An Adaptive Control Method for Cyber-Physical Systems Against Injection and Deception Attacks

Abstract

An adaptive control method for cyber-physical systems (CPS) subjected to injection and deception attacks includes the following steps: S1: Constructing a control system model under a cyber-physical framework; S2: Defining actuator attacks when the system's sensors and actuators are subjected to adversary injection and deception attacks; S3: Defining sensor attacks when the system is subjected to sensor attacks; S4: Rewriting the system model under cyberattacks; S5: Based on the rewritten system model, obtaining the adaptive control law u using the BackStepping method; S6: Further deriving that all signals in the closed-loop system are globally bounded based on the adaptive control law u in S5, and designing a controller by introducing Nussbaum even functions and their variable derivatives. When the system is subjected to injection and deception attacks, the control parameters are adjusted to make the adjustment error arbitrarily small. This invention can ensure that the adjustment error can be arbitrarily small under injection and deception attacks by adjusting the control parameters.

Description

Technical Field

[0001] This invention relates to the field of cyber-physical system control methods, specifically to an adaptive control method for cyber-physical systems against injection and deception attacks. Background Technology

[0002] A cyber-physical system (CPS) is a complex system that tightly integrates information systems with physical systems. It achieves real-time control, monitoring, and optimization of the physical world through embedded systems and network technologies.

[0003] With the development of network technology, cyber-physical systems (CPS) are increasingly widely used in transportation systems, unmanned factories, power systems, and other fields, making their operational security crucial. Control systems within the cyber-physical framework play a vital role in critical infrastructure and are potential targets for cyberattacks. Cyberattacks can be broadly categorized into three types: denial-of-service (DoS) attacks, replay attacks, and injection / spoofing attacks. In a DoS attack, attackers can overwhelm the communication network by sending a massive amount of data, preventing devices from sending or receiving information from sensors or actuators, thus causing the control system to malfunction. A replay attack is an attack strategy that maliciously repeats the sending and receiving of the same data over a period of time. Unlike DoS attacks, replay attacks can be conducted covertly. Injection / spoofing attacks involve modifying data from sensors and actuators during transmission, causing users to receive false data. All three types of attacks can lead to control system failure and even disaster. Therefore, addressing attacks on control systems is receiving increasing attention.

[0004] In practical applications, control systems within a cyber-physical framework need to acquire data from sensors and send control signals to the system via communication networks. Communication networks provide a convenient means for attacks, threats, and the extraction of information from sensor transmissions within these networks. Therefore, addressing control problems within a cyber-physical framework under different types of attacks is a critical issue.

[0005] Current research has yielded many results related to network attack problems. For example, the paper "State Estimation under False Data Injection Attacks: Security Analysis and System Protection" considers the state estimation problem of network control systems under injection attacks and proposes a system protection scheme. This scheme requires only a few (not all) communication channels to be protected against injection attacks. However, a limitation of this research is that it focuses on linear systems, while most real-world control systems are nonlinear, thus limiting the proposed method.

[0006] The paper "An adaptive control architecture for mitigating sensor and actuator attacks in cyber-physical systems" investigates the adaptive control problem for a class of Lipschtz nonlinear systems subjected to injection and spoofing attacks. The proposed adaptive control method guarantees the uniform eventual boundedness of the closed-loop system even under simultaneous sensor and actuator attacks. However, the model addressed by this method is relatively simple and cannot be directly generalized to nonlinear systems with uncertainties.

[0007] In summary, the shortcomings of existing technologies are that the models they focus on are often linear systems or relatively simple nonlinear systems. There is little research on the cybersecurity issues of nonlinear system models in cyber-physical systems among the proposed control schemes, and they cannot be directly extended to nonlinear systems with uncertainties. Summary of the Invention

[0008] To overcome the above technical problems, the present invention aims to provide an adaptive control method for cyber-physical systems against injection and deception attacks. This control method can adjust control parameters to ensure that the adjustment error can be arbitrarily small when subjected to injection and deception attacks. It also introduces a series of special nonlinear feedback signals to deal with the control difficulties caused by unknown time-varying gain, thereby achieving better security control performance. This enables the cyber-physical control system to adapt to various uncertainties and cyber attacks, and achieve high-performance, safe and stable control.

[0009] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0010] An adaptive control method for cyber-physical systems against injection and deception attacks includes the following steps;

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

[0012] S2: Based on the system model, when the system's executor is subjected to adversary injection and deception attacks, the attack definition for the executor is as follows:

[0013] S3: Definition of injection and spoofing attacks when the system's sensors are under attack;

[0014] S4: Based on the aforementioned control system model, actuator attack definition, and sensor attack definition, rewrite the control system model under network attack;

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

[0016] S6: Based on the adaptive control law u, it is deduced that all signals in the closed-loop system are globally bounded. Using a processing method based on Nussbaum technology, a controller is designed by introducing Nussbaum even functions and their variable derivatives. 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 refers to the system model and the parameters within the model, defined as follows:

[0018]

[0019] in,, These represent the real state vectors of the network physical system in two different dimensions. Indicates the state of the system. Indicates control input, Indicates control output. φ represents an uncertain system parameter. i : It is a nonlinear smooth function, i = 1, 2; These represent the actual state vectors of the network physical system. The first derivative.

[0020] Specifically, S2 is:

[0021] An executor attack is defined as:

[0022]

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

[0024] Specifically, S3 is:

[0025] The true state of the system when a sensor attack occurs. and It is unknown, and the sensor attack is defined as:

[0026]

[0027] Where i = 1, 2, and w(t) is the unknown time-varying gain. It is the signal injected into the sensor, therefore the output of the sensor is injected. With actual state signal Different, define λ(t) = 1 + w(t), then we have

[0028] Specifically, S4 is:

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

[0030]

[0031] Step S5 specifically involves:

[0032] S51: Let z1 = x1. According to the parameter definitions in S1, S2, S3, and S4, find the time derivative of z1. We have:

[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 gain And λθ1(t), the following nonlinear function is introduced:

[0037]

[0038] Where i = 1, 2, and δ i The given positive constant is h. i (x i ) and (|z i |-δ i ) 2 f i It is C 1 The function has:

[0039]

[0040] Consider the following Lyapunov function:

[0041]

[0042] Its time derivative is:

[0043]

[0044] Where Θ1 is The boundary, 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 It is an estimate of Θ. Indicates the estimation error;

[0050] Define Lyapunov functions

[0051]

[0052] Define parameter estimator

[0053]

[0054] Then there is:

[0055]

[0056] S52: Find the time derivative with respect to z2:

[0057]

[0058] Consider the following Lyapunov function:

[0059]

[0060] Taking its time derivative, we have:

[0061]

[0062] Let the upper bounds of v(t) and θ2(t) be respectively and So there are

[0063]

[0064] in

[0065] The controller u is designed as follows:

[0066]

[0067] in

[0068] It 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, then we get:

[0077]

[0078] The above formula always holds true, so we get:

[0079]

[0080] We can obtain the following from S5:

[0081]

[0082] The above formula yields the conditions for Lyapunov stability of the system under network attacks.

[0083] Specifically, S6 is:

[0084] The Nussbaum function used is:

[0085]

[0086] For a positive integer m, the Nussbaum function is positive in X∈(4m-1,4m+1) and negative in X∈(4m+1,4m+3). Consider 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 inequalities must be satisfied:

[0088]

[0089] definition

[0090]

[0091] Depend on

[0092]

[0093] Where l1 = 4m + 1 - χ0 > 0. For N(χ)≤0 and

[0094]

[0095] Where Ψ∈(0,1);

[0096] get:

[0097]

[0098] in l3=2Ψ>0

[0099] In conclusion:

[0100]

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

[0102] χ and It is bounded, and ultimately obtains...

[0103]

[0104] Therefore:

[0105] |z1|≤δ1,|x2|≤δ2

[0106] Therefore, the adjustment errors x1 and z2 can be arbitrarily reduced by adjusting the control parameters δ1 and δ2.

[0107] The beneficial effects of this invention are:

[0108] (1) This invention addresses a class of nonlinear systems with parameter uncertainties, considering the impact of injection and deception attacks on the system, and proposes an adaptive control scheme to minimize the convergence radius of all system outputs. This invention can handle more complex nonlinear systems.

[0109] (2) To address the problem of time-varying unknown parameters in the system, this invention employs two functions h i (z i ) and f i (z i This allows the norm of the time-varying unknown parameter θ(t) to be estimated.

[0110] (3) To address the time-varying parameters and unknown control direction problems caused by injection attacks and deception attacks, this invention introduces an adaptive feedback control scheme based on the Lyapunov function. For attacks involving unknown actuators, the Nussbaum function method is used to handle the time-varying unknown control direction problem. This invention proposes a new feedback control scheme that employs a novel Lyapunov function to address the non-integrable residual term problem present in the original Lyapunov function.

[0111] (4) The adaptive control scheme proposed in this invention can maintain the stability of the system under attack and make the adjustment error arbitrarily small. This method can make the adjustment error of the system arbitrarily small by adjusting the control parameters, thereby improving the control performance and control accuracy of the system. Attached Figure Description

[0112] Figure 1 This is a schematic diagram of the sensor and actuator of the system provided in the embodiment of the present invention when subjected to adversary injection and deception attacks.

[0113] Figure 2 This is a simulation result diagram of the system state in Embodiment 1 of the present invention.

[0114] Figure 3 This is a simulation result diagram of parameter estimation in Embodiment 1 of the present invention.

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

[0116] Figure 5 This is a simulation result diagram of parameter estimation for the robot manipulator system model in Embodiment 2 of the present invention.

[0117] Figure 6 This is a simulation result diagram of parameter estimation for the robot manipulator system model in Embodiment 2 of the present invention.

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

[0119] Figure 8 This is a simulation result diagram of parameter estimation for the single-arm robotic arm system in Embodiment 3 of the present invention.

[0120] Figure 9 This is a simulation result diagram of the system state of the ship motion model in Embodiment 4 of the present invention.

[0121] Figure 10 This is a simulation result diagram of the control input of the ship motion model in Embodiment 4 of the present invention.

[0122] Figure 11This is a simulation result diagram of the system state of the underwater robot model in Embodiment 5 of the present invention.

[0123] Figure 12 This is a simulation result diagram of parameter estimation for the underwater robot model in Embodiment 5 of the present invention. Detailed Implementation

[0124] The present invention will now be described in further detail with reference to the accompanying drawings.

[0125] An adaptive control method for cyber-physical systems against injection and deception attacks includes the following steps;

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

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

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

[0129]

[0130] In this invention, Assumption 1 is reasonable because if w(t) = -1, it means that the state is completely canceled and no signal is available 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 exist 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 exists an unknown positive constant. And a known smooth function ω(x)≥1, such that

[0139]

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

[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 It is bounded.

[0143] S1: A control system model under a cyber-physical framework was constructed. This step, to construct the control system model under a cyber-physical framework, introduces a class of second-order strictly feedback nonlinear systems with parameter uncertainties and provides the corresponding parameter definitions. The system model and parameter definitions are as follows:

[0144]

[0145] in, These represent the system's state, control input, and output, respectively. φ represents an uncertain system parameter. i : It is a nonlinear smooth function, i = 1, 2;

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

[0147]

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

[0149] S3: Based on S1 and S2, the true state of the system when a sensor attack occurs. and It is unknown, and the sensor attack is defined as:

[0150]

[0151] Where i = 1, 2, and w(t) is the unknown time-varying gain. It is the signal injected into the sensor, therefore the output of the sensor is injected. With actual state signal Different, define λ(t) = 1 + w(t), then we have

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

[0153] Specifically, S4 is:

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

[0155]

[0156] S5: Based on the system model under network attack proposed in step S4, to solve the system control problem, the BackStepping method is adopted to obtain the adaptive control law u(t). In the presence of nonlinear sensor and actuator attacks, a series of special nonlinear feedback control signals are introduced to handle the control difficulties caused by the unknown time-varying gain, and the closed-loop system stability is established using the Lyapunov function. This step constructs a system model under network attack that satisfies the Lyapunov stability condition.

[0157] S6: Based on step S5, since the control direction may become completely uncertain under network attacks, the Nussbaum technique is adopted to design the controller by introducing Nussbaum even functions and their variable derivatives.

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

[0159] Step S5 specifically involves:

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

[0161] Based on the parameter definitions in steps S1, S2, S3, and S4, the time derivative with respect to z1 is obtained as follows:

[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 gain And λθ1(t), the following nonlinear function is introduced:

[0166]

[0167] Where i = 1, 2, and δ i The given positive constant is h. i (z i ) and (|z i |-δ i ) 2 f i It is C 1 The function has:

[0168]

[0169] Consider the following Lyapunov function:

[0170]

[0171] Its time derivative is:

[0172]

[0173] Where Θ1 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 It is an estimate of Θ. Indicates the estimation error;

[0179] Define Lyapunov functions

[0180]

[0181] Define parameter estimator

[0182]

[0183] Then there is:

[0184]

[0185] S52: Find the time derivative with respect to z2:

[0186]

[0187] Consider the following Lyapunov function:

[0188]

[0189] Taking its time derivative, we have:

[0190]

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

[0192]

[0193] in

[0194] The controller u is designed as follows:

[0195]

[0196] in It 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 obtain:

[0205]

[0206] The above formula always holds true, so we get:

[0207]

[0208] We can obtain the following through step S5:

[0209]

[0210] The above formula yields the conditions for Lyapunov stability of the system under network attacks.

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

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

[0213]

[0214] 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 inequalities must be satisfied:

[0216]

[0217] definition

[0218]

[0219] Depend on

[0220]

[0221] Where l1 = 4m + 1 - χ0 > 0. For N(χ)≤0 and

[0222]

[0223] Where Ψ∈(0,1).

[0224] get:

[0225]

[0226] in l3=2Ψ>0

[0227] In conclusion:

[0228]

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

[0230] According to Lemma 2, we have: χ and It is bounded, and ultimately obtains...

[0231]

[0232] Therefore:

[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] Example (1) considers a class of second-order strictly feedback nonlinear systems and adopts the adaptive control scheme designed in this invention. The effectiveness of the proposed control scheme is proved by numerical simulation.

[0236] Examples (ii), (iii), (iv), and (v) respectively selected different actual system models and adopted the adaptive control scheme designed in this invention. The applicability of this invention was further demonstrated through numerical simulation.

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

[0238] (a) To verify the effectiveness of the proposed control scheme, the following simulations were performed.

[0239] The model of a second-order strictly feedback nonlinear system is as follows:

[0240]

[0241] The unknown system parameters are designed as θ1(t) = 4 + sin(t) and θ2 = 1 + 4cos(2t). The initial values ​​of i = 1 and 2 are respectively 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. Furthermore, the injection attack and the deception attack are w(t)=2+sin(t)cos(2t), v(t)=2, b(t)=1+0.1sin(5t), respectively.

[0243] like Figure 1 As shown, the system's sensors and actuators are subjected to injection and spoofing attacks by attackers. The system model corresponds to S1 in this invention, the actuator attack corresponds to S2 in this invention, and the sensor attack corresponds to S3 in this invention. 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 estimates are as follows: Figure 2 , 3 As shown, from the appendix 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 adjustment error is arbitrarily small.

[0245] (ii) Considering the robotic arm system:

[0246]

[0247] Where q and Let R represent the rotation angle and angular velocity of the robotic arm, D represent the system attenuation coefficient, M represent the mass of the link, g represent the gravitational acceleration, l represent the length from the connection point to the center of gravity, and u represent the control torque. Let R = 1, D = 2 + sin(t), and Mgl = 10.

[0248] Let x1 = q and The system model can then be represented as:

[0249]

[0250] The injection attack and the deception attack are respectively 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 through the above-described steps of the invention are as follows: Figure 4-6 As shown.

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

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

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

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

[0256] Select a set of single-arm robotic arms; their dynamics can be represented as follows:

[0257]

[0258] Where, θ i , and These represent the angular position, velocity, and acceleration of the connecting rod, respectively. It is the moment of inertia, m i For the quality of the robotic arm, l i D is the distance between the center of mass and the center of rotation of the connecting rod. i It is the coefficient of friction, N i =m i gl i This is the gravity term, where g is the gravitational coefficient, and u is the gravitational term. i It is a control signal. Define x. i,1 =θ i , The robotic arm model can then be represented as:

[0259]

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

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

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

[0263] like Figure 8 As shown in the figure, the adaptive control scheme designed according to the steps of the invention is illustrated. The estimated curves of parameters Ξ1, Ξ2, Ξ3, and Ξ4 are given in the figure. 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] Where 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 disturbance.

[0267] Choose the state variable x1 = ψ, Given u = δ, the state equation for the ship's motion can be obtained as follows:

[0268]

[0269] y = x1,

[0270] In the formula, The injection attack and the deception attack are respectively w(t)=2+sin(t)cos(2t), v(t)=2, b(t)=1+0.1sin(5t), The adaptive control scheme designed through the above-described steps of the invention yields the following simulation results for the system state and control input: Figure 9 , 10 As shown.

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

[0272] like Figure 10 As shown, the curve of the system's control input u is presented.

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

[0274]

[0275] Where 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 the deception attack are w(t) = 2 + sin(t)cos(2t), v(t) = 2, and b(t) = 1 + 0.1sin(5t), respectively. The simulation results obtained by the adaptive control scheme designed through the above-described steps of the invention are as follows: Figure 12 As shown.

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

[0280] like Figure 12As shown in the figure, the adaptive control scheme designed according to the steps of the invention is illustrated. The estimated curves of parameters Ξ1, Ξ2, Ξ3, and Ξ4 are given in the figure. It can be seen from the figure that the closed-loop signal Ξ is bounded.

Claims

1. An adaptive control method for cyber-physical systems against injection and deception attacks, characterized in that, Includes the following steps; S1: Construct a control system model under a cyber-physical framework; S2: Based on the control system model, when the system's actuators are subjected to adversary injection and deception attacks, the attack definition for the actuators is as follows: S3: Definition of sensor attack when the system's sensors are susceptible to injection and spoofing attacks; S4: Based on the aforementioned control system model, actuator attack definition, and sensor attack definition, rewrite the control system model under network attack; S5: Based on the rewritten system model, the adaptive control law of the system is obtained using the BackStepping method. ; S6: In the adaptive control law Based on this, 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 to adjust the control parameters when the system is subjected to injection and deception attacks, so that the adjustment error can be made arbitrarily small. Specifically, S4 is: The system model under network attack is rewritten as follows: ； These represent the real state vectors of the network physical system in two different dimensions. , These represent the actual state vectors of the network physical system. The first derivative; Specifically, S5 is: controller The design is as follows: in yes The estimate, and satisfies: definition Consider the following Lyapunov function: Taking its time derivative, we have: make ,get: The above formula always holds true, so we get: ； We obtain the following from S5: The above formula yields the conditions for a system to satisfy Lyapunov stability under network attacks. Specifically, S6 is: The Nussbaum function used is: The following inequalities must be satisfied: definition Depend on get: In conclusion: and It is bounded, and ultimately obtains... Therefore: By adjusting the control parameters and This can reduce errors and Arbitrarily small; Indicates uncertain system parameters, It is a nonlinear smooth function. ; , These represent the actual state vectors of the network physical system. The first derivative; in For the control to be designed, For unknown time-varying gain, It is a nonlinear function.

2. The adaptive control method for cyber-physical systems against injection and deception attacks according to claim 1, characterized in that, Specifically, S1 is: The system model and the parameters in the model are defined as follows: in, These represent the real state vectors of the network physical system in two different dimensions. Indicates the state of the system. Indicates control input, This indicates the control output.

3. The adaptive control method for cyber-physical systems against injection and deception attacks according to claim 2, characterized in that, Specifically, S2 is: An executor attack is defined as: It is a time-varying unknown parameter with an unknown sign; Specifically, S3 is: The true state of the system when a sensor attack occurs. and It is unknown; a sensor attack is defined as: in , It is an unknown time-varying gain. It is the signal injected into the sensor, and the output of the sensor. With actual state signal Different, definition So there are .

4. A model for implementing the method according to any one of claims 1-3, characterized in that, Robotic manipulator system: ， in, and These are the robotic arm's rotation angle and angular velocity, respectively. This represents the moment of inertia of the servo motor. Represents the system attenuation coefficient. Indicates the mass of the connecting rod. Represents gravitational acceleration. The length from the connection point to the center of gravity. It is the control torque; make and The system model is then represented as: , Injection attacks and deception attacks are respectively , , , .

5. A model for implementing the method according to any one of claims 1-3, characterized in that, Consider a set of single-arm robotic systems: Select a group of single-arm robotic arms, whose dynamic representation is as follows: in, , and These represent the angular position, velocity, and acceleration of the connecting rod, respectively. It is the moment of inertia. For the quality of the robotic arm, It is the distance between the center of mass and the center of rotation of the connecting rod. It is the coefficient of friction. It is a gravity term. It is the gravity coefficient. It is a control signal, defined , Then the robot model is represented as Injection attacks and deception attacks are respectively , , , .

6. A model for implementing the method according to any one of claims 1-3, characterized in that, Consider the mathematical model of ship motion in, For heading angle, As the rudder angle, , For ship model parameters, For system gain, External interference; Selecting state variables , , Then the state equation of the ship's motion is obtained as follows: ， ； In the formula, , Injection attacks and deception attacks are respectively , , , .

7. A model for implementing the method according to any one of claims 1-3, characterized in that, The dynamic model of the underwater robot is represented as follows: ， in, It's about the quality of the underwater robot. It is the damping coefficient. It is the stiffness coefficient of the underwater robot. That's the location of the underwater robot. It controls the input force; make Then there is ， definition , Injection attacks and deception attacks are respectively , , , .

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