A multi-agent preset-time cooperative control system against DoS based on multi-value fuzzy approximation and state-dependent asynchronous triggering

Abstract

This invention relates to a DoS-resistant multi-agent pre-time cooperative control system based on multi-valued fuzzy approximation and state-dependent asynchronous triggering, belonging to the field of multi-agent system cooperative control technology. Addressing the problems of uncontrollable convergence time, high parameter coupling difficulty, easy collisions caused by transient deviations, wasted communication bandwidth and vulnerability to denial-of-service attacks leading to crashes, and heavy computational burden on high-order systems in existing control algorithms, this invention constructs a time-varying unsteady network topology and generates link health discrimination variables. Collision avoidance planning is achieved through pre-set time performance envelopes and asymmetric security barriers. Disturbances are perceived using non-smooth multi-valued logic fuzzy approximation and differential topology flow. Asynchronous triggering sequences are generated based on a dynamic energy pool and link states, combined with instruction filtering compensation to generate control laws. This system achieves pre-set convergence independent of initial states, improves security constraints, reduces communication bandwidth consumption, enhances anti-attack security, and eliminates Zeno's phenomenon.

Description

Technical Field

[0001] This invention belongs to the field of multi-agent system cooperative control technology, and relates to a DoS-resistant multi-agent pre-time cooperative control system based on multi-valued fuzzy approximation and state-dependent asynchronous triggering. Background Technology

[0002] In pioneering fields such as modern industrial manufacturing, smart microgrids, and unmanned transportation, heterogeneous distributed collaborative swarm intelligence networks have become a core research direction due to their significant advantages in improving task execution fault tolerance, system-level robustness, and distributed resource scheduling. Typical applications include collaborative search and rescue and high-dynamic target 3D encirclement by drone swarms under complex weather conditions, power quality regulation of massive distributed renewable energy inverters in smart grids, ultra-dense platooning of connected autonomous vehicles on highways, and precise visual collaborative control of multi-degree-of-freedom endoscopic robots in minimally invasive surgery.

[0003] In realizing the above applications, the cooperative control technology of multi-agent systems is the core to ensure the successful completion of tasks. Existing technologies mainly revolve around traditional event-triggered mechanisms, predetermined-time control theory, and backstepping theory for handling high-order nonlinear systems. However, in deeply coupled practical physical applications, these underlying control algorithms still face many theoretical bottlenecks and engineering challenges.

[0004] First, the convergence time of existing control algorithms is uncontrollable and parameter coupling is difficult. The convergence upper limit of traditional asymptotically stable or finite-time control is highly dependent on the magnitude of the deviation of the initial state of the system. Once the initial error is too large, the convergence time cannot be guaranteed. Although fixed-time control provides a time upper limit independent of the initial state, this time boundary is deeply intertwined with the extremely complex physical control gain parameters inside the system, making it impossible for engineers to directly specify the physical time limit for task completion using a single macroscopic parameter.

[0005] Secondly, even if the system eventually converges, if the algorithm cannot impose hard physical constraints on the transient trajectory during the convergence process, the drone or robot is very likely to deviate from the safety corridor and be damaged, which may lead to obstacle avoidance overstepping or collision accidents between intelligent agents.

[0006] Furthermore, existing continuous-time triggering mechanisms are extremely wasteful of network bandwidth. Even early static event triggering mechanisms are prone to infinite triggering when faced with severe external disturbances, i.e., the Zeno phenomenon. In particular, when the system suffers from a deliberate denial-of-service (DoS) attack that causes channel congestion, it is highly susceptible to system stack overflow and system crash.

[0007] Furthermore, the inherent unmodeled nonlinearities of high-order physical entities and unknown disturbances such as gust shear can easily lead to saturation of the actuators in traditional controllers. At the same time, the traditional backstepping method requires repeated differentiation when deriving the virtual control law, which can easily cause an explosion in computational complexity, making it impossible for low-power controllers to handle their real-time computational load.

[0008] In summary, how to achieve preset time convergence, full-time domain security constraints, communication bandwidth optimization, and reduced computational load in multi-agent systems under complex environments with denial-of-service attacks, unknown nonlinear dynamics, and external compound disturbances remains an urgent technical problem to be solved. Summary of the Invention

[0009] In view of this, the purpose of the present invention is to provide a DoS-resistant multi-agent pre-time collaborative control system based on multi-valued fuzzy approximation and state-dependent asynchronous triggering.

[0010] To achieve the above objectives, the present invention provides the following technical solution: A DoS-resistant multi-agent pre-time cooperative control system based on multi-valued fuzzy approximation and state-dependent asynchronous triggering includes a communication topology modeling module, a collision avoidance and constraint planning module, a disturbance sensing module, a triggering decision module, and a control law synthesis module. The communication topology modeling module is used to construct a time-varying unsteady network topology that includes high-impedance state information shielding the time domain, and to generate link health discrimination variables; The collision avoidance restrictive planning module is used to generate asymmetric obstacle dual-transformation mapping projective manifold variables based on a preset time performance envelope manifold and asymmetric safety barrier boundaries; The disturbance sensing module is used to output the approximation value of the unknown nonlinear function and the estimated value of the composite disturbance of the external environment based on nonsmooth multivalued logic fuzzy approximation and differential topological flow. The triggering decision module is used to generate an asynchronous triggering sampling discrete timestamp sequence based on dynamic energy pool capacity variables and link health discrimination variables; The control law synthesis module is used to generate the final servo physical control law based on the asymmetric obstacle double transformation mapping projected manifold variable, the estimated value of the external environment composite disturbance, the asynchronous trigger sampling discrete timestamp sequence, and the augmented state command filtering compensation.

[0011] Furthermore, the communication topology modeling module is configured as follows: Define the high-resistivity state information shielding time domain within the observation time window as: ,in Representing the k The starting point of the DoS attack intrusion time. Representing the k Duration of the DoS attack; Define link health discrimination variables ,when Time represents intelligent agent i Intelligent agents with neighbors j The communication link is in a healthy communication window, when This indicates that the communication link is in a DoS blocking state; The time-varying adjacency weight is updated based on the link health discriminant variable. ,in Set the adjacency weights for the original values.

[0012] Furthermore, the collision avoidance restriction planning module is configured as follows: Construct a predefined time-performance envelope manifold function ,in To preset an independent time constant, This represents the maximum spatial location divergence at system startup. For steady-state high-frequency noise oscillation range, It is the power order; Define positional cooperative error components ,in For intelligent agents i The output observed variables, , It is the physical distance constant relative to the target; Introducing a preset time forced hedging function ,in It is the power order; Based on the preset time performance envelope manifold function, position cooperative error components, and preset time forced hedging function, the asymmetric safety barrier boundary is established. ,in , For asymmetric safety adjustment coefficients; generate asymmetric barrier dual transformation mapping projected manifold variables. .

[0013] Furthermore, the disturbance sensing module is configured as follows: An unknown nonlinear function is approximated using a Gaussian kernel multi-valued adaptive approximation mapping engine. ,in The optimal fuzzy rule parameter matrix, The Gaussian fuzzy membership degree basis function vector. To approximate the residual by truncating the intrinsic eigenvalue; Construct a full-dimensional exogenous perturbation perceptron using the formula Output the estimated value of unknown composite interference in the external environment, where For the auxiliary state variables of the full-dimensional perceptron, The core high-frequency sensing gain constant, For intelligent agentsi The k First-order state components; The auxiliary state variable of the full-dimensional sensor is expressed by the formula Evolution, in which Given the input stream of known terms, for hour ,for hour , To approximate the online estimation vector of the weight parameters.

[0014] Furthermore, the triggering decision module is configured as follows: When link health discriminant variables When this happens, the cached state of the most recently successfully received neighbor is invoked, and the cache reliability decay factor is applied. Calculate the cooperative error, where For the most recent successful reception of neighbors j The timing of the status packet This is the sensitivity coefficient; Define the core dynamic energy pool capacity variable The first-order adaptive nonlinear differential evolution equation is: ,in For damping parameters, To supplement the gain coefficient, To adaptively trigger the elastic adjustment threshold, For the cumulative divergence deviation vector, The time scale for the most recent broadcast status; The projection operator is used to limit the dynamic energy pool capacity variable to the minimum safe capacity. With maximum capacity between; when At that time, the trigger determination logic is activated and the asynchronous trigger sampling discrete timestamp sequence is recorded. .

[0015] Furthermore, the adaptive trigger elastic adjustment threshold Configured as ,in The lower limit of the basic damping trigger threshold. To dynamically adjust the adaptive weight constant, For state learning coupled gain, This is the online estimation vector for the highest-order approximation weight parameters.

[0016] Furthermore, the control law synthesis module is configured as follows: Embedded first-order instruction low-pass filter, through formula Generate smooth augmented state variables ,in The filter bandwidth time constant, For the first k -1st order virtual control law; Construct a calculus feedforward error compensation channel, using the formula Generate dynamic compensation signal ,in This is the feedforward compensation attenuation adjustment constant. ; Constructing a full-dimensional recursive backstepping composite tracking manifold variable , ,in , n The total order of the system dynamics; Generate the final servo physical control law of the highest execution layer ,in For proportional control gain, This is the maximum 2 norm estimate of the neural fuzzy weight matrix. For fault-tolerant self-compensating damping parameters, This is the highest-order estimate of the combined external environmental disturbances.

[0017] Furthermore, the control law synthesis module is also configured as follows: Generate adaptive weight self-learning evolution update law and ,in and To adaptively update the online parameter feedback and adjust the sensitivity constant, and This is a forced leakage factor.

[0018] Furthermore, the system is configured to utilize a multidimensional tensor product-type composite barrier Lyapunov energy functional. Verify the stability of the preset time, among which To adaptively update the deviation for the parameters, To estimate the bias of the weight matrix, To prevent interference estimation bias, N The total number of intelligent agents.

[0019] A DoS-resistant multi-agent pre-time cooperative control method based on multi-valued fuzzy approximation and state-dependent asynchronous triggering includes the following steps: Construct a time-varying nonsteady-state network topology that includes high-impedance state information to mask the time domain and generate link health discrimination variables; Asymmetric barrier double transformation mapping projected manifold variables are generated based on the preset time performance envelope manifold and asymmetric safety barrier boundary; Based on nonsmooth multivalued logic fuzzy approximation and differential topology flow, output the approximation value of the unknown nonlinear function and the estimate of the combined disturbance of the external environment; Asynchronous trigger sampling discrete timestamp sequence is generated based on dynamic energy pool capacity variables and link health discrimination variables; The final servo physical control law is generated based on the asymmetric obstacle dual-number transformation mapping projected manifold variable, the estimated value of the external environment composite disturbance, the asynchronous trigger sampling discrete timestamp sequence, and the augmented state command filtering compensation.

[0020] The beneficial effects of this invention are as follows: (1) Through the synergistic effect of the preset time performance envelope manifold and the preset time forced hedging function, the system can decouple the initial physical deviation and force convergence to near the residual zero point within the user-specified task time limit. At the same time, based on the asymmetric safety barrier boundary and the asymmetric obstacle double transformation mapping projection manifold, the system can impose hard constraints on the agent's motion trajectory in the entire time domain. When the cooperative error attempts to approach the physical collision avoidance boundary, the spatial boundary repulsion gain will generate a reverse correction pull, forcibly pulling the agent back before reaching the boundary, thus completely avoiding boundary collision accidents.

[0021] (2) By using a Gaussian kernel multi-valued adaptive approximation mapping engine to approximate unknown complex nonlinear functions, and combining a differential topological flow full-dimensional disturbance sensor to perform real-time estimation and feedforward cancellation of complex disturbances in the external environment, the system can effectively cope with unmodeled nonlinearities and time-varying disturbances in higher-order dynamics without precise modeling. At the same time, the state-dependent discrete triggering decision mechanism ensures that the agent only broadcasts state packets when the accumulated divergence deviation exceeds the adaptive threshold, which greatly reduces the ineffective activation of radio frequency components and saves communication bandwidth resources.

[0022] (3) When the communication link is interrupted due to intermittent denial-of-service attacks, the dynamic energy pool can act as an elastic buffer to absorb the energy of cooperative error oscillation, avoid the main control chip blindly triggering the radio frequency components, and avoid the risk of system stack overflow deadlock. At the same time, the trigger threshold design based on the evolution of the dynamic energy pool ensures that the wireless radio frequency transmission module has an absolutely positive safe operating interval under any disturbance, thus eliminating the self-locking crash fault of the microprocessor's infinite high-frequency sampling from the source.

[0023] (4) By embedding a first-order instruction low-pass filter in the Lyapunov recursive surface, the filtered low-pass derivative is directly extracted to replace the chain partial derivatives of the traditional backstepping method, thus completely avoiding the differential explosion problem caused by repeated differentiation. The synchronously constructed calculus feedforward error compensation channel feeds back the control energy filtered out by the low-pass filter to the control loop in the form of integral reconstruction, eliminating the steady-state phase lag caused by filtering, and enabling the system to deploy high-precision control under low-power hardware conditions.

[0024] Other advantages, objectives, and features of the invention will be set forth in part in the description which follows, and in part will be apparent to those skilled in the art from the following examination, or may be learned from practice of the invention. The objectives and other advantages of the invention can be realized and obtained through the following description. Attached Figure Description

[0025] To make the objectives, technical solutions, and advantages of the present invention clearer, the preferred embodiments of the present invention will be described in detail below with reference to the accompanying drawings, wherein: Figure 1 For the time series of denial-of-service attacks; Figure 2 A block diagram of the time-domain decoupled self-hedging logarithmic obstacle manifold space collision avoidance restricted programming algorithm; Figure 3 This is a schematic diagram of the algorithm for nonsmooth multi-valued logic fuzzy approximation and differential topological flow full-dimensional perturbation sensing. Figure 4 State-dependent adaptive discrete triggering and network resilience anti-attack decision mechanism Figure 5 A command filtering feedforward recursive compensation channel for resisting differential explosion and steady-state phase correction; Figure 6 This is a block diagram of a multi-agent pre-time collaborative control system for resisting DoS based on multi-valued fuzzy approximation and state-dependent asynchronous triggering. Detailed Implementation

[0026] The following specific examples illustrate the implementation of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and various details in this specification can be modified or changed 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 representations of the basic concept of the present invention. Unless otherwise specified, the following embodiments and features can be combined with each other.

[0027] The accompanying drawings are for illustrative purposes only and are schematic diagrams, not actual pictures. They should not be construed as limiting the invention. To better illustrate the embodiments of the invention, some parts in the drawings may be omitted, enlarged, or reduced, and do not represent the actual product dimensions. It is understandable to those skilled in the art that some well-known structures and their descriptions may be omitted in the drawings.

[0028] In the accompanying drawings of the embodiments of the present invention, the same or similar reference numerals correspond to the same or similar components. In the description of the present invention, it should be understood that if terms such as "upper," "lower," "left," "right," "front," and "rear" indicate the orientation or positional relationship based on the orientation or positional relationship 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 orientation, or be constructed and operated in a specific orientation. Therefore, the terms used to describe positional relationships in the drawings are only for illustrative purposes and should not be construed as limiting the present invention. For those skilled in the art, the specific meaning of the above terms can be understood according to the specific circumstances.

[0029] I. Topological Modeling of the Information Interaction Space Accompanying DoS Attacks Multi-robot systems based on distributed control strategies lack a central controller; therefore, each agent can only make local decisions based on information about itself and its neighbors. For leaderless systems, the communication topology of the agent cluster consists of an undirected graph. It means that among them It is a set of nodes. It is an edge set. It is a weighted adjacency matrix. If... So ,otherwise and have .node The neighbor set is .picture The Laplace matrix is ,in ,when hour In a graph, a path is a sequence of edges, for example... An undirected graph is connected if there is at least one path between every pair of nodes. In the case where a leader exists in the system, the leader is represented by node 0, and the followers are represented by node 1. This indicates that the topology of the followers is still composed of an undirected graph. With Laplace matrix Representation. A leader-follower graph consists of a set of nodes. Directed graph It indicates. Leaders and followers. Communication between them is unidirectional, from leader to follower, and the edge weights are... If followers Connecting with leaders ,otherwise .make For the leader's adjacency matrix and If from node To the node If there is a directed edge, then the node It is the parent node, the node A node is a child node. A directed tree is a graph in which every node has only one parent node except the root node, and the root node has directed paths to every node. For a directed graph, a directed spanning tree is a directed tree formed by the edges connecting all nodes in the graph. A directed graph has a directed spanning tree if at least one node has a path to all other nodes.

[0030] To address intermittent denial-of-service (DoS) network congestion attacks deliberately launched by adversaries in real-world adversarial environments, this algorithm designs a time-varying, non-stationary network topology evolution mechanism. Here, the union of all effective DoS attack time segments is defined as the high-impedance information-masking time domain. The timeline is shown below. Figure 1 As shown.

[0031] (1) (2) in Indicates the observation time window Within this interval, the union of all effective DoS attack time segments. Within this interval, the elements of the communication adjacency matrix are physically blocked and forced to decay to 0, resulting in complete loss of topology interaction; Representing the The precise intrusion time starting point of the enemy's DoS malicious blocking attack; Representing the The duration of a DoS attack, i.e., the attack pulse width; For the complement set, it represents a healthy communication window indicating that the network has not been attacked.

[0032] To enable each agent to autonomously identify whether the current communication link is under a DoS attack without a central controller, this invention further introduces a link health discrimination variable. For follower agents... Its neighboring intelligent agents Define link health criteria variables for communication links between them. ,in Represents intelligent agents Able to receive neighboring intelligent agents within the allowed communication time limit Valid status information, This indicates that the communication link is in a timeout, packet loss, or physical blockage state. (For leader-to-follower agents) A one-way communication link is defined. Based on this link health criterion variable, the time-varying adjacency weight affected by the DoS attack is updated as follows: The leader's adjacency weight is updated to .when or When this occurs, it indicates that the corresponding communication link is determined to be in a DoS blocking or equivalent failure state, and the corresponding topology interaction weight is set to zero; when or When this occurs, it indicates that the corresponding link is in a healthy communication window, and the corresponding topology weight is restored to its original set value.

[0033] Here the definition of the first The rigorous nonlinear dynamic equations for each autonomous node are as follows: (3) in Representing the The first follower node Higher-order phase space dynamics manifold components, A complete, full-dimensional state vector representing the current node; Represents a low-order state subvector; This represents the total order of the system dynamics at the current node; The final control input command for the servo motor or thruster acting on the intelligent agent; For measurable output observation variables; It refers to the inherent nonlinear dynamic function that objectively exists in the system but is difficult to model precisely using mathematics; This represents a complex disturbance of the external environment with highly time-varying characteristics. Here, it is assumed that its first derivative objectively has an energy upper limit, that is, it strictly satisfies the boundary condition: ,in The upper limit of an unknown positive real number. The expected evolution model of the leader is defined as follows: (4) It represents a continuous, smooth, and bounded global guidance path issued by the upper-level system.

[0034] II. Temporal Decoupling Self-Hydraulic Logarithmic Obstacle Manifold Space Collision-Avoidance Constrained Programming Algorithm Existing technologies generally only guarantee convergence when the time is reached. However, in real physics, excessive transient deviations during the convergence process can lead to mechanical damage. To address the theoretical deficiency in conventional control algorithms where the cooperative convergence time is highly dependent on the initial deviation, and to completely eliminate potential agent collisions during rapid transitions, this invention proposes a time-domain decoupled self-hedge logarithmic obstacle manifold space collision avoidance restricted programming algorithm. Its structural block diagram is shown below. Figure 2 As shown.

[0035] This algorithm integrates a pre-defined performance envelope manifold with a logarithmic asymmetric state projection transformation technique, enabling the control system to possess pre-defined convergence characteristics independent of the initial state. It aims to completely decouple the system's convergence time from the initial position divergence and implement hard, asymmetric safety constraints on the agent's physical trajectory across the entire time domain. The algorithm constructs an asymmetric time-domain decoupled deterministic measure time performance envelope manifold function completely governed by a single macroscopically specified physical task time limit, forcing the system to converge within a pre-defined time. Smooth, continuous design of switching points prevents abrupt acceleration changes in the underlying servo mechanism. The introduced pre-defined time-forced hedging function forcibly extends the upper and lower limits of the constraints at the initial moment, completely eliminating the possibility of violating inequality constraints due to excessive initial errors, ensuring that the control law does not undergo abrupt changes at the initial moment. Finally, by mapping the projected manifold variables through asymmetric obstacle double transformation, the constrained planning problem is transformed into an unconstrained control form. When the agent's trajectory attempts to approach the preset asymmetric collision avoidance safety threshold, the denominator of the spatial boundary repulsion gain coefficient rapidly converges to zero, causing the gain to grow exponentially towards physical infinity. This generates a strong reverse correction force in the underlying algorithm, forcibly pulling the agent back to the safe region. The pseudocode for the algorithm flow is as follows:

[0036] First, define a time that is completely subject to a single macroscopic specification. Dominant, asymmetric time-domain decoupling deterministic measure time performance envelope manifold function : (5) in, To pre-set an independent time constant, representing the absolute physical task completion time limit given by the user, the system algorithm will completely decouple the initial physical deviation and force convergence within the preset time. This represents the maximum spatial divergence that the system can tolerate at startup; and The maximum allowable steady-state high-frequency noise oscillation range after the task is completed is defined; This ensured that the curve was at the switching point. The first and second time derivatives at the point are absolutely smooth and continuous, preventing the underlying servo mechanism from experiencing sudden acceleration changes at the moment the task time expires, which could cause shocks.

[0037] Based on the above, the position coordination error component with formation configuration constant calculated by the current node based on the network algebraic topology protocol is defined as follows: (6) in , This represents the pre-defined relative target physical distance constant between each follower and between a follower and the leader, used to establish a specific formation geometry. To ensure that no obstacle avoidance overshoot or agent collisions occur across the entire time domain due to large-scale overshoot, the actual cooperative error must be strictly limited by the asymmetric safety adjustment coefficient. and Within the defined asymmetric security barrier boundary, i.e.: (7) in and The collision avoidance safety threshold for asymmetry in the direction of the agent's movement is specified; The newly introduced preset time-forced hedging function is used to completely eliminate the step impact caused by the initial divergence at the initial moment. This forced hedging function is defined as follows: (8) Generally speaking, the power order in equation (8) Obviously, at the initial moment This forces the upper and lower limits of the constraints to be extended at the initial moment, eliminating the possibility of violating inequality constraints due to excessive initial error. It ensures that the initial error of the system can be completely canceled after introducing this function, preventing abrupt changes in the control law at the initial moment and eliminating the initial step shock of the system. Furthermore, when the time exceeds the user-defined absolute task completion time limit... hour, This means that the system's cooperative tracking error It has been forcibly pulled back to the steady-state small neighborhood.

[0038] To theoretically reduce the requirements for initial feasibility values ​​and transform the constrained programming problem with hard obstacle avoidance boundaries into an unconstrained control form, this algorithm designs an asymmetric obstacle dual-transformation mapping projected manifold variable. as follows: (9) Taking the first-order complete derivative of the above asymmetric mapping manifold variables in time, we derive its time evolution differential equation as follows: (10) In the formula and These represent nonlinear algebraic time-varying mapping operators, and they are defined as follows: (11) (12) From the perspective of the physical mechanism of the controller, the partial derivative mapping operator It acts as a spatiotemporally damped dynamic repulsive force field in the entire system control loop. The spatial boundary repulsive gain coefficient is defined. as follows: (13) When the cooperative position error of an intelligent agent system attempts to approach a preset asymmetric physical collision avoidance boundary under unknown external composite perturbations, i.e. or The terms in the denominator of equation (13) will rapidly converge to zero, resulting in a repulsive gain coefficient. It grows towards physical infinity at a super-exponential slope. This divergent behavior generates a powerful reverse correction force in the underlying algorithm of the servo controller in a very short time, thus forcibly pulling the agent back before it reaches the physical boundary, theoretically ensuring that the physical entity does not experience any boundary collisions.

[0039] III. Non-smooth multi-valued logic fuzzy approximation and differential topological flow full-dimensional perturbation sensing algorithm Facing the high-dimensional indeterminate boundary eigendynamic divergence that is prevalent in higher-order dynamics And unknown high-frequency multi-source field composite disturbances This invention designs a nonsmooth multi-valued logic fuzzy approximation and differential topological flow full-dimensional perturbation sensing algorithm. The algorithm principle block diagram is as follows: Figure 3 As shown.

[0040] This algorithm combines a universal approximator with a delay-free differential topology observer, achieving real-time sensing and precise feedforward cancellation of unknown dynamics and environmental disturbances without sacrificing the controller's high-frequency noise suppression performance. The algorithm's pseudocode is as follows:

[0041] For the unknown complex nonlinear functions inside the dynamic equation (3) The system utilizes a Gaussian kernel multi-valued adaptive approximation mapping engine based on continuous compact set expansion for approximation description, specifically in the following form: (14) in, The constant real matrix represents the optimal fuzzy rule parameters in the multi-valued inference space, which represents the ideal solution that reconstructs the actual unknown dynamics within a compact set; Indicates the total number of rule nodes; This represents the Gaussian fuzzy membership basis function vector, whose basis elements satisfy a smooth Gaussian kernel distribution; The intrinsic truncation approximation residual, resulting from a finite number of nodes, strictly satisfies the following bounded condition: (15) in This represents the maximum upper limit of a small, objectively existing intrinsic approximation deviation. The corresponding real-time approximation output signal. The structure is as follows: (16) Among them To approximate the online real-time update of the estimated vector for the weight parameters.

[0042] In order to achieve the effect of resisting external complex interference without high-frequency noise excitation. Real-time estimation and reverse hedging are achieved. The system constructs a full-dimensional exogenous disturbance perceptron with a differential topology at the state observation layer, with the specific algebraic form as follows: (17) (18) In equation (17) This is the estimated value of the unknown complex interference in the external environment output by the sensor, which is used for direct feedforward hedging. For the auxiliary state variables of the full-dimensional perceptron; This represents the core high-frequency sensing gain constant used to determine the observation bandwidth. In the control law recursion, the known input stream is generally defined as: for low-order states ( ), For the highest execution layer ( ), .

[0043] Through algebraic differential derivation, substituting equations (3), (14), (17), and (18) into the equation yields the interference estimation bias of the sensor. It satisfies the following differential convergent flow evolution rule: (19) in The error estimation bias is calculated using the following formula: the parameter adaptive update bias is defined as follows. (20) This differential equation shows that as long as the derivative of the time-varying disturbance... And the approximation bias is bounded, resulting in a larger perceptron gain. This will be achieved through algebraic damping terms. By forcibly locking the estimated residuals within an extremely small and compact convergence channel, the algorithm can achieve online hedging of all-dimensional perturbations without delay.

[0044] IV. Anti-DoS State-Dependent Discrete Triggering Decision and Augmented State Command Filtering Compensation Algorithm Traditional static trigger thresholds can cause countless invalid infinite loops during network DoS attacks. To reduce the continuous occupancy of RF network bandwidth during long-term operation, and to ensure that the control system does not crash or fall into Zeno deadlock due to wireless link interruption during malicious DoS attacks, this invention constructs a DoS attack-resistant state-dependent discrete trigger decision and augmented state command filtering compensation algorithm. The algorithm pseudocode is as follows:

[0045] Furthermore, the algorithm also designs a trigger threshold based on a dynamic energy pool, which can remain silent for a long time when the network is healthy, and only absorb oscillating energy to achieve secure communication between secure agents when the network is maliciously blocked or errors are out of control. At the same time, a first-order dynamic surface phase delay correction low-pass instruction filter is introduced to eliminate the problem of insufficient computing power for higher-order chain derivatives.

[0046] First, to prevent control input shocks caused by sudden changes in neighbor states or invalid zeroing during a DoS attack-induced communication link interruption, this algorithm employs a neighbor state cache retention mechanism. Each agent receives and stores the state information and timestamp of the most recently successfully broadcast neighbor agent in real time within a healthy communication window. When a DoS-blocked state is detected, the agent no longer waits for new neighbor state packets but instead uses the most recently successfully received neighbor state cache to participate in the cooperative error calculation. To avoid outdated neighbor information misleading the control law due to prolonged communication interruptions, a cache reliability decay factor is introduced. : (twenty one) in Represents intelligent agents The most recent successful reception of neighbors The timing of the status packet; This is a sensitivity coefficient. This factor monotonically decays with the duration of the communication interruption, ensuring that the neighbor buffer state maintains its cooperative reference function during short-term interruptions, while gradually weakening its influence during long-term interruptions, thereby ensuring that the system can maintain local safe and stable operation until the link is restored.

[0047] Since the local microprocessor of the agent node only starts the RF transceiver chip to broadcast its status packet to the outside when the trigger judgment logic is met, its asynchronous trigger sampling discrete timestamp sequence is defined here. as follows: (twenty two) in The time scale for the underlying microcontroller to send the next data packet; This is the cumulative divergence deviation vector between the current full-dimensional physical state of the agent and the state of the most recent radio frequency network broadcast transmission during the discrete operation of the system. This represents the adaptive adjustment elastic limit threshold triggered by the network. These refer to the exponential filter damping time constants that control the energy pool consumption rate and the replenishment leakage rate, respectively.

[0048] To provide energy filtering and protection against disordered temporal divergence caused by DoS attacks, a core dynamic energy pool capacity variable for DoS attack-resistant network resilience is introduced into the main control microprocessor. Its first-order adaptive nonlinear differential evolution equation is defined as: (twenty three) The initial conditions must meet the safety boundary requirements. ; and These refer to the attenuation damping parameter and the supplementary gain coefficient, respectively, which are the damping time constants used to control the capacitive charging and discharging efficiency of the module.

[0049] To ensure that the dynamic energy pool variable always has a clear physical meaning during the discrete implementation process, the algorithm implements an energy pool capacity projection protection mechanism. The allowed value range for the dynamic energy pool capacity variable is... ,in The minimum safe capacity to prevent the energy pool from being completely depleted. To prevent the maximum capacity from expanding indefinitely beyond the trigger threshold, a projection operator is used each time a temporary capacity value is obtained based on the energy pool differential evolution equation. This limits the dynamic energy pool to the aforementioned range. This ensures that even under conditions of continuous DoS attacks, drastic changes in external disturbances, or numerical integration errors, the dynamic energy pool will not experience negative values, unbounded growth, or threshold failure.

[0050] Here, the adaptive trigger elastic adjustment threshold will be used. Designed as follows: (twenty four) In the formula The lower limit of the basic damping trigger threshold is used to ensure that the system does not experience zero-interval communication. This represents a dynamically adjusted adaptive weight constant. The state learning coupling gain.

[0051] The algorithm described above demonstrates strong resistance to DoS attacks. Within the health window and when control is in a steady state, The energy level is much lower than the threshold, and the dynamic energy pool spontaneously replenishes and maintains itself at an extremely high level. Continuous accumulation leads to a proactive widening of the trigger threshold, causing the RF chip to remain in a deep silent state. Once subjected to intermittent DoS malicious electromagnetic suppression by the enemy, the physical communication channel is completely severed. Due to the inability to obtain the neighborhood state, the cooperative deviation surges, leading to... Rapid divergence. At this point, the accumulated capacity in the dynamic energy pool will be rapidly negatively consumed, acting as a highly elastic buffer. This prevents the main control chip from blindly and repeatedly triggering the radio frequency components until the electromagnetic interference dissipates and the system safely restores connectivity, thus avoiding the risk of deadlock due to system stack overflow. Its structural block diagram is as follows: Figure 4 As shown.

[0052] In the recursive control of various orders of local dynamics of intelligent agents, to avoid the high-order backstepping method from being used in deriving virtual control laws... To address the differential explosion problem caused by repeatedly differentiating nonlinear functions, the following first-order instruction low-pass filter is embedded in parallel within the Lyapunov recursive surface: (25) (26) Among them The output is a smoothed augmented state variable after filtering, and its low-pass derivative can be directly extracted in subsequent calculations. To replace the chain partial derivative; The filter bandwidth time constant is generally: .

[0053] To completely eliminate the cumulative tracking accuracy loss caused by the physical phase lag introduced by low-pass filtering, a calculus-based feedforward error compensation channel mechanism is synchronously constructed at the system's underlying layer, with its dynamic compensation signal... The adaptive evolution equation is designed as follows: (27) in, This is the feedforward compensation attenuation adjustment constant; for the highest-order dynamics layer of a multi-agent system, due to the direct action of the actual physical control signal, it is set to... The feedforward compensation channel can losslessly feed back the useful control energy filtered out by the low-pass filter to the next-level control loop in the form of integral reconstruction. This saves a lot of multi-order derivative calculations and successfully eliminates the steady-state phase lag caused by filtering, thus enabling the deployment of high-precision control under low-power hardware conditions.

[0054] To avoid additional initial shocks to the command filter at system startup, the algorithm performs consistent initialization of the states of filters at each order. For the agent... The Virtual control Its filtered output The initial value is set to This ensures that the initial filtering error is zero. For the feedforward compensation channel, its initial compensation state value is set to zero, i.e. For the highest-level execution layer, since the actual control input directly acts on the agent's physical actuator, there is no need to pass virtual control compensation to the next level. Therefore, it is set... The above initialization method ensures that the command filter, compensation channel, and backstepping recursive control law remain consistent at the initial moment, avoiding sudden changes in control input caused by filter mismatch. The block diagram for this part is shown below. Figure 5 As shown.

[0055] V. Spatial Mapping Closed-Loop Control Law Synthesis and Multidimensional Tensor Composite Li's Pre-Time Stable Algorithm By performing deep algebraic decoupling on all the aforementioned perception and recognition, logarithmic obstacle avoidance, anti-DoS dynamic event triggering, and feedforward phase correction filtering modules, and through rigorous Lyapunov recursive logic derivation, we propose a recursive backstepping space mapping closed-loop control law synthesis and multidimensional tensor composite Lyapunov predetermined time stable algorithm.

[0056] First, construct the full-dimensional recursive backstepping composite tracking manifold variable as follows: (28) (29) In the recursive calculation of the th Within the design steps, i.e. Virtual regulatory law It can be constructed as: (30) Among them For proportional gain, it includes the previous stage bias mapping operator. In mathematical recursion, this is used to completely offset the coupling cross-interference energy between high and low order states. For The initial boundary of the time, the algorithm setting The corresponding highest execution layer final actual servo physical control law synthesis equation is designed as follows: (31) Meanwhile, the adaptive weight self-learning evolution update law and the parameter anti-drift elastic leakage law are designed as follows: (32) (33) In equation (31) This represents the proportional control gain of the servo closed-loop negative feedback. The maximum 2 norm of the neural fuzzy weight matrix for online real-time learning is estimated and used to achieve univariate solution of parameters to save controller overhead. For fault-tolerant self-compensating damping parameters; and The feedback adjustment sensitivity constant represents the adaptive online parameter update parameter; while and Representing the forced leakage factor, it is specifically designed to prevent the endless integral drift of the update weights caused by external measurement noise, thus serving as a physical constraint.

[0057] To make a final determination of the stability of the multidimensional time-varying dynamics of the entire heterogeneous swarm intelligence network, a multidimensional tensor product-type composite barrier Lyapunov energy functional is constructed. as follows: (34) For the above total energy functional The time derivative is performed along the system trajectory, substituted into all dynamic modules, and Young's scaling inequality is used to limit and eliminate nonlinear mismatch coupling disturbances such as the estimation error and the tracking state: (35) (36) Through algebraic induction of global terms, the following multidimensional Lyapunov asymptotic energy dissipation evolution inequality can be precisely derived: (37) The convergence decay constant in the above equation satisfies , This represents a small source of disturbance due to the accumulation of residuals from finite approximation and perception errors. Within the interval... : (38) It can be concluded that as the runtime approaches the user-specified task deadline, that is, when... When, the first term on the right side of the inequality satisfies and Therefore, the global total energy of a multidimensional tensor system must converge to near the residual zero, i.e. This means that no matter what kind of strong spatial divergence and adversarial interference the system encounters in its initial state, the multi-agent cluster will definitely converge to the predetermined high-precision formation target point in an absolutely safe manner when the user-preset time scale is reached, perfectly achieving the preset time coordination stability.

[0058] Regarding the safety justification for the event triggering interval, the adaptive learning weights and estimates are always bounded due to the existence of leakage damping, and for nonlinear states within two consecutive discrete sampling time intervals... By performing limit integration, it can be proven that there is always the following absolutely positive operating safety interval between its radio frequency transmission pulses: (39) In the formula, Represents the local Lipschitz constant within a compact set of physical dynamics; This represents the upper limit of the slope of the external disturbance. This analytical theorem physically confirms that no matter how severe the external environment and DoS network blocking attacks are, the system's wireless radio frequency transmission module will never experience a self-locking crash due to the microprocessor's infinite high-frequency sampling, thus fundamentally eliminating the Zeno self-locking phenomenon.

[0059] In practical embedded controller deployment, this invention unifies the continuous-time control law, dynamic energy pool equation, disturbance sensor equation, adaptive weight update law, first-order instruction filter, and feedforward compensation channel into a discrete sampling form. Let the controller sampling period be... Discrete time is For any continuous dynamic variable Its differential equation Discretized using the forward Euler method (40) For a dynamic energy pool, it can be discretized as: (41) Variables such as adaptive weights and trigger thresholds, which need to maintain physical boundedness, are also limited in their value range using projection operators after discrete updates. This transforms the continuous-time theoretical control algorithm into a recursive calculation process suitable for real-time microprocessor operation, while avoiding parameter drift, threshold failure, or abrupt changes in control input caused by numerical integration errors.

[0060] Figure 6 This is a block diagram of a multi-agent pre-time collaborative control system for resisting DoS based on multi-valued fuzzy approximation and state-dependent asynchronous triggering.

[0061] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A DoS-resistant multi-agent pre-time cooperative control system based on multi-valued fuzzy approximation and state-dependent asynchronous triggering, characterized in that: It includes a communication topology modeling module, a collision avoidance and constraint planning module, a disturbance perception module, a trigger decision module, and a control law synthesis module; The communication topology modeling module is used to construct a time-varying unsteady network topology that includes high-impedance state information shielding the time domain, and to generate link health discrimination variables; The collision avoidance restrictive planning module is used to generate asymmetric obstacle dual-transformation mapping projective manifold variables based on a preset time performance envelope manifold and asymmetric safety barrier boundaries; The disturbance sensing module is used to output the approximation value of the unknown nonlinear function and the estimated value of the composite disturbance of the external environment based on nonsmooth multivalued logic fuzzy approximation and differential topological flow. The triggering decision module is used to generate an asynchronous triggering sampling discrete timestamp sequence based on dynamic energy pool capacity variables and link health discrimination variables; The control law synthesis module is used to generate the final servo physical control law based on the asymmetric obstacle double transformation mapping projected manifold variable, the estimated value of the external environment composite disturbance, the asynchronous trigger sampling discrete timestamp sequence, and the augmented state command filtering compensation.

2. The anti-DoS multi-agent pre-time cooperative control system based on multi-valued fuzzy approximation and state-dependent asynchronous triggering as described in claim 1, characterized in that: The communication topology modeling module is configured as follows: Define the high-resistivity state information shielding time domain within the observation time window as: ,in Representing the k The starting point of the DoS attack intrusion time. Representing the k Duration of the DoS attack; Define link health discrimination variables ,when Time represents intelligent agent i Intelligent agents with neighbors j The communication link is in a healthy communication window, when This indicates that the communication link is in a DoS blocking state; The time-varying adjacency weight is updated based on the link health discriminant variable. ,in Set the adjacency weights for the original values.

3. The anti-DoS multi-agent pre-time cooperative control system based on multi-valued fuzzy approximation and state-dependent asynchronous triggering as described in claim 1, characterized in that: The collision avoidance restriction planning module is configured as follows: Construct a predefined time-performance envelope manifold function ,in To preset an independent time constant, This represents the maximum spatial location divergence at system startup. The steady-state high-frequency noise oscillation range, It is the power order; Define positional cooperative error components ,in For intelligent agents i The output observed variables, , It is the physical distance constant relative to the target; Introducing a preset time forced hedging function ,in It is the power order; Based on the preset time performance envelope manifold function, position cooperative error components, and preset time forced hedging function, the asymmetric safety barrier boundary is established. ,in , For asymmetric safety adjustment coefficients; generate asymmetric barrier dual transformation mapping projected manifold variables. .

4. The anti-DoS multi-agent pre-time cooperative control system based on multi-valued fuzzy approximation and state-dependent asynchronous triggering as described in claim 1, characterized in that: The disturbance sensing module is configured as follows: An unknown nonlinear function is approximated using a Gaussian kernel multi-valued adaptive approximation mapping engine. ,in The optimal fuzzy rule parameter matrix, The Gaussian fuzzy membership degree basis function vector. To approximate the residual by truncating the intrinsic eigenvalue; Construct a full-dimensional exogenous perturbation perceptron using the formula Output the estimated value of unknown composite interference in the external environment, where For the auxiliary state variables of the full-dimensional perceptron, The core high-frequency sensing gain constant, For intelligent agents i The k First-order state components; The auxiliary state variable of the full-dimensional sensor is expressed by the formula Evolution, in which Given the input stream of known terms, for hour ,for hour , To approximate the online estimation vector of the weight parameters.

5. The anti-DoS multi-agent pre-time cooperative control system based on multi-valued fuzzy approximation and state-dependent asynchronous triggering as described in claim 1, characterized in that: The trigger decision module is configured as follows: When link health discriminant variables When this happens, the most recently successfully received neighbor state cache is invoked, and the cache reliability decay factor is applied. Calculate the cooperative error, where For the most recent successful reception of neighbors j The timing of the status packet This is the sensitivity coefficient; Define the core dynamic energy pool capacity variable The first-order adaptive nonlinear differential evolution equation is: ,in For damping parameters, To supplement the gain coefficient, To adaptively trigger the elastic adjustment threshold, For the cumulative divergence deviation vector, The time scale for the most recent broadcast status; The projection operator is used to limit the dynamic energy pool capacity variable to the minimum safe capacity. With maximum capacity between; when At that time, the trigger determination logic is activated and the asynchronous trigger sampling discrete timestamp sequence is recorded. .

6. The anti-DoS multi-agent pre-time cooperative control system based on multi-valued fuzzy approximation and state-dependent asynchronous triggering as described in claim 5, characterized in that: The adaptive trigger elastic adjustment threshold Configured as ,in The lower limit of the basic damping trigger threshold. To dynamically adjust the adaptive weight constant, For state learning coupled gain, This is the online estimation vector for the highest-order approximation weight parameters.

7. The anti-DoS multi-agent pre-time cooperative control system based on multi-valued fuzzy approximation and state-dependent asynchronous triggering as described in claim 1, characterized in that: The control law synthesis module is configured as follows: Embedded first-order instruction low-pass filter, through formula Generate smooth augmented state variables ,in The filter bandwidth time constant, For the first k -1st order virtual control law; Construct a calculus feedforward error compensation channel, using the formula Generate dynamic compensation signal ,in This is the feedforward compensation attenuation adjustment constant. ; Constructing a full-dimensional recursive backstepping composite tracking manifold variable , ,in , n The total order of the system dynamics; Generate the final servo physical control law of the highest execution layer ,in For proportional control gain, This is the maximum 2 norm estimate of the neural fuzzy weight matrix. For fault-tolerant self-compensating damping parameters, This is the highest-order estimate of the combined external environmental disturbances.

8. The anti-DoS multi-agent pre-time cooperative control system based on multi-valued fuzzy approximation and state-dependent asynchronous triggering according to claim 7, characterized in that: The control law synthesis module is also configured as follows: Generate adaptive weight self-learning evolution update law and ,in and To adaptively update the online parameter feedback and adjust the sensitivity constant, and This is a forced leakage factor.

9. The anti-DoS multi-agent pre-time cooperative control system based on multi-valued fuzzy approximation and state-dependent asynchronous triggering according to any one of claims 1 to 8, characterized in that: The system is configured to utilize a multidimensional tensor product-type composite barrier Lyapunov energy functional. Verify the stability of the preset time, among which To adaptively update the deviation for the parameters, To estimate the bias of the weight matrix, To prevent interference estimation bias, N The total number of intelligent agents.

10. A method for anti-DoS multi-agent pre-time cooperative control based on multi-valued fuzzy approximation and state-dependent asynchronous triggering, characterized in that: Includes the following steps: Construct a time-varying nonsteady-state network topology that includes high-impedance state information to mask the time domain and generate link health discrimination variables; Asymmetric barrier double transformation mapping projected manifold variables are generated based on the preset time performance envelope manifold and asymmetric safety barrier boundary; Based on nonsmooth multivalued logic fuzzy approximation and differential topology flow, output the approximation value of the unknown nonlinear function and the estimate of the combined disturbance of the external environment; Asynchronous trigger sampling discrete timestamp sequence is generated based on dynamic energy pool capacity variables and link health discrimination variables; The final servo physical control law is generated based on the asymmetric obstacle dual-number transformation mapping projected manifold variable, the estimated value of the external environment composite disturbance, the asynchronous trigger sampling discrete timestamp sequence, and the augmented state command filtering compensation.

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