CN114895559B - A reliable control method for cyber-physical systems under malicious attacks - Google Patents

Abstract

Translated fromChinese

本发明提供一种面向恶意攻击下的信息物理系统可靠控制方法，属于信息安全技术领域。所述方法包括：建立恶意攻击下带有外部扰动的信息物理系统面向控制的动力学模型；基于建立的动力学模型，根据系统的实际输出和理想输出确定跟踪误差，并设计变结构控制方法中所需的系统切换表面；构建高斯径向基函数神经网络，基于确定的跟踪误差，对恶意攻击和外部扰动进行在线实时预估和重构；基于李雅普诺夫稳定性定理，确定高斯径向基函数神经网络的自适应法则，根据确定的自适应法则和切换表面设计自适应神经网络有限时间控制器，实现恶意攻击下对信息物理系统的可靠控制。采用本发明，能够确保系统输出在有限时间内准确跟踪到理想输出。

The present invention provides a reliable control method for an information-physical system under malicious attacks, and belongs to the field of information security technology. The method comprises: establishing a control-oriented dynamic model for an information-physical system with external disturbances under malicious attacks; based on the established dynamic model, determining the tracking error according to the actual output and ideal output of the system, and designing the system switching surface required in the variable structure control method; constructing a Gaussian radial basis function neural network, and based on the determined tracking error, performing online real-time prediction and reconstruction of malicious attacks and external disturbances; based on the Lyapunov stability theorem, determining the adaptive law of the Gaussian radial basis function neural network, and designing an adaptive neural network finite time controller according to the determined adaptive law and the switching surface, so as to realize reliable control of the information-physical system under malicious attacks. The present invention can ensure that the system output accurately tracks the ideal output within a limited time.

Description

Reliable control method of information physical system oriented to malicious attack

Technical Field

The invention relates to the technical field of information security, in particular to a reliable control method of an information physical system facing malicious attack.

Background

At present, along with the rapid development of technologies such as sensing, computing, communication and control, an information physical system integrating factors such as people, machines, objects, environment and information in a physical space and an information space is generated, becomes a research front in the current automation field, and is widely applied to the field of actual engineering, such as smart power grids, intelligent network automobiles, industrial Internet, intelligent medical treatment and the like. The typical characteristic of the information physical system is that the control layer and the perception execution layer need to communicate through the data transmission layer, so that a malicious attacker can launch a plurality of and complex information-physical cross-domain attack behaviors aiming at the attack of the information physical system, and aims at detecting, invading and hijacking the information system, thereby causing serious non-contact damage to the physical system.

In recent years, home and abroad scholars start from different angles, a series of ideas for reliable control of an information physical system facing malicious attacks are provided, and although progress and achievements are achieved, the defect still exists that most methods only realize progressive stabilization of the information physical system under the malicious attacks, and few researches can realize online real-time prediction and reconstruction of the malicious attacks and external disturbance. Meanwhile, the limited time stability difficulty of the information physical system with external disturbance under the malicious attack is high due to the existence of the malicious attack and the external disturbance, so that a limited time control method of the information physical system with external disturbance under the malicious attack is needed to be designed.

Disclosure of Invention

The embodiment of the invention provides a reliable control method of an information physical system facing malicious attack, which can ensure that the system output is accurately tracked to ideal output in a limited time. The technical scheme is as follows:

The embodiment of the invention provides a reliable control method of an information physical system facing malicious attack,

Establishing a control-oriented dynamic model of an information physical system with external disturbance under malicious attack;

based on the established dynamic model, determining tracking error according to the actual output and the ideal output of the system, and designing a system switching surface required in the variable structure control method;

Constructing a Gaussian radial basis function neural network, and carrying out online real-time estimation and reconstruction on malicious attack and external disturbance based on the determined tracking error;

Based on Lyapunov stability theorem, the adaptive rule of the Gaussian radial basis function neural network is determined, and the adaptive neural network finite time controller is designed according to the determined adaptive rule and the switching surface, so that reliable control of an information physical system under malicious attack is realized.

Further, the established dynamic model of the information physical system with external disturbance under the malicious attack is as follows:

Where t represents time, ζ (t) represents an information physical system state variable,.., Ζ^(n-1)(t)、ξ⁽ⁿ⁾ (t) denote in sequence the first, second, third, etc. derivative of ζ (t) with respect to time t, where n denotes that the system is an n-th order nonlinear system, p (-) and q (-) are known real continuous nonlinear functions with respect to system state variables, y (t) denotes the actual output of the system, C denotes the coefficient matrix, u_a (t) denotes the malicious attack, u (t) denotes the system input, the malicious attacker intends to achieve the purpose of the malicious attack by superimposing u_a (t) on the system input u (t), d (t) denotes the external disturbance present in the control object, |d (t) | < β, β is a positive constant;

Converting the kinetic model into the following form:

Wherein,The n-dimensional state vector of the information physical system after conversion is represented, ζ₁ (t) and ζ (t) represent the same meaning, each represent 1 st dimension in n-dimensional state variables of the information physical system, ζ₂(t)、ξ₃(t)、ξ₄(t)、…、ξ_n (t) respectively represent first derivative, second derivative, third derivative and third derivative of ζ (t) with respect to time t, n-1 th derivative, and a (t) =ψ (xi, t) =q (xi) u_a (t) represents the energy of malicious attack suffered by the information physical system;

according to the attack energy bounded theory, the method comprises the following steps:

Wherein phi_i >0, i=1, 2,..n represents the upper energy bound for malicious attacks to the information physical system,.., Ψ⁽ⁿ⁾ (xi, t) represent, in order, the first derivative, the second derivative, the third derivative, the fourth derivative of ψ (xi, t) with respect to time t.

Further, the determining tracking error according to the actual output and the ideal output of the system based on the established dynamics model, and designing the system switching surface required in the variable structure control method includes:

based on the established dynamics model, determining the tracking error of the system according to the actual output and the ideal output of the system as follows:

Wherein,Representing the tracking error of the system, y_d (t) representing the ideal output of the system, and y (t) representing the actual output of the system;

the tracking error dynamics of the system are described as:

Wherein,Representing the nth derivative of the ideal output y_d (t) with respect to time t,Respectively representFirst derivative, second derivative, and third derivative of time t third derivative, n-1, n derivative,Respectively representFirst, second, third, n-1 derivatives over time t;

the control targets of the system are described as:

wherein, pi (t) is in a shorthand form,The expression of the expression vector is European norms, T represents the adjustment time of the system, and epsilon represents the preset tracking precision;

defining a switching surface as:

Wherein W (t) represents the switching surface and v represents the conversion rate of the switching surface;

according to the newton's expansion formula, the switching surface is written specifically as follows:

Wherein,Respectively representFirst derivative, second derivative, n-3, n-2, n-1 derivatives over time t;

converting the switching surface into, according to the tracking error dynamics of the system:

Wherein,Representing a tracking error of the system;

after the first derivative of the switching surface with respect to time t is obtained, the following steps are obtained:

Further, the constructing the gaussian radial basis function neural network, based on the determined tracking error, performing online real-time prediction and reconstruction on the malicious attack and the external disturbance comprises:

constructing a Gaussian radial basis function neural network;

will track errorsTraining weights Q between hidden layers and output layers in the constructed Gaussian radial basis function neural network as input so as to estimate the sum of malicious attack and external disturbance by the trained Gaussian radial basis function neural network

Wherein S (-) represents a Gaussian function,Respectively representing the weights between the estimated hidden layer and the output layer, the center of the hidden layer neuron and the standard deviation of the hidden layer neuron, X (t) represents the input vector of the Gaussian radial basis function neural network,

Defining the estimated error of the weight Q between the hidden layer and the output layer of the Gaussian radial basis function neural networkThe method comprises the following steps:

Wherein,The estimated weight of the Gaussian radial basis function neural network constructed in the embodiment is Q^*, and the existing weight between the optimal hidden layer and the output layer is the estimated weight.

Further, the adaptive rule of the gaussian radial basis function neural network is expressed as:

Based on Lyapunov stability theorem, determining the adaptive rule of the Gaussian radial basis function neural network:

Wherein,Representation ofFor the first derivative of time t, μ=μ^*,τ＝τ^*, μ, τ represent the center μ^* of the optimal hidden layer neuron and the standard deviation τ^* of the optimal hidden layer neuron, respectively.

Further, the designed adaptive neural network finite time controller is expressed as:

wherein sgn (·) represents a sign function, k is a normal number, k is equal to or greater than α+β, β is an upper bound of external disturbance d (t) existing in the system, α is a normal number, and q (Σ) is not equal to 0.

The technical scheme provided by the embodiment of the invention has the beneficial effects that at least:

1) Aiming at an information physical system with external disturbance under malicious attack, a reliable control method of the information physical system is provided to ensure that the system output is accurately tracked to ideal output in a limited time;

2) The Gaussian radial basis function neural network constructed in the embodiment is a self-adaptive neural network predictor, and can realize online prediction and reconstruction of external disturbance and malicious attack existing in a system;

3) The reliable control method of the information physical system provided by the embodiment is designed aiming at the n-order nonlinear information physical system, so that the method can be applied to the safety control of various nonlinear information physical systems;

4) The embodiment fuses the Lyapunov stabilization theory, ensures the stability of the information physical system, and effectively improves the control performance.

Drawings

In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings required for the description of the embodiments will be briefly described below, and it is apparent that the drawings in the following description are only some embodiments of the present invention, and other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.

FIG. 1 is a schematic diagram of an information physical system according to an embodiment of the present invention;

fig. 2 is a flow chart of a reliable control method of an information physical system facing malicious attack provided by the embodiment of the invention;

FIG. 3 is a schematic diagram of a finite time control strategy of an adaptive neural network according to an embodiment of the present invention;

FIG. 4 is a schematic diagram of a malicious attack according to an embodiment of the present invention;

FIG. 5 is a schematic diagram of external disturbance according to an embodiment of the present invention;

FIG. 6 is a schematic diagram of an adaptive neural network predictor for predicting effects according to an embodiment of the present invention;

FIG. 7 is a schematic diagram of a simulation result of the automobile speed according to an embodiment of the present invention;

fig. 8 is a schematic diagram of a switching surface simulation result according to an embodiment of the present invention.

Detailed Description

For the purpose of making the objects, technical solutions and advantages of the present invention more apparent, the embodiments of the present invention will be described in further detail with reference to the accompanying drawings.

In this embodiment, the structure diagram of the information physical system with external disturbance under the malicious attack is shown in fig. 1, the communication mode in the system is wireless communication, the controller sends a control instruction to the actuator through the wireless communication network, the actuator acts on the control object, the external disturbance exists in the control object all the time, the sensor measures the signal in the control object and sends the signal to the controller through the wireless communication network, the malicious attack intends to send the control instruction u (t) (i.e. system input) to the actuator through the wireless communication network, and then the malicious attack signal u_a (t) is added, so that the purpose of the malicious attack is achieved.

S101, establishing a control-oriented dynamic model of an information physical system with external disturbance under malicious attack so as to mathematically characterize the malicious attack and the existing external disturbance of the information physical system;

In this embodiment, the dynamic model of the information physical system with external disturbance under the malicious attack is:

Where t represents time, ζ (t) represents information physical system state variables such as vehicle speed, vehicle-to-vehicle distance, etc.,.., Ζ^(n-1)(t)、ξ⁽ⁿ⁾ (t) denote in order that ζ (t) is a first derivative, a second derivative, a third derivative, a.i., n-1 order, n-order derivative of time t, n denotes that the system is an n-order nonlinear system, p (, q () is a known real continuous nonlinear function of system state variables, y (t) denotes an actual output of the system, such as vehicle speed, vehicle acceleration, etc., C denotes a coefficient matrix, c= [1, 0]^T,u_a (t) denotes a malicious attack, u (t) denotes a system input, a malicious attacker intends to achieve the purpose of the malicious attack by superimposing u_a (t) on the system input u (t), d (t) denotes an external disturbance present in the control object, |d (t) | < β, β is a positive constant;

Converting the kinetic model into the following form:

Wherein,The n-dimensional state vector of the information physical system after conversion is represented, ζ₁ (t) and ζ (t) represent the same meaning, each represent 1 st dimension in n-dimensional state variables of the information physical system, ζ₂(t)、ξ₃(t)、ξ₄(t)、...、ξ_n (t) respectively represent first derivative, second derivative, third derivative and third derivative of ζ (t) with respect to time t, n-1 th derivative, and a (t) =ψ (xi, t) =q (xi) u_a (t) represents the energy of malicious attack suffered by the information physical system;

according to the attack energy bounded theory, the method comprises the following steps:

Wherein phi_i >0, i=1, 2,..n represents the upper energy bound for malicious attacks to the information physical system,.., Ψ⁽ⁿ⁾ (xi, t) represent, in order, the first derivative, the second derivative, the third derivative, the fourth derivative of ψ (xi, t) with respect to time t.

S102, determining tracking errors according to actual output and ideal output of a system based on the established dynamic model, and designing a system switching surface required in a variable structure control method;

In this embodiment, the tracking error of the system is:

Wherein,Representing the tracking error of the system, y_d (t) representing the ideal output of the system, and y (t) representing the actual output of the system;

the tracking error dynamics of the system are described as:

Wherein,Representing the nth derivative of the ideal output y_d (t) with respect to time t,...、Respectively representFirst derivative, second derivative, and third derivative of time t third derivative, n-1, n derivative,Respectively representFirst, second, third, n-1 derivatives over time t;

The control objective of this embodiment is to ensure that, for any initial state of the system, the system output can be accurately tracked to the ideal output within a limited time, and the control objective of the system can be written as:

wherein, pi (t) is in a shorthand form,The expression vector is European norms, T >0 represents the adjustment time of the system, and epsilon >0 represents the preset tracking precision;

defining a switching surface as:

Wherein W (t) represents the switching surface, and v >0 represents the conversion rate of the switching surface;

according to the newton's expansion formula, the switching surface is written specifically as follows:

Wherein,Respectively representFirst derivative, second derivative, n-3, n-2, n-1 derivatives over time t;

converting the switching surface into, according to the tracking error dynamics of the system:

Wherein,Representing a tracking error of the system;

after the first derivative of the switching surface with respect to time t is obtained, the following steps are obtained:

S103, constructing a Gaussian radial basis function neural network, and carrying out online real-time prediction and reconstruction on malicious attacks and external disturbance based on the determined tracking error, so as to realize the purposes of online prediction and reconstruction on the external disturbance and the malicious attacks of the system;

In this embodiment, according to the global approximation theorem, for the sum of external disturbance and malicious attack, a_d (t) =a (t) +d (t), there is always a gaussian radial basis function neural network, so that for any approximation accuracy, the following equation always holds:

Wherein S (-) represents a Gaussian function,Representing the estimated result of the Gaussian radial basis function neural network constructed in the embodiment, specifically, the sum of external disturbance and malicious attack, χ >0 represents the approximation accuracy, Q^*、μ^*、τ^* represents the weight between the optimal hidden layer and the output layer, the center of the hidden layer neuron and the standard deviation of the hidden layer neuron respectively, X (t) represents the input vector of the Gaussian radial basis function neural network,

The above equation indicates that there is always an optimal Q^*,μ^*,τ^* so that the above equation is satisfied, and for the Gaussian radial basis function neural network constructed in this embodiment, the estimated result of A_d (t)Can be expressed as follows:

Wherein,Respectively representing the weights between the predicted hidden layer and the output layer, the center of the hidden layer neuron and the standard deviation of the hidden layer neuron;

It is worth noting that the gaussian radial basis function neural network constructed in the embodiment is trained only for the weight Q between the hidden layer and the output layer, and the designed gaussian radial basis function neural network is used as a self-adaptive neural network predictor, so as to realize online prediction and reconstruction of external disturbance and malicious attack existing in the system.

In this embodiment, the following estimation error is defined with respect to the weight Q between the hidden layer and the output layer of the Gaussian radial basis function neural networkThe method comprises the following steps:

Wherein,The estimated weight of the Gaussian radial basis function neural network constructed in the embodiment is Q^*, and the existing weight between the optimal hidden layer and the output layer is the estimated weight.

S104, based on the Lyapunov stability theorem, determining the self-adaptive rule of the Gaussian radial basis function neural network, and designing a finite time controller of the self-adaptive neural network according to the determined self-adaptive rule and the switching surface to realize reliable control of an information physical system under malicious attack. Therefore, the Lyapunov stability theory is fused, the stability of the information physical system is ensured, and the control performance is effectively improved.

In this embodiment, based on the lyapunov stability theorem, an adaptive rule of the gaussian radial basis function neural network is determined:

Wherein,Representation ofFor the first derivative of time t, since the present embodiment only trains for weights between hidden layer to output layer, μ, τ represent the center of the optimal hidden layer neuron and the standard deviation of the optimal hidden layer neuron, i.e., μ=μ^*,τ＝τ^*, respectively;

According to the global approximation theorem, an optimal Gaussian radial basis function neural network always exists and can accurately approximate A_d (t), namely the following formula holds:

A_d(t)＝Q^*TS(X(t),μ,τ)

therefore, an adaptive neural network finite time controller is designed as follows:

wherein sgn (·) represents a sign function, k is a normal number, k is equal to or greater than α+β, β is an upper bound of external disturbance d (t) existing in the system, α is a normal number, and q (Σ) is not equal to 0.

The system stability proving process is as follows:

The following form of lyapunov function was selected:

deriving the Lyapunov function to obtain:

Will beSubstituting the formula:

the finite time controller of the adaptive neural network constructed by the embodiment is brought into the formula to obtain:

Further simplification of the above formula can be obtained:

according to the global approximation theorem:

Then willThe simplification is as follows:

Substituting the adaptive rule determined in this embodiment into the above formula yields:

further simplifying and obtaining:

according to the lyapunov theorem, the system output can accurately track the ideal output in a limited time.

The reliable control method for the information physical system facing malicious attack provided by the embodiment of the invention has at least the following advantages:

1) Aiming at an information physical system with external disturbance under malicious attack, a reliable control method of the information physical system is provided to ensure that the system output is accurately tracked to ideal output in a limited time;

2) The Gaussian radial basis function neural network constructed in the embodiment is a self-adaptive neural network predictor, and can realize online prediction and reconstruction of external disturbance and malicious attack existing in a system;

3) The reliable control method of the information physical system provided by the embodiment is designed aiming at the n-order nonlinear information physical system, so that the method can be applied to the safety control of various nonlinear information physical systems;

4) The embodiment fuses the Lyapunov stabilization theory, ensures the stability of the information physical system, and effectively improves the control performance.

For better understanding of the present invention, the reliable control method for the information physical system under malicious attack provided by the embodiment of the present invention is described with ζ (t) =v (t), where v (t) represents the vehicle speed of the heavy-duty car, as shown in fig. 3, in this embodiment,

y(t)=v(t),u(t)=T_e(t)

Wherein,M_a＝40000kg,m_a denotes the mass of the car, m_t denotes the total mass of the heavy vehicle system, J_w＝32.9kgm²,J_w denotes the rotational inertia of the car tyre, r_w＝0.5m,r_w denotes the radius of the vehicle wheel,In relation to the wheel inertia, lambda_G＝1,λ_G denotes the gearbox, lambda_F＝2.71,λ_F denotes the transmission ratio of the main transmission gear, eta_G＝0.97,η_G denotes the gearbox, eta_F＝0.97,η_F denotes the main transmission efficiency factor,In relation to the inertia of the flywheel,Representing the transmission coefficient of the force generated by the engine,Z_a denotes an air resistance coefficient, c_d denotes a resistance coefficient, a_a＝10m²,A_a denotes a front area of the vehicle, ρ_a＝1.29kg/m³,ρ_a denotes an air density, z_r＝c_rm_ag,c_r＝0.007,c_r denotes a sliding friction coefficient, g=9.82, g denotes a gravitational constant, z_r denotes a resistance coefficient due to vehicle gravity, z_g＝m_ag,z_g denotes vehicle gravity, J_e＝3.5kgm², α(s) denotes a slope road angle (which is a function of a position s on a road where the vehicle is located), T_e (T) denotes an engine torque, v (T) denotes a speed of the vehicle, y (T) =v (T) denotes a speed of the vehicle as a system output, and a (T) and d (T) respectively denote a malicious attack and an external disturbance suffered by the vehicle;

firstly, establishing a control-oriented dynamic model of an information physical system with external disturbance under malicious attack, wherein the control-oriented dynamic model comprises the following steps:

y(t)=v(t)

Wherein a (t) and d (t) are shown in fig. 4 and 5, respectively.

Secondly, determining the tracking error as follows:

wherein y_d (t) represents the ideal speed, y_d (t) =22.2 m/s;

Then, the switching surface of the system is determined as:

Thirdly, constructing a Gaussian radial basis function neural network to estimate the sum of malicious attack and external disturbance, wherein the input of the neural network is thatThe output isThe number of neurons of an hidden layer of the designed neural network is 5, the Gaussian radial basis function neural network constructed in the embodiment is trained only for the weight Q between the hidden layer and an output layer, and the designed Gaussian radial basis function neural network is used as a self-adaptive neural network estimator to realize online estimation and reconstruction of external disturbance and malicious attack existing in a system.

Fourth, the following adaptive rules are determined:

then, an adaptive neural network finite time controller is designed as follows:

wherein k is equal to or greater than α+β, β is the upper bound of the external disturbance d (t) present in the system, α=0.5, and q (Σ) noteq0.

In this embodiment, the built adaptive neural network predictor performs online prediction on external disturbance and malicious attack existing in the system, the prediction result is shown in fig. 6, and obviously, the adaptive neural network predictor built in this embodiment can accurately estimate and reconstruct the malicious attack and the external disturbance, in addition, the automobile speed v (t) and the operation curve result of the switching surface W (t) obtained by simulating the heavy automobile system implementation case are shown in fig. 7 and 8, it is known from fig. 7 and 8 that the automobile speed v (t) tracks to the ideal speed v_cc =22.2 m/s in a limited time, and the switching surface W (t) is converted into 0 in a limited time.

The foregoing description of the preferred embodiments of the invention is not intended to limit the invention to the precise form disclosed, and any such modifications, equivalents, and alternatives falling within the spirit and scope of the invention are intended to be included within the scope of the invention.

Claims (4)

Translated fromChinese

1.一种面向恶意攻击下的信息物理系统可靠控制方法，其特征在于，包括：1. A reliable control method for a cyber-physical system under malicious attacks, comprising:建立恶意攻击下带有外部扰动的信息物理系统面向控制的动力学模型；Establish a control-oriented dynamic model for cyber-physical systems with external disturbances under malicious attacks;基于建立的动力学模型，根据系统的实际输出和理想输出确定跟踪误差，并设计变结构控制方法中所需的系统切换表面；Based on the established dynamic model, the tracking error is determined according to the actual output and ideal output of the system, and the system switching surface required in the variable structure control method is designed;构建高斯径向基函数神经网络，基于确定的跟踪误差，对恶意攻击和外部扰动进行在线实时预估和重构；Construct a Gaussian radial basis function neural network to perform online real-time estimation and reconstruction of malicious attacks and external disturbances based on the determined tracking error;基于李雅普诺夫稳定性定理，确定高斯径向基函数神经网络的自适应法则，根据确定的自适应法则和切换表面设计自适应神经网络有限时间控制器，实现恶意攻击下对信息物理系统的可靠控制；Based on Lyapunov's stability theorem, the adaptive law of Gaussian radial basis function neural network is determined. According to the determined adaptive law and switching surface, an adaptive neural network finite time controller is designed to achieve reliable control of cyber-physical systems under malicious attacks.其中，建立的恶意攻击下带有外部扰动的信息物理系统面向控制的动力学模型为：Among them, the control-oriented dynamic model of the cyber-physical system with external disturbance under malicious attack is established as follows:其中，t表示时间，ξ(t)表示信息物理系统状态变量，依次表示ξ(t)对时间t的一阶导数、二阶导数、三阶导数、…、n-1阶、n阶导数，n表示系统为n阶非线性系统，p(.)和q(.)是已知的关于系统状态变量的实连续非线性函数，y(t)表示系统的实际输出，C表示系数矩阵，u_a(t)表示恶意攻击，u(t)表示系统输入，恶意攻击者意图通过给系统输入u(t)叠加u_a(t)从而实现恶意攻击的目的，d(t)表示控制对象中存在的外部扰动，|d(t)|<β，β为正常数；Where t represents time, ξ(t) represents the state variable of the cyber-physical system, represents the first-order derivative, second-order derivative, third-order derivative, …, n-1-order, and n-order derivative of ξ(t) with respect to time t, n represents the system is an n-order nonlinear system, p(.) and q(.) are known real continuous nonlinear functions of the system state variables, y(t) represents the actual output of the system, C represents the coefficient matrix,_ua (t) represents a malicious attack, u(t) represents the system input, and the malicious attacker intends to achieve the purpose of the malicious attack by superimposing_ua (t) on the system input u(t), d(t) represents the external disturbance existing in the control object, |d(t)|<β, and β is a positive constant;将所述动力学模型转化为如下形式：The kinetic model is transformed into the following form:其中，表示经过转化之后的信息物理系统的n维状态向量，ξ₁(t)与ξ(t)代表相同含义，均表示信息物理系统n维状态变量中的第1维，ξ₂(t)、ξ₃(t)、ξ₄(t)、...、ξ_n(t)分别表示ξ(t)对时间t的一阶导数、二阶导数、三阶导数、…、n-1阶导数，A(t)＝Ψ(Ξ,t)＝q(Ξ)u_a(t)表征信息物理系统所遭受恶意攻击的能量；in, represents the n-dimensional state vector of the cyber-physical system after transformation, ξ₁ (t) and ξ(t) have the same meaning, both representing the first dimension of the n-dimensional state variable of the cyber-physical system, ξ₂ (t), ξ₃ (t), ξ₄ (t), ..., ξ_n (t) represent the first-order derivative, second-order derivative, third-order derivative, ..., n-1-order derivative of ξ(t) with respect to time t, respectively, A(t) = Ψ(Ξ, t) = q(Ξ)u_a (t) represents the energy of malicious attacks suffered by the cyber-physical system;根据攻击能量有界理论，得到：According to the bounded attack energy theory, we get:其中，φ_i>0,i＝1,2,…,n表征信息物理系统所遭受恶意攻击的能量上界，依次表示Ψ(Ξ,t)对时间t的一阶导数、二阶导数、三阶导数、...、n阶导数；Among them, φ_i >0, i＝1,2,…,n represents the upper bound of the energy of malicious attacks suffered by cyber-physical systems, represents the first-order derivative, second-order derivative, third-order derivative, ..., n-order derivative of Ψ(Ξ,t) with respect to time t in turn;其中，所述基于建立的动力学模型，根据系统的实际输出和理想输出确定跟踪误差，并设计变结构控制方法中所需的系统切换表面包括：Wherein, based on the established dynamic model, determining the tracking error according to the actual output and the ideal output of the system, and designing the system switching surface required in the variable structure control method include:基于建立的动力学模型，根据系统的实际输出和理想输出确定系统的跟踪误差为：Based on the established dynamic model, the tracking error of the system is determined according to the actual output and ideal output of the system:其中，表示系统的跟踪误差，y_d(t)表示系统的理想输出，y(t)表示系统的实际输出；in, represents the tracking error of the system, y_d (t) represents the ideal output of the system, and y(t) represents the actual output of the system;将系统的跟踪误差动力描述为：The tracking error dynamics of the system is described as:其中，表示理想输出y_d(t)对时间t的n阶导数，分别表示对时间t的一阶导数、二阶导数、三阶导数、…、n-1阶、n阶导数，分别表示对时间t的一阶导数、二阶导数、三阶导数、…、n-1阶导数；in, represents the nth-order derivative of the ideal output y_d (t) with respect to time t, Respectively The first derivative, second derivative, third derivative, ..., n-1 derivative, n derivative at time t, Respectively The first derivative, second derivative, third derivative, ..., n-1 derivative with respect to time t;将系统的控制目标描述为：The control objective of the system is described as:其中，Π(t)为简写形式，.||表示向量的欧式范数，T代表系统的调节时间，ε代表预先设定的跟踪精度；Among them, Π(t) is a short form, .|| represents the Euclidean norm of the vector, T represents the adjustment time of the system, and ε represents the preset tracking accuracy;定义切换表面为：Define the switching surface as:其中，W(t)表示切换表面，υ表示切换表面的转化速率；Where W(t) represents the switching surface, and υ represents the conversion rate of the switching surface;根据牛顿展开公式，将切换表面具体写为如下形式：According to Newton's expansion formula, the switching surface is specifically written as follows:其中，分别表示对时间t的一阶导数、二阶导数、…、n-3阶、n-2阶、n-1阶导数；in, Respectively The first derivative, second derivative, ..., n-3, n-2, and n-1 derivatives with respect to time t;根据系统的所述跟踪误差动力，将切换表面转化为：According to the tracking error dynamics of the system, the switching surface is transformed into:其中，表示系统的跟踪误差；in, Represents the tracking error of the system;将切换表面对时间t求取一阶导数后，得到：After taking the first-order derivative of the switching surface with respect to time t, we obtain:2.根据权利要求1所述的面向恶意攻击下的信息物理系统可靠控制方法，其特征在于，所述构建高斯径向基函数神经网络，基于确定的跟踪误差，对恶意攻击和外部扰动进行在线实时预估和重构包括：2. The reliable control method for a cyber-physical system under malicious attacks according to claim 1 is characterized in that the step of constructing a Gaussian radial basis function neural network to perform online real-time prediction and reconstruction of malicious attacks and external disturbances based on a determined tracking error comprises:构建高斯径向基函数神经网络；Construct a Gaussian radial basis function neural network;将跟踪误差作为输入，对构建的高斯径向基函数神经网络中的隐含层与输出层之间的权重Q进行训练，以便训练好的高斯径向基函数神经网络预估恶意攻击和外部扰动的和Tracking Error As input, the weight Q between the hidden layer and the output layer in the constructed Gaussian radial basis function neural network is trained so that the trained Gaussian radial basis function neural network can estimate the sum of malicious attacks and external disturbances.其中，S(.)表示高斯函数，分别表示预估出的隐含层与输出层之间的权重，隐含层神经元的中心和隐含层神经元的标准差；X(t)表示高斯径向基函数神经网络的输入向量，Among them, S(.) represents the Gaussian function, They represent the estimated weights between the hidden layer and the output layer, the center of the hidden layer neurons, and the standard deviation of the hidden layer neurons; X(t) represents the input vector of the Gaussian radial basis function neural network,定义高斯径向基函数神经网络隐含层到输出层之间权重Q的预估误差为：Define the estimated error of the weight Q between the hidden layer and the output layer of the Gaussian radial basis function neural network for:其中，是构建的高斯径向基函数神经网络所预估出的权重，Q^*是存在的最优的隐含层到输出层之间的权重。in, is the weight estimated by the constructed Gaussian radial basis function neural network, and Q^* is the optimal weight between the hidden layer and the output layer.3.根据权利要求2所述的面向恶意攻击下的信息物理系统可靠控制方法，其特征在于，所述高斯径向基函数神经网络的自适应法则表示为：3. The reliable control method for a cyber-physical system under malicious attacks according to claim 2 is characterized in that the adaptive law of the Gaussian radial basis function neural network is expressed as:基于李雅普诺夫稳定性定理，确定高斯径向基函数神经网络的自适应法则：Based on Lyapunov's stability theorem, the adaptive law of Gaussian radial basis function neural network is determined:其中，表示对时间t的一阶导数，μ＝μ^*，τ＝τ^*，μ,τ分别代表最优的隐含层神经元的中心μ^*和最优的隐含层神经元的标准差τ^*。in, express The first-order derivative with respect to time t is μ=μ^* , τ=τ^* , where μ and τ represent the center μ^* of the optimal hidden layer neuron and the standard deviation τ^* of the optimal hidden layer neuron, respectively.4.根据权利要求2所述的面向恶意攻击下的信息物理系统可靠控制方法，其特征在于，设计的自适应神经网络有限时间控制器表示为：4. The reliable control method for cyber-physical systems under malicious attacks according to claim 2 is characterized in that the designed adaptive neural network finite time controller is expressed as:其中，sgn(·)表示符号函数，k为正常数，k≥α+β，β为系统中存在的外部扰动d(t)的上界，α为正常数，且q(Ξ)≠0。where sgn(·) represents a sign function, k is a positive constant, k ≥ α + β, β is the upper bound of the external disturbance d(t) in the system, α is a positive constant, and q(Ξ) ≠ 0.