Unmanned aerial vehicle cluster cooperative hunting control method based on event triggering mechanism

Abstract

The invention discloses an unmanned aerial vehicle cluster cooperative hunting control method based on an event trigger mechanism, relates to the technical field of unmanned aerial vehicle cluster cooperative hunting control, and aims to solve the problem that unmanned aerial vehicle cluster cooperative hunting control is unstable. Through reasonable design of control gain and triggering conditions, the cooperative hunting ability of the cluster can still be maintained, the robustness of the system in a complex communication environment is improved, in combination with Lyapunov analysis of a potential field method, it is ensured that the distance between the unmanned aerial vehicles is always larger than a safety threshold value in the hunting process, communication links are kept communicated, and the hunting efficiency of the unmanned aerial vehicles is improved. Task failure caused by collision or disconnection is avoided, safety and reliability of the system are enhanced, connectivity is maintained through attraction, stability of the convex hull structure is ensured, the controller combines continuous relative position data and sampling speed data, control continuity is ensured, high-frequency communication requirements are reduced, data transmission pressure is reduced, and the reliability of the system is improved. After triggering, the error is reset to be zero, and the effectiveness of each communication update is ensured.

Description

Technical Field

[0001] The present invention relates to the technical field of cooperative hunting control for unmanned aerial vehicle swarms, and particularly to a cooperative hunting control method for unmanned aerial vehicle swarms based on an event-triggered mechanism. Background Art

[0002] Cooperative hunting control of unmanned aerial vehicle swarms refers to using a group of unmanned aerial vehicles (UAVs) to perform cooperative operations to achieve the purpose of hunting and controlling a certain target.

[0003] A Chinese patent with the publication number CN116736883B discloses a method for intelligent cooperative motion planning of unmanned flight swarms. By introducing a target trajectory prediction (deep long short-term memory neural network) algorithm, the unmanned flight swarm can quickly strike a target under speed constraints, effectively solving the impact of target dynamics and task environment complexity on the effectiveness of the motion planning of the unmanned flight swarm, realizing fast and intelligent motion planning for multiple agents, and designing a decision network framework for cooperative strikes of unmanned flight swarms with variable numbers of members, namely a coronary bidirectional connected network with target prediction ability, which extends the generalization of traditional reinforcement learning methods and effectively solves the problem of cooperative strikes of an indefinite number of multi-agents. Although the above scheme solves the problem of cooperative control, there are still the following problems in actual operation:

[0004] 1. Most control strategies rely on pre-set formation functions to form specific configurations of UAVs, which are not suitable for hunting mobile targets in complex environments.

[0005] 2. ETC strategies are usually designed based on formation errors without considering the implicit task characteristics of the system.

[0006] 3. There is no problem of more detailed and careful analysis of the stability of the UAV swarm. Summary of the Invention

[0007] The purpose of the present invention is to provide a cooperative hunting control method for unmanned aerial vehicle swarms based on an event-triggered mechanism. By reasonably designing control gains and trigger conditions, the cooperative hunting ability of the swarm can still be maintained, the robustness of the system in a complex communication environment can be improved, combined with the Lyapunov analysis of the potential field method, it is ensured that the distance between UAVs is always greater than the safety threshold during the hunting process, and the communication link remains connected, avoiding task failures caused by collisions or loss of connection, enhancing the safety and reliability of the system. By maintaining connectivity through attraction, the convex hull structure is ensured to be stable. The controller combines continuous relative position data with sampled speed data, reducing the high-frequency communication demand while ensuring control continuity, reducing the data transmission pressure, resetting the error to zero after triggering, and ensuring the effectiveness of each communication update, which can solve the problems in the prior art.

[0008] To achieve the above object, the present invention provides the following technical solutions:

[0009] A cooperative pursuit control method for unmanned aerial vehicle clusters based on an event-triggered mechanism, comprising:

[0010] First, establish an unmanned aerial vehicle dynamics model and a dynamic network topology, define a flight convex hull and a pursuit error, design a fixed-time differential state observer, use the target position data measured by the unmanned aerial vehicle to estimate the speed and acceleration of the target, design a distributed pursuit controller, including a navigation feedback control term, a speed consensus term, and a collision avoidance and connectivity maintenance term, where the collision avoidance and connectivity maintenance term is based on a potential field method, dynamically adjust the distance between unmanned aerial vehicles through a single potential function, design a double-threshold event-triggered mechanism, design trigger conditions based on the speed consistency deviation and the pursuit error, dynamically adjust the communication frequency, introduce a minimum trigger interval coefficient to eliminate Zeno behavior, and construct a Lyapunov function for stability analysis.

[0011] Preferably, establishing an unmanned aerial vehicle dynamics model and a dynamic network topology, and defining a flight convex hull and a pursuit error, includes:

[0012] Considering a cluster system composed of n fixed-wing unmanned aerial vehicles in a three-dimensional space, the model formula of the i-th unmanned aerial vehicle is Formula 1, and Formula 1 is as follows:

[0013]

[0014] Where p i (t)=[x i (t), y i (t), z i (t)] T represents the position of the UAV i in the inertial coordinate system, V i (t), γ i (t) and ψ i (t) respectively represent the speed, flight path angle and heading angle of the UAV i . m i is the mass, g is the acceleration due to gravity, and the actual control input u ic (t)=[T i (t), n i (t), φ i (t)] T are respectively the engine thrust, overload and tilt angle. L i (t), D i (t) are respectively the lift and drag;

[0015] Among them, the relevant variables and control inputs need to satisfy the constraint conditions, and the constraint conditions are as follows:

[0016] V min ≤V i (t)≤V max ,ψ min ≤ψ i (t)≤ψ max ,γ min ≤γ i (t)≤γ max ,T min ≤T i (t)≤T max ,n min ≤n i (t)≤n max ,φ min ≤φ i (t)≤φ max ;

[0017] Meanwhile, design the encirclement strategy, including that the axial velocity of the UAV is axial virtual control quantity u i (t) = [u ix (t), u iy (t), u iz (t)] T ;

[0018] And, convert the relationship between u i (t) and the actual control input. The relationship conversion includes Formula 2, and Formula 2 is as follows:

[0019]

[0020] Course angle ψ i (t) and flight path angle γ i (t) are respectively obtained by calculation.

[0021] Preferably, establish the UAV dynamics model and dynamic network topology, define the flight convex hull and the encirclement error, and also include:

[0022] Design a controller to enable the cluster to achieve cooperative encirclement of a maneuvering target in the form of a flight convex hull, and during this process, the relative distance between each UAV and the target is automatically maintained under the action of the controller;

[0023] Define the flight convex hull formed by multiple UAVs. The definition of the flight convex hull includes Formula 3, and Formula 3 is as follows:

[0024]

[0025] The definition of the flight convex hull formed by multiple UAVs includes Formula 4, and Formula 4 is as follows:

[0026]

[0027] The distance between the target and the flight convex hull includes Equation 5, and Equation 5 is as follows:

[0028]

[0029] is a point within the convex hull co(p) that has a distance from the target, where p T represents the position vector of the target;

[0030] When and only when H(p) = 0, p T ∈ co(p), indicating that the UAV swarm has achieved the encirclement control of the target;

[0031] The information interaction between UAVs is described by the graph G = {v, ε, A}, where v = {1, 2, …, n} is the set of points of the graph, used to represent the set of UAVs in the swarm, is the edge set of the graph, used to represent the interaction relationship between UAVs, A = [a ij ∈ R n×n is the adjacency matrix;

[0032] If UAV i can receive information from UAV j, then a ij > 0; otherwise, a ij = 0. The degree matrix of graph G is D = diag{d1, d2, …, d n}, where Then the Laplacian matrix of graph G is defined as L = D - A;

[0033] The dynamic neighbor set of UAV i includes Equation 6, and Equation 6 is as follows:

[0034] M i (t) = {j ∈ {1, 2, …, n}, ||p ij || ≤ μ, j ≠ i}

[0035] where, ||p ij || = ||p i - p j ||, representing the Euclidean distance between UAV i and j.

[0036] Preferably, a fixed-time differential state observer is designed to estimate the velocity and acceleration of the target using the target position data measured by the UAVs, including:

[0037] Accurately estimate the velocity and acceleration of the target within a fixed time, that is where V T (t) is the velocity vector of the target, respectively represent the estimates of the target velocity and acceleration by the i-th UAV;

[0038] The speed of each drone remains consistent and converges to the target speed, that is

[0039] Collision avoidance and connectivity maintenance: 2r in <||p ij (t)||≤μ, where r in represents the body radius;

[0040] The target can be captured by the drone swarm, that is

[0041] If there is task suddenness or a non - cooperative relationship between the drones and the target, and the maneuver form of the target is unknown, drone i can measure the target position through on - board sensing equipment and design a fixed - time state observer to estimate the target speed and acceleration. The estimation includes Equation (7), and Equation (7) is as follows:

[0042]

[0043] where k = 1, 2, 3 represents the estimated values of the i - th drone pair (i.e., p T (t), V T (t) and u T (t)); Satisfy α i ∈(1 - ε1, 1), ε1 is a sufficiently small positive number; Satisfy β i ∈(1, 1 + ε2), ε2 is a sufficiently small positive number;

[0044] Control gains and are both positive numbers and respectively satisfy the polynomials and are Hurwitz;

[0045] The unstructured data and the fixed time of drone i include Equation (8), and Equation (8) is as follows:

[0046]

[0047] The observation of the target speed V T (t) and acceleration u T (t) can be achieved within. Where are both symmetric positive definite matrices, are respectively the solutions of the Lyapunov equations and respectively,

[0048] Preferably, a distributed pursuit controller is designed, which includes a navigation feedback control term, a velocity consensus term, and a collision avoidance and connectivity maintenance term. Among them, the collision avoidance and connectivity maintenance term is based on the potential field method, and the distance between UAVs is dynamically adjusted through a single potential function, including:

[0049] The error representation between the UAV and the target includes Equation (9), and Equation (9) is as follows:

[0050]

[0051] The controller includes continuous relative position data and sampled velocity data;

[0052] The design of the controller includes Equation (10), and Equation (10) is as follows:

[0053]

[0054] where the control gains c1, c2, c3 > 0, represents the potential function, is the gradient along p i (t); represents the event trigger instant of the UAV.

[0055] Preferably, a double-threshold event-triggering mechanism is designed. Based on the velocity consistency deviation and the pursuit error, the trigger condition is designed to dynamically adjust the communication frequency, and the minimum trigger interval coefficient is introduced to eliminate Zeno behavior, including:

[0056] The initial position of the UAV satisfies

[0057] The error between the current value and the latest sampled velocity is defined, including Equation (13), and Equation (13) is as follows:

[0058]

[0059] The design of the event trigger condition for balancing the pursuit task and the cluster control result includes Equation (14), Equation (15), and Equation (16). Equation (14) is as follows:

[0060]

[0061] Equation (15) is as follows:

[0062]

[0063] Equation (17) is as follows:

[0064]

[0065] where K is the feedback gain matrix, and k i is the triggering function to be designed;

[0066] Combined with Equation (14), Equation (15), and Equation (16), the trigger will not trigger at trigger;

[0067] If f i (t)>0 ∨ g i (t)>0, the event trigger will be activated, and then the speed information will be updated, and e qi (t) will be reset to zero.

[0068] Preferably, a Lyapunov function is constructed for stability analysis, including:

[0069] The cooperative target enclosing of the UAV swarm is realized through distributed event-triggered control;

[0070] If (A, B) is stable, then for there exists a positive definite matrix P>0 that satisfies the Riccati inequality. The positive definite matrix includes Equation (17), and Equation (17) is as follows:

[0071] A T P + PA - 2αPBB T P + αI2 < 0

[0072] When the UAV swarm performs target enclosing based on Equation (10), the parameters satisfy: k i ≤n 2 ρ′, K = B T P, (1 - 2κ 2 )>0,

[0073] Define the Lyapunov candidate function including Equation (18), and Equation (18) is as follows:

[0074]

[0075] According to the definition of the neighbor set, the communication topology is time-varying, that is, V c (t) is a piecewise continuous function;

[0076] The control input sequence is denoted as l = 0, 1, 2,..., represents the time sequence of Equation (14) represents the topology switching time sequence;

[0077] If and T0 = 0, the derivative of V c (t) at t ∈ [T0, T1) includes Equation (19), and Equation (19) is as follows:

[0078]

[0079] Formula twenty is obtained according to Young's inequality, and formula twenty is as follows:

[0080]

[0081] Based on formula twenty, formula twenty-one and formula twenty-two are further obtained. Formula twenty-one is as follows:

[0082]

[0083] Formula twenty-two is as follows:

[0084]

[0085] Substitute formula twenty-one and formula twenty-two into formula twenty to obtain formula twenty-three, and formula twenty-three is as follows:

[0086]

[0087] Meanwhile, formula twenty-four is derived according to formula fourteen, and formula twenty-four is as follows:

[0088]

[0089] Since (1 - 2κ 2 ) > 0, formula twenty-five can be obtained, and formula twenty-five is as follows:

[0090]

[0091] Therefore, formula twenty-five is transformed into formula twenty-six, and formula twenty-six is as follows:

[0092]

[0093] When the parameters meet the corresponding requirements, it is obtained that indicating that V c (t) ≤ V c (T0),

[0094] According to formula twenty-six and the definition of, there is no collision and loss of connectivity during the process of [T0, T1);

[0095] If V1(t) is still continuous, and T1 is expressed as the initial topology moment, and V c (T1 + ) < ∞, V c (t) is discontinuous;

[0096] If the communication topology G is initially connected and G is ultimately fixed, and V c (t) is a uniformly continuous and differentiable function;

[0097] Then is an invariant set, and all solutions of Equation (27) converge to the largest invariant set

[0098] Equation (27) is as follows:

[0099]

[0100] Therefore, That is, q1(t) = q2(t) =... = q n (t) = q T (t);

[0101] When the event-triggering mechanism exhibits Zeno behavior, the characteristic of Zeno behavior is that an infinite sequence of triggering events occurs within a finite time frame;

[0102] Under the action of Equation (14), there is no Zeno behavior in the UAV swarm.

[0103] Preferably, constructing a Lyapunov function for stability analysis further includes:

[0104] When the measurement error ||e qi (t)|| 2 exceeds , the event is updated, including Equation (28), and Equation (28) is as follows:

[0105]

[0106] ||e qi (t)|| 2 The Dini derivative of

[0107]

[0108] According to the definition, e qi (t) includes Equation (30), and Equation (30) is as follows:

[0109]

[0110] Let It can be obtained that: D + ||e qi (t)|| 2 ≤||e qi (t)|| 2 +2Δ 1i Δ2i

[0111] At the trigger moment Including Formula 31, and Formula 31 is as follows:

[0112]

[0113] In addition, when Including Formula 32, and Formula 32 is as follows:

[0114]

[0115] When is satisfied, the time interval If There is When the collaborative task is not completed, Indicates Therefore, there is no Zeno behavior under the action of Formula 14;

[0116] According to the stability requirements of the target encirclement, the encirclement error is processed according to Formula 15;

[0117] The encirclement error includes Formula 33, and Formula 33 is as follows:

[0118]

[0119] Let Then the fence error system includes Formula 34, and Formula 34 is as follows:

[0120] Where According to the definition of dynamic topology, the communication between UAVs is undirected, that is And

[0121] The definition of the Lyapunov candidate function includes Formula 35, and Formula 35 is as follows:

[0122]

[0123] The time derivative of Formula 35 includes Formula 36, and Formula 36 is as follows:

[0124]

[0125] Introduce Given And Get Formula 37, and Formula 37 is as follows:

[0126]

[0127] Formula 38 is obtained according to Young's inequality, and Formula 38 is as follows:

[0128]

[0129] Formula 37 is transformed into Formula 39, and Formula 39 is as follows:

[0130]

[0131] An inequality is obtained according to Formula 39, and the inequality includes Formula 40, and Formula 40 is as follows:

[0132]

[0133] Among them, an inequality is obtained according to F = PBK, and the inequality includes Formula 41, and Formula 41 is as follows:

[0134]

[0135] Formula 42 is obtained according to Formula 41, and Formula 42 is as follows:

[0136]

[0137] If Formula 40 holds, then combined with Formula 17 and considering the coefficient That is It includes Formula 43, and Formula 43 is as follows:

[0138]

[0139] Formula 45 is proved according to Formula 43, and Formula 45 is as follows:

[0140]

[0141] If k i ≤n 2 ρ′ holds, then Formula 45 holds, thus proving the validity of Formula 42 and of.

[0142] Preferably, a Lyapunov function is constructed for stability analysis, and it also includes:

[0143] Design the minimum trigger interval coefficient τ i , so that the trigger time interval is jointly determined by the two and Formula 15, that is, the trigger interval includes Formula 46, and Formula 46 is as follows:

[0144]

[0145] Wherein represents the time interval determined by (15);

[0146] The conditions for selecting Equation 40 include Equation 47, and Equation 47 is as follows:

[0147]

[0148] Equation 48 is obtained according to Equation 47, and Equation 48 is as follows:

[0149]

[0150] τ i can be described as determined by the lower bound of the time interval from 0 to when;

[0151] For determining the lower limit of time, the calculation formula includes Equation 49 and Equation 50, and Equation 49 is as follows:

[0152]

[0153] Equation 50 is as follows:

[0154]

[0155] Let Then Equation 50 includes Equation 51, and Equation 51 is as follows:

[0156]

[0157] where β1 = 2||A||, β0 = n||KB 2 ||;

[0158] For Equation 51, Θ(t) ≤ θ(t, θ0) is satisfied, where θ(t, θ0) represents the solution of the equation;

[0159] The initial value problem includes Equation 52, and Equation 52 is as follows:

[0160]

[0161] Equation 53 is obtained according to Equation 52, and Equation 53 is as follows:

[0162]

[0163] According to and under the action of Equation 15, the maximum adjustable trigger time interval coefficient includes Equation 54, and Equation 54 is as follows:

[0164]

[0165] Preferably, constructing a Lyapunov function for stability analysis further includes:

[0166] According to D i (t) and L i (t) are calculated according to Equation 500,000, and Equation 500,000 is as follows:

[0167]

[0168] where S w = 1.37 m 2 , ρ0 = 1.225 kg / m 3 , and C D0 = 0.02 are the wing area, air density, and zero-lift drag coefficient respectively, k n = 1, k d = 0.1, m i = 20 kg, r1 = 10 m, and μ = 100 m. The constraint of u ia (t) is -1.5 ≤ n i ≤ 2.0, 10 N ≤ T i ≤ 125 N, and -80° ≤ φ i ≤ 80°;

[0169] The formula for the first maneuvering target is as follows:

[0170] u T (t) = [0.2sin(πt / 20), 0.2cos(πt / 20), 0.01sin(πt / 5)] T

[0171] The formula for the second maneuvering target is as follows:

[0172] u T (t) = [sin(πt / 10), 0.5cos(πt / 10), 0.01sin(πt / 5)] T .

[0173] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0174] 1. A method for cooperative pursuit control of an unmanned aerial vehicle cluster based on an event-triggered mechanism provided by the present invention transforms the pursuit task of the unmanned aerial vehicle cluster into a dynamic adjustment problem of the distance between the target and the convex hull through the convex hull mathematical definition (Equations 3 to 5), uses graph theory to describe the communication relationship of the unmanned aerial vehicles, and the dynamic neighbor set enables the unmanned aerial vehicles to perceive the positions of neighboring individuals in real time, providing data support for control items such as collision avoidance and velocity consensus. Each unmanned aerial vehicle independently estimates the target state and reaches a consensus through the communication network, avoiding the single-point failure problem of centralized estimation.

[0175] 2. The cooperative pursuit control method for unmanned aerial vehicle (UAV) swarms based on an event-triggered mechanism provided by the present invention adjusts the UAV spacing dynamically through a single potential function for the potential field collision avoidance term. When the distance is too close, a repulsive force is generated to avoid collisions. At the same time, connectivity is maintained through an attractive force to ensure the stability of the convex hull structure. The controller combines continuous relative position data and sampled velocity data, reducing the high-frequency communication requirements while ensuring control continuity, alleviating the data transmission pressure, resetting the error to zero after triggering, ensuring the effectiveness of each communication update, and avoiding the influence of stale data on control accuracy.

[0176] 3. The cooperative pursuit control method for UAV swarms based on an event-triggered mechanism provided by the present invention can still maintain the cooperative pursuit ability of the swarm and enhance the robustness of the system in complex communication environments by reasonably designing the control gain and triggering conditions. Combining the Lyapunov analysis of the potential field method, it ensures that the distance between UAVs is always greater than the safety threshold during the pursuit process, and the communication links remain connected, avoiding mission failures caused by collisions or disconnections, and enhancing the safety and reliability of the system. Description of the Drawings

[0177] Figure 1 is a schematic diagram of the cooperative pursuit process of the present invention;

[0178] Figure 2 is a schematic diagram of the UAV neighborhood of the present invention;

[0179] Figure 3 is a schematic diagram of the cooperative pursuit control scheme of the present invention;

[0180] Figure 4 is a schematic diagram of the first flight trajectory of the present invention;

[0181] Figure 5 is a schematic diagram of the second flight trajectory of the present invention;

[0182] Figure 6 is a schematic diagram of the pursuit error of the present invention;

[0183] Figure 7 is a schematic diagram of the relative distance between UAVs of the present invention;

[0184] Figure 8 is a schematic diagram of the flight speed of the present invention;

[0185] Figure 9 is a schematic diagram of the relative distance between a UAV and a target of the present invention;

[0186] Figure 10 is a schematic diagram of the heading angle of the present invention;

[0187] Figure 11 is a schematic diagram of the flight path angle of the present invention;

[0188] Figure 12 Schematic diagram of the actual control input of the present invention;

[0189] Figure 13 Schematic diagram of the trigger distribution of the present invention;

[0190] Figure 14 Schematic diagram of the first faulty flight trajectory of the present invention;

[0191] Figure 15 Schematic diagram of the second faulty flight trajectory of the present invention;

[0192] Figure 16 Schematic diagram of the faulty enclosure error of the present invention;

[0193] Figure 17 Schematic diagram of the faulty flight speed of the present invention;

[0194] Figure 18 Schematic diagram of the faulty flight path angle of the present invention;

[0195] Figure 19 Schematic diagram of the faulty heading angle of the present invention;

[0196] Figure 20 Schematic diagram of the faulty actual control input of the present invention;

[0197] Figure 21 Schematic diagram of the faulty trigger distribution of the present invention. Detailed implementation manners

[0198] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

[0199] To solve the problem in the prior art that most control strategies rely on pre-set formation functions to form specific configurations of unmanned aerial vehicles and are not suitable for maneuvering target enclosure in complex environments, please refer to Figures 1 - 2 , the following technical solutions are provided in this embodiment:

[0200] A method for cooperative enclosure control of unmanned aerial vehicle clusters based on an event-triggered mechanism, including:

[0201] First, establish the UAV dynamics model and dynamic network topology, define the flight convex hull and the pursuit error, design a fixed-time differential state observer, estimate the target's velocity and acceleration using the target position data measured by the UAVs, and design a distributed pursuit controller, which includes a navigation feedback control term, a velocity consensus term, and a collision avoidance and connectivity maintenance term. The collision avoidance and connectivity maintenance term is based on the potential field method, and dynamically adjusts the distance between UAVs through a single potential function. Design a double-threshold event-triggering mechanism, design the triggering condition based on the velocity consistency deviation and the pursuit error, dynamically adjust the communication frequency, introduce a minimum triggering interval coefficient to eliminate Zeno behavior, and construct a Lyapunov function for stability analysis.

[0202] Specifically, abandon the limitations of preset formation parameters (such as fixed formation, desired distance / azimuth) in traditional methods. By defining the "flight convex hull" as the pursuit target, use the self-organization principle to enable the UAV swarm to dynamically adjust the relative positions, automatically form a stable configuration around the target, adapt to complex environments and maneuvering targets, without the need for prior formation planning, improve the task flexibility and robustness. When individual UAVs fail or lose contact, the remaining UAVs autonomously reconstruct the formation (such as changing from a regular tetrahedron to an equilateral triangle) by dynamically adjusting the potential function and neighbor set, maintain the continuity of the pursuit task, enhance the system fault tolerance and distributed cooperation ability. Only relying on the target position data measured locally by the UAVs, without network communication, can accurately estimate the target's velocity and acceleration within a fixed time, solve the problem of unmeasurable target states, provide real-time state feedback for maneuvering target pursuit, improve the control accuracy. Simultaneously handle the collision avoidance (repulsive force) and connectivity maintenance (attractive force) between UAVs through a single potential function, avoid the complexity of separate designs in traditional methods, reduce the system computational overhead, ensure that the UAVs dynamically adjust within a safe distance, and maintain the stability of the communication link. Design the triggering condition based on the velocity consistency deviation and the pursuit error, and trigger communication only when the error exceeds the dynamic threshold, avoid the resource waste of continuous communication, significantly reduce the communication frequency (such as the number of trigger times in the simulation is reduced by about 86% compared with the case without the trigger mechanism), reduce the network load, introduce a minimum triggering interval coefficient, ensure that the triggering time interval has a positive lower bound, avoid the problem of infinite triggering within a finite time, and ensure the engineering feasibility of the event-triggering mechanism and improve the system real-time performance.

[0203] Establish the UAV dynamics model and dynamic network topology, define the flight convex hull and the pursuit error, including:

[0204] Consider a swarm system composed of n fixed-wing UAVs in three-dimensional space. The model formula of the i-th UAV is Formula 1, and Formula 1 is as follows:

[0205]

[0206] where p i (t)=[xi (t), y i (t), z i (t)] T represents the position of the UAV i in the inertial coordinate system, and V i (t), γ i (t) and ψ i respectively represent the velocity, flight path angle and heading angle of the UAV i . m i is the mass, g is the acceleration due to gravity, and the actual control input u ic (t) = [T i (t), n i (t), φ i (t)] T are respectively the engine thrust, overload and tilt angle. L i (t), D i (t) are respectively the lift and drag forces;

[0207] Among them, the relevant variables and control inputs need to satisfy the constraint conditions, and the constraint conditions are as follows:

[0208] V min ≤ V i (t) ≤ V max , ψ min ≤ ψ i (t) ≤ ψ max , γ min ≤ γ i (t) ≤ γ max , T min ≤ T i (t) ≤ T max , n min ≤ n i (t) ≤ n max , φ min ≤ φ i (t) ≤ φ max ;

[0209] Meanwhile, the encirclement strategy is designed, including the axial velocity of the UAV being the axial virtual control quantity u i (t) = [u ix (t), u iy (t), u iz (t)] T ;

[0210] And, a relationship conversion is carried out between u i (t) and the actual control input, and the relationship conversion includes Equation 2, and Equation 2 is as follows:

[0211]

[0212] Course angle ψ i (t) and flight path angle γ i (t) are respectively obtained by Calculation.

[0213] Design a controller to enable the cluster to achieve cooperative encirclement of a maneuvering target in the form of a flight convex hull. During this process, the relative distance between each UAV and the target is automatically maintained under the action of the controller;

[0214] Define the flight convex hull formed by multiple UAVs. The flight convex hull includes Formula 3, and Formula 3 is as follows:

[0215]

[0216] The definition of the flight convex hull formed by multiple UAVs includes Formula 4, and Formula 4 is as follows:

[0217]

[0218] The distance between the target and the flight convex hull includes Formula 5, and Formula 5 is as follows:

[0219]

[0220] Is a point within the convex hull co(p) that has a distance from the target, where p T Represents the position vector of the target;

[0221] When and only when H(p) = 0, p T ∈co(p), indicating that the UAV cluster has achieved encirclement control of the target;

[0222] Describe the information interaction between UAVs with a graph G = {v, ε, A}, where v = {1, 2,..., n} is the set of points of the graph, used to represent the set of UAVs in the cluster, Is the edge set of the graph, used to represent the interaction relationship between UAVs, A = [a ij ∈ R n×n Is the adjacency matrix;

[0223] If UAV i can receive information from UAV j, then a ij > 0; otherwise, a ij = 0. The degree matrix of graph G is D = diag{d1, d2,..., d n}), where Then the Laplacian matrix of graph G is defined as L = D - A;

[0224] The dynamic neighbor set of UAV i includes Formula 6, and Formula 6 is as follows:

[0225] M i\(\tau(i)=\{j\in\{1,2,\ldots,n\},\vert\vert p ij \vert\vert\leq\mu,j\neq i\}

[0226] where \(\vert\vert p ij \vert\vert=\vert\vert p i - p j \vert\vert\), representing the Euclidean distance between UAVs \(i\) and \(j\).

[0227] Specifically, by establishing a three - dimensional dynamic model (Equation 1) that includes position, velocity, flight path angle, and heading angle, the physical relationships between UAV thrust, overload, tilt angle, etc. and lift and drag are clarified, providing an accurate mathematical basis for subsequent controller design. The introduction of constraint conditions (such as engine thrust range, overload limit) ensures the feasibility of control inputs, prevents UAVs from exceeding physical limits, and improves system safety. Through the convex hull mathematical definition (Equations 3 - 5), the pursuit task of the UAV swarm is transformed into a dynamic adjustment problem of the distance between the target and the convex hull. When the convex hull contains the target (i.e., \(H(p)=0\)), it indicates that the pursuit is successful. This geometric modeling method provides a unified objective function for distributed cooperative control, facilitating each UAV to achieve the global pursuit effect through local information interaction. Using graph theory to describe the UAV communication relationship (adjacency matrix, Laplacian matrix), the dynamic neighbor set (Equation 6) enables UAVs to perceive the positions of neighboring individuals in real time, providing data support for control items such as collision avoidance and velocity consensus. This distributed architecture reduces the dependence on the central node, improves the robustness and fault tolerance of the swarm. Even if some UAVs' communications are interrupted, the pursuit task can still be maintained through local topology adjustment. The pursuit method based on self - organizing behavior can make full use of the autonomy of each UAV. When a UAV is unable to continue its task due to a fault or external factors, the remaining UAVs can reconfigure the formation in a short time to achieve the cooperative target pursuit. This requires UAVs to be able to autonomously adjust the distance between them to ensure collision avoidance and connection maintenance. To facilitate the realization of the above functions, the adjacent area of each UAV is defined as Figure 2 shown, where \(r_1\) is the body radius, \(r_2\) is the collision avoidance radius, and \(\mu\) is the sensing radius. The position distribution of UAVs changes with the planned trajectory, and UAVs with a sensing range of \(\mu\) move continuously in three - dimensional space. Therefore, the neighbor set of each UAV will be continuously updated, forming a dynamic communication topology. Assuming that each UAV is equipped with the same on - board sensor, once a UAV enters the sensing range \(\mu\) of another UAV, the two can communicate with each other. Therefore, the communication between UAVs is bidirectional, and the Laplacian matrix is positive semi - definite.

[0228] Design a fixed - time differential state observer to estimate the velocity and acceleration of the target using the target position data measured by the UAV, including:

[0229] Accurately estimate the speed and acceleration of the target within a fixed time, that is where V T (t) is the velocity vector of the target, respectively represent the estimates of the target speed and acceleration by the i-th UAV;

[0230] The speed of each UAV remains consistent and converges to the target speed, that is

[0231] Collision avoidance and connectivity maintenance: where r in represents the body radius;

[0232] The target can be captured by the UAV swarm, that is

[0233] If the task is sudden or there is a non - cooperative relationship between the UAVs and the target, and the maneuver form of the target is unknown, UAV i can measure the target position through on - board sensing equipment and design a fixed - time state observer to estimate the target speed and acceleration. The estimation includes Equation (7), and Equation (7) is as follows:

[0234]

[0235] where k = 1, 2, 3 represents the estimate of the i - th UAV for (that is, p T (t), V T (t) and u T (t)); Satisfy α i ∈(1 - ε1, 1), ε1 is a sufficiently small positive number; Satisfy β i ∈(1, 1 + ε2), ε2 is a sufficiently small positive number;

[0236] The control gains and are both positive numbers and respectively satisfy the polynomials and are Hurwitz;

[0237] The unstructured data and the fixed time of UAV i include Equation (8), and Equation (8) is as follows:

[0238]

[0239] Realize the observation of the target speed V T (t) and acceleration u T (t) within. Where are all symmetric positive definite matrices, are respectively the solutions of the Lyapunov equations and respectively.

[0240] Specifically, the fixed-time state observer (Equations 7 and 8) is designed through non-linear control gains to ensure accurate estimation of the target velocity and acceleration within a finite time without relying on prior knowledge of the target motion pattern. This feature is particularly applicable to sudden tasks or non-cooperative target scenarios (such as unknown target maneuvers), enabling the UAVs to quickly respond to target changes and shorten the encirclement time. Each UAV independently estimates the target state and reaches a consensus through the communication network, avoiding the single-point failure problem of centralized estimation. The design of the observer parameters satisfies the Hurwitz stability condition, ensuring that the estimation error decays exponentially over time, providing reliable target motion information for the subsequent controller and improving the encirclement accuracy. Through collision avoidance constraints and connectivity maintenance, it is ensured that while estimating the target state, the UAVs maintain a safe distance and communication link, avoiding internal collisions or disconnections within the cluster and ensuring the continuity and reliability of the encirclement task. The UAVs need to perform cooperative escort or encirclement of high-value flying targets. During this period, to ensure the safety of the cluster, the UAVs should possess autonomous collision avoidance and obstacle avoidance capabilities. In addition, the premise for multiple UAVs to cooperatively execute the encirclement task is the existence of a complete communication link within the system. Therefore, maintaining the connectivity of the UAV cluster dynamic network is of crucial importance. Constrained by the on-board performance, the velocity and acceleration of the target may not be measurable. To ensure the precise encirclement of a maneuvering target, both need to be estimated, and a cooperative control scheme based on a distributed event-triggered mechanism consisting of a state observer and an encirclement controller is constructed for the UAVs to complete the target encirclement task.

[0241] To solve the problem in the prior art that ETC strategies are usually designed based on formation errors without considering the implicit task characteristics of the system, please refer to Figures 3 - 21 This embodiment provides the following technical solutions:

[0242] Design a distributed encirclement controller, which includes a navigation feedback control term, a velocity consensus term, and a collision avoidance and connectivity maintenance term. The collision avoidance and connectivity maintenance term is based on the potential field method and dynamically adjusts the distance between UAVs through a single potential function, including:

[0243] The error representation between the UAV and the target includes Equation 9, and Equation 9 is as follows:

[0244]

[0245] The controller includes continuous relative position data and sampled velocity data;

[0246] The design of the controller includes Equation (10), which is as follows:

[0247]

[0248] where the control gains \(c_1, c_2, c_3>0\), represents the potential function, is the gradient along \(p\) i (t); represents the event-triggering instant of the UAV.

[0249] Specifically, (Equation (9)) directly drives the UAV to track the target position error, ensuring that the overall swarm approaches the target. The velocity consensus term promotes the convergence of the UAV velocity to the target velocity, achieving swarm motion consistency and avoiding the destruction of the encirclement structure caused by velocity differences. The potential field collision avoidance term dynamically adjusts the UAV spacing through a single potential function (such as a repulsive potential field), generating a repulsive force when the distance is too close to avoid collisions, and maintaining connectivity through an attractive force to ensure the stability of the convex hull structure. The controller combines continuous relative position data and sampled velocity data (Equation (10)), reducing the high-frequency communication requirements while ensuring control continuity and reducing data transmission pressure. The introduction of the potential function gradient enables the UAV to autonomously adjust its motion based on local information, enhancing the autonomy and flexibility of distributed control. Through the design of potential function parameters (such as the action range and repulsive intensity), the UAV can maintain a safe distance in a dense environment and maintain communication connectivity in a sparse environment, adapting to the encirclement requirements in different scenarios and improving the system generalization ability.

[0250] Design a dual-threshold event-triggering mechanism, design the triggering conditions based on the velocity consistency deviation and the encirclement error, dynamically adjust the communication frequency, and introduce a minimum triggering interval coefficient to eliminate Zeno behavior, including:

[0251] The initial position of the UAV satisfies

[0252] Define the error between the current value and the latest sampled velocity, including Equation (13), which is as follows:

[0253]

[0254] The design of the event-triggering conditions for balancing the encirclement task and the swarm control result includes Equation (14), Equation (15), and Equation (16). Equation (14) is as follows:

[0255]

[0256] Equation (15) is as follows:

[0257]

[0258] Equation (17) is as follows:

[0259]

[0260] where K is the feedback gain matrix, and k i is the triggering function to be designed;

[0261] Combined with Equation (14), Equation (15), and Equation (16), the trigger will not trigger at the trigger;

[0262] If f i (t) > 0 ∨ g i (t) > 0, the event trigger will be activated, and then the speed information will be updated, and e qi (t) will be reset to zero.

[0263] Specifically, through the dual-threshold triggering conditions (Equation (14) and Equation (15)), communication is activated only when the speed consistency deviation or the enclosing error exceeds the set threshold, avoiding redundant data transmission in periodic communication, significantly reducing energy consumption and communication bandwidth occupancy, extending the flight time of the UAVs, especially suitable for large-scale cluster scenarios. The minimum trigger interval coefficient (Equation (46)) ensures the lower limit of the trigger time interval, avoiding the Zeno problem of infinite triggering within a finite time, and ensuring the real-time performance and physical realizability of the control system. After triggering, the error is reset to zero (such as ∈qt(t) = 0), ensuring the effectiveness of each communication update and avoiding the influence of stale data on the control accuracy. The design of the threshold parameters (such as κ, λ2) can be dynamically adjusted according to the task requirements, increasing the communication frequency when high enclosing accuracy is required and decreasing the frequency when the target is stable, achieving the optimal balance between performance and resources, and enhancing the adaptability of the system in different task phases.

[0264] Construct a Lyapunov function for stability analysis, including:

[0265] Achieve cooperative target enclosing of UAV swarms through distributed event-triggered control;

[0266] If (A, B) is stable, then for there exists a positive definite matrix P > 0 that satisfies the Riccati inequality. The positive definite matrix includes Equation (17), and Equation (17) is as follows:

[0267] A T P + PA - 2αPBB T P + αI2 < 0

[0268] When the UAV swarm performs target enclosing based on Equation (10), the parameters satisfy: k i ≤ n 2 ρ′, K = B T P, (1 - 2κ 2 ) > 0,

[0269] Define the Lyapunov candidate function to include Equation (18), and Equation (18) is as follows:

[0270]

[0271] According to the definition of the neighbor set, the communication topology is time-varying, that is, V c (t) is a piecewise continuous function;

[0272] The control input sequence is denoted as l = 0, 1, 2, …, Denote the time series of Equation (14) Denote the topological switching time series;

[0273] If and T0 = 0, obtain the derivative of V c (t) at t ∈ [T0, T1) to include Equation (19), and Equation (19) is as follows:

[0274]

[0275] According to the Young's inequality, obtain Equation (20), and Equation (20) is as follows:

[0276]

[0277] According to Equation (20), further obtain Equation (21) and Equation (22), and Equation (21) is as follows:

[0278]

[0279] Equation (22) is as follows:

[0280]

[0281] Substitute Equation (21) and Equation (22) into Equation (20) to obtain Equation (23), and Equation (23) is as follows:

[0282]

[0283] Meanwhile, derive Equation (24) according to Equation (14), and Equation (24) is as follows:

[0284]

[0285] Since (1 - 2κ 2 ) > 0, obtain Equation (25), and Equation (25) is as follows:

[0286]

[0287] Therefore, Formula 25 is transformed into Formula 26, and Formula 26 is as follows:

[0288]

[0289] When the parameters meet the corresponding requirements, we get indicating that V c (t) ≤ V c (T0),

[0290] According to Formula 26 and 's definition, no collision and loss of connectivity occur during the process of [T0, T1);

[0291] If V1(t) is still continuous, and V c (T1 - ) = V c (T1 + ) < V c (T0), , T1 is represented as the initial topological moment, and V c (T1 + ) < ∞, V c (t) is discontinuous;

[0292] If the communication topology G is initially connected and G is finally fixed, V c (t) is a uniformly continuous and differentiable function;

[0293] Then is an invariant set, and all solutions of Formula 27 converge to the largest invariant set

[0294] Formula 27 is as follows:

[0295]

[0296] Therefore, that is, q1(t) = q2(t) = … = q n (t) = q T (t);

[0297] When the event-triggering mechanism exhibits Zeno behavior, the characteristic of Zeno behavior is that an infinite sequence of triggering events occurs within a finite time frame;

[0298] Under the action of Formula 14, there is no Zeno behavior in the UAV swarm.

[0299] When the measurement error ||e qi (t)|| 2 exceeds When the event is updated, it includes Equation (28), and Equation (28) is as follows:

[0300]

[0301] ||e qi (t)|| 2 The Dini derivative of... includes Equation (29), and Equation (29) is as follows:

[0302]

[0303] According to the definition, e qi (t) includes Equation (30), and Equation (30) is as follows:

[0304]

[0305] Let We can get: D + ||e qi (t)|| 2 ≤||e qi (t)|| 2 +2Δ 1i Δ 2i

[0306] At the trigger moment it includes Equation (31), and Equation (31) is as follows:

[0307]

[0308] In addition, when it includes Equation (32), and Equation (32) is as follows:

[0309]

[0310] When is satisfied, the time interval If there is When the collaborative task is not completed, it means Therefore, there is no Zeno behavior under the action of Equation (14);

[0311] According to the stability requirements of target encirclement, the encirclement error is processed according to Equation (15);

[0312] The encirclement error includes Equation (33), and Equation (33) is as follows:

[0313]

[0314] Let Then the fence error system includes Equation (34), and Equation (34) is as follows:

[0315] Among them According to the definition of dynamic topology, the communication between UAVs is undirected, that is and

[0316] The definition of the Lyapunov candidate function includes Equation (35), and Equation (35) is as follows:

[0317]

[0318] The time derivative of Equation (35) includes Equation (36), and Equation (36) is as follows:

[0319]

[0320] Introduce Given and We get Equation (37), and Equation (37) is as follows:

[0321]

[0322] According to Young's inequality, we get Equation (38), and Equation (38) is as follows:

[0323]

[0324] Convert Equation (37) into Equation (39), and Equation (39) is as follows:

[0325]

[0326] According to Equation (39), we get an inequality, and the inequality includes Equation (40), and Equation (40) is as follows:

[0327]

[0328] Among them, according to F = PBK, we get an inequality, and the inequality includes Equation (41), and Equation (41) is as follows:

[0329]

[0330] According to Equation (41), we get Equation (42), and Equation (42) is as follows:

[0331]

[0332] If Equation (40) holds, then combining Equation (17) and considering the coefficient That is It includes Equation (43), and Equation (43) is as follows:

[0333]

[0334] Prove formula forty-five according to formula forty-three. Formula forty-five is as follows:

[0335]

[0336] If k i ≤n 2 ρ′ holds, then formula forty-five holds, thus proving the validity of formula forty-two and .

[0337] Design the minimum trigger interval coefficient τ i such that the trigger time interval is jointly determined by the two and formula fifteen, that is, the trigger interval includes formula forty-six. Formula forty-six is as follows:

[0338]

[0339] where represents the time interval determined by (15);

[0340] The conditions for selecting formula forty include formula forty-seven. Formula forty-seven is as follows:

[0341]

[0342] According to formula forty-seven, formula forty-eight is obtained. Formula forty-eight is as follows:

[0343]

[0344] τ i can be described as determined by the lower bound of the time interval from 0 increasing to ;

[0345] Calculate the lower limit of the determined time. The calculation formulas include formula forty-nine and formula fifty. Formula forty-nine is as follows:

[0346]

[0347] Formula fifty is as follows:

[0348]

[0349] Let then formula fifty includes formula fifty-one. Formula fifty-one is as follows:

[0350]

[0351] where β1 = 2||A||, β0 = n||KB 2 ||;

[0352] For Equation 51, Θ(t) ≤ θ(t, θ0) is satisfied, where θ(t, θ0) represents the solution of the equation;

[0353] The initial value problem includes Equation 52, and Equation 52 is as follows:

[0354]

[0355] Equation 53 is obtained from Equation 52, and Equation 53 is as follows:

[0356]

[0357] According to And under the action of Equation 15, the maximum adjustable trigger time interval coefficient includes Equation 54, and Equation 54 is as follows:

[0358]

[0359] According to D i (t) and L i (t) are calculated according to Equation 500,000, and Equation 500,000 is as follows:

[0360] L i (t) = m i gn i (t)

[0361] where S w = 1.37m 2 , ρ0 = 1.225kgm 3 , and C D0 = 0.02 are the wing area, air density, and zero-lift drag coefficient respectively, k n = 1, k d = 0.1, m i = 20kg, r1 = 10m, and μ = 100m. u ia (t) constraints are -1.5 ≤ n i ≤ 2.0, 10N ≤ T i ≤ 125N, and -80° ≤ φ i ≤ 80°;

[0362] The formula for the first maneuvering target is as follows:

[0363] u T (t) = [0.2sin(πt20), 0.2cos(πt20), 0.01sin(πt5)] T

[0364] The formula for the second maneuvering target is as follows:

[0365] uT \(\mathbf{\xi}(t) = [\sin(\pi t / 10), 0.5\cos(\pi t / 10), 0.01\sin(\pi t / 5)]\) T 。

[0366] Specifically, by constructing the Lyapunov candidate function (Equation XVIII) and analyzing its derivative (Equations XIX to XXVI), the stability of the UAV swarm under event-triggered control is strictly proven, ensuring that state variables such as the pursuit error and velocity consistency error converge to zero over time, guaranteeing the feasibility of the scheme at the theoretical level. For the dynamic communication topology (piecewise continuous function), the stability analysis considers the impact of topology switching on the system and proves that even in the case of time-varying communication links, by reasonably designing the control gain (such as \(K = B\) T \(P\)) and trigger conditions, the cooperative pursuit ability of the swarm can still be maintained, enhancing the robustness of the system in complex communication environments. Combining the Lyapunov analysis with the potential field method (such as Equation XXVI) ensures that the distance between UAVs is always greater than the safety threshold (\(2r\) min ), and the communication links remain connected, avoiding mission failures caused by collisions or disconnections and enhancing the safety and reliability of the system. Through the Dini derivative analysis (Equation XXIX) and trigger conditions (Equation XXVIII), the robustness of the system to measurement errors is proven, and even in the presence of sensor noise or data quantization errors, the state can still be dynamically updated through the event-triggered mechanism to maintain the pursuit accuracy. The derivation of the minimum trigger interval (Equations LI to LIV) provides a clear parameter design basis for engineering implementation, ensuring that the trigger interval is measurable and controllable. The pursuit error system is modeled as a linear time-varying system (Equation XXXIV), and the feedback gain is designed through the Riccati inequality (Equation XVII) and Hurwitz conditions to ensure the exponential stability of the error dynamics. This linearization facilitates the tuning of controller parameters in engineering applications. Combining a nonlinear observer and a trigger mechanism, efficient control of the nonlinear system is achieved. By setting different maneuvering targets (such as sinusoidal motion) and UAV parameters (such as wing area, air density), the stability analysis covers a variety of scenarios, proving the adaptability of the scheme to fast maneuvering targets and complex environments and providing extensive theoretical support for practical engineering applications. By solving differential equations (Equations LII to LIII), it is clear that the lower bound of the trigger interval is determined by system parameters (such as control gain \(\beta_1\), initial error \(\theta_0\)), providing an accurate mathematical model for the timing design of the communication module in hardware implementation and avoiding communication congestion caused by too short a trigger interval or control lag caused by too long a trigger interval. By adjusting the trigger function parameters (such as \(\rho\), \(\alpha\)), a trade-off can be made among the pursuit speed, accuracy, and energy consumption. For example, reducing \(\rho\) can improve the trigger sensitivity and is suitable for high-dynamic targets; increasing \(\rho\) can reduce the communication frequency and is suitable for stable targets, achieving fine-tuning of system performance. Through specific physical parameters (such as UAV mass \(m\)i = 20 kg, wing area S = 1.37 m 2 ) and the substitution of the target motion equation (such as sinusoidal acceleration), the stability analysis results can directly guide the selection of UAV hardware (such as the engine thrust range) and the implementation of software algorithms, shortening the conversion cycle from theory to engineering.

[0367] In summary: A dynamic model of a fixed-wing UAV in three-dimensional space is established to clarify the relationships between state variables such as position, velocity, and flight path angle and control inputs such as engine thrust and overload. At the same time, physical constraints (such as thrust range and overload limit) are incorporated to ensure control feasibility. The conversion relationship between the axial virtual control quantity and the actual control input is defined. Through the dynamic calculation of the heading angle and flight path angle, precise control of the UAV's motion attitude is achieved. The information interaction between UAVs is described using graph theory, and a dynamic network topology is constructed through the adjacency matrix and Laplacian matrix. The dynamic neighbor set is used to real-time sense the positions of neighboring UAVs, providing data support for distributed control. The geometric concept of "flight convex hull" is introduced to transform the pursuit task into a dynamic adjustment problem of the distance between the target and the convex hull. When the convex hull contains the target (i.e., \(H(p)=0\)), it is determined that the pursuit is successful, and a unified distributed cooperative objective function is formed. A nonlinear differential observer is designed. Based on the target position data measured locally by the UAV, the velocity and acceleration of the target are accurately estimated within a fixed time without relying on prior knowledge of the target motion mode, adapting to sudden tasks or non-cooperative target scenarios. The observer parameters are optimized through the Hurwitz stability condition to ensure that the estimation error decays exponentially, providing reliable target motion information for the controller. The UAVs are directly driven to track the target position error, prompting the entire cluster to approach the target. The velocity of the UAVs converges to the target velocity through the consensus algorithm to maintain the motion consistency of the cluster and avoid the destruction of the pursuit structure. A single potential function is designed based on the potential field method to dynamically adjust the distance between UAVs - a repulsive force is generated to avoid collisions when the distance is too close, and the communication connectivity is maintained through the attractive force to ensure the stability of the convex hull structure. The controller combines continuous position data and sampled velocity data to reduce the communication frequency while ensuring control continuity. A dual-threshold trigger condition based on the velocity consensus deviation and pursuit error is designed, and communication is activated only when the error exceeds the dynamic threshold, avoiding the waste of resources caused by high-frequency communication and significantly reducing the data transmission pressure. A minimum trigger interval coefficient is introduced to ensure that the trigger time interval has a positive lower bound, excluding Zeno behavior (infinitely many triggers within a finite time) and ensuring the real-time performance and engineering feasibility of the system. After triggering, the error is reset to zero to avoid the influence of stale data on control accuracy. A Lyapunov candidate function containing the pursuit error, velocity error, and potential field energy is constructed, and the stability of the system is proven through derivative analysis, ensuring that state variables such as the pursuit error and velocity consensus error converge to zero over time. Considering the time-varying characteristics of the dynamic communication topology, it is proven that when the communication link switches, the cooperative ability of the cluster can still be maintained through reasonable design of the control gain and trigger conditions, enhancing the robustness in complex environments.Combined with the analysis of the potential field method, ensure that the distance between UAVs is greater than the safety threshold to avoid collisions and disconnections, enhance the system security, optimize the control gain through the Riccati inequality and Hurwitz conditions, combine the physical parameters of UAVs (such as mass, wing area) and the target motion equation, realize the engineering tuning of the controller parameters, solve the lower bound of the triggering interval through differential equations, dynamically adjust the threshold parameters according to the mission requirements (such as triggering sensitivity, communication frequency), and achieve the optimal balance among the enclosure accuracy, speed and energy consumption.

[0368] It should be noted that in this article, relational terms such as first and second are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any actual relationship or order between these entities or operations. Moreover, the term "comprising", "including" or any other variant thereof is intended to cover non-exclusive inclusion, so that a process, method, article or device comprising a series of elements not only includes those elements, but also includes other elements not expressly listed, or further includes elements inherent to such process, method, article or device.

[0369] Although the embodiments of the present invention have been shown and described, those of ordinary skill in the art can understand that various changes, modifications, substitutions and variations can be made to these embodiments without departing from the principles and spirit of the present invention.

Claims

1. A collaborative enclosing control method for a swarm of unmanned aerial vehicles based on an event-triggered mechanism, characterized in that Including: First, establish the UAV dynamics model and dynamic network topology, define the flight convex hull and the pursuit error, design a fixed-time differential state observer, use the target position data measured by the UAVs to estimate the velocity and acceleration of the target, design a distributed pursuit controller, which includes a navigation feedback control term, a velocity consensus term, and a collision avoidance and connectivity maintenance term. Among them, the collision avoidance and connectivity maintenance term is based on the potential field method, and dynamically adjusts the distance between UAVs through a single potential function. Design a double-threshold event-triggering mechanism, design the triggering condition based on the velocity consistency deviation and the pursuit error, dynamically adjust the communication frequency, introduce a minimum triggering interval coefficient to exclude Zeno behavior, and construct a Lyapunov function for stability analysis.

2. The collaborative surrounding control method for unmanned aerial vehicle clusters based on an event-triggered mechanism according to claim 1, characterized in that Establish the UAV dynamics model and dynamic network topology, define the flight convex hull and the pursuit error, including: In a three-dimensional space, consider a swarm system composed of n fixed-wing UAVs. The model formula of the i-th UAV is Formula 1, and Formula 1 is as follows: where p i (t) = [x i (t), y i (t), z i (t)] T represents the position of the UAV i in the inertial coordinate system, V i (t), γ i (t) and ψ i (t) respectively represent the velocity, flight path angle and heading angle of the UAV i , m i is the mass, g is the acceleration due to gravity, and the actual control input u ic (t) = [T i (t), n i (t), φ i (t)] T are respectively the engine thrust, overload and tilt angle, L i (t), D i (t) are respectively the lift and drag; Among them, the relevant variables and control inputs need to satisfy the constraint conditions, and the constraint conditions are as follows: V min ≤V i (t)≤V max ,ψ min ≤ψ i (t)≤ψ max ,γ min ≤γ i (t)≤γ max ,T min ≤T i (t)≤T max ,n min ≤n i (t)≤n max ,φ min ≤φ i (t)≤φ max ; Meanwhile, design the encirclement strategy, including the axial velocity of the UAV as axial virtual control quantity u i (t) = [u ix (t), u iy (t), u iz (t)] T ; And, convert the relationship between u i (t) and the actual control input, and the relationship conversion includes Formula 2, and Formula 2 is as follows: Course angle ψ i (t) and flight path angle γ i (t) are respectively obtained by calculation.

3. A cooperative encirclement control method for an unmanned aerial vehicle cluster based on an event-triggered mechanism according to claim 2, characterized in that Establish the UAV dynamics model and dynamic network topology, define the flight convex hull and the pursuit error, and also include: Design a controller to enable the swarm to achieve cooperative pursuit of a maneuvering target in the form of a flight convex hull, and during this process, the relative distance between each UAV and the target is automatically maintained under the action of the controller; Define the flight convex hull formed by multiple UAVs. The flight convex hull includes Formula 3, and Formula 3 is as follows: The definition of the flight convex hull formed by multiple UAVs includes Formula 4, and Formula 4 is as follows: The distance between the target and the flight convex hull includes Formula 5, and Formula 5 is as follows: is a point within the convex hull co(p) that has a distance from the target, where p T represents the position vector of the target; When and only when H(p) = 0, p T ∈ co(p), indicating that the UAV swarm has achieved the encirclement control of the target; The information interaction between UAVs is described by a graph \(G = \{v,\varepsilon,A\}\), where \(v=\{1,2,\cdots,n\}\) is the set of vertices of the graph, which is used to represent the set of UAVs in the cluster. \(\varepsilon\) is the set of edges of the graph, which is used to represent the interaction relationship between UAVs, and \(A = [a_{ij}]\in R^{n\times n}\) ij is the adjacency matrix. n×n ​ If drone i can receive information from drone j, then a ij > 0; otherwise, a ij = 0. The degree matrix of graph G is D = diag{d1, d2, …, d n}, where Then the Laplacian matrix of graph G is defined as L = D - A; The dynamic neighbor set of UAV i includes Formula 6, and Formula 6 is as follows: M i (t) = {j ∈ {1, 2, …, n}, ||p ij || ≤ μ, j ≠ i} where ||p ij || = ||p i -p j || represents the Euclidean distance between drones i and j.

4. A cooperative pursuit control method for an unmanned aerial vehicle cluster based on an event-triggered mechanism according to claim 3, characterized in that Design a fixed-time differential state observer, use the target position data measured by the UAVs to estimate the velocity and acceleration of the target, including: Accurately estimate the velocity and acceleration of the target within a fixed time, that is where V T (t) is the velocity vector of the target, respectively represent the estimates of the target velocity and acceleration by the i-th UAV; The speed of each UAV remains consistent and converges to the target speed, i.e., Collision avoidance and connectivity maintenance: where r in represents the body radius; The target can be captured by the UAV swarm, that is If the task is sudden or there is a non-cooperative relationship between the UAVs and the target, and the maneuvering form of the target is unknown, UAV i can measure the target position through on-board sensing equipment and design a fixed-time state observer to estimate the target velocity and acceleration. The estimation includes Formula 7, and Formula 7 is as follows: Among them represents the estimation value of the i-th unmanned aerial vehicle pair (i.e., p T (t), V T (t) and u T (t)); Satisfy α i ∈(1 - ε1, 1), where ε1 is a sufficiently small positive number; Satisfy β i ∈(1, 1 + ε2), where ε2 is a sufficiently small positive number; Control gain and are both positive numbers and respectively satisfy the polynomials and in the Hurwitz form; Unstructured data and the fixed time that UAV i can include Formula 8, and Formula 8 is as follows: Realize the observation of the target speed V T (t) and the acceleration u T (t), where are both symmetric positive definite matrices, are the solutions of the Lyapunov equations and respectively, 5. A cooperative encirclement control method for an unmanned aerial vehicle cluster based on an event-triggered mechanism according to claim 4, characterized in that, Design a distributed pursuit controller, which includes a navigation feedback control term, a velocity consensus term, and a collision avoidance and connectivity maintenance term. Among them, the collision avoidance and connectivity maintenance term is based on the potential field method, and dynamically adjusts the distance between UAVs through a single potential function, including: The error representation between the UAV and the target includes Formula 9, and Formula 9 is as follows: The controller includes continuous relative position data and sampled velocity data; The design of the controller includes Formula 10, and Formula 10 is as follows: Among them, the control gains c1, c2, c3 > 0, represents the potential function, is the gradient along p i (t); represents the event trigger instant of the UAV.

6. A cooperative pursuit control method for an unmanned aerial vehicle cluster based on an event-triggered mechanism according to claim 5, characterized in that, Design a double-threshold event-triggering mechanism, design the triggering condition based on the velocity consistency deviation and the pursuit error, dynamically adjust the communication frequency, introduce a minimum triggering interval coefficient to exclude Zeno behavior, including: The initial position of the drone satisfies Define the error between the current value and the latest sampled velocity, including Formula 13, and Formula 13 is as follows: The design of the event-triggering condition for balancing the pursuit task and the swarm control result includes Formulas 14, 15, and 16. Formula 14 is as follows: Formula 15 is as follows: Equation XVII is as follows: Among them K is the feedback gain matrix, and k i is the triggering function to be designed; Combined with Equation XIV, Equation XV, and Equation XVI, the trigger will not trigger at trigger; If f i (t) > 0 ∨ g i (t) > 0, the event trigger will be activated, and subsequently the speed information will be updated and e qi (t) will be reset to zero.

7. A cooperative pursuit control method for an unmanned aerial vehicle cluster based on an event-triggered mechanism according to claim 6, wherein Construct a Lyapunov function for stability analysis, including: Achieve cooperative target enclosing of the UAV swarm through distributed event-triggered control; If (A, B) is stable, then for there exists a positive definite matrix P > 0 that satisfies the Riccati inequality. The positive definite matrix includes Formula XVII, and Formula XVII is as follows: A T P + PA - 2αPBB T P + αI2 < 0 When the UAV swarm conducts target encirclement based on Equation (10), the parameters satisfy: k i ≤n 2 ρ′,K=B T P,(1 - 2κ 2 )>0, Define the Lyapunov candidate function including Equation XVIII, and Equation XVIII is as follows: According to the definition of the neighbor set, the communication topology is time-varying, i.e., V c (t) is a piecewise continuous function; The control input sequence is denoted as the time series representing Formula XIV representing the topological switching time series; If and T0 = 0, we obtain V c (t) whose derivative with respect to t ∈ [T0, T1) includes Equation XIX, which is as follows: Obtain Equation XX according to Young's inequality, and Equation XX is as follows: Further obtain Equation XXI and Equation XXII according to Equation XX, and Equation XXI is as follows: Equation XXII is as follows: Substitute Equation XXI and Equation XXII into Equation XX to obtain Equation XXIII, and Equation XXIII is as follows: Meanwhile, derive Equation XXIV according to Equation XIV, and Equation XXIV is as follows: Since (1 - 2κ 2 ) > 0, Formula 25 can be obtained. Formula 25 is as follows: Therefore, transform Equation XXV into Equation XXVI, and Equation XXVI is as follows: When the parameters meet the corresponding requirements, it indicates that According to Formula 26 and the definition, no collision and loss of connectivity occur during the [T0, T1) process; If V1(t) remains continuous, and V c (T1 - ) = V c (T1 + ) < V c (T0), T1 is represented as the initial topological instant, and V c (T1 + ) < ∞, V c (t) is discontinuous; If the communication topology G is initially connected and G is ultimately fixed, V c (t) is a uniformly continuous and differentiable function; Then is an invariant set, and all solutions of Equation (27) converge to the largest invariant set Equation XXVII is as follows: Therefore, that is, q1(t) = q2(t) = … = q n (t) = q T (t); When the event-triggering mechanism exhibits Zeno behavior, the characteristic of Zeno behavior is an infinite sequence of triggering events occurring within a finite time frame; Under the action of Equation XIV, there is no Zeno behavior in the UAV swarm.

8. A cooperative pursuit control method for an unmanned aerial vehicle cluster based on an event-triggered mechanism according to claim 7, characterized in that Construct a Lyapunov function for stability analysis, which also includes: When the measurement error ||e qi (t) || 2 exceeds , the event is updated, including Equation 28, which is as follows: ||e qi (t)|| 2 The Dini derivative of () includes Equation (29), which is as follows: According to the definition e qi (t) includes Equation (30), and Equation (30) is as follows: Let It can be obtained that: D + ||e qi (t)|| 2 ≤||e qi (t)|| 2 +2Δ 1i Δ 2i At the trigger moment Including Formula 31, and Formula 31 is as follows: In addition, when including Formula 32, Formula 32 is as follows: When is satisfied, the time interval If there is When the collaborative task is not completed, indicate Therefore, there is no Zeno behavior under the action of Equation XIV; According to the stability requirements of target enclosing, process the enclosing error according to Equation XV; The enclosing error includes Equation XXXIII, and Equation XXXIII is as follows: Let Then the fence error system includes Equation (34), which is as follows: Among them According to the definition of dynamic topology, the communication between UAVs is undirected, that is and The definition of the Lyapunov candidate function includes Equation XXXV, and Equation XXXV is as follows: The time derivative of Equation XXXV includes Equation XXXVI, and Equation XXXVI is as follows: Introduction Given and Formula 37 is obtained as follows: Obtain Equation XXXVIII according to Young's inequality, and Equation XXXVIII is as follows: Transform Equation XXXVII into Equation XXXIX, and Equation XXXIX is as follows: Obtain an inequality according to Equation XXXIX, and the inequality includes Equation XL, and Equation XL is as follows: Among them, obtain an inequality according to F = PBK, and the inequality includes Equation XLI, and Equation XLI is as follows: Obtain Equation XLII according to Equation XLI, and Equation XLII is as follows: If Equation (40) holds, then combining with Equation (17) and considering the coefficient That is including Equation (43), and Equation (43) is as follows: Prove Equation XLV according to Equation XLIII, and Equation XLV is as follows: If k i ≤ n 2 ρ' holds, then Equation (45) holds, proving the validity of Equation (42) and .

9. A method for collaborative pursuit control of an unmanned aerial vehicle cluster based on an event-triggered mechanism according to claim 8, characterized in that Construct a Lyapunov function for stability analysis, which also includes: Design the minimum trigger interval coefficient τ i , so that the trigger time interval is jointly determined by the sum of the two and Equation 15, that is, the trigger interval includes Equation 46, and Equation 46 is as follows: where represents the time interval determined by (15); The conditions for selecting Equation XL include Equation XLVII, and Equation XLVII is as follows: Obtain Equation XLVIII according to Equation XLVII, and Equation XLVIII is as follows: τ i can be described as determined by the lower bound of the time interval from 0 to when it increases; For the determination of time calculate the lower limit, and the calculation formula includes Formula 49 and Formula 50. Formula 49 is as follows: Equation L is as follows: Suppose Then Formula 50 includes Formula 51, and Formula 51 is as follows: where β1 = 2||A|| and β0 = n||KB 2 ||; For Equation LI, satisfy Θ(t) ≤ θ(t,θ0), where θ(t,θ0) represents the solution of the equation; The initial value problem includes Equation LII, and Equation LII is as follows: θ(0) = θ0 Obtain Equation LIII according to Equation LII, and Equation LIII is as follows: According to Under the action of Equation (15), the maximum adjustable trigger time interval coefficient includes Equation (54), and Equation (54) is as follows:

10. A method for collaborative pursuit control of an unmanned aerial vehicle cluster based on an event-triggered mechanism according to claim 9, characterized in that Construct a Lyapunov function for stability analysis, which also includes: According to D i (t) and L i (t) is calculated according to Equation Five Hundred Thousand, and Equation Five Hundred Thousand is as follows: L i L(t)=m i gn i L(t) Among them, S w = 1.37 m 2 , ρ0 = 1.225 kg / m 3 , and C D0 = 0.02 are the wing area, air density, and zero-lift drag coefficient respectively, k n = 1, k d = 0.1, m i = 20 kg, r1 = 10 m, and μ = 100 m, u ia (t) The constraints are -1.5 ≤ n i ≤ 2.0, 10 N ≤ T i ≤ 125 N, and -80° ≤ φ i ≤ 80°; The formula for the first maneuvering target is as follows: u T u(t) = [0.2sin(πt / 20), 0.2cos(πt / 20), 0.01sin(πt / 5)] T The formula for the second maneuvering target is as follows: u T u(t) = [sin(πt / 10), 0.5cos(πt / 10), 0.01sin(πt / 5)] T 。

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