Elastic intermittent control method and system for single-link manipulator system under deception attack

Abstract

The application discloses a resilient intermittent control method and system for a single-link mechanical arm system under a deception attack, and the method comprises the following steps: constructing a model of the single-link mechanical arm system; under the deception attack, constructing an event triggering mechanism for the single-link mechanical arm system model; based on the single-link mechanical arm system model and the event triggering mechanism, constructing a fuzzy state estimator; based on the event triggering mechanism and the fuzzy state estimator, constructing a resilient adaptive controller by using a backstepping method; inputting the rotational inertia, the link mass and the link length of the single-link mechanical arm into the model of the single-link mechanical arm system, inputting the angle variable between the link after triggering the attack and the horizontal ground, the estimated angular velocity of the mechanical arm joint and the adaptive parameter value as the input values of the resilient adaptive controller, obtaining the output value of the resilient adaptive controller, and controlling the action of the single-link mechanical arm system based on the output value.

Description

Technical Field

[0001] This invention relates to the field of industrial automatic control technology, and in particular to an elastic intermittent control method and system for a single-link robotic arm system under deception attack. Background Technology

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

[0003] Given the limited public resources such as communication, computing, and energy available for network transmission, there is an urgent need to improve the energy efficiency of individual feedback controls. This requires minimizing the occupation and consumption of public resources by individual feedback controls while ensuring acceptable system performance, thereby ensuring system reliability. Furthermore, for confidentiality and security reasons, it is sometimes necessary to minimize information communication and control / decision updates. These energy efficiency and security objectives place higher demands on the fundamental theory of feedback control for uncertain systems and the control technologies based on it, presenting new challenges.

[0004] Furthermore, with the cross-penetration of control, computing, and communication technologies, network security has become an issue that cannot be ignored and deserves serious attention in the field of automation. Deception attacks, a type of malicious attack during network transmission, can affect the steady-state performance of a system, leading to instability. Therefore, developing resilient control methods to effectively address the impact of deception attacks is a crucial issue.

[0005] In the process of realizing this invention, the inventors discovered the following technical problems in the prior art:

[0006] (1) In the traditional single-link robotic arm system control method, the controller design is based on all state information. Therefore, the observability of the system must be guaranteed, that is, all states must be measurable, which increases the cost of practical application and makes it more difficult to implement.

[0007] (2) Existing single-link robotic arm systems are based on continuous signal transmission. Considering the limited energy of sensors and the limited communication bandwidth resources in practical applications, continuous signal transmission will lead to the consumption of many unnecessary communication resources, increasing the network communication burden and reducing work efficiency. In addition, in the existing event-triggered robotic arm system control methods, the event triggering mechanism only acts on the controller-actuator end, but the signal transmitted at the sensor-controller end is still continuous, which greatly increases the bandwidth occupation and consumption of feedback control.

[0008] (3) With the increasing openness within and between cyber-physical systems, existing technologies for single-link robotic arm systems rarely consider cybersecurity issues. In practical network control and communication systems, sensors are highly vulnerable to malicious cyberattacks during signal transmission, which has a significant impact on the security and stability of the system. Summary of the Invention

[0009] To address the shortcomings of existing technologies, this invention provides an elastic intermittent control method and system for a single-link robotic arm system under deception attacks; this invention also provides an observer-based elastic adaptive control algorithm for cyber-physical systems under deception attacks, which enables the steady-state error signal of the cyber-physical system under deception attacks to be within an adjustable bounded range, and ensures that all signals of the closed-loop system are bounded.

[0010] On the one hand, a method for elastic intermittent control of a single-link robotic arm system under deception attacks is provided, including:

[0011] Construct a model of a single-link robotic arm system;

[0012] Under deception attacks, an event triggering mechanism is constructed for a single-link robotic arm system model;

[0013] Based on the single-link robotic arm system model and event triggering mechanism, a fuzzy state estimator is constructed.

[0014] Based on the event-triggered mechanism and fuzzy state estimator, an elastic adaptive controller is constructed using the backstepping method;

[0015] The moment of inertia, mass, and length of the link at the joint of the single-link robotic arm are input into the model of the single-link robotic arm system. The angle variable between the link and the horizontal ground after the triggered attack, the estimated angular velocity of the robotic arm joint, and the adaptive parameter values ​​are used as the input values ​​of the elastic adaptive controller to obtain the output value of the elastic adaptive controller. The action of the single-link robotic arm system is controlled based on the output value.

[0016] On the other hand, a flexible intermittent control system for a single-link robotic arm system under deception attacks is provided, including:

[0017] The model building module is configured to build a model of a single-link robotic arm system.

[0018] The triggering mechanism construction module is configured to: construct an event triggering mechanism for a single-link robotic arm system model under a deception attack;

[0019] The estimator building module is configured to: build a fuzzy state estimator based on a single-link robotic arm system model and an event triggering mechanism;

[0020] The controller building module is configured to construct an elastic adaptive controller based on an event-triggered mechanism and a fuzzy state estimator, using a backstepping method.

[0021] The output module is configured to input the moment of inertia, link mass, and link length at the joint of the single-link robotic arm into the model of the single-link robotic arm system. It uses the angle variable between the link and the horizontal ground after the triggered attack, the estimated angular velocity of the robotic arm joint, and the adaptive parameter values ​​as input values ​​to the elastic adaptive controller to obtain the output value of the elastic adaptive controller. Based on the output value, it controls the action of the single-link robotic arm system.

[0022] Furthermore, an electronic device is also provided, including:

[0023] Memory, used for non-transitory storage of computer-readable instructions; and

[0024] Processor, for executing the computer-readable instructions,

[0025] When the computer-readable instructions are executed by the processor, they perform the method described in the first aspect above.

[0026] In another aspect, a storage medium is also provided for non-transitory storage of computer-readable instructions, wherein when the non-transitory computer-readable instructions are executed by a computer, the instructions of the method described in the first aspect are executed.

[0027] In another aspect, a computer program product is also provided, including a computer program that, when run on one or more processors, is used to implement the method described in the first aspect above.

[0028] One of the above technical solutions has the following advantages or beneficial effects:

[0029] This invention addresses the challenges of malicious spoofing attacks, unpredictable states, and limited communication bandwidth in practical single-link systems. It constructs a novel fuzzy state estimator using intermittent spurious outputs and fuzzy logic systems (FLSs). Based on this estimator, a novel coordinate transformation of error variables based on erroneous outputs and estimated states is proposed, along with a new observer-based elastic adaptive fuzzy control scheme. Furthermore, this invention incorporates dynamic surface techniques into the backstepping design framework to eliminate the "complexity explosion" problem.

[0030] This invention addresses the problem of non-differentiability of virtual control signals caused by discrete state variables in single-link systems. It develops an alternative method to address the issue of non-differentiability of intermittent spurious output information: first, a continuous spurious output signal is used for feedback mechanism design, and then the continuous spurious output is replaced with an intermittent spurious output. This avoids the problem of directly differentiating the intermittent spurious output signal and establishes a corresponding compensation mechanism, thereby solving the problem of designing feedback control and analyzing system stability using only intermittent spurious output. Attached Figure Description

[0031] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an improper limitation of the invention.

[0032] Figure 1 This is a block diagram of the elastic control of a nonlinear cyber-physical system under deception attack based on the present invention;

[0033] Figure 2 This is a model diagram of the single-link robotic arm system disclosed in Embodiment 1 of the present invention;

[0034] Figure 3 This is a waveform diagram of the trajectory of the output, estimated output, and triggered attack output signal of the single-link robotic arm system disclosed in Embodiment 1 of the present invention.

[0035] Figure 4 The above is a waveform diagram of the system state and estimated state disclosed in Embodiment 1 of the present invention;

[0036] Figure 5 The waveform diagram shows the control input of the single-link robotic arm system disclosed in Embodiment 1 of the present invention under a deception attack. Detailed Implementation

[0037] It should be noted that the following detailed descriptions are exemplary and intended to provide further illustration of the invention. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains.

[0038] Where there is no conflict, the embodiments and features in the embodiments of the present invention can be combined with each other.

[0039] All data acquisition in this embodiment is carried out in accordance with laws and regulations and with user consent, and the data is used legally.

[0040] Example 1

[0041] This embodiment provides an elastic intermittent control method for a single-link robotic arm system under deception attacks;

[0042] like Figure 1 and Figure 2 As shown, the elastic intermittent control method for a single-link robotic arm system under deception attack includes:

[0043] S101: Construct a model of a single-link robotic arm system;

[0044] S102: Under deception attack, construct an event triggering mechanism for a single-link robotic arm system model;

[0045] S103: Construct a fuzzy state estimator based on a single-link robotic arm system model and event triggering mechanism;

[0046] S104: Based on the event-triggered mechanism and fuzzy state estimator, an elastic adaptive controller is constructed using the backstepping method;

[0047] S105: Input the moment of inertia, link mass, and link length at the joint of the single-link robotic arm into the model of the single-link robotic arm system. Use the angle variable between the link and the horizontal ground after the triggered attack, the estimated angular velocity of the robotic arm joint, and the adaptive parameter value as the input values ​​of the elastic adaptive controller to obtain the output value of the elastic adaptive controller. Control the action of the single-link robotic arm system based on the output value; the output value refers to torque.

[0048] Further, S101: Constructing a model of a single-link robotic arm system includes:

[0049]

[0050] Where x1 is the angle between the link and the horizontal ground, in rad; x2 is the angular velocity of the robotic arm joint; and M is the moment of inertia at the link connection, in kg / m. 2 u is the input torque, N; g is the acceleration due to gravity, m / s². 2 m is the mass of the connecting rod, kg; l is the length of the connecting rod, m. Let y be the acceleration of the robotic arm joint, and y be the output of the single-link robotic arm. It is the angle between the connecting rod and the horizontal ground after being attacked, ω s (t,x1) represents a spoofing attack on the angle sensor, which can be represented by the parameter ω. s (t,x1)=ρ(t)x1(t), where ρ(t) is an unknown time-varying weight.

[0051] It is important to note that when the system's angle sensor is subjected to a spoofing attack, the true angle information between the linkage and the horizontal ground is unavailable. Users can only obtain the false angle information after the attack to achieve system stability.

[0052] Furthermore, in S102: Under a deception attack, for a single-link robotic arm system model, an event triggering mechanism is constructed, including:

[0053]

[0054]

[0055] Where t>0 represents time, t k >0 represents the update time, t k+1 >0 indicates the (k+1)th time, where m>0 is a positive constant in the design. It is the angle variable between the link and the horizontal ground after the attack is triggered. It is the angle between the connecting rod and the horizontal ground after being attacked. Indicates t k The angle between the link and the horizontal ground after being attacked at any moment, where inf is the infimum.

[0056] Further, in step S103: based on the single-link robotic arm system model and event triggering mechanism, a fuzzy state estimator is constructed, including:

[0057]

[0058]

[0059] For i = 1, 2, For x i The estimate, f i The estimate, f i For an unknown nonlinear function, f1 = 0. l i For positive design parameters, a fuzzy logic system (FLS) is introduced to estimate the unknown nonlinear function f. i And satisfy For the ideal weight vector, Let φ be the fuzzy basis function vector. i yes The estimated value, δ i To estimate the error, Ω i It is a tight cluster.

[0060] Next, we define the estimation error. Its derivative is:

[0061]

[0062] in, Let L be the Herwitz matrix, where L = [l1, l2]. T , To estimate the error, Let K1 be the real number field, and K1 = [1, 0]. T K2 = [0,1] T ,

[0063] Further, S104: Based on the event-triggered mechanism and fuzzy state estimator, a resilient adaptive controller is constructed using the backstepping method, including:

[0064] S104-1: Establish a new coordinate transformation as follows:

[0065]

[0066]

[0067] in, The error variable after the attack. η1 is the error variable triggered by the attack, and η2 is the state variable obtained through the low-pass filter. For the triggered variable, Let the rate of change of the state variable obtained through the low-pass filter be expressed as: Where α1 is the virtual controller before triggering, and κ2>0 is the design parameter.

[0068] S104-2: Choose the Lyapunov function V as:

[0069]

[0070] Where P>0 is a positive definite matrix, and λ=(1+ρ) -1 For the unknown time-varying attack gain, z1 = x1, Ξ2 = η2 - α1 is the boundary error, and the design parameters are... It is an estimate of θ. It is an estimate of ζ, and Θ1 is... The estimate, To estimate the error;

[0071] Its derivative is:

[0072]

[0073] Where ∈ > 0, ∈ is a design constant, Q > 0, and Q is a two-dimensional matrix. To estimate the error δ i The upper boundary.

[0074] S104-3: Design the virtual controller α1 before triggering and the virtual controller after triggering. as follows:

[0075]

[0076]

[0077] Where k1>0 is the design parameter, and τ>0 is a known constant;

[0078] S104-4: Design an elastic adaptive controller and adaptive parameter update law as follows:

[0079]

[0080]

[0081]

[0082]

[0083] Where k2,τ1,τ2,s1,s2,d1 are positive design parameters;

[0084] in, φ1, Θ1, and φ2 are adaptive parameters;

[0085] Based on S104-3 and S104-4, we obtain:

[0086]

[0087] in σ1 and σ2 are auxiliary variables.

[0088] Further, in step S105: the rotational inertia, link mass, and link length related system parameter values ​​at the link connection of the single-link robotic arm are input into the system; the angle variable between the link and the horizontal ground after the triggered attack, the estimated angular velocity of the robotic arm joint, and the adaptive parameter value are used as input values ​​for the elastic adaptive controller to obtain the output value of the elastic adaptive controller; and the action of the single-link robotic arm system is controlled based on the output value; the output value is the torque.

[0089] For the purpose of stability analysis, we first propose two important lemmas:

[0090] Lemma 1 and α1 and The boundedness of the following is a summary:

[0091]

[0092]

[0093] in, m is the design parameter.

[0094] Lemma 2 states that the following inequality holds:

[0095]

[0096]

[0097]

[0098] Where Δζ, Δφ1, ΔΘ1, Δθ, and Δφ2 are design parameters related to event triggering.

[0099] With the help of Lemma 1-2, we can obtain:

[0100]

[0101] Define a set and in because There exists a maximum value M2 such that |π2|≤M2. Therefore, we obtain

[0102]

[0103] in,

[0104] make get

[0105]

[0106] Therefore, all signals in a closed-loop system are bounded.

[0107] Next, to verify the effectiveness of the proposed method, the designed controller was input into the single-link robotic arm system for simulation experiments.

[0108] The design parameters and initial values ​​are selected as follows:

[0109] x1(0)=0.1, x2(0)=0.2, k1=5, k2=13, l1=5, l2=4, τ1=τ2=0.5, κ2 = 0.05.

[0110] The parameters for the single-link robotic arm system are selected as follows: M = 0.5, g = 9.8, m = 1, l = 1.

[0111] Simulation results are as follows Figures 3-5 As shown. From Figure 3 In the figure, we show the trajectories of the output, estimated output, and triggered attack output signal. As shown in the figure, we can see that the system output achieves steady-state performance under attack conditions.

[0112] Figure 4 The system state and estimated state curves are shown. The state estimator can estimate the system state well, and the system state and estimated state are bounded.

[0113] Figure 5 This is a graph of the controller input. From Figure 3 , Figure 4 and Figure 5 It can be seen that the controller designed in this invention can ensure that all signals are stable, that all states of the existing system under network attack are bounded, and that the steady-state error can converge to a very small region.

[0114] This invention discloses an observer-based elastic adaptive control algorithm for a single-link robotic arm system under unknown sensor spoofing attacks. First, a novel fuzzy state estimator is constructed using intermittent spurious outputs and fuzzy logic systems (FLSs). Then, based on the fuzzy state estimator and coordinate transformations involving the attack and estimated state variables, a novel observer-based elastic adaptive fuzzy control scheme is developed. The stabilization error of the proposed elastic adaptive output event-triggered control converges to the residual set near zero, and all signals of the entire system remain bounded. Finally, the proposed algorithm is applied to a single-link robotic arm system, verifying the effectiveness of the proposed method.

[0115] Example 2

[0116] This embodiment provides an elastic intermittent control system for a single-link robotic arm system under deception attacks, including:

[0117] The model building module is configured to build a model of a single-link robotic arm system.

[0118] The triggering mechanism construction module is configured to: construct an event triggering mechanism for a single-link robotic arm system model under a deception attack;

[0119] The estimator building module is configured to: build a fuzzy state estimator based on a single-link robotic arm system model and an event triggering mechanism;

[0120] The controller building module is configured to construct an elastic adaptive controller based on an event-triggered mechanism and a fuzzy state estimator, using a backstepping method.

[0121] The output module is configured to input the moment of inertia, link mass, and link length at the joint of the single-link robotic arm into the model of the single-link robotic arm system. It uses the angle variable between the link and the horizontal ground after the triggered attack, the estimated angular velocity of the robotic arm joint, and the adaptive parameter values ​​as input values ​​to the elastic adaptive controller to obtain the output value of the elastic adaptive controller. Based on the output value, it controls the action of the single-link robotic arm system.

[0122] It should be noted that the examples and application scenarios implemented by the above modules and corresponding steps are the same, but are not limited to the content disclosed in Embodiment 1 above. It should also be noted that the above modules, as part of a system, can be executed in a computer system such as a set of computer-executable instructions.

[0123] The descriptions of each embodiment in the above embodiments have different focuses. For parts not described in detail in a certain embodiment, please refer to the relevant descriptions in other embodiments.

[0124] The proposed system can be implemented in other ways. For example, the system embodiments described above are merely illustrative, and the division of modules described above is only a logical functional division. In actual implementation, there may be other division methods. For example, multiple modules may be combined or integrated into another system, or some features may be ignored or not executed.

[0125] Example 3

[0126] This embodiment also provides an electronic device, including: one or more processors, one or more memories, and one or more computer programs; wherein, the processor is connected to the memory, and the one or more computer programs are stored in the memory. When the electronic device is running, the processor executes the one or more computer programs stored in the memory to cause the electronic device to perform the method described in Embodiment 1.

[0127] It should be understood that in this embodiment, the processor can be a central processing unit (CPU), or it can be other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. The general-purpose processor can be a microprocessor or any conventional processor, etc.

[0128] Memory may include read-only memory and random access memory, and provides instructions and data to the processor. A portion of memory may also include non-volatile random access memory. For example, memory may also store information about the device type.

[0129] In the implementation process, each step of the above method can be completed by the integrated logic circuits in the processor hardware or by software instructions.

[0130] The method in Embodiment 1 can be directly implemented by a hardware processor, or implemented by a combination of hardware and software modules within the processor. The software modules can reside in readily available storage media in the art, such as random access memory, flash memory, read-only memory, programmable read-only memory, electrically erasable programmable memory, or registers. This storage medium is located in memory; the processor reads information from the memory and, in conjunction with its hardware, completes the steps of the above method. To avoid repetition, a detailed description is not provided here.

[0131] Those skilled in the art will recognize that the units and algorithm steps described in connection with the various examples of this embodiment can be implemented in electronic hardware or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of this invention.

[0132] Example 4

[0133] This embodiment also provides a computer-readable storage medium for storing computer instructions, which, when executed by a processor, complete the method described in Embodiment 1.

[0134] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for elastic intermittent control of a single-link robotic arm system under deception attack, characterized by: include: S1. Construct a model of a single-link robotic arm system, including: in, Let be the angle between the connecting rod and the horizontal ground, in rad; Let be the angular velocity of the robotic arm joint. The moment of inertia at the connecting rod joint is expressed in kg / m. 2 ; Input torque, N; The acceleration due to gravity is m / s². 2 ; The mass of the connecting rod is in kg; Let the length of the link be m. For the acceleration of the robotic arm joints, For the output of a single-link robotic arm, It is the angle between the connecting rod and the horizontal ground after being attacked. For angle sensors, spoofing attacks can be performed using parameters such as , The time-varying weights are unknown; S2. Under deception attacks, construct an event triggering mechanism for a single-link robotic arm system model, including: in, For time, For update time, This indicates that at time k+1, m>0 is a positive constant of the design. It is the angle variable between the linkage and the horizontal ground after the attack is triggered; It is the angle between the connecting rod and the horizontal ground after being attacked. express The angle between the linkage and the horizontal ground after being attacked. The infimum; S3. Based on the single-link robotic arm system model and event triggering mechanism, a fuzzy state estimator is constructed, including: Among them, for , for The estimate, for The estimate, For an unknown nonlinear function, , , For positive design parameters, a fuzzy logic system is introduced to estimate the unknown nonlinear function. And satisfy , For the ideal weight vector, For fuzzy basis function vectors, yes The estimated value, To estimate the error; , For a compact set; Next, we define the estimation error. Its derivative is: in, The Herwitz matrix is... , To estimate the error, For the real number field, , , , ; S4. Based on the event-triggered mechanism and fuzzy state estimator, a resilient adaptive controller is constructed using the backstepping method, including: (1): Establish a new coordinate transformation as follows: in, , The error variable after the attack. , The error variable triggered after the attack. The state variables are obtained through a low-pass filter. For the triggered variable, Let the rate of change of the state variable obtained through the low-pass filter be expressed as: ,in For the virtual controller before triggering, For design parameters; (2): Choose Lyapunov function for: in, It is a positive definite matrix. An attack buff that varies over an unknown period of time. , Design parameters for boundary layer error , , , , , yes The estimate, yes The estimate, yes The estimate, , , , , To estimate the error; Its derivative is: in, , For design constants, , It is a two-dimensional matrix. , To estimate the error The upper bound; (3): Design the virtual controller before triggering and the virtual controller after triggering as follows: in, For design parameters, It is a known constant; (4): The design of the elastic adaptive controller and the adaptive parameter update law are as follows: in, Positive design parameters; in, , , , and It is an adaptive parameter; Based on (3) and (4), we obtain: in , and As an auxiliary variable, , ; S5. Input the moment of inertia, link mass, and link length at the joint of the single-link robotic arm into the model of the single-link robotic arm system. Use the angle variable between the link and the horizontal ground after the triggered attack, the estimated angular velocity of the robotic arm joint, and the adaptive parameter value as the input values ​​of the elastic adaptive controller to obtain the output value of the elastic adaptive controller. Control the action of the single-link robotic arm system based on the output value.

2. The elastic intermittent control system for a single-link robotic arm system under deception attack as described in claim 1, characterized in that, include: The model building module is configured to build a model of a single-link robotic arm system. The triggering mechanism construction module is configured to: construct an event triggering mechanism for a single-link robotic arm system model under a deception attack; The estimator building module is configured to: build a fuzzy state estimator based on a single-link robotic arm system model and an event triggering mechanism; The controller building module is configured to construct an elastic adaptive controller based on an event-triggered mechanism and a fuzzy state estimator, using a backstepping method. The output module is configured to input the moment of inertia, link mass, and link length at the joint of the single-link robotic arm into the model of the single-link robotic arm system. It uses the angle variable between the link and the horizontal ground after the triggered attack, the estimated angular velocity of the robotic arm joint, and the adaptive parameter values ​​as input values ​​to the elastic adaptive controller to obtain the output value of the elastic adaptive controller. Based on the output value, it controls the action of the single-link robotic arm system.

3. An electronic device, characterized in that it comprises: Memory is used to store computer-readable instructions in a non-transitory manner. as well as Processor, for executing the computer-readable instructions, When the computer-readable instructions are executed by the processor, they perform the method described in claim 1.

4. A storage medium, characterized in that, Non-transitory storage of computer-readable instructions, wherein, when executed by a computer, the instructions of the method of claim 1 are executed.

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