Network physical system adaptive control method for injection and spoofing attacks

Abstract

The invention discloses a network physical system adaptive control method for injection and spoofing attacks. The method comprises the following steps: S1, constructing a control system model under a network physical framework; s2, when a sensor and an actuator of the system are subjected to opponent injection and spoofing attacks, defining the attack of the actuator; s3, when a sensor attack exists in the system, defining the sensor attack; s4, rewriting the system model under the network attack; s5, on the basis of the rewritten system model, a BackStepping method is adopted, and an adaptive control law u of the system is obtained; and S6, further deducing that all signals in the closed-loop system are globally bounded on the basis of the adaptive control law u in the step S5, designing a controller by introducing a Nussbaum even function and a variable derivative thereof, and when the system is subjected to injection and spoofing attacks, adjusting control parameters so as to enable an adjustment error to be arbitrarily small. The method can ensure that the adjustment error can be randomly small under the condition of injection and spoofing attacks, and is realized by adjusting the control parameters.

Description

Technical Field

[0001] The present invention relates to the technical field of network-physical system control methods, and in particular to a network-physical system adaptive control method for injection and deception attacks. Background Art

[0002] Cyber-physical system (CPS) refers to a complex system that closely integrates information system with physical system. It realizes real-time control, monitoring and optimization of the physical world through embedded system and network technology.

[0003] With the development of network technology, cyber-physical systems are increasingly used in transportation systems, unmanned factories, power systems and other fields, and their operational safety is of vital importance. Control systems under the cyber-physical framework play an important role in critical infrastructure and may become targets of cyber attacks. Cyber ​​attacks can be roughly divided into three categories: denial of service attacks, replay attacks, and injection and spoofing attacks. In a denial of service attack, an attacker can block the communication network by sending a maximum amount of data through the network to prevent the device from sending or receiving information from sensors or actuators in the network, thereby causing the control system to fail. A replay attack is an attack strategy that maliciously sends and receives the same data repeatedly over a period of time. Unlike a denial of service attack, a replay attack may be carried out secretly. An injection and spoofing attack is an attack that may modify data from sensors and actuators during transmission, causing the user to receive false data. All three types of attacks may cause the control system to fail and lead to disasters. Therefore, how to solve the problem of attacks in control systems has received increasing attention.

[0004] In practical applications, control systems in a cyber-physical framework need to collect data from sensors and send control signals to the system through a communication network. Communication networks provide a convenient way to attack, threaten, and extract information from sensor transmissions in communication networks. Therefore, solving control problems in a cyber-physical framework under different types of attacks is a key issue.

[0005] Current research has achieved many results related to the problem of network attacks. For example, in "State Estimation under False Data Injection Attacks: Security Analysis and System Protection", the injection attack state estimation problem of network control systems was considered, and a system protection scheme was proposed, through which only a few (rather than all) communication channels need to be protected against injection attacks. However, the shortcoming of this study is that the research focuses on linear systems, while actual control systems are mostly nonlinear systems, so the proposed method has certain limitations.

[0006] In “An adaptive control architecture for mitigating sensor and actuator attacks in cyber-physical systems”, the adaptive control problem for a class of Lipschtz nonlinear systems with injection and deception attacks is studied. The proposed adaptive control method can guarantee the consistent ultimate boundedness of the closed-loop system under the simultaneous presence of sensor and actuator attacks. However, the model focused on by this method is relatively simple and cannot be directly generalized to nonlinear systems with uncertainty.

[0007] In summary, the defects of the existing technology are that the models of concern are often linear systems or relatively simple nonlinear systems, and there is little research on the network security issues of nonlinear system models in cyber-physical systems in the proposed control schemes, and they cannot be directly extended to nonlinear systems with uncertainties. Summary of the invention

[0008] In order to overcome the above technical problems, the purpose of the present invention is to provide an adaptive control method for a cyber-physical system against injection and deception attacks. The control method can adjust the control parameters to ensure that the adjustment error can be arbitrarily small when subjected to injection and deception attacks, and introduce a series of special nonlinear feedback signals to deal with the control difficulties caused by unknown time-varying gains, thereby achieving better safety control performance, enabling the cyber-physical control system to adapt to various uncertainties and network attacks, and achieving high-performance, safe and stable control.

[0009] In order to achieve the above object, the technical solution adopted by the present invention is:

[0010] The method for adaptive control of a cyber-physical system against injection and deception attacks comprises the following steps;

[0011] S1: Construct a control system model under the cyber-physical framework;

[0012] S2: Based on the system model, when the system's actuator is subjected to injection and deception attacks by the adversary, the actuator attack definition is performed;

[0013] S3: When there is a sensor attack on the system's sensors, the definition of injection and deception attacks;

[0014] S4: rewriting the control system model under the network attack based on the control system model, the actuator attack definition and the sensor attack definition;

[0015] S5: Based on the rewritten system model, the BackStepping method is used to obtain the adaptive control law u of the system;

[0016] S6: Based on the adaptive control law u, it is deduced that all signals in the closed-loop system are globally bounded. A processing method based on Nussbaum technology is adopted. By introducing the Nussbaum even function and its variable derivatives, a controller is designed. When the system is subjected to injection and deception attacks, the control parameters are adjusted to make the adjustment error arbitrarily small.

[0017] Specifically, S1 is as follows: the system model and the parameters in the model are defined as:

[0018]

[0019] in,, Represent the real state vectors of the cyber-physical system in two different dimensions, Indicates the status of the system. represents the control input, Indicates the control output, represents the uncertain system parameters, φ i : is a nonlinear smooth function, i=1,2; Represent the real state vector of the cyber-physical system The first derivative of .

[0020] The S2 is specifically:

[0021] An actuator attack is defined as:

[0022]

[0023] Where u is the control to be designed, is the unknown time-varying gain, is a nonlinear function, b(t) is a time-varying unknown parameter with an unknown sign.

[0024] The S3 is specifically:

[0025] When the system is attacked by sensors, the real state of the system and is unknown, the sensor attack is defined as:

[0026]

[0027] where i = 1, 2, w(t) is the unknown time-varying gain, is the signal injected into the sensor, so the output of the sensor is The actual status signal Different, define λ(t)=1+w(t), then we have

[0028] The S4 is specifically:

[0029] The system model under network attack is rewritten as:

[0030]

[0031] The step S5 is specifically as follows:

[0032] S51: Let z1 = x1. According to the parameter definitions in S1, S2, S3 and S4, the time derivative of z1 is obtained: +-

[0033]

[0034] Let x2 = α + z2, where α is the virtual control and z2 is the virtual control error, then:

[0035]

[0036] To handle unknown time-varying gains and λθ1(t), the following nonlinear function is introduced:

[0037]

[0038] where i = 1, 2, and δ i is a positive constant to be given. In addition, h i (x i ) and (|z i |-δ i ) 2 f i It is C 1 function, and has:

[0039]

[0040] Consider the following Lyapunov function:

[0041]

[0042] Its time derivative is:

[0043]

[0044] where Θ1 is is the boundary of λθ1(t), θ2 is the boundary of λθ1(t), σ is a small positive constant, and the virtual control α is designed as

[0045]

[0046] in

[0047]

[0048] Θ=[Θ1,Θ2] T

[0049] and is an estimate of Θ, represents the estimation error;

[0050] Defining the Lyapunov function

[0051]

[0052] Defining parameter estimators

[0053]

[0054] Then there are:

[0055]

[0056] S52: Find the time derivative of z2:

[0057]

[0058] Consider the following Lyapunov function:

[0059]

[0060] Taking its time derivative, we have:

[0061]

[0062] The upper bounds of v(t) and θ2(t) are set to be and Then there is

[0063]

[0064] in

[0065] The design of controller u is:

[0066]

[0067] in

[0068] is an estimate of Ξ and satisfies:

[0069]

[0070] definition

[0071]

[0072] Consider the following Lyapunov function:

[0073]

[0074] Taking its time derivative, we have:

[0075]

[0076] Let δ1≥δ2, we get:

[0077]

[0078] The above formula is always established, and we get:

[0079]

[0080] Through S5, you can get:

[0081]

[0082] Through the above formula, the conditions for the system to satisfy Lyapunov stability under network attack are obtained.

[0083] The S6 is specifically:

[0084] The Nussbaum function used is:

[0085]

[0086] Where, for a positive integer m, the Nussbaum function is positive in X∈(4m-1,4m+1) and negative in X∈(4m+1,4m+3), considering the following two time intervals, where [χ0,χ1]=[χ0,4m+1], [χ1,χ2]=[4m+1,4m+3], χ0>0, and m is a sufficiently large positive integer;

[0087] The following inequality is satisfied:

[0088]

[0089] definition

[0090]

[0091] Depend on

[0092]

[0093] Where l1=4m+1-χ0>0. N(χ)≤0 and

[0094]

[0095] where Ψ∈(0,1);

[0096] get:

[0097]

[0098] in l3=2Ψ>0

[0099] In summary, we can get:

[0100]

[0101] Among them, l2=2Ψcos(πΨ / 2)>0, Ψ∈(0,1), l3=2Ψ>0

[0102] χ and is bounded, and we end up with

[0103]

[0104] Thus:

[0105] |z1|≤δ1,|x2|≤δ2

[0106] Therefore, the regulation errors x1 and z2 are made arbitrarily small by adjusting the control parameters δ1 and δ2.

[0107] Beneficial effects of the present invention:

[0108] (1) The present invention is aimed at a class of nonlinear systems with parameter uncertainty, takes into account the impact of injection and deception attacks on the system, and proposes an adaptive control scheme to make the convergence radius of all outputs of the system as small as possible. The present invention can handle more complex nonlinear systems.

[0109] (2) The present invention uses two functions h to solve the problem of time-varying unknown parameters in the system. i (z i ) and f i (z i ), so that the norm of the time-varying unknown parameter θ(t) can be estimated.

[0110] (3) The present invention introduces an adaptive feedback control scheme based on the Lyapunov function to address the time-varying parameters and unknown control direction problems caused by injection attacks and deception attacks. For attacks on unknown actuators, the Nussbaum function method is used to deal with the time-varying unknown control direction problem. The present invention proposes a new feedback control scheme that uses a new type of Lyapunov function to address the problem of non-integrable residual terms in the original Lyapunov function.

[0111] (4) The adaptive control scheme proposed by the present invention can maintain the stability of the system under attack and make the adjustment error as small as possible. This method can make the adjustment error of the system as small as possible by adjusting the control parameters, thereby improving the control performance and control accuracy of the system. BRIEF DESCRIPTION OF THE DRAWINGS

[0112] Figure 1 It is a schematic diagram of the sensors and actuators of the system provided by the embodiment of the present invention when they are subjected to injection and deception attacks by an adversary.

[0113] Figure 2 This is a diagram of the system status simulation results of Example 1 of the present invention.

[0114] Figure 3 4 is a diagram of parameter estimation simulation results of Example 1 of the present invention.

[0115] Figure 4 This is a diagram of the system state simulation results of the robot manipulator system model of Example 2 of the present invention.

[0116] Figure 5 It is a diagram of the parameter estimation simulation results of the robot manipulator system model of Example 2 of the present invention.

[0117] Figure 6 It is a diagram of the parameter estimation simulation results of the robot manipulator system model of Example 2 of the present invention.

[0118] Figure 7 This is a diagram of the system state simulation results of the single-arm manipulator system of Example 3 of the present invention.

[0119] Figure 8 This is a diagram of parameter estimation simulation results of the single-arm manipulator system of Example 3 of the present invention.

[0120] Fig. 9 4 is a diagram of the system state simulation results of the ship motion model of Example 4 of the present invention.

[0121] Fig.10 4 is a control input simulation result diagram of the ship motion model of embodiment 4 of the present invention.

[0122] Fig.114 is a diagram of the system state simulation result of the underwater robot model of Example 5 of the present invention.

[0123] Fig.12 4 is a diagram of the parameter estimation simulation results of the underwater robot model according to Example 5 of the present invention. DETAILED DESCRIPTION

[0124] The present invention will be further described in detail below in conjunction with the accompanying drawings.

[0125] The method for adaptive control of a cyber-physical system against injection and deception attacks comprises the following steps;

[0126] In the present invention, the following two assumptions are introduced for subsequent proof.

[0127] Assumption 1: For the attack signal w(t), w(t) = -1. In addition, there are two unknown and positive constants. λ0, so that

[0128] Assumption 2: For the time-varying gain b(t), there are two unknown constants and So that the following inequality is always satisfied:

[0129]

[0130] In the present invention, assumption 1 is reasonable because if w(t)=-1, it means that the state is completely canceled and no signal can be used for feedback control; in this case, the system is uncontrollable; assumption 2 means that the control system does not have a singularity problem.

[0131] In this invention, two lemmas are introduced to facilitate control design;

[0132] Lemma 1: For any continuous function There always exists α(x)>0 and β(y)>0 such that

[0133] |γ(x,y)|≤α(x)β(y)

[0134] By applying Lemma 1, there exists an unknown constant and a known smooth function ψ i (x1,x2)≥1, such that

[0135]

[0136] and

[0137]

[0138] In addition, there is an unknown positive constant and a known smooth function ω(x)≥1, such that

[0139]

[0140] Lemma 2: For a positive unbounded Lyapunov function V(t), the following inequality is satisfied:

[0141]

[0142] where b≠0, its sign is also unknown and c is an unknown constant for t∈[0,∞], then for t∈[0,∞], V(t), χ and is bounded.

[0143] S1: Construct a control system model under the network-physical framework; In order to construct the control system model under the network-physical framework, this step introduces a second-order strict feedback nonlinear system with parameter uncertainty and gives the corresponding parameter definition. The system model and parameter definitions are:

[0144]

[0145] in, They represent the state, control input and output of the system respectively. represents the uncertain system parameters, φ i : is a nonlinear smooth function, i=1,2;

[0146] S2: Based on the system model proposed in S1, when the sensors and actuators of the system are subjected to injection and deception attacks by the adversary, the actuator attack is defined as:

[0147]

[0148] Where u is the control to be designed, is the unknown time-varying gain, is a nonlinear function, b(t) is a time-varying unknown parameter with an unknown sign;

[0149] S3: Based on S1 and S2, the real state of the system when there is a sensor attack on the system and is unknown, the sensor attack is defined as:

[0150]

[0151] where i = 1, 2, w(t) is the unknown time-varying gain, is the signal injected into the sensor, so the output of the sensor is The actual status signal Different, define λ(t)=1+w(t), then we have

[0152] S4: system model, actuator attack definition, and sensor attack definition obtained based on S1, S2, and S3 respectively;

[0153] The S4 is specifically:

[0154] The system model under network attack is rewritten as:

[0155]

[0156] S5: Based on the system model under network attack proposed in step S4, in order to solve the control problem of the system, the BackStepping method is used to obtain the adaptive control law u(t) of the system; in the presence of nonlinear sensor and actuator attacks, a series of special nonlinear feedback control signals are introduced to deal with the control difficulties caused by unknown time-varying gains, and the closed-loop system stability is established through the Lyapunov function. This step constructs the system model under network attack to meet the conditions of Lyapunov stability.

[0157] S6: Based on step S5, since the control direction is completely likely to become uncertain under a network attack, the Nussbaum technology processing method is adopted to design the controller by introducing the Nussbaum even function and its variable derivatives.

[0158] This step proves that under Assumptions 1 and 2, all closed-loop signals in the system under cyber attack are globally bounded, and the regulation error can be made arbitrarily small by adjusting the control parameters.

[0159] The step S5 is specifically as follows:

[0160] S51: Let the tracking variable of the system state x1 be z1, satisfying z1=x1.

[0161] According to the parameter definitions in steps S1, S2, S3 and S4, the time derivative of z1 is obtained: +-

[0162]

[0163] Let x2 = α + z2, where α is the virtual control and z2 is the virtual control error, then:

[0164]

[0165] To handle unknown time-varying gains and λθ1(t), the following nonlinear function is introduced:

[0166]

[0167] where i = 1, 2, and δ i is a positive constant to be given. In addition, h i (z i ) and (|z i |-δ i ) 2 f i It is C 1 function, and has:

[0168]

[0169] Consider the following Lyapunov function:

[0170]

[0171] Its time derivative is:

[0172]

[0173] where Θ1 is is the boundary of , Θ2 is the boundary of λθ1(t), and σ is a small positive constant. The virtual control α is designed as

[0174]

[0175] in

[0176]

[0177] Θ=[Θ1,Θ2] T

[0178] and is an estimate of Θ, represents the estimation error;

[0179] Defining the Lyapunov function

[0180]

[0181] Defining parameter estimators

[0182]

[0183] Then there are:

[0184]

[0185] S52: Find the time derivative of z2:

[0186]

[0187] Consider the following Lyapunov function:

[0188]

[0189] Taking its time derivative, we have:

[0190]

[0191] Assume that the upper bounds of v(t) and θ2(t) are

[0192]

[0193] in

[0194] The design of controller u is:

[0195]

[0196] in is an estimate of Ξ and satisfies:

[0197]

[0198] definition

[0199]

[0200] Consider the following Lyapunov function:

[0201]

[0202] Taking its time derivative, we have:

[0203]

[0204] Let δ1≥δ2, we can get:

[0205]

[0206] The above formula is always established, and we get:

[0207]

[0208] Through step S5, we can get:

[0209]

[0210] Through the above formula, the conditions for the system to satisfy Lyapunov stability under network attack are obtained.

[0211] Step S6 further deduces on the basis of step S5 that all signals in the closed-loop system are globally bounded, and the regulation error can be made arbitrarily small by adjusting the control parameters.

[0212] In step S6, the Nussbaum function used is:

[0213]

[0214] Here, for a positive integer m, the Nussbaum function is positive in χ∈(4m-1,4m+1) and negative in χ∈(4m+1,4m+3). Consider the following two time intervals, where [χ0,χ1]=[χ0,4m+1], [X1,X2]=[4m+1,4m+3], χ0>0, and m is a sufficiently large positive integer.

[0215] The following inequality is satisfied:

[0216]

[0217] definition

[0218]

[0219] Depend on

[0220]

[0221] Where l1=4m+1-χ0>0. N(χ)≤0 and

[0222]

[0223] where Ψ∈(0,1).

[0224] get:

[0225]

[0226] in l3=2Ψ>0

[0227] In summary, we can get:

[0228]

[0229] Among them, l2=2Ψcos(πΨ / 2)>0, Ψ∈(0,1), l3=2Ψ>0

[0230] According to Lemma 2, we can get: is bounded, and we end up with

[0231]

[0232] Thus:

[0233] |z1|≤δ1,|z2|≤δ2

[0234] Therefore, the adjustment errors z1 and z2 can be made arbitrarily small by adjusting the control parameters δ1 and δ2.

[0235] Embodiment (I) considers a second-order strict feedback nonlinear system, adopts the adaptive control scheme designed in the present invention, and proves the effectiveness of the proposed control scheme through numerical simulation;

[0236] Embodiments (two), (three), (four) and (five) respectively selected different actual system models and adopted the adaptive control scheme designed in the present invention, and further proved the applicability of the present invention through numerical simulation.

[0237] The embodiments of the present invention are as follows:

[0238] (i) In order to verify the effectiveness of the proposed control scheme, the following simulations are carried out.

[0239] The second-order strict feedback nonlinear system model is as follows:

[0240]

[0241] The unknown system parameters are designed to be θ1(t)=4+sin(t) and θ2=1+4cos(2t). The initial values ​​of i=1,2 are Ξ1(0)=2, Ξ1(0)=3, Ξ1(0)=1, Ξ1(0)=1,

[0242] The control parameter is designed as δ i =0.1,i=1,2. In addition, the injection attack and deception attack are w(t)=2+sin(t)cos(2t), v(t)=2, b(t)=1+0.1sin(5t),

[0243] like Figure 1 As shown, the sensors and actuators of the system are subjected to injection and deception attacks by attackers. The system model corresponds to S1 in the present invention, the actuator attack corresponds to S2 in the present invention, the sensor attack corresponds to S3 in the present invention, and adaptive controllers are designed for S4, S5, and S6 to ensure the stability of the system under network attacks.

[0244] The system state and parameter estimation are respectively Figure 2 , 3 As shown in the attached Figure 2 , 3 It can be seen that in the presence of injection attacks and spoofing attacks, the closed-loop signal is bounded and the regulation error is arbitrarily small.

[0245] (ii) Consider the robot manipulator system:

[0246]

[0247] Among them, q and are the rotation angle and angular velocity of the robot arm, R represents the moment of inertia of the servo motor, D represents the system attenuation coefficient, M represents the mass of the connecting rod, g represents the acceleration of gravity, l represents the length from the connection to the center of gravity, and u represents the control torque. Take R=1, D=2+sin(t), Mgl=10.

[0248] Let x1 = q and Then the system model can be expressed as:

[0249]

[0250] The injection attack and spoofing attack are w(t)=2+sin(t)cos(2t), v(t)=2, b(t)=1+0.1sin(5t),

[0251] The simulation results obtained by the adaptive control scheme designed by the above steps of the invention are as follows: Figure 4-6 shown.

[0252] like Figure 4 As shown, under the action of the given control signal u, the system state eventually reaches a steady state;

[0253] like Figure 5 As shown, the adaptive control scheme designed according to the steps of the invention content, the estimated curves of parameters Ξ1, Ξ2, Ξ3, Ξ4 are respectively given in the figure, and it can be seen from the figure that the closed-loop signal Ξ is bounded;

[0254] like Figure 6 As shown, the adaptive control scheme designed according to the steps of the invention content gives the estimated curves of parameters Θ1 and Θ2 respectively. It can be seen from the figure that the closed-loop signal Θ is bounded.

[0255] (III) Consider a set of single-arm manipulator systems:

[0256] Select a group of single-arm manipulators, whose dynamics can be expressed as

[0257]

[0258] Among them, θ i , and denote the angular position, velocity and acceleration of the connecting rod, respectively. is the moment of inertia, m i is the mass of the robot, l i is the distance between the center of mass and the center of rotation of the connecting rod, D i is the friction coefficient, N i =m i gl i is the gravity term, g is the gravity coefficient, u i is the control signal. Define x i,1 =θ i , Then the robot model can be expressed as

[0259]

[0260] The physical parameters of the system are chosen as m i =1.5kg, g i =9.8m / s 2 , l i =0.5m, D i =2. The injection attack and spoofing attack are w(t)=2+sin(t)cos(2t), ν(t)=2, b(t)=1+0.1sin(5t),

[0261] The simulation results obtained by the adaptive control scheme designed by the above steps of the invention are as follows: Figure 7 , 8 shown.

[0262] like Figure 7 As shown, under the action of the given control signal u, the system state eventually reaches a steady state;

[0263] like Figure 8 As shown, the adaptive control scheme designed according to the steps of the invention content, the estimated curves of parameters Ξ1, Ξ2, Ξ3, Ξ4 are respectively given in the figure, and it can be seen from the figure that the closed-loop signal Ξ is bounded;

[0264] (IV) Considering the mathematical model of ship motion

[0265]

[0266] Among them, ψ is the heading angle, δ is the rudder angle, T and α are the ship model parameters, k is the system gain, and d is the external interference.

[0267] Select the state variable x1 = ψ, u=δ, then the state equation of the ship's motion can be obtained as

[0268]

[0269] y=x1,

[0270] In the formula, The injection attack and deception attack are w(t)=2+sin(t)cos(2t), v(t)=2, b(t)=1+0.1sin(5t), The adaptive control scheme designed by the above steps of the invention obtains the system state and control input simulation results as shown in the following figure: Fig. 9 , 10 shown.

[0271] like Fig. 9 As shown, under the action of the given control signal u, the system state eventually reaches a steady state;

[0272] like Fig.10 As shown, the variation curve of the control input u of the system is given.

[0273] (V) The dynamic model of the underwater robot can be expressed as:

[0274]

[0275] Among them, m is the mass of the underwater robot, c is the damping coefficient, k is the stiffness coefficient of the underwater robot, x is the position of the underwater robot, and u is the control input force.

[0276] Let x1 = x, Then there is

[0277]

[0278] Define c = 5 (1 + cos 2x), k = 2 + sinx, m = 5. The injection attack and spoofing attack are w (t) = 2 + sin (t) cos (2t), v (t) = 2, b (t) = 1 + 0.1 sin (5t), The simulation results obtained by the adaptive control scheme designed by the above steps of the invention are as follows: Fig.12 shown.

[0279] like Fig.11 As shown, under the action of the given control signal u, the system state eventually reaches a steady state;

[0280] like Fig.12As shown, the adaptive control scheme designed according to the steps of the invention content, the figure gives the estimated curves of parameters Ξ1, Ξ2, Ξ3, Ξ4 respectively, and it can be seen from the figure that the closed-loop signal Ξ is bounded.

Claims

1. Adaptive control method for cyber-physical systems against injection and spoofing attacks, characterized in that: The steps include: S1: Construct a control system model under the cyber-physical framework; S2: Based on the control system model, when the actuator of the system is subjected to injection and deception attacks by the adversary, an attack definition on the actuator is made; S3: When the system's sensors are attacked by injection and deception attacks, the sensor attack definition; S4: rewriting the control system model under the network attack based on the control system model, the actuator attack definition and the sensor attack definition; S5: Based on the rewritten system model, the BackStepping method is used to obtain the adaptive control law u of the system; S6: Based on the adaptive control law u, it is deduced that all signals in the closed-loop system are globally bounded. A processing method based on Nussbaum technology is adopted. By introducing Nussbaum even functions and their variable derivatives, a controller is designed. When the system is subjected to injection and deception attacks, the control parameters are adjusted to make the adjustment error arbitrarily small.

2. The method for adaptive control of cyber-physical systems against injection and spoofing attacks according to claim 1, characterized in that: The S1 is specifically: The system model and the parameters in the model are defined as: in, Represent the real state vectors of the cyber-physical system in two different dimensions, Indicates the status of the system. represents the control input, Indicates the control output, represents uncertain system parameters, is a nonlinear smooth function, i=1,2; Represent the real state vector of the cyber-physical system The first derivative of .

3. The method for adaptive control of cyber-physical systems against injection and spoofing attacks according to claim 2, characterized in that: The S2 is specifically: An actuator attack is defined as: Where u is the control to be designed, is the unknown time-varying gain, is a nonlinear function, b(t) is a time-varying unknown parameter with an unknown sign; The S3 is specifically: When the system is attacked by sensors, the real state of the system and is unknown, sensor attacks are defined as: where i = 1, 2, w(t) is the unknown time-varying gain, is the signal injected into the sensor, and the output of the sensor The actual status signal Different, define λ(t)=1+w(t), then we have 4. The method for adaptive control of a cyber-physical system against injection and spoofing attacks according to claim 3, characterized in that: The S4 is specifically: The system model under network attack is rewritten as:

5. The method for adaptive control of a cyber-physical system against injection and spoofing attacks according to claim 4, characterized in that: The S5 is specifically: The design of controller u is: in is an estimate of Ξ and satisfies: definition Consider the following Lyapunov function: Taking its time derivative, we have: Let δ1≥δ2, we get: The above formula is always established, and we get: Through S5, we get: Through the above formula, the conditions for the system to satisfy Lyapunov stability under network attack are obtained.

6. The method for adaptive control of a cyber-physical system against injection and spoofing attacks according to claim 5, characterized in that: The S6 is specifically: The Nussbaum function used is: The following inequality is satisfied: definition Depend on get: In summary, we can get: χ and is bounded, and we end up with Thus: |z1|≤δ1,|z2|≤δ2 The regulation errors z1 and z2 can be made arbitrarily small by adjusting the control parameters δ1 and δ2.

7. A model for implementing the method according to any one of claims 1 to 6, characterized in that: Robot Manipulator System: Among them, q and are the rotation angle and angular velocity of the robot arm, R represents the moment of inertia of the servo motor, D represents the system attenuation coefficient, M represents the mass of the connecting rod, g represents the acceleration of gravity, l represents the length from the connection to the center of gravity, and u represents the control torque; Let x1 = q and The system model is expressed as: The injection attack and deception attack are w(t)=2+sin(t)cos(2t), ν(t)=2, b(t)=1+0.1sin(5t), 8. A model for implementing the method according to any one of claims 1 to 6, characterized in that: Consider a system of single-arm manipulators: Select a group of single-arm manipulators, whose dynamic representation is Among them, θ i , and denote the angular position, velocity and acceleration of the connecting rod, respectively. is the moment of inertia, m i is the mass of the robot, l i is the distance between the center of mass and the center of rotation of the connecting rod, D i is the friction coefficient, N i =m i gl i is the gravity term, g is the gravity coefficient, u i is the control signal, define x i,1 =θ i , The robot model is expressed as The injection attack and deception attack are w(t)=2+sin(t)cos(2t), ν(t)=2, b(t)=1+0.1sin(5t), 9. A model for implementing the method according to any one of claims 1 to 6, characterized in that: Considering the mathematical model of ship motion Among them, ψ is the heading angle, δ is the rudder angle, T and α are the ship model parameters, k is the system gain, and d is the external interference; Select the state variable x1 = ψ, u=δ, then the state equation of the ship's motion is y = x1; In the formula, The injection attack and deception attack are w(t)=2+sin(t)cos(2t), ν(t)=2, b(t)=1+0.1sin(5t), 10. A model for implementing the method according to any one of claims 1 to 6, characterized in that: The dynamic model of the underwater robot is expressed as: Among them, m is the mass of the underwater robot, c is the damping coefficient, k is the stiffness coefficient of the underwater robot, x is the position of the underwater robot, and u is the control input force; Let x1 = x, Then there is Define c = 5(1+cos 2x), k = 2+sinx, injection attack and spoofing attack are w(t) = 2+sin(t)cos(2t), v(t) = 2, b(t) = 1+0.1sin(5t),

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