Multi-mobile-robot intermittent formation tracking control method for denial of service attack

Abstract

The invention relates to a multi-mobile-robot intermittent formation tracking control method for denial of service attack, and belongs to the technical field of multi-mobile-robot control. Aiming at the problems of poor anti-interference performance, waste of communication computing resources, uncontrollable convergence time and strong model dependence in the prior art, a remote control terminal and ultrasonic radio station cooperative anti-attack switching scheme is provided, a distributed observer is adopted to realize leader state estimation, resource consumption is reduced by combining intermittent communication and an intermittent control mechanism, and the reliability of the system is improved. And a preset time adjustment function ensures user-defined convergence, and a reinforcement learning network optimization control strategy is introduced. The anti-attack capability and the self-adaptive performance of the system are improved, high-precision formation tracking is realized, the communication and calculation burden is remarkably reduced, and the expansibility is high.

Description

Technical Field

[0001] The invention belongs to the technical field of multi-mobile robot control and relates to an intermittent formation tracking control method for multi-mobile robots that are under denial of service attack. Background Art

[0002] With the advancement of industrial automation and intelligent systems, multi-mobile robot systems are increasingly being used in logistics and warehousing, disaster relief, military reconnaissance, and other fields. These systems utilize distributed collaborative control to achieve formation, path tracking, and task coordination. Their performance relies on efficient communication networks and robust control algorithms. However, existing technologies for multi-mobile robot systems still have significant shortcomings in terms of interference immunity, communication efficiency, computational resource optimization, and adaptability to dynamic environments.

[0003] Existing systems often rely on wireless communication technologies, such as Wi-Fi or Bluetooth, but lack effective protection against denial-of-service attacks. Attackers can cause robots to lose connection or control failure by blocking communication channels. Traditional anti-interference methods, such as frequency-hopping communication, can only mitigate weak interference and are unable to cope with high-intensity or sustained attacks. Furthermore, current formation control strategies typically require followers to directly access leader information. If communication is interrupted or the topology changes, the system cannot adapt, resulting in reduced formation stability or even failure.

[0004] In terms of distributed observer design, existing solutions can reduce reliance on central nodes, but they are computationally complex and struggle to guarantee accurate estimations when communication resources are limited. Regarding communication mechanisms, traditional time-triggered control requires robots to continuously exchange data, which can lead to bandwidth waste and network congestion. While event-triggered control can reduce communication times, its triggering conditions are complex to design, and the frequent execution of threshold calculations increases the processor burden.

[0005] Control algorithms also lack resource efficiency. For example, traditional methods such as PID or model predictive control use a fixed-period update of the control variable. This means that even if the system state hasn't changed significantly, calculations continue, leading to unnecessary consumption of computing resources. Furthermore, the convergence time of finite-time or fixed-time control often depends on the system's initial state or parameters and cannot be directly set by the user, limiting its application in time-sensitive scenarios.

[0006] Model dependency is another challenge. Model-based control methods, such as sliding mode control or adaptive control, rely on precise dynamic models and struggle to cope with unknown friction, external disturbances, or sudden load changes. While existing neural networks can approximate unknown dynamics, their lack of collaborative optimization with reinforcement learning results in suboptimal control inputs, impacting tracking accuracy and overall system performance.

[0007] In summary, existing technologies have significant bottlenecks in the anti-attack capability, communication and computing resource optimization, convergence time controllability and model adaptability of multi-mobile robot systems. There is an urgent need for a new control method that can balance safety, efficiency and accuracy. Summary of the Invention

[0008] In view of this, the object of the present invention is to provide a multi-mobile robot intermittent formation tracking control method for denial of service attacks.

[0009] Aiming at the problem that multi-mobile robot systems are unable to communicate with each other due to denial of service attacks, a remote control terminal-ultrasonic radio-multi-mobile robot control scheme is proposed to ensure user control over the multi-mobile robot system.

[0010] Aiming at the problem that followers in a multi-mobile robot system cannot obtain leader information, a distributed observer is proposed, which enables all followers in the multi-mobile robot system to estimate the leader information through neighbor information interaction.

[0011] Aiming at the problem of limited communication resources in multi-mobile robot systems, an intermittent communication mechanism is proposed to intermittently interact with intelligent agents in the multi-mobile robot system and alleviate the burden of communication resources.

[0012] In response to the system convergence rate requirements, a preset time adjustment function is introduced in the distributed observer, controller and neural network weight update rate, so that the system state can accurately converge to the expected value within the time preset by the user.

[0013] In response to the control accuracy requirements and the unknown dynamics in the system, a reinforcement learning identification-execution-evaluation network is introduced, which uses neural networks to approximate the unknown dynamics while optimizing the system control input.

[0014] Aiming at the problem of computing resource waste caused by redundant control input of mobile robots, an intermittent control mechanism is proposed to intermittently input the control of mobile robots and reduce the burden of computing resources.

[0015] In order to achieve the above object, the present invention provides the following technical solutions:

[0016] A method for tracking and controlling a multi-mobile robot intermittent formation in a denial-of-service attack environment comprises the following steps:

[0017] S1: When a denial of service (DoS) attack is detected, the control of the multi-mobile robot system is switched to the remote control terminal, which sends control commands to the mobile robots through the local area network constructed by the ultrasonic radio;

[0018] S2: Through the distributed observer, the follower mobile robot estimates the position and velocity state of the leader based on the information interaction of the neighboring nodes. The expression of the distributed observer is:

[0019]

[0020] in, β(t) is the preset time adjustment function, a i,j is the communication topology weight;

[0021] S3: Adopting an intermittent communication mechanism, the neighbor node information is updated only under trigger conditions. The trigger conditions are:

[0022]

[0023] S4: Design an optimal controller based on a reinforcement learning network, including an identification network, an execution network, and an evaluation network. The identification network is used to approximate the unknown dynamics of the system, the execution network generates control inputs, and the evaluation network optimizes the control strategy.

[0024] S5: Through the intermittent control mechanism, the control input is updated only at the triggering moment, which is determined by the dynamic relationship between the speed tracking error and the control input derivative.

[0025] Furthermore, in S1, the communication parameters of the ultrasonic radio station include:

[0026] The RF output power is 4W×2, the bandwidth is 10MHz, the operating frequency is 2.4GHz, the maximum communication distance is 20km, and the communication delay T=T1+T2 satisfies T≤15.426ms, where T1 is the encoding and decoding delay and T2 is the transmission delay.

[0027] Furthermore, in S1, the expression of the preset time adjustment function β(t) is:

[0028]

[0029] Where T * It is the convergence time set by the user, and p is a constant.

[0030] Furthermore, in S2, the convergence of the distributed observer is verified by Lyapunov's stability theorem, and the neighbor information update is suspended during the DoS attack.

[0031] Furthermore, in S4, the expression of the identification network is:

[0032]

[0033] Among them, i =[p i(t),v i (t)] T , S(·) is the basis function, is the neural network weight.

[0034] Furthermore, the neural network weights The update law is:

[0035]

[0036] Among them, γ fi is the learning rate, σ i is the attenuation coefficient.

[0037] Furthermore, in S5, the triggering condition for intermittent control is:

[0038]

[0039] Among them, ω i,1 、ω i,2 、ω i,3 is the weight coefficient.

[0040] Furthermore, in S4, the value function of the evaluation network is:

[0041]

[0042] where Q i 、R i is a positive definite weight matrix.

[0043] Furthermore, in S3, the intermittent communication mechanism adopts space-time coding technology when communication is restored, with a coding delay of 5ms and a decoding delay of 10ms.

[0044] Furthermore, in S1, the remote control terminal receives the status information and environment image of the mobile robot in real time, and feeds it back to the user end via the ultrasonic radio.

[0045] The beneficial effects of the present invention are:

[0046] (1) Through the collaborative control scheme of the remote control terminal and the ultrasonic radio, seamless switching of control rights is achieved when a denial of service attack occurs, ensuring the safety and controllability of the multi-mobile robot system under extreme interference and avoiding the risk of formation failure or loss of control due to communication interruption.

[0047] (2) The designed distributed observer allows all followers to estimate the leader's state only through local neighbor information interaction, transforming the complex multi-agent coordination problem into a single robot tracking control problem, significantly reducing the system complexity and improving the robustness, while reducing the dependence on the central node.

[0048] (3) An intermittent communication mechanism is introduced to dynamically adjust the frequency of information exchange between multiple mobile robots through a self-triggering strategy, triggering communication updates only when necessary, significantly reducing network bandwidth occupancy and energy consumption, and alleviating the communication congestion problem of large-scale cluster systems.

[0049] (4) A preset time adjustment function is embedded in the observer, controller, and neural network, so that signals such as system tracking error and parameter estimation error are forced to converge within a fixed time defined by the user, breaking through the limitations of traditional methods that rely on initial states or system parameters and meeting the requirements of high-timeliness tasks.

[0050] (5) The identification-execution-evaluation network architecture that integrates reinforcement learning achieves high-precision tracking control by online approximation of unknown dynamics and collaborative optimization of control strategies. At the same time, it reduces model dependence, effectively copes with uncertainties such as friction and disturbances, and improves the system's adaptability.

[0051] (6) An intermittent control mechanism is adopted, combined with trigger conditions to dynamically predict the control input update time, avoiding the redundant calculations caused by traditional continuous control or fixed-period updates, significantly reducing the processor load, and is particularly suitable for resource-constrained embedded mobile robot platforms.

[0052] (7) Through modular design, it integrates anti-attack control, distributed estimation and optimization algorithms, and can adapt to heterogeneous robot clusters and diversified task scenarios, providing a general solution for multi-robot collaborative applications in industrial automation, intelligent warehousing and other fields.

[0053] Other advantages, objects, and features of the present invention will be described in part in the following description and, in part, will be apparent to those skilled in the art upon examination of the following description or may be learned from practice of the present invention. The objects and other advantages of the present invention may be realized and obtained through the following description. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] In order to make the purpose, technical solutions and advantages of the present invention more clear, the present invention will be described in detail below with reference to the accompanying drawings, in which:

[0055] Figure 1 To protect against communication topology changes under denial of service attacks;

[0056] Figure 2 Time series for denial of service attacks;

[0057] Figure 3 Provide control solutions for denial of service attacks;

[0058] Figure 4 Optimal intermittent control scheme for mobile robots based on reinforcement learning;

[0059] Figure 5 It is a flow chart of the present invention. DETAILED DESCRIPTION

[0060] The following describes the embodiments of the present invention by means of specific examples, and those skilled in the art can easily understand other advantages and effects of the present invention from the contents disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and the details in this specification can also be modified or changed in various ways based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that the illustrations provided in the following embodiments are only schematic illustrations of the basic concept of the present invention, and the following embodiments and features in the embodiments can be combined with each other without conflict.

[0061] Among them, the accompanying drawings are only for illustrative purposes and represent only schematic diagrams rather than actual pictures, and should not be understood as limiting the present invention. In order to better illustrate the embodiments of the present invention, some parts of the accompanying drawings may be omitted, enlarged or reduced, and do not represent the dimensions of actual products. For those skilled in the art, it is understandable that some well-known structures and their descriptions may be omitted in the accompanying drawings.

[0062] The same or similar numbers in the drawings of the embodiments of the present invention correspond to the same or similar parts; in the description of the present invention, it should be understood that if there are terms such as "upper", "lower", "left", "right", "front", "back", etc. indicating directions or positional relationships, they are based on the directions or positional relationships shown in the drawings. They are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific direction, be constructed and operate in a specific direction. Therefore, the terms describing the positional relationship in the drawings are only used for illustrative purposes and cannot be understood as limiting the present invention. For ordinary technicians in this field, the specific meanings of the above terms can be understood according to specific circumstances.

[0063] 1. Kinematic Model of Multiple Mobile Robots and Denial of Service Attack

[0064] (1) Kinematic model of mobile robot

[0065] A multi-mobile robot system refers to an intelligent group of multiple autonomous or semi-autonomous robots that complete complex tasks in a shared environment through collaborative control and communication networks. This type of system achieves collaboration through technologies such as distributed perception, task allocation, and path planning. It has the advantages of high efficiency, flexibility, and robustness, and is widely used in logistics warehousing, intelligent manufacturing, disaster relief, agricultural inspections, and military reconnaissance. With the development of 5G communications, edge computing, and swarm intelligence algorithms, multi-mobile robot systems are evolving towards heterogeneous collaboration, adaptive learning, and large-scale clustering, becoming a key technical support for the construction of smart cities. The kinematic model of mobile robots is:

[0066]

[0067] Where: p i ∈R n is the position state; v i ∈R n is the speed state; u i ∈R n is the control input; f i (p i (t),v i (t))∈R n It is the unknown dynamic of the system;

[0068] The leader kinematic model of the multi-mobile robot system is:

[0069]

[0070] (2) Denial of Service Attack Model

[0071] Denial of service attacks are one of the most common types of network attacks, primarily exploiting vulnerabilities in network protocols to exhaust target resources. Figure 1 This paper demonstrates a scenario in which a mobile robot cluster is subjected to a denial of service attack. It is clear that when a communication channel is attacked by a denial of service (DoS) attack, information on that channel becomes unavailable during the attack, implying a detrimental impact on the communication of the multi-mobile robot system. Typically, resources for DoS attacks are limited, and the attack requires a continuous supply of energy. Therefore, during the dormant period of a DoS attack, the communication mechanism can be quickly restored. Without loss of generality, the initial communication topology of the multi-mobile robot cluster is assumed to be strongly connected. Furthermore, it is assumed that after a communication channel is attacked by a DoS attack, the mobile robot can abandon communication on that channel; until the communication topology is restored, the mobile robot becomes uncontrollable and discards information from neighboring drones.

[0072] To facilitate analysis, the denial of service attack is mathematically modeled as follows:

[0073]

[0074] Where: Δ m The time interval between denial of service attacks on multiple mobile robot systems;

[0075] Denial of service attack time series Figure 2 shown.

[0076] 2. Remote Control of Multi-Mobile Robot Systems Under Denial of Service Attacks

[0077] When the system is attacked by a denial of service, the mobile robot will be out of control. To ensure the security of the system, the present invention proposes a remote control terminal-ultrasonic radio-multi-mobile robot system control scheme. During the denial of service attack period, the remote control terminal is used to take over the control of the system to ensure the security of the system and complete the formation task. In order to solve the problem of beyond visual range between the remote control terminal and the multi-mobile robot system, an ultrasonic radio is used to establish a large-scale local area network, realize TCP / UDP communication, delegate control instructions, receive mobile robot information, and monitor the surrounding images of the mobile robot in real time, helping users to complete the control of the mobile robot. The control scheme is as follows: Figure 3 shown.

[0078] The relevant technical specifications of the ultrasonic radio are as follows: RF output power S1 = 4W × 2, bandwidth B = 10MHz, and operating frequency f = 2.4GHz. Assuming the maximum communication range of the remote control terminal-multi-mobile robot system is d = 20km, calculate the free-space path loss at an ultrashort wave radio operating frequency f of 2.4GHz.

[0079] FSPL=20lg(d)+20lg(f)-147.55=126.07dB (4)

[0080] When the bandwidth B of the ultra-short wave radio is 10MHz, calculate the corresponding noise power.

[0081] P noise =k·T·B (5)

[0082] Where k is the Boltzmann constant. Assuming the temperature T is 290K (room temperature), the noise power P is calculated as noise =4.002×10 -16 W; Calculate the data transmission channel capacity of ultra-short wave radio stations based on the Shannon-Hartley theorem

[0083]

[0084] The calculated value is C = 94.07 Mbps.

[0085] The communication delay based on ultra-short wave radio consists of two parts: encoding and decoding delay and transmission delay. The encoding and decoding delay is the delay caused by the ultra-short wave radio using space-time coding technology. The space-time coding process involves converting the data stream. The ultra-short wave radio uses a complex coding scheme (Alamouti coding). The transmission of each time slot or symbol needs to rely on the previous symbol to generate redundant information. For Alamouti coding, the coding delay is mainly reflected in the synchronization and processing of signals from multiple antennas. The delay of the coding process is usually related to the transmission period of each symbol (such as the symbol period). Assume that the transmission period of each symbol is T s, the coding delay is roughly the length of each symbol period (approximately 5ms). The decoding process for Alamouti coding is relatively simple, typically using least squares estimation (LS) or maximum likelihood detection (MLD), which have low computational complexity. For a 2x2 receive matrix, the decoding delay is typically constant (approximately 10ms), independent of the number of antennas or symbol length. The estimated coding / decoding delay T1 is 15ms.

[0086] The transmission delay can be calculated based on the ultra-short wave radio data transmission channel capacity and the transmission data size obtained above. Assuming that the data size of the multi-mobile robot system status information (including position, speed, etc.) is 5000 bytes, then when the ultra-short wave radio data transmission channel capacity is, the transmission encoding and decoding delay T2 = 0.426ms.

[0087] The calculation above shows that the communication delay for the remote control terminal-multi-mobile robot system based on the ultrashort wave radio is T = T1 + T2 = 15.426ms, which meets the communication requirements. The above discussion demonstrates the feasibility of the proposed control scheme for the remote control terminal-ultrasonic radio-multi-mobile robot system under denial of service attacks.

[0088] 3. Distributed Observation Algorithm for Multi-Mobile Robot Systems under Intermittent Communication

[0089] The distributed observer in a multi-mobile robot system is an intelligent state estimation tool based on local communication and collaboration. Its core goal is to estimate the leader's information through information interaction and data fusion between mobile robots. Each mobile robot relies only on its own information feedback and limited information from neighboring nodes, and gradually approaches the leader's information estimate through a consistent distributed estimation method. The distributed observer reduces the communication burden and avoids the centralized observer's dependence on the central node. It also has strong robustness and can maintain effective estimation when some nodes fail or communication is interrupted. The distributed observer can be used to transform the complex coordinated control problem of the multi-agent system into a simple single-agent tracking control problem. For agents in the multi-mobile robot system that cannot directly communicate with the leader, the distributed observer is designed as follows:

[0090]

[0091] Where: β(t) is the preset time adjustment function, which is expressed as follows;

[0092]

[0093] According to the above distributed observer, the leader information estimate can be obtained As a reference trajectory for the subsequent design of tracking controller for mobile robots, for A vector consisting of the first n rows of .

[0094] The aforementioned distributed observer requires agents to communicate with neighboring nodes in real time to obtain local state information and complete leader estimation. However, limited communication resources are a common challenge in multi-agent systems. Intermittent communication mechanisms, which trigger information exchange only when necessary, offer significant advantages. Intermittent communication refers to a system in which nodes in a multi-agent system exchange information only under specific conditions (such as when the state error exceeds a threshold or reaches a preset time interval), rather than continuously communicating. By reducing the frequency of unnecessary communication, this mechanism significantly reduces network load, energy consumption, and computational overhead while still ensuring system collaboration. Its core benefits include: reducing bandwidth usage and energy consumption, making it suitable for multi-agent systems with limited communication resources; avoiding performance degradation caused by communication congestion in large-scale systems; and maintaining system stability in the event of communication delays or packet loss through local prediction or event-triggered strategies. Intermittent communication is often combined with event-triggered or self-triggered control and is widely used in fields such as drone formations, distributed sensor networks, and smart grids. It is a key technology for achieving efficient collaboration in multi-agent systems.

[0095] Compared to event-triggered mechanisms, self-triggering mechanisms exhibit significant advantages in the communication and control of multi-agent systems. By predicting the next trigger moment based on the current state, the self-triggering mechanism avoids the continuous state monitoring required by event-triggered mechanisms and completely eliminates the computational overhead of real-time sensor detection. This characteristic makes it particularly suitable for embedded systems with limited processor resources. Secondly, by presetting a lower limit on the trigger time interval, the self-triggering mechanism can strictly avoid the Zeno phenomenon (infinite triggering) and ensure system stability. However, event-triggered mechanisms theoretically still carry the risk of high-frequency triggering due to noise interference. Furthermore, under the same control accuracy, the self-triggering mechanism can significantly reduce the number of communications, which is particularly critical for energy-constrained mobile robot clusters.

[0096]

[0097] Where:

[0098] The triggering conditions of this self-triggering mechanism are related to the consistency error of the multi-mobile robot system, the observer output at the previous moment, and its derivative. The triggering conditions, designed based on the Lyapunov stability theorem, ensure the convergence of the distributed observer under intermittent communication. The next communication moment is directly calculated based on the current observer state information, eliminating the need for continuous communication. During the non-triggering interval, the observer's neighbor node information remains at the value at the previous triggering moment, with the signal updated only at the end of the interval. If a denial of service (DoS) attack is detected, the triggering mechanism is proactively suspended, and control of the mobile robot is transferred to the remote control terminal to avoid invalid observations. This intermittent communication based on the self-triggering mechanism can limit the number of communications and alleviate the communication burden of the multi-mobile robot system.

[0099] 4. Optimal intermittent control algorithm for a single mobile robot based on reinforcement learning

[0100] The above-mentioned distributed observer transforms the coordinated control problem of multiple mobile robot systems into a tracking control problem of a single mobile robot. In response to the efficient control problem of a single mobile robot, the present invention proposes an optimal intermittent control algorithm that integrates backstepping and reinforcement learning. Through the collaborative design of identification-execution-evaluation network, preset time convergence and self-triggering mechanism, high-precision and low-energy autonomous control is achieved. Through the backstepping framework, the recursive Lyapunov function design is adopted to process the nonlinear dynamics of the system in steps to ensure control stability and provide a structural basis for reinforcement learning strategy optimization. In the identification-execution-evaluation network, the identification network is responsible for online estimation of the unknown dynamic parameters of the robot to enhance the adaptability of the model; the actuator network is responsible for generating intermittent optimal control instructions based on environmental interaction experience; the evaluation network is responsible for evaluating the state-action value and guiding the strategy update to minimize the long-term cost. The tracking error is strictly constrained to converge within a fixed time defined by the user through the time adjustment function to meet the needs of time-sensitive tasks. The triggering moment of the next control update is dynamically predicted according to the system state, and the control input is calculated only at the triggering moment, which significantly reduces the consumption of computing resources while ensuring stability. The control scheme is as follows Figure 4 shown.

[0101] 5. Optimal Controller Design Process Based on Reinforcement Learning

[0102] The position tracking error and velocity tracking error of the mobile robot are defined as follows:

[0103]

[0104] Where: η i Set position intervals for the formation;

[0105] Differentiating the above error, we get:

[0106]

[0107] Step 1: Design a first-order optimal virtual controller:

[0108] Define the following optimal value function:

[0109]

[0110] The cost function expression is: p (e i,p ,α i )=Q i (e i,p )+α i T R i α i ,

[0111] Its Hamilton-Jacobi-Bellman equation is:

[0112]

[0113] The first-order optimal virtual controller can be obtained by differentiating the Hamilton-Jacobi-Bellman equation

[0114]

[0115] First, design as follows:

[0116]

[0117]

[0118] The first-order virtual optimal controller is designed as follows:

[0119]

[0120] The term is highly nonlinear, so a neural network is used to approximate it:

[0121]

[0122] Introducing the execution-evaluation network, It can be expressed as:

[0123]

[0124] The first-order optimal virtual controller is designed as follows:

[0125]

[0126] The execution-evaluation network weight update rate is designed as follows:

[0127]

[0128] Step 2: Design a second-order optimal practical controller

[0129] Define the following optimal value function:

[0130]

[0131] The cost function expression is: p (e i,v ,α i )=Q i (e i,v )+α i T R i α i , Its Hamilton-Jacobi-Bellman equation is

[0132]

[0133] The second-order optimal actual controller can be obtained by differentiating the Hamilton-Jacobi-Bellman equation

[0134]

[0135] First, due to the existence of unknown dynamics f in the system i (p i (t),v i (t)), so the identification neural network is used to approximate it

[0136]

[0137] Where: i =[p i (t),v i (t)] T ;

[0138] Secondly, design as follows:

[0139]

[0140] The second-order actual optimal controller is designed as follows:

[0141]

[0142] The term is highly nonlinear, so a neural network is used to approximate it:

[0143]

[0144] Introducing the execution-evaluation network, It can be expressed as:

[0145]

[0146] The second-order optimal actual controller is designed as follows:

[0147]

[0148] The weight update rate of the identification-execution-evaluation network is designed as follows:

[0149]

[0150] It should be noted that the above-mentioned first-order virtual optimal controller, second-order actual optimal controller, identification, execution, and evaluation of the neural network update rate design process all take into account the preset time adjustment function β(t); in order to solve the problem that the convergence time of traditional adaptive control depends on the initial state of the system, the present invention innovatively embeds the preset time adjustment function into the weight update law of the neural network and the controller design, and realizes the strict preset time convergence of all signals of the closed-loop system (including tracking error, neural network estimation error and control input). Make the system state at a fixed time T defined by the user * The function is forced to converge to the equilibrium point (regardless of the initial conditions). At the same time, the function dynamically adjusts the learning rate of the neural network to ensure that the parameter estimation and control are synchronized, fast and stable. It has precise convergence time guarantee, breaking through the limitations of asymptotic convergence or finite time convergence. The convergence time T * It can be directly specified in advance and does not depend on the initial state or the disturbance amplitude; at the same time, the computing resources are optimized, and the time-varying function is * After that, it automatically degenerates into a constant, and the neural network switches to static mode, saving online computing overhead; In addition, the time parameter T * It can serve as a direct debugging interface, facilitating the trade-off between convergence speed and control energy consumption based on task requirements. However, the aforementioned optimal controller based on reinforcement learning requires real-time calculation of control inputs, resulting in computational redundancy and resource waste caused by high-frequency updates. To address this issue, the present invention introduces a self-triggering mechanism that triggers control updates only when necessary, achieving intelligent intermittent control input.

[0151] Intermittent control based on a self-triggering mechanism is a new type of intelligent control strategy. Its core idea is to autonomously determine the update time of the control signal through preset trigger conditions (such as system state error or time threshold), rather than traditional periodic sampling or continuous control. This mechanism activates the controller only when the trigger condition is met, thereby effectively reducing the computational burden and communication resource consumption, while ensuring the stability and control accuracy of the system. Compared with traditional event-triggered control, the self-triggering mechanism further avoids the communication overhead of real-time monitoring by predicting the next trigger moment. Its advantages include: significantly reducing the control update frequency and improving energy and computing efficiency; reducing communication congestion in networked control systems; being suitable for resource-constrained embedded systems and distributed multi-agent collaborative control; balancing system performance and energy consumption through adaptive triggering strategies, and having important application value in multi-mobile robot formation systems.

[0152] The intermittent control strategy based on the self-triggering mechanism is designed as follows:

[0153]

[0154] The triggering conditions of the self-triggering mechanism are linked to the mobile robot's velocity error, the previous control input, and the derivative of the control input. The triggering conditions are designed based on the Lyapunov stability theorem, ensuring the convergence of the mobile robot under intermittent control. The next trigger moment is directly calculated from the current state information, eliminating the need for continuous monitoring of the system state. The mobile robot only needs to sample the system state at the trigger moment and update the control input. During the non-triggering interval, the controller output remains at the value at the previous trigger moment, with the signal updated only at the end of the interval. If a denial of service (DoS) attack is detected, the triggering mechanism is proactively suspended, and control of the mobile robot is transferred to the remote control terminal, ensuring system security while avoiding invalid communication. Intermittent control based on the self-triggering mechanism effectively reduces the number of sampling times and alleviates the burden on system computing resources.

[0155] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not limiting. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solutions of the present invention can be modified or replaced by equivalents without departing from the purpose and scope of the technical solutions, which should all be included in the scope of the claims of the present invention.

Claims

1. A method for tracking and controlling multiple mobile robots in intermittent formations against denial of service attacks, characterized by: The following steps are involved: S1: When a denial of service (DoS) attack is detected, the control of the multi-mobile robot system is switched to the remote control terminal, which sends control commands to the mobile robots through the local area network constructed by the ultrasonic radio; S2: Through the distributed observer, the follower mobile robot estimates the position and velocity state of the leader based on the information interaction of the neighboring nodes. The expression of the distributed observer is: in, β(t) is the preset time adjustment function, a i,j is the communication topology weight; S3: Adopting an intermittent communication mechanism, the neighbor node information is updated only under trigger conditions. The trigger conditions are: S4: Design an optimal controller based on a reinforcement learning network, including an identification network, an execution network, and an evaluation network. The identification network is used to approximate the unknown dynamics of the system, the execution network generates control inputs, and the evaluation network optimizes the control strategy. S5: Through the intermittent control mechanism, the control input is updated only at the triggering moment, which is determined by the dynamic relationship between the speed tracking error and the control input derivative.

2. The method for tracking and controlling multiple mobile robots in intermittent formations against a denial of service attack according to claim 1, characterized in that: In S1, the communication parameters of the ultrasonic radio station include: The RF output power is 4W×2, the bandwidth is 10MHz, the operating frequency is 2.4GHz, the maximum communication distance is 20km, and the communication delay T=T1+T2 satisfies T≤15.426ms, where T1 is the encoding and decoding delay and T2 is the transmission delay.

3. The method for tracking and controlling multiple mobile robots in intermittent formations against a denial of service attack according to claim 1, wherein: In S1, the expression of the preset time adjustment function β(t) is: Where T * It is the convergence time set by the user, and p is a constant.

4. The method for tracking and controlling multiple mobile robots in intermittent formations against a denial of service attack according to claim 1, wherein: In S2, the convergence of the distributed observer is verified by Lyapunov stability theorem, and neighbor information updates are suspended during DoS attacks.

5. The method for tracking and controlling multiple mobile robots in intermittent formations against denial of service attacks according to claim 1, characterized in that: In S4, the expression of the identification network is: Among them, i =[p i (t),v i (t)] T , S(·) is the basis function, is the neural network weight.

6. The method for tracking and controlling multiple mobile robots in intermittent formations for denial of service attacks according to claim 5, characterized in that: The neural network weights The update law is: Among them, γ fi is the learning rate, σ i is the attenuation coefficient.

7. The method for tracking and controlling multiple mobile robots in intermittent formations against a denial of service attack according to claim 1, wherein: In S5, the triggering conditions for intermittent control are: Among them, ω i,1 、ω i,2 、ω i,3 is the weight coefficient.

8. The method for tracking and controlling multiple mobile robots in intermittent formations against denial of service attacks according to claim 1, wherein: In S4, the value function of the evaluation network is: where Q i 、R i is a positive definite weight matrix.

9. The method for tracking and controlling multiple mobile robots in intermittent formations against a denial of service attack according to claim 1, wherein: In S3, the intermittent communication mechanism adopts space-time coding technology when communication is restored, with a coding delay of 5ms and a decoding delay of 10ms.

10. The method for tracking and controlling multiple mobile robots in intermittent formations against denial of service attacks according to claim 1, characterized in that: In S1, the remote control terminal receives the status information and environment image of the mobile robot in real time, and feeds it back to the user end through the ultrasonic radio.

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