Sliding mode control method and system for single-link mechanical arm under multi-node DoS attack

Abstract

The invention relates to the field of mechanical arm control, and discloses a sliding mode control method and system for a single-link mechanical arm under multi-node DoS attack, and the method comprises the steps: 1, constructing a dynamic model of the single-link mechanical arm, and constructing a T-S fuzzy switching model of the single-link mechanical arm as a controlled object; step 2, constructing a multi-node DoS attack model and acting on a communication channel between the sensor and the controller; step 3, introducing an RR communication protocol into a communication channel between the controller and the actuator; 4, constructing a fuzzy sliding mode controller; a closed-loop control system is integrated, and sliding mode control over the single-connecting-rod mechanical arm system is achieved. According to the method, T-S fuzzy modeling, the average residence time switching strategy, the sliding mode control law and the RR communication protocol are combined, the problems of high system nonlinearity, frequent working mode switching, limited communication resources, multi-node DoS attacks and the like in the posture control process of the mechanical arm are solved, and the safety, stability and control precision of the single-connecting-rod mechanical arm under complex working conditions are improved.

Description

Technical Field

[0001] This application belongs to the field of robotic arm control technology, and specifically relates to a sliding mode control method and system for a single-link robotic arm under multi-node DoS attacks. Background Technology

[0002] With the rapid development of robotics and intelligent manufacturing, robotic arms, as typical mechatronic equipment, are widely used in industrial scenarios such as assembly, handling, grasping, and precision operation. Among these applications, robotic arm posture control is one of the key technologies to ensure its motion accuracy, stability, and safety. Single-link robotic arms, as the most basic robotic arm structure, are characterized by strong system nonlinearity and easily changing parameters, and are often used as an important object for research and engineering verification of posture control methods. However, under complex working conditions and external disturbances, traditional linear control methods struggle to simultaneously achieve both control accuracy and system robustness.

[0003] In recent years, with the development of the Industrial Internet and networked control systems, robotic arm posture control has gradually evolved from local closed-loop control to a networked control architecture. Under this architecture, sensors, controllers, and actuators interact through communication networks. While this improves system flexibility and resource utilization, it also introduces problems such as limited communication bandwidth, data latency, and packet loss. Especially in multi-node systems, communication protocols such as Round-Robin (RR) are often used to schedule control signals, causing the control input to fail to update synchronously at each sampling moment, thus adversely affecting the performance and stability of robotic arm posture control.

[0004] Furthermore, the open network environment exposes robotic arm control systems to potential cybersecurity risks, among which Denial-of-Service (DoS) attacks are a common and highly destructive form of cyberattack. DoS attacks maliciously monopolize communication resources or block data transmission, preventing the timely transmission of attitude information from sensors to the controller, thus leading to decreased control performance or even system instability. In practical applications, the probability and timing of attacks on different communication nodes are random, making it difficult for a single attack model to accurately characterize attack behavior in a multi-node network environment.

[0005] Existing robotic arm posture control methods often assume a reliable communication environment or only analyze a single attack channel, making it difficult to simultaneously handle complex coupled issues such as the nonlinear characteristics of the robotic arm system, working mode switching, multi-node random DoS attacks, and communication protocol constraints. Therefore, there is an urgent need for a robust control method for networked robotic arm posture control that can still guarantee system stability and control performance while considering communication scheduling and multi-node DoS attacks.

[0006] It should be noted that the information disclosed in the background section above is only used to enhance the understanding of the background of this application, and therefore may include information that does not constitute prior art known to those skilled in the art. Summary of the Invention

[0007] To address or at least mitigate one or more of the above-mentioned problems, a sliding mode control method and system for a single-link robotic arm under multi-node DoS attacks is provided. This robotic arm posture control method can guarantee system stability and control performance without relying on the assumption of complete reliability of the communication environment. By constructing a unified system model capable of characterizing different operating conditions of the robotic arm, and comprehensively considering communication scheduling constraints and information loss caused by network attacks in the controller design, this invention achieves robust control of the posture of a single-link robotic arm, thereby improving the system's security, stability, and engineering applicability in complex network environments.

[0008] To achieve the above objectives, according to the first aspect of this application, a sliding mode control method for a single-link robotic arm under multi-node DoS attacks is provided, comprising: Step 1: Construct a dynamic model of a single-link robotic arm. Based on the constructed dynamic model of the single-link robotic arm, construct a TS fuzzy switching model of the single-link robotic arm, i.e., the single-link robotic arm system as the controlled object. Step 2: Construct a multi-node DoS attack model and apply it to the communication channel between the sensor and the controller; Step 3: Based on the constructed multi-node DoS attack model, introduce the RR communication protocol into the communication channel between the controller and the actuator: Step 4: Based on the constructed single-link robotic arm system and multi-node DoS attack model, construct a fuzzy sliding mode controller; The control signal output by the fuzzy sliding mode controller is applied to the single-link robotic arm system described in step 1 through the RR communication protocol. Based on the single-link robotic arm system, multi-node DoS attack model and fuzzy sliding mode controller constructed in the previous steps, a closed-loop control system is integrated and system stability and reachability analysis are performed to finally realize the sliding mode control of the single-link robotic arm system.

[0009] To achieve the above objectives, according to the second aspect of this application, a sliding mode control system for a single-link robotic arm under multi-node DoS attacks is provided, comprising: The first unit is used to construct a dynamic model of a single-link robotic arm. Based on the constructed dynamic model of the single-link robotic arm, a TS fuzzy switching model of the single-link robotic arm is constructed, that is, the single-link robotic arm system is used as the controlled object. The second unit is used to construct a multi-node DoS attack model and apply it to the communication channel between the sensor and the controller. The third unit is used to introduce the RR communication protocol into the controller-actuator communication channel based on the constructed multi-node DoS attack model: The fourth unit is used to build a fuzzy sliding mode controller for the constructed single-link robotic arm system; The closed-loop control unit applies the control signal output by the fuzzy sliding mode controller to the single-link robotic arm system through the RR communication protocol. Based on the single-link robotic arm system, multi-node DoS attack model, and fuzzy sliding mode controller constructed by the aforementioned unit, a closed-loop control system is integrated and system stability and reachability analysis are performed to ultimately achieve sliding mode control of the single-link robotic arm system.

[0010] To achieve the above objectives, according to a third aspect of this application, a computer-readable storage medium is provided storing a computer program, which, when executed by a processor, is used to implement the sliding mode control method for a single-link robotic arm under a multi-node DoS attack as described above.

[0011] By adopting the above technical solution, this application has the following beneficial effects compared with the prior art: This application utilizes the TS fuzzy model to describe the nonlinear dynamic characteristics of a single-link manipulator, and combines the RR communication protocol and sliding mode control strategy to improve the adaptability and stability of the control system. This invention introduces a multi-node DoS attack model, using Markov processes to model the attack states of each sensor node, effectively characterizing the attack states during network communication. Simultaneously, the RR communication protocol is used to schedule control signals, improving network resource utilization efficiency under bandwidth-constrained conditions. The TS fuzzy switching system, as an effective tool for handling nonlinear problems, represents the dynamic behavior of the manipulator under different operating states as a weighted combination of several linear sub-models, and achieves unified modeling and control design of the entire system through a switching mechanism. A sliding mode control strategy is introduced to enhance the system's ability to suppress external disturbances, model uncertainties, and network attacks. The proposed method can improve the system's adaptability to communication-constrained and random attack environments while ensuring attitude control accuracy, reducing control design complexity, and thus achieving the safety, real-time performance, and engineering feasibility of manipulator attitude control.

[0012] The specific embodiments of this application will be described in further detail below with reference to the accompanying drawings. Attached Figure Description

[0013] The accompanying drawings, which form part of this application, are used to provide a further understanding of the application. The illustrative embodiments and descriptions of the application are used to explain the application, but do not constitute an undue limitation of the application. Obviously, the drawings described below are merely some embodiments, and those skilled in the art can obtain other drawings based on these drawings without creative effort.

[0014] In the attached diagram: Figure 1 This is a logical schematic diagram of the sliding mode control method for a single-link robotic arm under multi-node DoS attacks in this specific embodiment. Figure 2 This is a schematic diagram illustrating the situation where the sensor-to-actuator channel 1 is subjected to a DoS attack in this specific embodiment; Figure 3 This is a schematic diagram illustrating the situation where the sensor-to-actuator channel 2 is subjected to a DoS attack in this specific embodiment; Figure 4 The simulation curve of the system state x(k) of the single-link robotic arm under sliding mode control in this specific embodiment is shown. Figure 5 The simulation curve of the control input u(k) of the single-link robotic arm under sliding mode control in this specific embodiment is shown. Figure 6 This is a simulation curve of the sliding mode variable s(k) of the single-link robotic arm under sliding mode control in this specific embodiment; Figure 7 This is a schematic diagram illustrating the switching process of the ADT-based subsystem in this specific embodiment. Detailed Implementation

[0015] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the technical solutions in the embodiments will be clearly and completely described below with reference to the accompanying drawings. The following embodiments are used to illustrate this application, but are not intended to limit the scope of this application.

[0016] Please see Figure 1 This application provides a sliding mode control method for a single-link robotic arm under multi-node DoS attacks, including: Step 1: Construct a dynamic model of a single-link robotic arm. Based on the constructed dynamic model of the single-link robotic arm, construct a discrete-time TS fuzzy switching model of the single-link robotic arm, i.e., the single-link robotic arm system as the controlled object. Step 2: Construct a multi-node DoS attack model and apply it to the communication channel between the sensor and the controller; Step 3: Based on the constructed multi-node DoS attack model, introduce the RR communication protocol into the communication channel between the controller and the actuator: Step 4: Based on the constructed single-link robotic arm system and multi-node DoS attack model, construct a fuzzy sliding mode controller; The control signal output by the fuzzy sliding mode controller is applied to the single-link robotic arm system described in step 1 via the RR communication protocol. Based on the single-link robotic arm system, multi-node DoS attack model, and fuzzy sliding mode controller constructed in the preceding steps, a closed-loop control system is integrated, and system stability and reachability analyses are performed. Ultimately, sliding mode control of the single-link robotic arm system is achieved.

[0017] Step 1, establish the dynamic model of the single-link robotic arm: A single-link robotic arm is a simple mechanical structure consisting of only one rigid link and one drive joint, primarily used to achieve rotational motion along the joint axis or oscillating motion in a specific direction. Its simple structure and low cost make it suitable for tasks such as grasping and transportation. Its continuous-time dynamic equations can be described by the following expression: (1); in, This indicates the joint angles of the robotic arm. Let be the angular velocity of the robotic arm, and be the angular acceleration of the robotic arm. Indicates control input, , , and These represent mass, arm length, moment of inertia, and damping, respectively. It is the acceleration due to gravity. For a moment.

[0018] Step 1: Establish the TS fuzzy switching model of the single-link robotic arm: The TS fuzzy switching system is a modeling method for describing nonlinear and multi-operating-state systems. By setting multiple fuzzy rules, it represents the dynamic behavior of the system under different operating states as corresponding linear sub-models. Membership functions are then used to weight or switch between these sub-models, thus achieving a unified description of the overall nonlinear system. This system effectively characterizes the changes in dynamic properties of system parameters caused by variations in operating states, and features a clear structure and flexible modeling.

[0019] In single-link robotic arm attitude control applications, the robotic arm's dynamic characteristics change with attitude angle, motion state, and load conditions. Using a TS fuzzy switching system to model the single-link robotic arm allows mapping the dynamic behavior of different attitude ranges or operating states to multiple linear subsystems. A smooth transition between system models is achieved through fuzzy weighting and switching mechanisms, thus reducing the complexity of control design and stability analysis while ensuring modeling accuracy. This modeling method is easily integrated with robust control strategies such as sliding mode control, which helps improve the stability and engineering feasibility of the robotic arm attitude control system under complex working conditions and uncertain environments.

[0020] The p-th fuzzy rule is: Fuzzy rule p:IF is and … and is THEN! (2); in, It is a state variable, and the state variable is taken as... It is a control input; It is an external interference, and satisfies , is a known constant; i represents the index number of the fuzzy rule. It is a switching signal. for abbreviated form, The time interval between switching is called the dwell time, where The time when the c-th switch occurs is... This is the moment immediately following the next switching event; , ..., It is a prerequisite variable. , ..., It is a fuzzy set; and Let the state matrix and input matrix of the system be known constant matrices, respectively; allowable uncertainty. satisfy , , It is a known constant matrix. It is an unknown time-varying matrix that satisfies Let I be the identity matrix; The known constant matrix is ​​represented as , Uncertainty is represented as ; Then, through TS fuzzy inference and with sampling period Discretization is performed to obtain the discrete-time TS fuzzy switching model of the single-link robotic arm, i.e., the single-link robotic arm system: (3); in, It is a normalized membership function, and ,satisfy , 1.

[0021] Step 2, establish a multi-node DoS attack model: In a networked control environment, a single-link robotic arm needs to transmit attitude information collected by multiple sensor nodes to the controller via a communication network during operation. Due to the openness and shared nature of communication networks, the transmission process may be affected by denial-of-service (DoS) attacks, causing some nodes to be unable to send data normally for a certain period. In practical applications, DoS attacks often do not only target a single communication node but may randomly occur on multiple nodes or communication channels, resulting in the loss or incompleteness of attitude information. To more realistically reflect the operating state of the robotic arm in a complex network environment, it is necessary to introduce a multi-node DoS attack model to uniformly describe the communication state of each node, providing a reasonable modeling foundation for subsequent controller design. Whether the current sensor-to-controller channel is under attack is indicated by: (4); in, p is a binary variable describing whether the current sensor-to-controller channel is under attack, where p is the order of the sensor-to-controller channel. variable Follows a two-state Markov chain with the following transition probabilities: (5); in, To start from the current state Transition to the next state The probability, This indicates that at the current time k, the state is... Under the premise that, at the next moment k+1, the state transitions to state. The probability, These represent the state of being attacked at the current moment and the state of being attacked at the next moment, respectively. It is the set of all possible attack states; The corresponding transition probability matrix of the p-th channel is expressed as: (6); in, ; Let p be the transition probability matrix of the p-th channel. The probability that the p-th channel is communicating normally at the current time and will remain so at the next time step. Let p be the probability that the p-th channel transitions from a normal communication state to a state subject to a DoS attack. Let p be the probability that the p-th channel recovers from a DoS attack state to a normal communication state. Let p be the probability that the p-th channel is in an attack state at the current time and will still be in an attack state at the next time. According to the defined Markov process, the steady-state probability of the DoS process for the p-th channel is calculated as follows: (7); in, Let represent the long-term probabilities of channel p being in a normal state and an attacked state, respectively. These steady-state distributions characterize the average availability and unavailability of communication networks over time.

[0022] In an unreliable network system, when a malicious DoS attack interferes with the p-th sensor-to-controller communication channel, the current state... The transmission may not reach the controller; At this point, the system will use the most recently received status information to compensate for the missing data, as follows: (8); When the p-th channel is operating normally Its current state It can be obtained directly; conversely, once a DoS attack occurs... The controller will use the last received state. As an alternative; This represents the state signal received by the controller at time k; The complete state vector obtained by the controller is represented as follows: (9); in, , , Represents a diagonal matrix; The attack on different communication channels is defined as occurring independently, i.e., n random variables. Since they are mutually independent, n independent Markov chains are used to characterize the random behavior of all transmission channels. For ease of subsequent analysis, a mapping method is used to map these n independent Markov chains to a unified Markov process. : (10); in, This is a mapping function.

[0023] Step 3, introduce the RR communication protocol: In networked control systems, the Round-Robin (RR) communication protocol is a communication method that polls and schedules multiple communication nodes in a predetermined order. It achieves a rational allocation of limited bandwidth by allowing only one node to obtain communication resources at each sampling time. This protocol has advantages such as simple scheduling rules, fair resource allocation, and ease of engineering implementation, and helps avoid communication conflicts and long-term channel occupancy by nodes. For the attitude control application of single-link robotic arms in a networked environment, since sensors and actuators share the communication network and communication resources are limited, adopting the RR communication protocol can effectively reduce the communication load and ensure that each node can obtain updated control information within a certain period of time, thus providing predictable communication conditions for controller design and system stability analysis.

[0024] The RR communication protocol is used to manage communication access between controller nodes. At each transmission time k, the protocol adjusts the communication based on the scheduling signal. Determine which controller node obtains the access token for the controller-actuator network; scheduling index. Update according to the following rules: (11); Where m is the total number of system controllers. The set of all controller serial numbers. This represents the modulo operation; When the scheduling signal satisfies That is, when At time k, only q actuators can receive the new control signal, where q is the actuator number; while the other actuators temporarily maintain their original control values ​​and will not receive any new updates. To mitigate the performance degradation that may be caused by communication constraints, for each actuator Define the corresponding compensation mechanism as follows: (12); in, For the q-th actuator, receive the control signal at the current moment. This represents the control signal output by the q-th controller at the current moment. The control signal received by the q-th actuator in the previous moment; this mechanism ensures that if the controller node fails to obtain an access token, its corresponding actuator will use the control value stored in the buffer of the previous step; Based on the RR communication protocol scheduling and potential DoS attacks, the available executor signal u(k) for the executor is represented as: (13); in, ; in, ;in, Let Kronecker function be denoted as Kronecker function; for convenience, let ... However, this does not lose its generality.

[0025] Step 4, for the single-link robotic arm system (3), design a fuzzy sliding mode controller: Sliding mode control is a robust nonlinear control method that constructs a suitable sliding surface to allow the system state to reach and remain near that surface within a finite time, thus effectively constraining the system's dynamic behavior. This method is insensitive to model parameter uncertainties and external disturbances, has a relatively simple control structure, and a fast response speed, making it particularly suitable for robotic arm control systems with nonlinear characteristics and uncertainties. In situations where network communication is limited and the system may be subject to disturbances or attacks, introducing sliding mode control strategies can help improve the stability and robustness of single-link robotic arm control systems, enhancing the system's engineering applicability.

[0026] The sliding surface is designed as follows: (14); Where G is the sliding mode matrix to be designed. It is the sliding surface. By adjusting this term, the system state can be made to approach the sliding surface and maintain the sliding mode. Probability correlation matrix and The definition is as follows: (15); in, and These represent the probabilities under normal transmission and DoS attack scenarios, respectively. Once the signal is transmitted Interrupted, the sliding variable in formula (14) Since it cannot be directly calculated, to ensure the feasibility of the controller in practical applications, the actual state will be considered in the subsequent control law design. It will be used with the corresponding value Replaced; based on the SMC framework and accessible system states, design the corresponding control law: (16); in, This represents the sliding mode control law at time k. Indicates and The relevant membership function, express norm, Represents a symbolic function. This represents the control gain matrix to be designed, used to stabilize the linear part of the system. For formula (14) Replace with The result; The closed-loop control system design for the single-link robotic arm is as follows: (17); in, Represents the relevant terms of the system state matrix. This represents time-varying terms related to system input; ; .

[0027] Step 5, System Stability Analysis: To ensure the stable operation of the single-link robotic arm, the mean square stability of the control system under different scheduling states needs to be verified using mathematical tools. The Lyapunov function method can be used to ensure stable convergence of the system in the desired sense.

[0028] To analyze the stability of the closed-loop system (17), the following Lyapunov function is selected: (18); in, It is the weight matrix of the current system state, used to measure the state energy of the system at the current moment, and its expected descent property can be used to judge the stability of the system; It is a compensation weight matrix for the "state lag" caused by DoS attacks, to prevent the Lyapunov function from not closing due to data loss; It is the weight matrix for controlling the input to maintain the error under the RR protocol, ensuring that the system is still analyzable when scheduling is limited.

[0029] Calculate the expected difference of the Lyapunov function: (19); in, Let represent a known constant that reflects the decay rate and satisfies ... , {*} represents the mathematical expectation operation. This indicates that the current system state is known. and attack signals Under the premise that, the Lyapunov function at the next moment The mathematical expectation; Verification yielded the following results: (20); Through the iterative equation, we can obtain: (twenty one); in, This represents the exponential decay factor related to the current switching path. Indicates the time of switching and the corresponding switching signal The Lyapunov function value below, Indicates the switching time. The switching signal indicating the switching time. It is a positive constant. Indicates the average length of stay; Indicates the time interval The number of times the internal switching signal σ is switched; Based on equation (18), we can obtain: (twenty two); (twenty three); (twenty four); Where a and b are the minimum and maximum amplification factors between the Lyapunov function and the system state norm, respectively, used to establish the upper and lower bounds between them to aid in stability analysis. If the following conditions are met... , If , then system (3) is mean square exponentially stable.

[0030] Step 6, Reachability Analysis: Sliding mode reachability analysis further demonstrates that the state of the single-link robotic arm system can approach the target control surface within a finite time, exhibiting good convergence and engineering feasibility.

[0031] Prove that the state trajectory of the TS fuzzy switching system (3) can reach the neighborhood of the specified sliding surface s(k) = 0 in the mean square sense. Sliding mode domain for: (25); in, for norm, The upper bound term caused by disturbances and communication scheduling is defined as follows: Sliding mode domain This indicates the small region near the sliding surface into which the state will be driven in the mean-square sense. Represents a positive definite matrix The smallest eigenvalue is used to define the lower bound of the growth of the Lyapunov function. This represents an intermediate variable in the LMI conditions related to the sliding surface, used to control the energy of the disturbance term; m is the total number of controllers. Indicates system state The square of the norm, Indicates the state acquired by the controller. The square of the norm.

[0032] From (14) and (17), we can obtain: (26); Choose the Lyapunov function as: (27); in It is the sliding surface energy weight matrix, used to characterize the distance from the system to the sliding surface.

[0033] calculate When the state trajectory remains in the region Other than: (28); It can be verified that: (29); Therefore, the Lyapunov function is monotonically decreasing outside the sliding mode domain. This means that the system's state trajectory will converge to the sliding mode domain within a finite time. middle.

[0034] The invention will be further explained below by providing relevant parameters of the single-link robotic arm system.

[0035] Select the length of the single-link robotic arm. Gravitational acceleration ; Select the initial system state as ; Select a TS fuzzy switching system containing two switching subsystems, each with two fuzzy rules, with the following system parameters: , , and These represent mass, arm length, moment of inertia, and damping, respectively.

[0036] Subsystem 1 (Light Load Mode): Load quality Moment of inertia Damping term ; , , , ; , , , ; , ; Subsystem 2 (High-speed flight mode): Load quality Moment of inertia Damping term ; , , , ; , , , ; , ; The membership function is chosen as follows:

[0037] ; Suppose there are two channels on the sensor-to-controller path that may be subject to DoS attacks. Each channel is modeled using a two-state Markov chain, and its transition matrix is ​​as follows: , ; The steady-state probabilities of DoS attacks for each corresponding channel are as follows: ; Select parameters in stability analysis .

[0038] Two actuators are used, and the update matrix in equation (13) is selected as follows. , .

[0039] The system was simulated under the above simulation conditions to verify its attitude control capability.

[0040] Figure 2 This demonstrates the frequency of DoS attacks suffered by the sensor-to-controller channel 1 of a single-link robotic arm. The horizontal axis represents simulation time in seconds; the vertical axis... This is the attack signal from the sensor to controller channel 1. Among them, This indicates that the system has been subjected to a DoS attack. This indicates that the system has not been attacked. During an attack, communication between the system and the controller will be maliciously interrupted.

[0041] Figure 3 This demonstrates the frequency of DoS attacks suffered by the sensor-to-controller channel 2 of a single-link robotic arm. The horizontal axis represents simulation time in seconds; the vertical axis... This is the attack signal from the sensor to controller channel 2. Among them, This indicates that the system has been subjected to a DoS attack. This indicates that the system has not been attacked. During an attack, communication between the system and the controller will be maliciously interrupted.

[0042] Figure 4 This reflects the time response of the system state variables of a single-link robotic arm. The horizontal axis represents the simulation time in seconds; the vertical axis represents the amplitude of the system state variables. (Dashed line curve) Angular velocity, in rad / s, represented by a dotted-dash curve. Angular acceleration, in rad / s² 2 .

[0043] Despite system parameter uncertainties, load switching, multi-channel DoS attacks, and RR communication scheduling constraints, the system state can still converge to near the equilibrium point in a short time without significant oscillations. This indicates that the designed sliding mode controller can effectively guarantee the mean square exponential stability of the single-link robotic arm system and has good dynamic response performance.

[0044] Figure 5 This demonstrates the control input of a single-link robotic arm. The horizontal axis represents simulation time in seconds; the vertical axis represents the control input. The solid curve represents the control input. The dashed-dot curve represents the control input. The figure shows that the designed sliding mode control strategy can avoid continuous large-amplitude control inputs while ensuring system stability, thereby achieving a control effect with low energy consumption and low actuator burden, and is suitable for robotic arm systems with communication constraints.

[0045] Figure 6 This reflects the changes in sliding mode variables of the single-link robotic arm system under the action of the sliding mode controller. The horizontal axis represents the simulation time in seconds; the vertical axis represents the sliding mode variables. The solid curve represents the sliding mode variables. The dashed-dot curve represents the sliding mode variable. The rapid convergence of the sliding mode variables indicates that the system state can quickly approximate the sliding surface, and the system enters the sliding mode dynamic process. This demonstrates that the proposed control method has good resistance to parameter uncertainties, network attacks, and strong system robustness, and the control strategy is reliable.

[0046] Figure 7 The figure illustrates the subsystem switching frequency based on the average residence time. The horizontal axis represents simulation time in seconds; the vertical axis represents the mode, i.e., the subsystem number. As can be seen from the figure, the system dynamically switches between two subsystems, and the switching frequency is constrained by the ADT (Active Time Transmission) constraint. No frequent high-frequency jumps occurred during the entire switching process. This figure demonstrates that the controller structure exhibits good switching logic stability under ADT control, effectively avoiding unstable behavior caused by excessively rapid switching.

[0047] Based on the same inventive concept, this application also provides a sliding mode control system for a single-link robotic arm under multi-node DoS attacks, the sliding mode control system comprising: The first unit is used to construct a dynamic model of a single-link robotic arm. Based on the constructed dynamic model of the single-link robotic arm, a TS fuzzy switching model of the single-link robotic arm is constructed, that is, the single-link robotic arm system is used as the controlled object. The second unit is used to construct a multi-node DoS attack model and apply it to the communication channel between the sensor and the controller. The third unit is used to introduce the RR communication protocol into the controller-actuator communication channel based on the constructed multi-node DoS attack model: The fourth unit is used to build a fuzzy sliding mode controller for the constructed single-link robotic arm system; The closed-loop control unit applies the control signal output by the fuzzy sliding mode controller to the single-link robotic arm system through the RR communication protocol. Based on the single-link robotic arm system, multi-node DoS attack model and fuzzy sliding mode controller constructed by the aforementioned unit, a closed-loop control system is integrated to ultimately realize the sliding mode control of the single-link robotic arm system.

[0048] Based on the same inventive concept, this application also provides a computer-readable storage medium storing a computer program, which, when executed by a processor, implements the sliding mode control method for a single-link robotic arm under a multi-node DoS attack as described above.

[0049] The program product of this application for implementing the above method may employ a portable compact disk read-only memory and include program code, and may run on a terminal device, such as a personal computer. However, the program product of this application is not limited thereto. In this application, the readable storage medium may be any tangible medium containing or storing a program that may be used by or in conjunction with an instruction execution system, system, or device.

[0050] It should be noted that a computer-readable storage medium may include data signals propagated in baseband or as part of a carrier wave, carrying readable program code. Such propagated data signals may take various forms, including but not limited to electromagnetic signals, optical signals, or any suitable combination thereof. A readable storage medium may also be any readable medium other than a readable storage medium, capable of sending, propagating, or transmitting programs for use by or in conjunction with an instruction execution system, system, or device. The program code contained on the readable storage medium may be transmitted using any suitable medium, including but not limited to wireless, wired, optical fiber, RF, etc., or any suitable combination thereof.

[0051] The above are merely preferred embodiments of this application and are not intended to limit this application in any way. Although this application has disclosed preferred embodiments as described above, it is not intended to limit this application. Any person skilled in the art can make some modifications or alterations to the above-mentioned technical content to create equivalent embodiments without departing from the scope of the technical solution of this application. The implementation schemes in the above embodiments can also be further combined or replaced. Any simple modifications, equivalent changes and alterations made to the above embodiments based on the technical essence of this application without departing from the content of the technical solution of this application shall still fall within the scope of this application.

Claims

1. A method for sliding mode control of a single-link manipulator under multi-node DoS attack, characterized in that, The method comprises the following steps: Step 1, constructing a single-link robot arm dynamics model, and constructing a discrete-time T-S fuzzy switching model of the single-link robot arm based on the single-link robot arm dynamics model, so that the single-link robot arm system serves as a controlled object; Step 2, constructing a multi-node DoS attack model and applying the model to a sensor-controller communication channel; Step 3, introducing an RR communication protocol into a controller-actuator communication channel based on the constructed multi-node DoS attack model; Step 4, constructing a fuzzy sliding mode controller based on the constructed single-link robot arm system and multi-node DoS attack model; The control signal output by the fuzzy sliding mode controller is applied to the single-link robot arm system of Step 1 through the RR communication protocol, and a closed-loop control system is integrated based on the single-link robot arm system, multi-node DoS attack model and fuzzy sliding mode controller constructed by the preceding steps, and system stability analysis and reachability analysis are performed, so as to finally realize sliding mode control of the single-link robot arm system.

2. The method of claim 1, wherein, The single-link robot arm dynamics model comprises: （1）； wherein, denotes the joint angle of the robot arm, is the angular velocity of the robot arm, is the angular acceleration of the robot arm, denotes the control input, , , and represent the mass, the arm length, the moment of inertia and the damping term, respectively, is the gravitational acceleration, is the time instant.

3. The method of claim 2, wherein, The discrete-time T-S fuzzy switching model of the single-link robot arm is constructed based on the single-link robot arm dynamics model, and the single-link robot arm system serves as a controlled object; The pth fuzzy rule is: Fuzzy rule p: IF is and … and is THEN; （2）； where is a state variable, taking values in the state variable set is a control input; is an external disturbance, and satisfies , is a known constant; i denotes the index number of the fuzzy rule, is a switching signal, is a short form of , the switching time interval between is the time instant of the cth switching, is the time instant of the next switching; , is a premise variable, , is a fuzzy set; and denote the state matrix and the input matrix of the system, respectively, are known constant matrices; the allowed uncertainty satisfies , , is a known constant matrix, is an unknown time-varying matrix satisfying , is the identity matrix; let , the known constant matrix is denoted as , , the uncertainty is denoted as ; Then, the T-S fuzzy inference is performed and the sampling period The discretization processing is performed to obtain a discrete-time T-S fuzzy switching model of the single-link robot arm, i.e., a single-link robot arm system: （3）； wherein is a normalized membership function satisfying , 1.

4. The method of claim 3, wherein, The multi-node DoS attack model is constructed and applied to the sensor-controller communication channel, and comprises: Whether the current sensor-to-controller channel is under attack is represented as: （4）； wherein, is a binary variable describing whether the current sensor-to-controller channel is under attack, is the order of the sensor-to-controller channel. Binary variable , denotes the index of the variable, following a two-state Markov chain with the following transition probabilities: （5）； wherein, is the probability of transitioning from the current state to the next state , denotes the probability of transitioning to state at the next time instant k+1 given that at the current time instant k the state is , denote the state under attack at the current time instant and the state under attack at the next time instant, respectively, is the set of all possible states under attack. The first corresponding transition probability matrix of the respective channel is represented as: (6)； wherein, ; is the transition probability matrix of the pth channel, the channel is in normal communication at the current time and remains normal at the next time, is the probability that the channel transitions from a normal communication state to a state suffering from a DoS attack, is the probability that the channel recovers from a DoS attack state to a normal communication state, is the probability that the channel is in an attack state at the current time and remains in an attack state at the next time; The steady state probability of the DoS process for the i th channel, is calculated as: (7)； wherein respectively represent a channel the long-term probabilities of being in a normal state and an attacked state, and ; In a network system where unreliability exists, when a malicious DoS attack interferes with the sensor-to-controller communication channel, the current state of transmission cannot reach the controller. ​ At this time, the system will use the most recently received state information to compensate for the missing data, as follows: (8)； When the When each channel is operating normally, that is Current state Direct acquisition; once a DoS attack occurs... The controller will use the last received state. As an alternative; Indicates the controller at time. Received status signals; The complete state vector obtained by the controller is represented as: (9)； wherein, , , denotes a diagonal matrix, denotes the state vector received by the 1st, 2nd,..., n controllers at time k, denotes a random binary variable for the 1st, 2nd,..., n sensor-to-controller channels; Attacks defining different communication channels are independent occurrences, i.e. a random binary variable are independent of each other; thus, the stochastic behavior of all transmission channels is represented by independent Markov chains; the mapping method is used to map the independent Markov chains into a unified Markov process : (10)； wherein is a mapping function.

5. The method of claim 4, wherein, The RR communication protocol is introduced into the controller-actuator communication channel based on the constructed multi-node DoS attack model, and comprises: The communication access between the controller nodes is managed using a RR communication protocol, which at each transmission instant determines which controller node gets the access token to the controller and actuator network according to a scheduling signal ; the scheduling index is updated according to the following rule: (11)； wherein, is the total number of system controllers, is a set of all controller sequence numbers, denotes a modulo operation; When the scheduling signal satisfies That is, when At that time, only Each actuator at transmission time Receive new control signals, This is the actuator's sequence number; other actuators will temporarily retain their original control values ​​and will not receive any new updates. For each actuator A compensation mechanism is defined for each actuator, as follows: (12)； in, For the first Each actuator receives the control signal at the current moment. For the first The control signal output by the controller at the current moment For the first The control signal received by each actuator in the previous moment; the compensation mechanism ensures that if the controller node fails to obtain an access token, the corresponding actuator of the controller node will use the control value stored in the buffer of the previous step; scheduling and potential DoS attacks based on the RR communication protocol, actuator signals available to the actuator is represented as: (13)； ; ; ； ； wherein, represents the original control signal outputted by the 1st, 2nd, …, mth controller at the kth moment, represents the control signal received by the 1st, 2nd, …, mth actuator at the kth moment, represents the scheduling weight coefficient of the 1st, 2nd, …, mth RR protocol, represents the Kronecker function.

6. The method of claim 3, wherein, The fuzzy sliding mode controller is constructed based on the constructed single-link robot arm system and multi-node DoS attack model, and comprises: The sliding mode surface is designed as: (14)； wherein G is a sliding mode matrix to be designed, is the sliding surface, by adjusting this term the system state tends to the sliding surface and maintains the sliding mode. Probability correlation matrix and is defined as follows: (15)； wherein, and respectively represent the probabilities under normal transmission and DoS attack scenarios; Once the transmission signal is interrupted, the sliding variable in equation (14) will not be directly calculated, to ensure the feasibility of the controller in practical applications, in the subsequent control law design, the actual state will be replaced by the corresponding value ; based on the SMC framework and the accessible system state, the corresponding control law is designed: （16）； wherein, denotes the sliding mode control law at time k, denotes the membership function associated with denotes the norm of denotes the sign function, denotes the control gain matrix to be designed for stabilizing the linear part of the system, is replaced by in formula (14) by resulting in;​ The closed-loop control system of the single-link robot arm is designed as follows: （17）； ； ； wherein, represents a system state matrix dependent term, represents a time varying term dependent on system inputs.

7. A sliding mode control system for a single-link manipulator under multi-node DoS attack, characterized by, The sliding mode control system comprises: A first unit is configured to construct a single-link robot arm dynamics model, and construct a T-S fuzzy switching model of the single-link robot arm based on the constructed single-link robot arm dynamics model, so that the single-link robot arm system serves as a controlled object; A second unit is configured to construct a multi-node DoS attack model and apply the model to a sensor-controller communication channel; A third unit is configured to introduce an RR communication protocol into a controller-actuator communication channel based on the constructed multi-node DoS attack model; A fourth unit is configured to construct a fuzzy sliding mode controller based on the constructed single-link robot arm system and multi-node DoS attack model; A closed-loop control unit is configured to apply the control signal output by the fuzzy sliding mode controller to the single-link robot arm system through the RR communication protocol, and integrate a closed-loop control system based on the single-link robot arm system, multi-node DoS attack model and fuzzy sliding mode controller constructed by the preceding units, and perform system stability analysis and reachability analysis, so as to finally realize sliding mode control of the single-link robot arm system.

8. A computer readable storage medium storing a computer program, characterized in that, The computer program, when executed by a processor, is configured to implement the sliding mode control method for a single-link robot arm under multi-node DoS attack according to any one of claims 1-6.

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