Adaptive sliding mode control method for a swing robot against false injection attacks

Abstract

The present invention discloses an adaptive sliding mode control method for a sway robot to resist false injection attacks, belonging to the technical field of sway robot control. The method comprises obtaining the initial trajectory tracking error equation of the sway robot based on the robot's dynamic model, a tracking trajectory reference signal, and the trajectory the sway robot needs to track; simulating the actuator attack signal using a neural network, obtaining the weight estimate of the neural network through a linear filter based on the Lyapunov stability theorem, and determining the actuator attack signal; determining the trajectory tracking error equation of the sway robot after being attacked by a false injection actuator based on the attack signal and the initial trajectory tracking error equation; and setting an adaptive integral sliding mode controller with the trajectory tracking error converging to 0 within a fixed time as the control goal to control the sway robot to achieve trajectory tracking. This method can ensure that trajectory tracking is not affected by attacks and interference, resolving the problem of insufficient protection against targeted attacks.

Description

Technical Field

[0001] The present invention relates to the technical field of vehicle-swing robot control, and in particular to an adaptive sliding mode control method for a vehicle-swing robot to resist false injection attacks. Background Art

[0002] The statements in this section merely mention background art related to the present invention and do not necessarily constitute prior art.

[0003] As a simple and fast-response robotic system, cart-swing robots are widely used in complex industrial fields such as intelligent manufacturing, agricultural and cultural production, logistics, and transportation. The task of a cart-swing robot is typically to keep the cart's movement path and the pendulum's deflection angle along a given reference trajectory. In other words, the task can be considered as tracking the trajectory between the cart and the pendulum. However, due to the widespread use of wireless devices in the industrial sector, cart-swing robot systems are highly vulnerable to hacker attacks, but current control schemes rarely consider the impact of hacker attacks. Furthermore, due to the complexity of the operating environment, cart-swing robot systems are inevitably affected by model uncertainty and external environmental interference. Therefore, ensuring that cart-swing robots maintain trajectory tracking despite cyberattacks and external interference is of great application significance.

[0004] In recent years, numerous researchers have proposed advanced control strategies to address trajectory tracking problems, such as adaptive control and sliding mode control. Adaptive control is a robust adaptive suppression control strategy for time-varying state-dependent disturbances. This control method can achieve online estimation of system model parameters and effectively compensate for errors caused by model parameter uncertainty. However, significant research remains to be done when considering attacks such as false data injection into actuators and external interference. Sliding mode control is a special nonlinear discontinuous control method characterized by fast response, ease of implementation, and strong robustness. However, due to the inherent characteristics of sliding mode control, the control signal is prone to chattering, meaning that the system does not converge completely along the sliding surface to the equilibrium point, but instead oscillates back and forth between the equilibrium points. Existing control schemes only require that the system converge to the equilibrium point within a finite time, which is dependent on the initial value of the system state. However, in practical industrial production, it is expected that the system can achieve the control target within a fixed time regardless of the initial value of the system. Summary of the Invention

[0005] To address the shortcomings of the existing technology, the present invention provides an adaptive sliding mode control method, system, electronic device and computer-readable storage medium for a vehicle-swinging robot to resist false injection attacks. By utilizing the nonlinear approximation capability of neural networks, nonlinear unknown network attacks are simulated using neural networks, the impact of actuator attacks on the system is accurately estimated, and a new control strategy is constructed to ensure that trajectory tracking is not affected by attacks and interference.

[0006] In a first aspect, the present invention provides an adaptive sliding mode control method for a vehicle-swinging robot to resist false injection attacks;

[0007] The adaptive sliding mode control method for the car-swing robot to resist false injection attacks includes:

[0008] According to the dynamic characteristics of the vehicle-mounted pendulum robot, a dynamic model of the vehicle-mounted pendulum robot is constructed; according to the dynamic model, the tracking trajectory reference signal and the trajectory that the vehicle-mounted robot needs to track, the initial trajectory tracking error equation of the vehicle-mounted pendulum robot is obtained;

[0009] A neural network is used to simulate the attack signal of a false injection actuator. Based on the Lyapunov stability theorem, the weight estimation value of the neural network is obtained through a linear filter to determine the attack signal of the false injection actuator.

[0010] According to the attack signal of the false injection actuator and the initial trajectory tracking error equation, the trajectory tracking error equation of the car-swing robot after being attacked by the false injection actuator is determined;

[0011] With the control objective of converging the trajectory tracking error to 0 within a fixed time, an adaptive integral sliding mode controller is set to control the car-swing robot to achieve trajectory tracking.

[0012] Furthermore, the initial trajectory tracking error equation of the vehicle-mounted robot is obtained according to the dynamic model, the tracking trajectory reference signal, and the trajectory that the vehicle-mounted robot needs to track, including:

[0013] Determine the dynamic model of the track to be tracked according to the track to be tracked by the vehicle-mounted robot and the track reference signal;

[0014] Determine the trajectory tracking error according to the tracking trajectory reference signal and the dynamic model of the trajectory to be tracked;

[0015] According to the dynamic model and trajectory tracking error of the car-swing robot, the initial trajectory tracking error equation of the car-swing robot is obtained.

[0016] Furthermore, the method of using a neural network to simulate a false injection actuator attack signal and obtaining a weight estimate of the neural network through a linear filter based on the Lyapunov stability theorem includes:

[0017] The trajectory error tracking equation of the car-swing robot after being attacked by the actuator is filtered by a linear filter, and an auxiliary matrix is ​​designed to extract weight information from the filtered equation.

[0018] Obtaining unknown weight estimates based on the activation function of the neural network and the estimated value of the unknown attack signal;

[0019] Based on Lyapunov's stability theorem, the adaptive update law of the unknown weight is determined so that the estimation error of the unknown weight converges to 0 and the estimated value of the unknown weight is determined;

[0020] The estimation error of the unknown weight is the difference between the weight information and the estimated value of the unknown weight.

[0021] Preferably, the adaptive update law of the unknown weight is expressed as:

[0022]

[0023] Where Φ is the positive definite gain matrix of the adaptive update law, I is a 4-dimensional unit vector, η and η0 are parameters for adjusting the adaptive update law and fixed time, and their values ​​are positive and satisfy S is the integral sliding mode function.

[0024] Furthermore, the trajectory tracking error equation of the vehicle-swing robot after being attacked by the false injection actuator is expressed as:

[0025]

[0026] Where A and B are the system parameter matrices, W is the unknown weight of the neural network associated with the false injection actuator attack signal, e(t) is the trajectory tracking error, Υ(e(t))=BΨ(e(t)), Ψ(e(t)) is the activation function of the neural network, δ1=δ f +d,δ f is the approximation error of neural network modeling, and d is the parameter uncertainty and external interference.

[0027] Furthermore, with the trajectory tracking error converging to 0 within a fixed time as the control goal, an adaptive integral sliding mode controller is set to control the car-swing robot to achieve trajectory tracking, including:

[0028] With the trajectory tracking error converging to 0 within a fixed time as the control goal, an integral sliding mode control function is designed;

[0029] Through the integral sliding mode control function, based on Lyapunov theorem and fixed time theorem, a control law is designed to control the car-swing robot to achieve trajectory tracking, so that the trajectory tracking error converges to 0 within a fixed time.

[0030] Preferably, the integral sliding mode control function is expressed as:

[0031]

[0032] Where L is the adjustable parameter matrix, A, B, and C are system parameter matrices, e(t) is the trajectory tracking error, t represents time, t0 is the initial time, e(t0) represents the trajectory tracking error at the initial time, and r is the integral variable.

[0033] In a second aspect, the present invention provides an adaptive sliding mode control system for a vehicle-swinging robot to resist false injection attacks;

[0034] The adaptive sliding mode control system of the car-swing robot to resist false injection attacks includes:

[0035] The trajectory tracking model building module is configured to: build a dynamic model of the vehicle-mounted pendulum robot based on the dynamic characteristics of the vehicle-mounted pendulum robot; obtain an initial trajectory tracking error equation of the vehicle-mounted pendulum robot based on the dynamic model, the tracking trajectory reference signal and the trajectory that the vehicle-mounted robot needs to track;

[0036] The false injection actuator attack simulation module is configured to: simulate the false injection actuator attack signal using a neural network, obtain the weight estimate of the neural network based on the Lyapunov stability theorem through a linear filter, and obtain the false injection actuator attack signal; and determine the trajectory tracking error equation of the vehicle-swinging robot after being attacked by the false injection actuator based on the false injection actuator attack signal and the initial trajectory tracking error equation;

[0037] The adaptive sliding mode control module is configured to set an adaptive integral sliding mode controller with the control target of converging the trajectory tracking error to 0 within a fixed time to control the vehicle-swing robot to achieve trajectory tracking.

[0038] In a third aspect, the present invention provides an electronic device;

[0039] An electronic device includes a memory and a processor, and computer instructions stored in the memory and executed on the processor. When the computer instructions are executed by the processor, the steps of the adaptive sliding mode control method for a vehicle-swinging robot to resist false injection attacks are completed.

[0040] In a fourth aspect, the present invention provides a computer-readable storage medium;

[0041] A computer-readable storage medium is used to store computer instructions. When the computer instructions are executed by a processor, the steps of the adaptive sliding mode control method for the above-mentioned vehicle-swing robot to resist false injection attacks are completed.

[0042] Compared with the prior art, the present invention has the following beneficial effects:

[0043] Existing research on trajectory tracking for vehicle-swing systems primarily focuses on the flaws caused by the uncertainty of the system's mathematical model, but is insufficient to protect against targeted attacks. The technical solution provided by this invention leverages the nonlinear approximation capabilities of neural networks to simulate nonlinear, unknown network attacks. This accurately estimates the impact of actuator attacks on the system and constructs a new control strategy to ensure trajectory tracking is immune to attacks and interference.

[0044] 2. Traditional adaptive control methods can only meet the requirement that parameter estimation errors are bounded. The technology provided by the present invention introduces a filtering operator and proposes an adaptive update law based on a neural network, which can achieve accurate estimation of unknown weights.

[0045] 3. The technical solution provided by the present invention addresses the chattering phenomenon of the sliding mode control scheme and proposes a new integral sliding mode control scheme, which ensures that the system state is at the equilibrium point of the sliding mode control from the beginning, thereby eliminating the impact of chattering on the control signal to the greatest extent.

[0046] 4. The technical solution provided by the present invention combines the fixed-time lemma and Lyapunov theorem to propose a fixed-time sliding mode control strategy. The fixed time is only related to the parameters selected by the system control strategy and is independent of the initial value of the system state. It can ensure that the system under any initial value can complete convergence within a fixed time. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] The accompanying drawings, which constitute a part of the present invention, are used to provide a further understanding of the present invention. The exemplary embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute improper limitations on the present invention.

[0048] Figure 1 A schematic diagram of a process flow provided by an embodiment of the present invention;

[0049] Figure 2 A schematic diagram of a filtering process according to an embodiment of the present invention;

[0050] Figure 3 A schematic diagram of a sliding mode control process according to an embodiment of the present invention;

[0051] Figure 4 A schematic diagram of a process for estimating neural network weights according to an embodiment of the present invention;

[0052] Figure 5 A schematic diagram of a flow chart of a control signal output according to an embodiment of the present invention;

[0053] Figure 6 A schematic diagram of a process for determining a trajectory tracking error according to an embodiment of the present invention;

[0054] Figure 7 A schematic diagram of a tracking error response curve for a SIMULINK simulation of a vehicle-swinging robot trajectory tracking according to an embodiment of the present invention;

[0055] Figure 8 A schematic diagram of a corresponding curve of a SIMULINK simulation trajectory for the trajectory tracking of a vehicle-swinging robot provided in an embodiment of the present invention;

[0056] Figure 9 A schematic diagram of a sliding mode function response curve for SIMULINK simulation of trajectory tracking of a car-swing robot provided in an embodiment of the present invention;

[0057] Figure 10 A schematic diagram of a SIMULINK simulation attack weight estimation response curve for trajectory tracking of a vehicle-swinging robot provided in an embodiment of the present invention;

[0058] Figure 11 Schematic diagram of the SIMULINK simulation control input response curve for the trajectory tracking of the vehicle-swing robot provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0059] It should be noted that the following detailed descriptions are exemplary and intended to provide further explanation of the present invention. Unless otherwise specified, all technical and scientific terms used in the present invention have the same meanings as those commonly understood by those skilled in the art to which the present invention belongs.

[0060] It should be noted that the terms used herein are only for describing specific embodiments and are not intended to limit exemplary embodiments according to the present invention. As used herein, unless the context clearly indicates otherwise, the singular form is also intended to include the plural form. In addition, it should be understood that the terms "including" and "having" and any variations thereof are intended to cover non-exclusive inclusions. For example, a process, method, system, product or device comprising a series of steps or units is not necessarily limited to those steps or units clearly listed, but may include other steps or units that are not clearly listed or inherent to these processes, methods, products or devices.

[0061] In the absence of conflict, the embodiments of the present invention and the features thereof may be combined with each other.

[0062] Example 1

[0063] In the prior art, during the control of a vehicle-swing robot, there are false data injection-type actuator attacks and external interference, which affect the control; therefore, the present invention provides an adaptive sliding mode control method for a vehicle-swing robot to resist false injection attacks.

[0064] Next, combine Figures 1-11The adaptive sliding mode control method for the vehicle-swing robot to resist false injection attacks disclosed in this embodiment is described in detail. The adaptive sliding mode control method for the vehicle-swing robot to resist false injection attacks includes the following steps:

[0065] S1. Construct a dynamic model of the vehicle-mounted pendulum robot based on its dynamic characteristics; obtain the initial trajectory tracking error equation of the vehicle-mounted pendulum robot based on the dynamic model, the tracking trajectory reference signal, and the trajectory that the vehicle-mounted robot needs to track. The specific steps include:

[0066] S101. Construct a dynamic model of the car-swing robot according to the dynamic characteristics of the car-swing robot, and simplify the dynamic model of the car-swing robot.

[0067] Furthermore, the dynamic model of the car-swing robot is as follows:

[0068]

[0069] Where δ is the parameter error, is the first-order derivative of x with respect to time, is the second-order derivative of x with respect to time. The meanings of other symbols are shown in Table 1.

[0070] Table 1: Dynamic model parameters of the car-pendulum robot

[0071] parameter symbol unit Carriage displacement x m Swing arm rotation angle θ rad moment of inertia I <![CDATA[kg·m 2 ]]> Center of gravity distance l m Car quality <![CDATA[m c ]]> kg Carriage motion viscosity coefficient <![CDATA[c m ]]> Ns / m Swing arm mass <![CDATA[M p ]]> m Viscosity coefficient of swing arm motion <![CDATA[c M ]]> Ns / m Control Input τ N·m Gravity g <![CDATA[m / s 2 ]]>

[0072] The above kinetic model can be simplified as follows

[0073]

[0074] Among them, q=[x;θ], D=(m c +M p )I+M p m c l 2 , E=[M p l 2 +I; -M p l], ω is the interference caused by the external environment and parameter modeling errors.

[0075] S102 : determining a trajectory tracking error according to the dynamic model of the vehicle-pendulum robot, a tracking trajectory reference signal, and the dynamic model of the trajectory to be tracked.

[0076] Among them, q d Represents the trajectory to be tracked, satisfying the following dynamic model:

[0077]

[0078] T represents the reference signal of the tracking trajectory, so the trajectory tracking error e(t) can be expressed as:

[0079]

[0080] Among them, q d is the trajectory that the car-swing robot needs to follow. T in formula (4) represents the transposition symbol in mathematics. e1 and e2 have the following relationship:

[0081]

[0082] The meanings of e1 and e2 are as shown in (4). is the first derivative of e1, is the first derivative of e2, V D =D -1 V, G D =D -1 G, E D =D -1 E,ω D =D -1 ω.

[0083] Therefore, the initial trajectory tracking error equation of the car-swing robot system can be expressed as

[0084]

[0085] in, is the first-order derivative of the trajectory tracking error e(t), A and B are the system parameter matrices, and d is the parameter uncertainty and external interference. At the same time, our control goal is to max The tracking error converges to 0, that is,

[0086] S2. Use a neural network to simulate a false injection actuator attack signal. Using a linear filter and Lyapunov's stability theorem, obtain the weight estimate of the neural network and determine the false injection actuator attack signal. Based on the false injection actuator attack signal and the initial trajectory tracking error equation, determine the trajectory tracking error equation of the vehicle-swinging robot after being attacked by the false injection actuator. Specific steps include:

[0087] S201. Use a neural network to simulate a false injection actuator attack signal.

[0088] Due to the attack of the fake injection actuator, the control signal received by the actuator is

[0089]

[0090] in, is the control signal after being attacked, σ aτ (t, e(t)) is the false control input information transmitted by the network hacker through the false injection attack. It is a nonlinear function related to time t and tracking error e(t). Due to the nonlinear approximation capability of the neural network, this interference can be represented by the following mathematical model:

[0091] σ aτ (t, e(t)) = Ψ(e(t))W + δ f (8)

[0092] Among them, Ψ(e(t)) is the activation function of the neural network, which can be obtained through multiple learning; W is the weight associated with the attack signal, δ f is the approximation error of neural network modeling.

[0093] S202. Filter the trajectory error tracking equation of the vehicle-swinging robot after being attacked by the actuator through a linear filter, design an auxiliary matrix, and extract weight information from the filtered equation; obtain the unknown weight estimate based on the activation function of the neural network and the estimated value of the unknown attack signal.

[0094] In this embodiment, an RBF neural network is used. RBF neural networks are nonlinear networks composed of a large number of nodes. Due to their ability to approximate nonlinear functions, they are often used to simulate arbitrary nonlinear functions. In this embodiment, they are used to learn the mapping relationship for a false injection actuator attack. The hidden layer activation function Ψ(e(t)) of the RBF neural network can be obtained by repeatedly learning attack samples. However, for an unknown actuator attack, the weights of the neural network are unknown, and information about these unknown weights must be extracted from the system state after the attack. Therefore, a linear filter is created to accurately estimate these unknown weights, thereby enabling accurate identification of unknown attacks.

[0095] Furthermore, according to S1, the trajectory tracking equation of the car-swing robot system after being attacked by the virtual actuator is:

[0096]

[0097] Among them, Υ(e(t))=BΨ(e(t)), δ1=δ f +d.

[0098] The linear filter is expressed as:

[0099]

[0100]

[0101]

[0102]

[0103] The filtered system equation is expressed as:

[0104]

[0105] In order to extract the weight information from the filtered equation, auxiliary matrices M, N and R are designed.

[0106]

[0107]

[0108]

[0109] The relationship between the auxiliary matrix and the weight is as follows:

[0110] N=MW-R (18)

[0111] For unknown false injection attack signal σ aτ The estimated value of (t, e(t)) is

[0112]

[0113] Represents the estimation of unknown weights, the estimated error of weights And there is the following relationship:

[0114]

[0115] Based on Lyapunov's stability theorem, an adaptive update law for unknown weights is derived, which can make the estimated error of the weights converge to 0.

[0116]

[0117] Where Φ is the positive definite gain matrix of the adaptive update law, I is a 4-dimensional unit vector, η and η0 are parameters for adjusting the adaptive update law and fixed time, and their values ​​are positive and satisfy S is the integral sliding mode function, sgn is the sign function, and the mathematical expression is approximately as follows:

[0118]

[0119] Where a is a positive constant. When a is large enough, the approximate error of the above formula is very small.

[0120] Substitute the determined unknown weight estimates into equations (8) and (9) to determine the trajectory tracking error equation of the car-swing robot after being attacked by the false injection actuator.

[0121] S3. With the trajectory tracking error converging to 0 within a fixed time as the control goal, an adaptive integral sliding mode controller is set to control the car-swing robot to achieve trajectory tracking. The specific steps include:

[0122] S301, with the trajectory tracking error converging to 0 within a fixed time as the control target, design an integral sliding mode control function, which is expressed as follows:

[0123]

[0124] Where e(t) is the trajectory tracking error, t represents time, t0 is the initial time, e(t0) represents the trajectory tracking error at the initial time, r is the integral variable, and L is an adjustable parameter matrix that only needs to satisfy det(LB)≠0, that is, the modulus of LB is not 0. The parameter matrix C can be obtained by solving the following linear matrix inequality:

[0125]

[0126] in, It is the inverse matrix of P, Q = CP -1 ,

[0127] S302. Design a control law based on the integral sliding mode control function, Lyapunov's theorem and the fixed time theorem, and control the vehicle-swing robot to achieve trajectory tracking, so that the trajectory tracking error converges to 0 within a fixed time.

[0128] Specifically, through the above integral sliding mode control function, based on Lyapunov theorem and fixed time theorem, the following control law is proposed:

[0129] τ=τ1+τ2+τ3 (24)

[0130] τ1=Ce(t) (25)

[0131]

[0132] τ3==-c1(LB) T S-c2sgn((LB) T S)-c3(LB) T S 2 -c4(LB) T sgn((LB) T S) (27)

[0133] Among them, c1, c2, c3, c4 are positive coefficients. This control law can make the tracking error e(t) within a fixed time T max Converges to 0 internally.

[0134]

[0135] Where Λ=LB, λ min Represents the smallest eigenvalue of the matrix.

[0136] Based on the above control law, the control signal is output to control the car-swing robot to achieve trajectory tracking and achieve a trajectory tracking error of 0 within a fixed time.

[0137] S4. Select Lyapunov function to verify the stability of the system.

[0138] Specifically, define the Lyapunov function as

[0139]

[0140] Among them, S T represents the transpose of S, represents the estimated error of the weight, express The transpose of .

[0141] Taking the derivative of the Lyapunov function, we can get

[0142]

[0143] Substituting the control law (24) and the weight adaptive update law (21) into (30), we can get

[0144]

[0145] Since V≥0 positive semidefinite, Semi-positive definite, it is proved that the closed-loop system is asymptotically stable in fixed time. That is, when t→T max When the sliding mode control function S and the weight estimation error approaches 0, so the trajectory tracking error e(t)→0,

[0146] A false injection attack occurs when an attacker obtains the system state and, based on that state, creates a false control signal that acts on the actuator. Because the attack signal varies with the actual system state, traditional control strategies and actuators have difficulty identifying it. To address this difficulty, this embodiment introduces a neural network to simulate the attack signal. Because neural networks have powerful nonlinear approximation and learning capabilities, they can identify this type of attack by repeatedly training on attack samples.

[0147] Sliding mode control means that the system's motion is constrained to remain within the sliding mode plane to achieve stability. Generally, the system's initial position is not on the sliding surface, and the system's state undergoes a transition from the initial point to the sliding surface. Therefore, traditional sliding mode control methods cannot guarantee that the system's state consistently meets the expected performance requirements from the initial state to the sliding surface. However, integral sliding mode control ensures that the system's initial state is already on the sliding surface, thereby improving the system's performance and anti-interference capabilities.

[0148] Conventional control strategies aim to achieve control objectives within a finite time. For example, in the case of trajectory tracking for a vehicle pendulum system, the tracking error e(t) converges within a finite time t. However, this finite convergence time is dependent on the system's initial values. In real life, it is often desirable to achieve convergence time that is not limited by these initial values. To achieve this, this embodiment incorporates the fixed-time theorem to improve the controller's control strategy, enabling convergence within a fixed time. This fixed time depends solely on the selected control law coefficients and is independent of the system's initial state.

[0149] To facilitate understanding, the following briefly explains the adaptive sliding mode control method of a vehicle-swinging robot to resist false injection attacks, taking a heavy-duty material handling robot as an example.

[0150] S1. Determine the initial trajectory tracking error equation of the heavy material handling robot

[0151]

[0152]

[0153] Wherein, d = 0.2sin(xt) + 0.3cos(θt), and the tracking target trajectory reference signal is T = 5sin(t).

[0154] S2. Simulation of Fake Injection Actuator Attack

[0155] σ aτ (t, e(t)) = Ψ(e(t))W

[0156] Ψ(e(t)) has been obtained through multiple learning attack samples. In this embodiment, the weight As an unknown weight for fake injection actuator attacks.

[0157]

[0158] Select L = [1.2 0.7 22.7 1], therefore, Λ = LB = 1.

[0159] By solving linear matrix inequalities:

[0160]

[0161] The feedback gain vector C = [-1.3575 16.3959 -4.5989 0.0090] is obtained.

[0162]

[0163] Among them, the initial value of the weight estimate The coefficient of the filter is ξ=0.001, and the vector Δ related to the estimation error information is obtained by using the filter and the auxiliary matrix, and then the weight estimation value is updated based on the adaptive update law of the weight.

[0164]

[0165] Φ=diag(0.5, 0.5, 0.5, 0.5), diag represents the diagonal matrix, η=6, η0=0.2, thus accurately estimating the attack signal

[0166] S3. Establish a controller.

[0167] τ1=Ce(t)

[0168]

[0169] τ3=-c1(LB) T S-c2sgn((LB) T S)-c3(LB) T S 2 -c4(LB) T sgn((LB) T S)

[0170] Among them, C=[-1.3575 16.3959 -4.5989 0.0090], c1=0.25, c2=1.7, c3=6, c4=5. By selecting the control parameters, the fixed time T can be calculated. max =106.1s.

[0171] Example 2

[0172] This embodiment discloses an adaptive sliding mode control system for a vehicle-swinging robot to resist false injection attacks, including:

[0173] The trajectory tracking model building module is configured to: build a dynamic model of the vehicle-mounted pendulum robot based on the dynamic characteristics of the vehicle-mounted pendulum robot; obtain an initial trajectory tracking error equation of the vehicle-mounted pendulum robot based on the dynamic model, the tracking trajectory reference signal and the trajectory that the vehicle-mounted robot needs to track;

[0174] The false injection actuator attack simulation module is configured to: simulate the false injection actuator attack signal using a neural network, obtain the weight estimate of the neural network based on the Lyapunov stability theorem through a linear filter, and obtain the false injection actuator attack signal; and determine the trajectory tracking error equation of the vehicle-swinging robot after being attacked by the false injection actuator based on the false injection actuator attack signal and the initial trajectory tracking error equation;

[0175] The adaptive sliding mode control module is configured to set an adaptive integral sliding mode controller with the control target of converging the trajectory tracking error to 0 within a fixed time to control the vehicle-swing robot to achieve trajectory tracking.

[0176] It should be noted that the trajectory tracking model construction module, the false injection actuator attack simulation module, and the adaptive sliding mode control module correspond to the steps in Example 1. The examples and application scenarios implemented by these modules and the corresponding steps are the same, but are not limited to the contents disclosed in Example 1. It should be noted that the above modules, as part of the system, can be executed in a computer system, such as a set of computer-executable instructions.

[0177] Example 3

[0178] Embodiment 3 of the present invention provides an electronic device, including a memory and a processor, and computer instructions stored in the memory and running on the processor. When the computer instructions are run by the processor, the steps of the above-mentioned adaptive sliding mode control method for the vehicle-swing robot to resist false injection attacks are completed.

[0179] Example 4

[0180] A fourth embodiment of the present invention provides a computer-readable storage medium for storing computer instructions. When the computer instructions are executed by a processor, the steps of the above-mentioned adaptive sliding mode control method for the vehicle-swing robot to resist false injection attacks are completed.

[0181] The present invention is described with reference to flowcharts and / or block diagrams of methods, devices (systems), and computer program products according to embodiments of the present invention. It should be understood that each process and / or block in the flowcharts and / or block diagrams, as well as combinations of processes and / or blocks in the flowcharts and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowcharts and / or block diagrams. Figure 1 a process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0182] These computer program instructions may also be stored in a computer readable memory that can direct a computer or other programmable data processing device to work in a specific manner, so that the instructions stored in the computer readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 a process or multiple processes and / or boxes Figure 1 The function specified in one or more boxes.

[0183] These computer program instructions can also be loaded onto a computer or other programmable data processing device, and a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, so that the instructions executed on the computer or other programmable device provide the functions for implementing the process. Figure 1 a process or multiple processes and / or boxes Figure 1 A step that specifies a function in one or more boxes.

[0184] The descriptions of the various embodiments in the above embodiments have different focuses. For parts not described in detail in a certain embodiment, reference can be made to the relevant descriptions of other embodiments.

[0185] The foregoing description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Those skilled in the art will readily appreciate that various modifications and variations of the present invention are possible. Any modifications, equivalent substitutions, or improvements made within the spirit and principles of the present invention are intended to be within the scope of protection of the present invention.

Claims

1. The adaptive sliding mode control method for a car-swing robot to resist false injection attacks is characterized by: include: According to the dynamic characteristics of the car-swing robot, the dynamic model of the car-swing robot is constructed; According to the dynamic model, the tracking trajectory reference signal and the trajectory that the car-swing robot needs to track, the initial trajectory tracking error equation of the car-swing robot is obtained; A neural network is used to simulate the attack signal of a false injection actuator. Based on the Lyapunov stability theorem, the weight estimation value of the neural network is obtained through a linear filter to determine the attack signal of the false injection actuator, including: The trajectory error tracking equation of the car-swing robot after being attacked by the actuator is filtered by a linear filter, and an auxiliary matrix is ​​designed to extract weight information from the filtered equation. Obtaining unknown weight estimates based on the activation function of the neural network and the estimated value of the unknown attack signal; Based on Lyapunov's stability theorem, the adaptive update law of the unknown weight is determined so that the estimation error of the unknown weight converges to 0 and the estimated value of the unknown weight is determined; Among them, the estimation error of the unknown weight is the difference between the weight information and the estimated value of the unknown weight; According to the attack signal of the false injection actuator and the initial trajectory tracking error equation, the trajectory tracking error equation of the car-swing robot after being attacked by the false injection actuator is determined; With the control objective of converging the trajectory tracking error to 0 within a fixed time, an adaptive integral sliding mode controller is set to control the car-swing robot to achieve trajectory tracking.

2. The adaptive sliding mode control method for a vehicle-swinging robot to resist false injection attacks according to claim 1 is characterized in that: The trajectory tracking error equation of the vehicle-swing robot is obtained according to the dynamic model, the tracking trajectory reference signal and the trajectory that the vehicle-swing robot needs to track, including: According to the trajectory that the car-swing robot needs to track and the tracking trajectory reference signal, the dynamic model of the trajectory that needs to be tracked is determined; Determine the trajectory tracking error according to the tracking trajectory reference signal and the dynamic model of the trajectory to be tracked; According to the dynamic model and trajectory tracking error of the car-swing robot, the trajectory tracking error equation of the car-swing robot is obtained.

3. The adaptive sliding mode control method for a vehicle-swinging robot to resist false injection attacks according to claim 1 is characterized in that: The adaptive update law of the unknown weight is expressed as: in, is the positive definite gain matrix of the adaptive update law, I is a 4-dimensional unit vector, L is the adjustable parameter matrix, B is the system parameter matrix, and To adjust the parameters of the adaptive update law and fixed time, the value is positive and satisfies , M is the auxiliary matrix, λmin represents the minimum eigenvalue of the matrix, Δ is the estimation error extraction function, and S is the integral sliding mode function.

4. The adaptive sliding mode control method for a vehicle-swinging robot to resist false injection attacks according to claim 1 is characterized in that: The trajectory tracking error equation of the vehicle-swing robot after being attacked by the false injection actuator is expressed as: in, 、 is the system parameter matrix, is the unknown weight of the neural network associated with the fake injected actuator attack signal, is the trajectory tracking error, , is the activation function of the neural network, , The approximation error for modeling neural networks, It is caused by parameter uncertainty and external interference.

5. The adaptive sliding mode control method for a vehicle-swinging robot to resist false injection attacks according to claim 1 is characterized in that: With the trajectory tracking error converging to 0 within a fixed time as the control goal, an adaptive integral sliding mode controller is set to control the car-swing robot to achieve trajectory tracking, including: With the trajectory tracking error converging to 0 within a fixed time as the control goal, an integral sliding mode control function is designed; Through the integral sliding mode control function, based on Lyapunov theorem and fixed time theorem, a control law is designed to control the car-swing robot to achieve trajectory tracking, so that the trajectory tracking error converges to 0 within a fixed time.

6. The adaptive sliding mode control method for a vehicle-swinging robot to resist false injection attacks according to claim 5 is characterized in that: The integral sliding mode control function is expressed as: in, is the adjustable parameter matrix, 、 、 is the system parameter matrix, is the trajectory tracking error, Represents time, is the initial moment, represents the trajectory tracking error at the initial moment, is the integration variable.

7. An adaptive sliding mode control system for a vehicle-swing robot that resists false injection attacks, using the adaptive sliding mode control method for a vehicle-swing robot that resists false injection attacks as described in any one of claims 1 to 6, characterized in that: include: The trajectory tracking model building module is configured to: build a dynamic model of the car-swing robot according to the dynamic characteristics of the car-swing robot; According to the dynamic model, the tracking trajectory reference signal and the trajectory that the car-swing robot needs to track, the initial trajectory tracking error equation of the car-swing robot is obtained; The false injection actuator attack simulation module is configured to: simulate the false injection actuator attack signal using a neural network, obtain the weight estimate of the neural network based on the Lyapunov stability theorem through a linear filter, and obtain the false injection actuator attack signal; and determine the trajectory tracking error equation of the vehicle-swinging robot after being attacked by the false injection actuator based on the false injection actuator attack signal and the initial trajectory tracking error equation; The adaptive sliding mode control module is configured to set an adaptive integral sliding mode controller with the control target of converging the trajectory tracking error to 0 within a fixed time to control the vehicle-swing robot to achieve trajectory tracking.

8. An electronic device, characterized in that: The method comprises a memory and a processor, and computer instructions stored in the memory and executed on the processor, wherein the steps described in any one of claims 1 to 6 are completed when the computer instructions are executed by the processor.

9. A computer-readable storage medium, characterized in that Used to store computer instructions, which, when executed by a processor, complete the steps described in any one of claims 1 to 6.

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