Flexible preset performance elastic optimization inclusion control method for unmanned aerial vehicle cluster
By adopting flexible preset performance elastic optimization and control method in the drone cluster, the problem of optimization and control inclusion under malicious attacks is solved, and fixed-time preset performance optimization and control are realized, improving system performance and robustness are improved, and the impact of control singularity and malicious attacks are avoided.
Patent Information
- Application Number
- CN202510183813.7
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-02-19
- Publication Date
- 2025-05-23
AI Technical Summary
The existing adaptive preset performance optimization control strategy based on reinforcement learning cannot effectively solve the problem of optimization and control of drone clusters under malicious attacks, resulting in the impairment of the robustness and security of closed-loop systems.
A flexible preset performance elastic optimization included control method for a drone cluster is adopted. By establishing a drone attitude dynamic model that is subjected to malicious attacks, constructing flexible preset performance functions, designing fixed time filters and adaptive dynamic surface control technology, establishing coordinate conversion equations, constructing Hamilton-Jacobby-Bellmann equations, solving the optimal virtual control law and intermediate control law, designing attack compensation signals, realizing online estimation and compensation, and finally obtaining adaptive fixed time flexible preset performance elastic optimization included controllers.
The fixed-time preset performance optimization and control of the drone cluster under malicious attacks is realized, which improves the transient and steady-state performance of the attitude system, avoids the control singularity problem, and effectively suppresses malicious network attacks, ensuring the fixed-time stability of the closed-loop attitude control system.
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Figure CN120029336A_ABST
Abstract
Description
Technical Field
[0001] The present invention belongs to the technical field of unmanned aerial vehicle control, and in particular, relates to a flexible preset performance elastic optimization control method for a cluster of unmanned aerial vehicles. Background Art
[0002] With the significant increase in mission complexity and scope of operations, people are gradually inclined to use drone swarms for collaborative operations to replace inefficient single-drone work schemes. The stability of the fleet attitude of drone swarms is crucial for safe flight and collaborative control. In particular, the inclusive control strategy with multiple leaders as the collaborative mode constrains the output trajectories of all followers to the convex hull formed by the output trajectory of the leader, effectively improving the stability of the formation and preventing the followers from deviating from the predetermined route. However, most existing inclusive control results focus on achieving the asymptotic stability of the closed-loop system, and the unquantifiable stabilization time limits the implementation of these control strategies to a certain extent.
[0003] In addition, the openness of the communication network makes it vulnerable to cyber attacks, undermining network security and data reliability. Malicious attacks can mislead the system into making wrong decisions by injecting carefully crafted multiplication-driven attack signals and addition-driven attack signals, which greatly damages the robustness and security of the closed-loop system. On the other hand, control performance and resource utilization should be given enough attention as key factors in engineering applications, but the existing adaptive preset performance optimization control strategy based on reinforcement learning may not be able to solve the optimization and control problem of drone clusters under malicious attacks.
[0004] Therefore, there is an urgent need to invent a flexible preset performance elastic optimization control method for drone clusters to achieve the fixed-time preset performance optimization control problem of drone clusters under malicious attacks. Summary of the invention
[0005] The purpose of the present invention is to provide a flexible preset performance elastic optimization inclusion control method for a drone cluster, which mainly solves the problem that the existing adaptive preset performance optimization control strategy based on reinforcement learning may not be able to solve the optimization inclusion control problem of a drone cluster under malicious attacks.
[0006] To achieve the above purpose, the technical solution adopted by the present invention is as follows:
[0007] A flexible preset performance elastic optimization control method for a drone cluster includes the following steps:
[0008] S1, establish the attitude dynamics model of the UAV subjected to malicious attacks and saturated input;
[0009] S2, establish a topological communication network between followers and leaders, and define the synchronization error S ij, i represents the i-th drone, j = 1, 2, 3;
[0010] S3, according to the synchronization error S ij , construct a flexible preset performance function Φ L，ij (t) and Φ U，ij (t), Φ L，ij (t) and Φ U，ij (t) respectively represent the lower constraint boundary and the upper constraint boundary of the flexible preset performance function, design a fixed time filter, and establish a coordinate transformation equation based on the adaptive dynamic surface control technology;
[0011] S4, constructing a first optimal cost function according to the coordinate transformation equation and the first Hamilton-Jacobi-Bellman equation is the first error variable, solving the Hamilton-Jacobi-Bellman equation Get the optimal virtual control law First parameter update law Second parameter update law First Critique Network Weight Update Law And the first execution network weight update law Online training to obtain an approximately optimal virtual controller
[0012] S5, constructing a second optimal cost function according to the coordinate transformation equation and the second Hamilton–Jacobi–Bellman equation is the second error variable, solving the second Hamilton-Jacobi-Bellman equation Get the optimal intermediate control law Design attack compensation signal and Realize online estimation and compensation of multiplication-driven attack signals and additive attack signals, and design the third parameter update law Second judgment network weight update law And the second execution network weight update law Online optimization to obtain the approximate optimal intermediate control law Then we get the adaptive fixed time flexible preset performance elastic optimization including controller
[0013] S6, based on Lyapunov stability theory, analyzes the stability of the closed-loop attitude control system, determines the control gain to be designed, and realizes the fixed-time preset performance elastic optimization inclusive control of the UAV cluster.
[0014] Furthermore, in step S1, the dynamics model of the attitude system of the i-th UAV is:
[0015]
[0016] Where i = 1, 2, ..., N, N represents the number of followers; φ i ,θ i and ψ i are the roll angle, pitch angle and yaw angle of the i-th UAV respectively; and are the angular velocities of the roll angle, pitch angle and yaw angle of the i-th UAV respectively; and are the angular accelerations of the roll angle, pitch angle and yaw angle of the i-th UAV respectively; Y iφ , Y iθ and Y iψ is the control torque; ix , iy and λ iz is the moment of inertia, Ω iφ ,Ω iθ and Ω iψ is the aerodynamic damping coefficient; and is an unknown external disturbance;
[0017] The malicious attack expression suffered by the i-th drone is:
[0018]
[0019] Where i = 1, 2, ..., N, represents the control input torque of the i-th UAV; represents the multiplication driven attack signal, t represents time, and Represent the multiplication drive attack signal and injection time; Indicates additive attack signal, and Additive attack signal and injection time; represents the actual control input torque subject to saturation input constraints; combined with the malicious attack expression suffered by the i-th UAV, the attitude system dynamics model of the i-th UAV is transformed into:
[0020]
[0021] in,
[0022]
[0023] The saturation input constraint suffered by the i-th UAV is:
[0024]
[0025] Among them, ρ ij,min and ρ ij,max Enter lower and upper bounds for known saturation.
[0026] Furthermore, in step S2, the specific steps of establishing a topological communication network between followers and leaders are as follows:
[0027] S21, using directed graph represents the topological communication network of N followers and M leaders in a drone cluster, where and denote the vertex set and directed edge set respectively; Indicates that there is a directed edge from the p-th drone to the i-th drone; is the neighbor set; the adjacency matrix is defined as Among them, when When ip =1; otherwise, a ip =0; the diagonal matrix is defined as and Directed Graph The Laplacian matrix of is defined as in
[0028] S22, based on the topological communication network and the leader's expected trajectory Definition of synchronization error S ij :
[0029]
[0030] Where i = 1, 2, ..., N, j = 1, 2, 3, is the output trajectory of the i-th UAV.
[0031] Furthermore, in step S3, the flexible preset performance function Φ L，ij (t) and φ U,ij The expression of (t) is:
[0032]
[0033] in,
[0034]
[0035] ε ij (t) is the fixed time preset performance function, Eij (0) is the initial value including the error, is a positive design parameter; among them, and is the auxiliary system; its expression is:
[0036]
[0037] in, k ij1 , k ij2 , and is a positive design parameter.
[0038] Further, in step S3, the expression of the fixed time filter is:
[0039]
[0040] in,
[0041] Output signal for fixed time filtering The derivative of ij is the filtering error, is the first error variable, For unknown parameters The estimated value of b ij , and g ij1 is a positive design parameter, β>1.
[0042] Furthermore, in step S4, the first optimal cost function The expression is:
[0043]
[0044] in, Ψ(Ω) is the admissible control set including the origin, is the optimal virtual control law, is the approximately optimal virtual controller;
[0045] The first Hamilton-Jacobi-Bellman equation The expression is:
[0046]
[0047] First parameter update law The expression is:
[0048]
[0049] Second parameter update law The expression is:
[0050]
[0051] First Critique Network Weight Update Law The expression is:
[0052]
[0053] First execute the network weight update law The expression is:
[0054]
[0055] in, and r ij1 is a positive design parameter, and is the learning rate, μ ij1 (x ij1 )and Respectively represent the input and The basis function of μ ij1 Estimated value, and for An estimated value of
[0056] Nearly Optimal Virtual Controller The expression is:
[0057]
[0058] in,
[0059]
[0060] and is a positive design parameter.
[0061] Further, in step S5, the expression of the second optimal cost function is:
[0062]
[0063] in, is the second error variable, is the optimal intermediate control law, is the approximate optimal intermediate control law;
[0064] The second Hamilton-Jacobi-Bellman equation The expression is:
[0065]
[0066] Among them, the attack compensation signal and The expressions are:
[0067]
[0068] in, and The unknown parameters δ are ij and χ ij The estimated value of and g ij2 is a positive design parameter;
[0069] The third parameter update law The expression is:
[0070]
[0071] Second judgment network weight update law The expression is:
[0072]
[0073] Second execution network weight update law The expression is:
[0074]
[0075] Among them, r ij2 is a positive design parameter, and is the learning rate, υ ij2 (x ij2 )and is the basis function, μ ij2 The estimated value of and for The estimated value of and are the angular velocities of the roll angle, pitch angle, and yaw angle of the i-th UAV respectively;
[0076] Approximately optimal intermediate control law The expression is:
[0077]
[0078] in, and is a positive design parameter;
[0079] Adaptive fixed time flexible preset performance elastic optimization including controller The expression is:
[0080]
[0081] in, is a positive design parameter.
[0082] Compared with the prior art, the present invention has the following beneficial effects:
[0083] (1) The flexible preset performance elastic optimization inclusion control method of the present invention achieves strict constraints on the inclusion error convergence behavior with lower control conservatism by constructing a performance area distributed on one side. Different from the traditional preset performance constraint scheme, an auxiliary system is constructed in the recursive design framework, and a feedback mechanism is established between the saturation constraint and the performance constraint, so that the performance envelope can be flexibly expanded and contracted according to the saturation error, which not only effectively improves the transient and steady-state performance of the attitude system, but also avoids the control singularity problem.
[0084] (2) The present invention introduces a fixed-time filter in the adaptive optimization recursive design framework to avoid the computational dimension explosion problem caused by iterative differentiation. Two attack compensation signals are designed to effectively suppress malicious network attacks from the actuator-controller channel, and no prior boundary information of the multiplicative drive attack signal and the additive attack signal is required. Different from the existing inclusive control results, by establishing an execution-judgment structure based on reinforcement learning, an adaptive fixed-time preset performance elastic optimization inclusive controller is designed to minimize the cost function to achieve fixed-time stability of the closed-loop attitude control system. BRIEF DESCRIPTION OF THE DRAWINGS
[0085] Figure 1 A schematic diagram of a flow chart of a flexible preset performance elastic optimization including a control method of a drone cluster according to the present invention;
[0086] Figure 2 Designing a block diagram of the controller for adaptive fixed-time flexible preset performance elastic optimization of drone clusters;
[0087] Figure 3 This is the topological communication network structure diagram of the drone cluster;
[0088] Figures 4 to 6 This is the attitude response curve of the UAV cluster;
[0089] Figures 7-10 Include error trajectory maps for drone swarms;
[0090] Figures 11 to 14 Execution-criticism network weight trajectory diagram for drone swarm;
[0091] Fig.15 , Fig.16 Input trajectory graph for drone swarm control. DETAILED DESCRIPTION
[0092] The present invention is further described below in conjunction with the accompanying drawings and embodiments. The embodiments of the present invention include but are not limited to the following embodiments.
[0093] Example
[0094] Please refer to Figure 1 and Figure 2 The present invention provides a flexible preset performance elastic optimization control method for a drone cluster, comprising the following steps:
[0095] Step S1: Establishing a posture dynamics model of a drone subjected to malicious attacks and saturated input, specifically including:
[0096] Establish the dynamics model of the attitude system of the i-th UAV:
[0097]
[0098] Where i = 1, 2, ..., N, N represents the number of followers; φ i ,θ i and ψ i are the roll angle, pitch angle and yaw angle of the i-th UAV respectively; and are the angular velocities of the roll angle, pitch angle and yaw angle of the i-th UAV respectively; and are the angular accelerations of the roll angle, pitch angle and yaw angle of the i-th UAV respectively; Y iφ , Y iθ and Y iψ is the control torque; ix , iy and λ iz is the moment of inertia, Ω iφ ,Ω iθ and Ω iψ is the aerodynamic damping coefficient; and
[0099] It is an unknown external disturbance.
[0100] Assuming that the i-th drone is attacked by an unknown malicious network, the dynamic model (1) will be transformed into:
[0101]
[0102] in,
[0103]
[0104] and denote the multiplication driving attack signal and the additive attack signal respectively, and They represent the time when the attack signal is injected, j=1,2,3 respectively.
[0105] The saturation input constraint suffered by the i-th UAV is:
[0106]
[0107] Among them, ρ ij,min and ρ ij,max Enter lower and upper bounds for known saturation.
[0108] Step S2: Establish a topological communication network between followers and leaders, and define the synchronization error S ij , specifically including:
[0109] Directed Graph represents the topological communication network of N followers and M leaders in a drone cluster, where and denote the vertex set and directed edge set respectively; Indicates that there is a directed edge from the p-th drone to the i-th drone; is the neighbor set; the adjacency matrix is defined as Among them, when When ip =1; otherwise, a ip = 0. The diagonal matrix is defined as and Directed Graph The Laplacian matrix of is defined as in
[0110] Communication network and leader desired trajectory according to the topology Definition of synchronization error S ij :
[0111]
[0112] Step S3: according to the synchronization error S ij , construct a flexible preset performance function Φ L,ij (t) and Φ U,ij(t), design a fixed time filter, and establish the coordinate transformation equation based on the adaptive dynamic surface control technology, including:
[0113] Construct the following flexible preset performance function Φ L,ij (t) and Φ U,ij (t) so that it satisfies Φ L,ij (t)<S ij <Φ U,ij (t):
[0114]
[0115] in, Fixed time preset performance function ε ij (t) Designed to:
[0116]
[0117] in, and T ij is a positive design parameter.
[0118] Assistance Systems and Designed for:
[0119]
[0120] in, k ij1 , k ij2 , and is a positive design parameter.
[0121] According to the flexible preset performance function Φ L,ij (t) and Φ U,ij (t) and formula (2), based on the adaptive dynamic surface control technology, the coordinate transformation equation is established as:
[0122]
[0123] Among them, ω ij is the filtering error, For the approximately optimal virtual controller to be designed, is the output signal of the fixed time filter, and are the first error variable and the second error variable respectively.
[0124] The fixed-time filter is designed as:
[0125]
[0126] in, Output signal for fixed time filtering The derivative of For unknown parameters The estimated value of b ij , and g ij1 is a positive design parameter.
[0127] Step S4: construct a first optimal cost function according to the coordinate transformation equation and the first Hamilton-Jacobi-Bellman equation Solving the Hamilton-Jacobi-Bellman equation Get the optimal virtual control law Design parameter update law Parameter update law Judging the network weight update law And execute the network weight update law Online training to obtain an approximately optimal virtual controller Specifically include:
[0128] In order to achieve the preset performance elastic optimization including control objectives, the following optimal cost function is defined
[0129]
[0130] in, Ψ(Ω) is the admissible control set including the origin, is the optimal virtual control law, is a nearly optimal virtual controller.
[0131] Based on the Bellman optimality principle, the first Hamilton-Jacobi-Bellman equation Defined as:
[0132]
[0133] By solving Get the optimal virtual control law
[0134]
[0135] Since there are unknown terms in equation (12) The optimal analytical solution cannot be obtained, so it is decomposed into:
[0136]
[0137] in, β>1, and is a positive design parameter, is the weight vector, υ ij1 (x ij1 ) is the input The basis function, σ ij1 (x ij1 ) is the approximate error, and
[0138]
[0139] According to equations (13) and (14), the optimal virtual controller is:
[0140]
[0141] Using Neural Network Online identification of unknown functions To satisfy:
[0142]
[0143] in, is the unknown weight vector, is the basis function, is the input vector, is an approximate error.
[0144] Furthermore, the execution network is constructed and judgement network Online learning can obtain a nearly optimal virtual controller
[0145]
[0146] in, μ ij1 Estimated value, and for The estimated value of .
[0147] Parameter update law Parameter update law Judging the network weight update law and execute the network weight update law Designed for:
[0148]
[0149] in, and r ij1 is a positive design parameter, and is the learning rate.
[0150] According to equations (12), (17) and (18), the first Hamilton-Jacobi-Bellman equation is is approximated as:
[0151]
[0152] Furthermore, the Hamiltonian approximation error ∈ ij1 Defined as:
[0153]
[0154] Since the solution of the Hamilton-Jacobi-Bellman equation is unique, the obtained approximate optimal virtual controller Purpose ij1 →0 holds true, then is equivalent to:
[0155]
[0156] Define a continuous positive definite function Available il1 = 0 is equivalent to equation (25). So we can get:
[0157]
[0158] Through the above analysis, we can get the designed execution-criteria network weight update law and Can guarantee il1 =0, so equation (25) holds.
[0159] Construct the first Lyapunov function for:
[0160]
[0161] in,
[0162] By taking the derivative of formula (27), we can get:
[0163]
[0164] The approximate optimal virtual controller Parameter update law Parameter update law Judging the network weight update law and execute the network weight update law Substituting into formula (28), we can get:
[0165]
[0166] in,
[0167] Step S5: construct a second optimal cost function according to the coordinate transformation equation and the second Hamilton–Jacobi–Bellman equation Solving the Hamilton-Jacobi-Bellman equation Get the optimal intermediate control law Design attack compensation signal and Realize online estimation and compensation of multiplication-driven attack signals and additive attack signals, and design parameter update laws Judging the network weight update law And execute the network weight update law Online optimization to obtain the approximate optimal intermediate control law Then we get the adaptive fixed time flexible preset performance elastic optimization including controller Specifically include:
[0168] According to the coordinate transformation equation, the second optimal cost function is defined as follows:
[0169]
[0170] in, is the optimal intermediate control law, is an approximate optimal intermediate control law.
[0171] The second Hamilton-Jacobi-Bellman equation Defined as:
[0172]
[0173] By solving The optimal intermediate control law can be obtained for:
[0174]
[0175] because Unknown, so decompose it into:
[0176]
[0177] in, and is a positive design parameter, is the ideal weight vector, υ ij2 (x ij2) is the basis function, σ ij2 (x ij2 ) to satisfy The approximate error of
[0178] Further calculations can be obtained:
[0179]
[0180] Using Neural Network Online identification of unknown functions We can get:
[0181]
[0182] in,
[0183] is the unknown weight vector, Represents input The basis function of is an approximate error.
[0184] Constructing a judgment network approximate We can get:
[0185]
[0186] in, is the unknown weight vector The estimated value of ij2 is a positive design parameter.
[0187] Constructing the execution network Obtaining a near-optimal intermediate control law via online learning
[0188]
[0189] Attack compensation signal and Designed for:
[0190]
[0191] in, and The unknown parameters are and The estimated value of Λ ij , and They are the lower bound of the multiplicative driving attack signal, the upper bound of the additive attack signal, and the upper bound of the external unknown disturbance, respectively. and is a positive design parameter.
[0192] Parameter update law Judging the network weight update law and execute the network weight update law Designed for:
[0193]
[0194] Among them, r ij2 is a positive design parameter, and is the learning rate.
[0195] According to the approximate optimal intermediate control law Design adaptive fixed time flexible preset performance elastic optimization including controller for:
[0196]
[0197] in, is a positive design parameter.
[0198] Construct the second Lyapunov function for:
[0199]
[0200] in,
[0201] Given that By taking the derivative of formula (44), we can get:
[0202]
[0203] The adaptive fixed time flexible preset performance elastic optimization includes the controller Attack compensation signal and Parameter update law Judging the network weight update law and execute the network weight update law Substituting into formula (45), we can get:
[0204]
[0205] in, is the upper bound of the multiplication driven attack signal.
[0206] Step S5: Analyze the stability of the closed-loop attitude control system based on Lyapunov stability theory, determine the control gain to be designed, and realize the fixed-time preset performance elastic optimization of the UAV cluster, including control, specifically including:
[0207] Constructing the overall Lyapunov function
[0208]
[0209] Select control parameters to satisfy and Defined as The minimum eigenvalue of , q=1,2.
[0210] Taking the derivative of equation (47) and simplifying it, we can get:
[0211]
[0212] in,
[0213]
[0214] Based on Lyapunov's fixed-time stability theory, the adaptive fixed-time flexible preset performance elastic optimization controller designed in the present invention can ensure the actual fixed-time stability of the closed-loop attitude control system when the drone cluster is subjected to malicious attacks and saturated input, so that the output trajectory of the follower evolves into the convex shell formed by the output trajectory of the leader, and the error is included in the preset time T ij Converge to performance range Achieve fixed-time preset performance elastic optimization of drone clusters with minimal control cost.
[0215] The following simulation experiments are carried out in the simulation software-MATLAB R2020a / SIMULINK to illustrate in detail the effectiveness and feasibility of the flexible preset performance elastic optimization control method designed by the present invention.
[0216] The parameters of the UAV attitude system are selected as: Ω iφ =Ω iθ =Ω iψ =0.6kg / rad,λ ix =λ iy =0.082kg·m 2 ,λ=0.149kg·m 2 .
[0217] The external unknown disturbance settings are:
[0218] The initial conditions of the UAV attitude system and parameter update law are selected as:
[0219] [φ 1 (0),θ 1 (0),ψ 1 (0)] = [1, 1.3, 0.5], [φ 2 (0),θ 2 (0),ψ 2 (0)] = [0.1, 0.75, 0.4],
[0220] [φ 3 (0),θ 3 (0),ψ 3 (0)]=[1.1,-0.3,0.6],[φ 4 (0),θ 4 (0),ψ 4 (0)] = [0.3, 1.3, -0.5].
[0221] The output trajectory of the leader is selected as:
[0222]
[0223] The controller parameters are chosen as: ij,min =-5,ρ ij,max =5α=7 / 9,β=11 / 9, T ij =2, b ij =0.2, g ijq =e -10t , r ijq =3,
[0224] The Gaussian function is chosen as: i=1,2,3,4, j=1,2,3, q=1,2.
[0225] Malicious attack signals are selected as follows:
[0226]
[0227]
[0228] The attack signal is injected starting from t=2s.
[0229] The considered drone swarm system consists of 2 leaders labeled L1 and L2 and 4 followers labeled F1-F4. The simulation results are plotted in Figures 3 to 16 . Figure 3 The topological communication network structure diagram of the drone cluster is depicted in the figure. Figures 4 to 6 The output trajectories of the roll angle, pitch angle, and yaw angle of the leaders L1 and L2 and the four followers are plotted respectively. It can be seen from the figure that even if the drone cluster is attacked maliciously and saturated with input, the output trajectories of the four followers all evolve into the convex hull formed by the output trajectories of the leaders L1 and L2. Figures 7-10 The error S ij From the figure, it can be found that the published flexible preset performance elastic optimization includes the control method to synchronize the error S ij At a given time T ij = Constrained to performance range within 2s In particular, the envelope of the flexible preset performance function is adaptively expanded and contracted according to the saturated input difference to prevent control singularity problems. Figures 11 to 14 The execution-criticism network weight trajectory diagrams of the four followers are plotted separately, and it can be found that all the execution-criticism network weights are bounded. Fig.15 , Fig.16 is the control input curve diagram.
[0230] Combined with the simulation experiment results, it can be concluded that the flexible preset performance elastic optimization inclusion control method of a drone cluster disclosed in the present invention realizes the convergence constraint of the inclusion error by designing a flexible preset performance function, thereby effectively improving the transient performance and the steady-state performance; introduces two attack compensation signals to realize the online estimation and compensation of the multiplication-driven attack signal and the additive attack signal; constructs an execution-judgment network structure, and realizes the fixed-time preset performance elastic optimization inclusion control of the drone cluster under malicious attacks with the minimum control cost.
[0231] The above embodiment is only one of the preferred implementation modes of the present invention and should not be used to limit the protection scope of the present invention. Any changes or modifications that are made to the main design concept and spirit of the present invention and have no substantive significance, and the technical problems they solve are still consistent with the present invention, should be included in the protection scope of the present invention.
Claims
1. A flexible preset performance elastic optimization control method for a drone cluster, characterized in that: The following steps are involved: S1, establish the attitude dynamics model of the UAV subjected to malicious attacks and saturated input; S2, establish a topological communication network between followers and leaders, and define the synchronization error S ij , i represents the i-th drone, j = 1, 2, 3; S3, according to the synchronization error S ij , construct a flexible preset performance function Φ L，ij (t) and Φ U，ij (t), Φ L，ij (t) and Φ U，ij (t) respectively represent the lower constraint boundary and the upper constraint boundary of the flexible preset performance function, design a fixed time filter, and establish a coordinate transformation equation based on the adaptive dynamic surface control technology; S4, constructing a first optimal cost function according to the coordinate transformation equation and the first Hamilton-Jacobi-Bellman equation ij1 is the first error variable, solving the Hamilton-Jacobi-Bellman equation Get the optimal virtual control law First parameter update law Second parameter update law First Critique Network Weight Update Law And the first execution network weight update law Online training to obtain an approximately optimal virtual controller S5, constructing a second optimal cost function according to the coordinate transformation equation and the second Hamilton–Jacobi–Bellman equation ij2 is the second error variable, solving the second Hamilton-Jacobi-Bellman equation Get the optimal intermediate control law Design attack compensation signal and Realize online estimation and compensation of multiplication-driven attack signals and additive attack signals, and design the third parameter update law Second judgment network weight update law And the second execution network weight update law Online optimization to obtain the approximate optimal intermediate control law Then we get the adaptive fixed time flexible preset performance elastic optimization including controller S6, based on Lyapunov stability theory, analyzes the stability of the closed-loop attitude control system, determines the control gain to be designed, and realizes the fixed-time preset performance elastic optimization inclusive control of the UAV cluster.
2. The flexible preset performance elastic optimization control method of a drone cluster according to claim 1 is characterized in that: In step S1, the dynamics model of the attitude system of the i-th UAV is: Where i = 1, 2, ..., N, N represents the number of followers; φ i ,θ i and ψ i are the roll angle, pitch angle and yaw angle of the i-th UAV respectively; and are the angular velocities of the roll angle, pitch angle, and yaw angle of the i-th UAV respectively; and are the angular accelerations of the roll angle, pitch angle and yaw angle of the i-th UAV respectively; Y iφ , Y iθ and Y iψ is the control torque; ix , iy and λ iz is the moment of inertia, Ω iφ ,Ω iθ and Ω iψ is the aerodynamic damping coefficient; and is an unknown external disturbance; The malicious attack expression suffered by the i-th drone is: Where i = 1, 2, ..., N, represents the control input torque of the i-th UAV; represents the multiplication driven attack signal, t represents time, and Represent the multiplication drive attack signal and injection time; Indicates additive attack signal, and Additive attack signal and injection time; represents the actual control input torque subject to saturation input constraint; Combined with the malicious attack expression suffered by the i-th UAV, the attitude system dynamics model of the i-th UAV is transformed into: in, The saturation input constraint suffered by the i-th UAV is: Among them, ρ ij,min and ρ ij,max Enter lower and upper bounds for known saturation.
3. The flexible preset performance elastic optimization control method of a drone cluster according to claim 2 is characterized in that: In step S2, the specific steps of establishing a topological communication network between followers and leaders are as follows: S21, using directed graph represents the topological communication network of N followers and M leaders in a drone cluster, where and denote the vertex set and directed edge set respectively; Indicates that there is a directed edge from the p-th drone to the i-th drone; is the neighbor set; the adjacency matrix is defined as Among them, when When ip =1; otherwise, a ip =0; the diagonal matrix is defined as and Directed Graph The Laplacian matrix of in S22, based on the topological communication network and the leader's expected trajectory Definition of synchronization error S ij : Where i = 1, 2, ..., N, j = 1, 2, 3, is the output trajectory of the i-th UAV.
4. The flexible preset performance elastic optimization control method of a drone cluster according to claim 3 is characterized in that: In step S3, the flexible preset performance function Φ L，ij (t) and Φ U，ij The expression of (t) is: in, ε ij (t) is the fixed time preset performance function, E ij (0) is the initial value including the error, is a positive design parameter; among them, and is the auxiliary system; its expression is in, k ij1 , k ij2 , and is a positive design parameter.
5. The flexible preset performance elastic optimization control method of a drone cluster according to claim 4 is characterized in that: In step S3, the expression of the fixed time filter is: in, Output signal for fixed time filtering The derivative of ij is the filtering error, l ij1 is the first error variable, For unknown parameters The estimated value of b ij , and g ij1 is a positive design parameter, β>
1.
6. The flexible preset performance elastic optimization control method of a drone cluster according to claim 5 is characterized in that: In step S4, the first optimal cost function The expression is: in, Ψ(Ω) is the admissible control set including the origin, is the optimal virtual control law, is the approximately optimal virtual controller; The first Hamilton-Jacobi-Bellman equation The expression is: First parameter update law The expression is: Second parameter update law The expression is: First Critique Network Weight Update Law The expression is: First execute the network weight update law The expression is: in, and r ij1 is a positive design parameter, and is the learning rate, μ ij1 (x ij1 )and Respectively represent the input and The basis function of μ ij1 Estimated value, and for An estimated value of Nearly Optimal Virtual Controller The expression is: in, and is a positive design parameter.
7. The flexible preset performance elastic optimization control method of a drone cluster according to claim 6 is characterized in that: In step S5, the expression of the second optimal cost function is: in, l ij2 is the second error variable, is the optimal intermediate control law, is the approximate optimal intermediate control law; The second Hamilton-Jacobi-Bellman equation The expression is: Among them, the attack compensation signal and The expressions are: in, and The unknown parameters δ are ij and χ ij The estimated value of and g ij2 is a positive design parameter; The third parameter update law The expression is: Second judgment network weight update law The expression is: Second execution network weight update law The expression is: Among them, r ij2 is a positive design parameter, and is the learning rate, v ij2 (x ij2 )and is the basis function, μ ij2 The estimated value of and for The estimated value of and are the angular velocities of the roll angle, pitch angle, and yaw angle of the i-th UAV respectively; Approximately optimal intermediate control law The expression is: in, and is a positive design parameter; Adaptive fixed time flexible preset performance elastic optimization including controller The expression is: in, is a positive design parameter.