is 0, it means that this channel is not under the FDI attack. υ(k) is a Bernoulli variable that satisfies the following equation:

[0079]

[0080]

[0081] Among them, i≥2 is a constant, represents υ(k)=1, represents υ(k)=0, r υ ∈[0,1] represents the expected value of the Bernoulli random variable υ(k).

[0082] For the FDI attack signal a(k), assume a(k)=l(Οx(k)), where Ο is a known matrix, and the vector function satisfies the unilateral Lipschitz condition and the quadratic inner boundary condition, and their definitions are as follows:

[0083] Definition 1: For If there exists a scalar such that the following inequality holds:

[0084] <l(Οx 1 )-l(Οx 2 ),Ο(x 1 -x 2 )>≤ι||Ο(x 1 -x 2 )|| 2 ;

[0085] Then the vector function satisfies the unilateral Lipschitz condition.

[0086] Definition 2: For If there exists a scalar such that the following inequality holds:

[0087]

[0088] Then the vector function satisfies the quadratic inner boundary condition.

[0089] The actuator fault f(k) has a known upper bound, i.e., where is a known positive function, ||·|| is the vector norm and satisfies Δf(k) = f(k + 1) - f(k).

[0090] In one embodiment, the cyber - physical system model is expressed as:

[0091]

[0092] where, is the system state vector; is the actuator input under FDI attack; is the measured output; is the external disturbance and satisfies the condition ω(k) ∈ L 2 [0, ∞); is the actuator fault, Δf(k) = f(k + 1) - f(k); g(x(k), k) is the system non - linear function, and are constant matrices respectively.

[0093] In one embodiment, the dynamic event - triggered communication mechanism is expressed as:

[0094]

[0095] where χ(k) is the internal dynamic variable and satisfies: χ(0) = χ 0 , χ 0 represents the initial state of χ(k); e y (k) = y(k i +j) - y(k i ), j represents the moment when the next measurement signal is triggered, j ≥ 1, Ω is the weight matrix and Ω > 0, ε ∈ (0, 1), θ ∈ (0, ∞), ρ ∈ (0, 1) are given positive scalars, and satisfy the following relational expressions:

[0096]

[0097] In one embodiment, the sensor - to - actuator system delay is expressed as:

[0098]

[0099] where d(k) is the system delay,τ = min{τ i | i = 0, 1, 2, ..., ∞} is the lower bound of the system delay, is the upper bound of the system delay, j = 1, 2, ..., j * - 1.

[0100] In one embodiment, in the above step S2, it specifically includes the following steps:

[0101] S21. Construct a state-fault estimator according to the cyber-physical system model; the state-fault estimator is expressed as:

[0102]

[0103] Wherein, represents the state estimation value at the k + 1 moment; represents the state estimation value at the current moment; represents the fault estimation value at the current moment; represents the measurement output estimation value at the current moment; y(k i ) represents the measurement output at the most recent trigger moment; y(k - d(k)) represents the measurement output at the current moment; represents the actuator input when under attack; L, M represent the estimation gain matrices; represents the system nonlinear estimation value;

[0104] S22. Based on the system state estimation value Combine the sliding mode gain matrix K to establish a discrete sliding mode function:

[0105]

[0106] The preset sliding mode surface can be obtained, expressed as:

[0107]

[0108] Wherein, s(k) = [s 1 (k), s 2 (k), …, s p (k)] T represents the sliding mode surface at the current moment, s(k + 1) represents the sliding mode surface at the k + 1 moment; b(k) represents the compensation term, b(0) = 0, G represents a constant matrix, and GB satisfies the non-singular condition; e y (k) = y(k i ) - y(k i + j), j = 1, 2, ..., j * - 1, j* represents the right bound of the total delay interval between the sensor and the actuator; e x(k) represents the difference between the state vector x(k) at the current moment and the state observation value at the current moment That is

[0109] In one embodiment, in the above step S3, it specifically includes the following content:

[0110] Based on the ideal sliding mode condition s(k + 1) = s(k) = 0, the system equivalent control law is expressed as:

[0111]

[0112] Where Represents the system equivalent control law;

[0113] The system sliding mode dynamics is expressed as:

[0114]

[0115] Where the matrix W = I - B(GB) -1 G, I represent the identity matrix.

[0116] The system error dynamics is expressed as:

[0117]

[0118] Where Represents the difference between the system nonlinearity at the current moment and its estimated value.

[0119] In one embodiment, in the above step S4, the augmented closed-loop system is expressed as:

[0120]

[0121] Where Are the augmented matrices respectively; ψ(k) = [ω T (k) Δf T (k)] T , Are the augmented vectors respectively, Represents the difference between the system nonlinearity at the current moment and its estimated value.

[0122] In one embodiment, in the above step S5, it specifically includes the following content:

[0123] The adaptive sliding mode controller based on the equivalent control law is expressed as:

[0124]

[0125] Where u(k) represents the adaptive sliding mode controller; Represents the estimated value of the system state at the current moment; Represents the measured output observation value at the current moment; s(k) represents the sliding mode function at the current moment; K represents the sliding mode gain matrix; L represents the estimation gain matrix; G represents a constant matrix, and GB is non-singular; κ and Both represent positive scalars; Represents the adaptive parameter; Represents the adaptive parameter variable value; And Both represent intermediate parameter variables; Is the expected value when an attack occurs.

[0126] In one embodiment, to make the above augmented closed-loop system asymptotically stable, this embodiment designs the mode-dependent sliding mode gain matrix K and the state-fault estimation gain matrices L and M, that is, using the Lyapunov-Krasovskii stability theory and the LMI analysis method, fully considering the augmented vector, the dynamic event-triggered communication mechanism, the system delay, and the Lipschitz condition of the nonlinear terms of the CPS to analyze the stability problem of the augmented system, and gives the solution algorithm for the gain matrix; the specific process is as follows:

[0127] Select the following Lyapunov-Krasovskii function for the above augmented closed-loop system:

[0128]

[0129] Among them, P represents a positive definite matrix, V(k) represents the selected Lyapunov function,

[0130]

[0131] ζ(k) represents the state of the augmented system, Q 1 、Q 2 、R 1 、R 2 、Ω and S are positive definite matrices respectively, Ψ 1 、Ψ 2 、 Y, U and L are arbitrary matrices respectively.

[0132] Taking the forward difference of V(k) along any trajectory of the augmented closed-loop system, we can get

[0133]

[0134] Among them, Is the augmented matrix, Is the augmented matrix, τ 1 = τ + 1, τ2 = d(k) + 1 - τ, Θ 1 (d(k)) = [μ 1 τ 1 μ 6 -μ 3 τ 2 μ 7 +τ 3 μ 8 -μ 4 -μ 5 , Θ 2 (d(k)) = [μ 2 τ 1 μ 6 -μ 2 τ 2 μ 7 +τ 3 μ 8 -μ 3 -μ 4 , Θ 3 = [μ 2 μ 3 μ 5 , Θ 4 = μ 1 -μ 2 , Λ 1 = diag{R 1 , 3R 1},Θ 5 = [μ 2 -μ 3 μ 2 +μ 3 -2μ 6 , Θ 6 = [μ 3 -μ 4 μ 3 +μ 4 -2μ 7 μ 4 -μ 5 μ 4 +μ 5 -2μ 8 = [D 1 D 2 ,

[0135] Using the Lyapunov-Krasovskii stability theory and the LMI analysis method, by introducing the following system performance evaluation indexes, judge the asymptotic stability problem of the above system.

[0136] That is, for the above augmented closed-loop system model:

[0137] When the augmented vector ψ(k) = 0, if ΔV(k) < 0 is satisfied, it means that the above augmented closed-loop system is in an asymptotically stable state;

[0138] Given that the above augmented closed-loop system is asymptotically stable when ψ(k) = 0, and a positive scalar γ > 0 is given. If the above augmented closed-loop system satisfies, for all disturbances ψ(k) ≠ 0, under the zero initial condition ζ(0) = 0:

[0139]

[0140] Then the above augmented closed-loop system is said to be asymptotically stable at the disturbance attenuation level γ of H ∞

[0141] Then, the sufficient condition for the existence of asymptotic stability of the augmented system is:

[0142]

[0143] where τ 1 = τ +1, τ 2 = d(k) + 1 - τ , are all scalars,

[0144] Θ 1 (d(k)) = [μ 1 τ 1 μ 6 -μ 3 τ 2 μ 7 +τ 3 μ 8 -μ 4 -μ 5 , Θ 2 (d(k)) = [μ 2 τ 1 μ 6 -μ 2 τ 2 μ 7 +τ 3 μ 8 -μ 3 -μ 4 , Θ 3 = [μ 2 μ 3 μ 5 , Θ 4 = μ 1 -μ 2 , Θ 5 = [μ 2 ​-μ 3 μ 2 +μ 3 -2μ 6 , Θ 6 =[μ 3 -μ 4 μ 3 +μ 4 -2μ 7 μ 4 -μ 5 μ 4 +μ 5 -2μ 8 , are matrices respectively, Λ 1 =diag{R 1 , 3R 1}, are augmented matrices respectively, is a known matrix, P, Q 1 , Q 2 , R 1 , R 2 and Ω are positive definite matrices respectively, Ψ and S are arbitrary matrices, γ m , γ n ∈(0, +∞) is a given scalar, then the augmented closed-loop system is said to be asymptotically stable and has an H ∞ disturbance rejection level γ.

[0145] Furthermore, solve for the unknown matrix and the unknown positive definite matrix, including:

[0146] Given scalar ε 1 ∈[0, 1), ε 2 ∈[0, 1), γ m , γ n ∈(0, +∞), positive definite matrices P, Q 1 , Q 2 , R 1 , R 2 , Ω and matrices S, Ψ 1 , Ψ 2 , Y, U and are all unknown, and use the LMI toolbox in MATLAB to solve the above inequalities. When there is a solution, the augmented system satisfies asymptotic stability. After matrix transformation, we can get Then the corresponding sliding mode gain matrix K and state-fault estimation matrices L, M are: K = Y -1 U,

[0147] Where, J 1 = [I 0 0] T , J 2 = [0 I 0],

[0148] When there is no solution, the sliding mode gain matrix K and the state-fault estimation matrices L, M are re-solved, and an adaptive sliding mode controller is constructed until the augmented closed-loop system is asymptotically stable and has an H ∞ disturbance rejection level γ.

[0149] Next, the embodiments of the present invention also verify the correctness and effectiveness of the above-mentioned proposed safety control strategy through simulation examples. The specific implementation method is as follows:

[0150] Consider the controlled object as a class of nonlinear discrete CPS, and the corresponding system parameters are

[0151]

[0152] ω(k) = 0.4e -0.5k sin(0.5k),

[0153]

[0154] Assume that the occurrence probability of the FDI attack is υ(k) = 0.25; the attack matrix T is a third-order identity matrix; the FDI attack energy signal a(k) satisfies f(Οx(k)) = [0.5sin(1.5x 1 (k) + x 2 (k))]. With the help of the LMI toolbox of Matlab, the state-fault estimation gain matrix, the control gain matrix, the optimal H∞ performance index, and the event-triggering weight matrix obtained by solving are respectively

[0155] M = [-0.3813 0.0022],

[0156] K = [-0.121 -0.121 -1.527], γ min = 0.2365,

[0157] Select the initial state of the system as x(0) = [-1 1 1.5] T , the upper and lower bounds of the random time delay are τ = 1, τ = 3, the positive scalar parameter ε 1 = 0.03, ε 2 = 0.15, ρ = 0.2, θ = 7.7.

[0158] Figure 2The schematic diagram of the network-induced delay distribution in the system is given.

[0159] Figure 3 The schematic diagram of the occurrence time of the FDI attack is given, where "0" indicates that the control channel is not under FDI attack, and "1" indicates that the control channel is under FDI attack.

[0160] Figure 4 The occurrence trajectory of the actuator fault and its estimation schematic diagram are given.

[0161] Figure 5 The schematic diagram of the communication time of the dynamic event trigger is given. From Figure 5 it can be seen that compared with the periodic communication mechanism, the dynamic event-triggered communication scheme adopted in this paper saves 75% of the communication resources.

[0162] Even under the influence of negative factors such as FDI attacks and actuator faults, the control method proposed in this paper can still make the system state converge to the equilibrium state in a short time and has good state estimation performance.

[0163] The above simulation results show that the cyber-physical system event-triggered adaptive sliding mode control method proposed in the present invention under FDI attacks and actuator faults is correct and effective.

[0164] From the above scheme, it can be seen that the present invention provides a cyber-physical system event-triggered adaptive sliding mode control method under FDI attacks and actuator faults, constructs a cyber-physical system model under FDI attacks and actuator faults, and on this basis, introduces a dynamic event-triggered mechanism and takes into account the network-induced delay between sensors and actuators; then, based on the sliding mode dynamics and error dynamics, an augmented closed-loop system model is established, and a discrete sliding mode function based on the state estimation value is designed; finally, a new adaptive sliding mode control law is adopted, and a cooperative control design strategy for event-triggered and adaptive sliding mode control is designed, so that the system state is driven into the quasi-sliding mode domain. The present invention can optimize the control performance by adjusting the adaptive factor and effectively cope with system uncertainties such as FDI attacks, actuator faults, and external disturbances; realizes the adaptive sliding mode control of the system, and effectively reduces the negative impact of FDI attacks, actuator faults, and external disturbances on the system control performance in the CPS.

[0165] Embodiment 2:

[0166] The second aspect of the embodiment of the present invention also provides a cyber-physical system event-triggered adaptive sliding mode control device under FDI attacks and actuator faults, which applies the cyber-physical system event-triggered adaptive sliding mode control method provided in the first aspect of the embodiment. The device includes:

[0167] The cyber-physical system model construction module is used to construct a cyber-physical system model with FDI attacks and actuator faults, introduce a dynamic event-triggered communication mechanism into the measurement channel of the cyber-physical system, and consider the system delay from the sensor to the actuator at the same time;

[0168] The discrete sliding mode surface design module is used to construct a state-fault estimator according to the cyber-physical system model; and establish a discrete sliding mode function according to the constructed state-fault estimator;

[0169] The augmented system model construction module is used to obtain the system sliding mode dynamics and the system equivalent control law based on the ideal sliding mode condition; and construct an augmented closed-loop system according to the system sliding mode dynamics and the system error dynamics;

[0170] The adaptive sliding mode control module is used to construct an adaptive sliding mode controller based on the system equivalent control law, and use the adaptive sliding mode controller to perform compensation control on the augmented closed-loop system.

[0171] Embodiment 3:

[0172] The third aspect of the embodiments of the present invention also provides a computer-readable storage medium, which stores a computer program. When the computer program is executed by a processor, it implements the cyber-physical system event-triggered adaptive sliding mode control method provided in the first aspect of the embodiment under FDI attacks and actuator faults.

[0173] The above has introduced in detail the CPS adaptive sliding mode control method and device under FDI attacks and actuator faults provided by the present invention. In this embodiment, specific examples are used to elaborate the principle and implementation manner of the present invention. The description of the above embodiments is only used to help understand the method and its core idea of the present invention; at the same time, for those of ordinary skill in the art, according to the idea of the present invention, there will be changes in the specific implementation manner and application scope. In summary, the content of this specification should not be construed as a limitation to the present invention.

[0174] The above description of the disclosed embodiments enables those skilled in the art to implement or use the present invention. Various modifications to these embodiments will be obvious to those skilled in the art. The general principles defined in this embodiment can be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention will not be limited to these embodiments shown in this embodiment, but will conform to the widest scope consistent with the principles and novel features disclosed in this embodiment.

Claims

1. A CPS adaptive sliding mode control method under FDI attack and actuator failure, characterized in that: The steps include: S1. Construct a cyber-physical system model with FDI attack and actuator failure, and introduce a dynamic event-triggered communication mechanism in the measurement channel of the cyber-physical system; S2. Based on the cyber-physical system model, a state-fault estimator is constructed by considering the system delay from sensor to actuator; A discrete sliding mode function is established according to the system state estimation value obtained by the constructed state-fault estimator; S3. Based on the discrete sliding mode function, obtain the system equivalent control law and the system sliding mode dynamics; S4, dynamically constructing an augmented closed-loop system according to the sliding mode of the system; S5. Constructing an adaptive sliding mode controller based on the system equivalent control law, and using the adaptive sliding mode controller to perform compensation control on the augmented closed-loop system.

2. The CPS adaptive sliding mode control method under FDI attack and actuator failure according to claim 1 is characterized in that: The FDI attack mode in S1 is expressed as: In the formula, represents the actuator control signal damaged by FDI attack; a(k) represents the FDI attack signal that satisfies the one-sided Lipschitz condition and the quadratic inner boundary condition; κ represents a positive scalar; represents the channel diagonal matrix and its order is equal to the system state dimension. Its diagonal element is 0, which means that the corresponding channel has not been attacked by FDI. Its diagonal element is 1, which means that the corresponding channel has been attacked by FDI. υ(k) represents a Bernoulli random variable. The actuator fault f(k) in S1 has a known upper bound.

3. The CPS adaptive sliding mode control method under FDI attack and actuator failure according to claim 1 is characterized in that: The cyber-physical system model in S1 is expressed as: In the formula, represents the system state vector; Indicates the actuator control signal damaged by FDI attack; Indicates the measurement output; represents external disturbance and satisfies the condition ω(k)∈L2[0,∞); represents the actuator failure, Δf(k)=f(k+1)-f(k); g(x(k),k) represents the nonlinear function of the system, and They represent constant matrices respectively.

4. The CPS adaptive sliding mode control method under FDI attack and actuator failure according to claim 3 is characterized in that: The dynamic event triggering communication mechanism in S1 is expressed as: Where χ(k) is an internal dynamic variable and satisfies: χ(0)=χ0, χ0 represents the initial state of χ(k); e y (k) = y(k i +j)-y(k i ), j represents the time when the next measurement signal is triggered, j ≥ 1, Ω is the weight matrix and Ω > 0, ε∈(0,1), θ∈(0,∞), ρ∈(0,1) are given positive scalars, and satisfy the following relationship:

5. The CPS adaptive sliding mode control method under FDI attack and actuator failure according to claim 3 is characterized in that: The S2 comprises the following steps: S21: Construct a state-fault estimator according to the cyber-physical system model, expressed as: In the formula, represents the estimated value of the state at time k+1; Represents the estimated value of the system state at the current moment; represents the fault estimation value at the current moment; Represents the estimated value of the measured output at the current moment; represents the estimated value of the measured output at the current moment considering the sensor-to-actuator delay d(k); represents the actuator input when attacked; L and M represent the estimated gain matrix; represents the nonlinear estimation value of the system; A, B, C and F represent constant matrices; S22, based on system state estimation Combined with the sliding mode gain matrix K, a discrete sliding mode function is established: Get the preset sliding surface, expressed as: Where, s(k)=[s1(k),s2(k),…,s p (k)] T represents the sliding mode function at the current moment, s(k+1) represents the sliding mode surface at the k+1 moment; b(k) represents the compensation term, b(0)=0, G represents the constant matrix, GB satisfies the non-singular condition; e y (k) = y(k i )-y(k i +j), j=1,2,...,j * -1, j* represents the right limit of the total delay interval between the sensor and the actuator; e x (k) represents the current state vector x(k) and the current state observation value The difference, that is 6. The CPS adaptive sliding mode control method under FDI attack and actuator failure according to claim 5 is characterized in that: The S3 comprises the following steps: Construct the equivalent control law of the system It is expressed as: The sliding mode dynamic representation of the system is constructed as: In the formula, matrix W = IB (GB) -1 G, represents the estimated value of the system nonlinearity, and I represents the identity matrix.

7. The CPS adaptive sliding mode control method under FDI attack and actuator failure according to claim 5 is characterized in that: The augmented closed-loop system in S4 is expressed as: in, are the augmented matrices respectively; ψ(k)=[ω T (k) Δf T (k)] T , Δf(k)=f(k+1)-f(k), are augmented vectors, I represents the identity matrix, Indicates an actuator failure. It represents the difference between the current system nonlinearity and its estimated value.

8. The CPS adaptive sliding mode control method under FDI attack and actuator failure according to claim 5 is characterized in that: The adaptive sliding mode controller constructed based on the equivalent control law of the system in S5 is expressed as: Where, u(k) represents the adaptive sliding mode controller; represents a positive scalar; represents the adaptive parameters; Represents the adaptive parameter variable value; and All represent intermediate parameter variables; is the expected value when an attack occurs.

9. The CPS adaptive sliding mode control method under FDI attack and actuator failure according to claim 7 is characterized in that: In the process of using the adaptive sliding mode controller to perform compensation control on the augmented closed-loop system, the sufficient condition for the augmented closed-loop system to satisfy asymptotic stability is expressed as: In the formula, τ1= τ +1,τ2=d(k)+1- τ , are scalars, τ =min{τ i |i=0,1,2,...,∞} is the lower bound of system delay, Θ1(d(k))=[μ1 τ1μ6-μ3 τ2μ7+τ3μ8-μ4-μ5], Θ2(d(k))=[μ2τ1μ6-μ2 τ2μ7+τ3μ8-μ3-μ4], Θ3=[μ2 μ3 μ5], Θ4=μ1-μ2, Θ5=[μ2-μ3 μ2+μ3-2μ6], Θ6=[μ3-μ4 μ3+μ4-2μ7 μ4-μ5 μ4+μ5-2μ8], are matrices, Λ1=diag{R1,3R1}, are the augmented matrices, is a known matrix, P, Q1, Q2, R1, R2 and Ω are unknown positive definite matrices, Ψ and S are arbitrary matrices, γ m ,γ n ∈(0,+∞) is a given scalar; Solve the inequality of the sufficient condition. When the unknown matrix has a solution, the augmented system satisfies asymptotic stability.

10. A CPS adaptive sliding mode control device according to any one of claims 1 to 9 using a CPS adaptive sliding mode control method under FDI attack and actuator failure, characterized in that: include: A cyber-physical system model building module, used to build a cyber-physical system model with FDI attacks and actuator failures, and introduce a dynamic event-triggered communication mechanism in the cyber-physical system measurement channel; A discrete sliding surface design module, used to construct a state-fault estimator based on the cyber-physical system model and taking into account the system delay from sensor to actuator; and establishing a discrete sliding mode function according to the system state estimation value obtained by the constructed state-fault estimator; An augmented system model building module is used to obtain the system sliding mode dynamics and the system equivalent control law based on the discrete sliding mode function; and to build an augmented closed-loop system according to the system sliding mode dynamics; The adaptive sliding mode control module is used to construct an adaptive sliding mode controller based on the system equivalent control law, and use the adaptive sliding mode controller to perform compensation control on the augmented closed-loop system.

Images