Adaptive integral concurrent learning consistency control method for unmanned aerial vehicle cluster

Abstract

The invention provides a self-adaptive integral concurrent learning consistency control method for an unmanned aerial vehicle cluster, and relates to the technical field of unmanned aerial vehicle control, and the method comprises the steps: building an unmanned aerial vehicle attitude dynamic model suffering from a hostile attack; a compensation variable and a first-order filter are introduced, and a coordinate conversion equation is established in combination with an adaptive dynamic surface control technology; an attack compensator is designed for online estimation and counteracting the influence of spoofing attacks on the system; an integral concurrent learning strategy and an event triggering control mechanism are fused, a memory event triggering interval type-2 fuzzy integral concurrent learning-based security consistency controller is designed, and the stability of a closed-loop attitude control system is analyzed based on a Lyapunov stability theory. Under the condition of limited excitation, the leadless attitude asymptotic consistency control under the unmanned aerial vehicle cluster spoofing attack is realized, the safety control problem under the condition that communication resources are limited in actual engineering application is effectively solved, and the robustness and the control precision of the unmanned aerial vehicle when the unmanned aerial vehicle is subjected to network attack are remarkably improved.

Description

Technical Field

[0001] The present invention relates to the field of unmanned aerial vehicle (UAV) control technology, and in particular to an adaptive integral concurrent learning consistency control method for a UAV cluster. Background Art

[0002] Consistency control technology for drone swarms has attracted considerable attention due to its high efficiency in executing large-scale dynamic missions and its advantages in wide-area operations. However, the fragility of open communication network architectures exposes these systems to serious security threats, particularly covert cyberattacks such as spoofing attacks, which exploit open network interfaces to steal real data and inject false commands, misleading the system into adopting erroneous control strategies. Existing adaptive consistency control methods designed in a non-attack-free environment often struggle to maintain system stability.

[0003] It is worth noting that traditional adaptive consensus control strategies [Paper 1: Cui G, Xu H, Xu S, et al. Predefined-time adaptive fuzzy bipartite consensus control for multiquadrotors under malicious attacks [J]. IEEE Transactions on Fuzzy Systems, 2024, 32(4): 2187-2197.] rely on instantaneous data to update parameter estimates, and their convergence depends on continuous excitation conditions that are difficult to obtain a priori. In addition, the periodic time-triggered communication mechanism may cause the limited airborne communication bandwidth to be continuously occupied by redundant data transmission, resulting in wasted communication resources and mechanical wear of the actuator. Summary of the Invention

[0004] To solve the above technical problems, the present invention provides an adaptive integral concurrent learning consistency control method for drone clusters, which solves the key problems of traditional adaptive consistency control methods in network security and resource efficiency. It not only effectively alleviates network bandwidth pressure, but also ensures that drone clusters can still achieve leaderless attitude consistency control when subjected to deception attacks.

[0005] To achieve the above technical objectives, the adopted technical solution is: an adaptive integral concurrent learning consistency control method for a UAV cluster, comprising the following steps: Step 1: Obtain a state-space equation based on the deformation of the UAV attitude dynamics model, and define the state signal of the UAV under deception attack through the state-space equation; Step 2: Establish a topological communication network and use it to design compensation variables Design based on adaptive dynamic surface control technology includes adaptive parameters A first-order filter, combined with compensation variables First-order filter and state space equations are used to construct coordinate transformation equations. Based on the state signal of the drone being attacked by deception, the coordinate transformation equations of the attacked state are constructed. Step 3: Construct the first Lyapunov function based on the first error variable of the coordinate transformation equation And the derivative is Define auxiliary variables in conjunction with the coordinate transformation equation of the attacked state Through auxiliary variables Design attack compensator Parameter update law Combined auxiliary variables Attack Compensator and parameter update law Get virtual controller Step 4: Use the interval type-2 model logic system to approximate the defined unknown function and obtain the derivative of the second error variable Based on the integral concurrent learning strategy, design the integral concurrent learning parameter update law According to the second error variable of the coordinate transformation equation, the second Lyapunov function is constructed And the derivative is Define auxiliary variables in conjunction with the coordinate transformation equation of the attacked state Through auxiliary variables Design parameter update law Parameter update law and Attack Compensator Combined auxiliary variables Parameter update law and Attack Compensator A concurrent learning safety consistency controller based on memory event-triggered interval type-2 fuzzy integral is obtained. Step 5: According to the first Lyapunov function and the second Lyapunov function Constructing a global Lyapunov function Based on Lyapunov stability theory, the stability of the closed-loop attitude control system is analyzed, the controller gains of the virtual controller and the safety consistency controller are determined, and the leaderless attitude consistency safety control of the UAV swarm under deception attack is realized.

[0006] Furthermore, the compensation variable for in, The i-th UAV can receive the information of the j-th UAV, denoted as a ij=1; otherwise, a ij =0; It is the first attack signal; and are the attitude output signals of the i-th UAV and the j-th UAV respectively.

[0007] The first-order filter is in, is the positive control gain to be designed, is the filtering error, is a time-varying bounded function, is the output signal of the first-order filter, is the derivative of the output signal of the first-order filter, is the input signal of the first-order filter, Unknown estimated value.

[0008] The virtual controller for in, and is the positive control gain to be designed, is the first error variable attacked, First attack signal The estimated value of is the compensation variable, represents the fuzzy basis function vector, is the weight vector estimated value.

[0009] The attack compensator and parameter update law for in, is a positive definite diagonal matrix, is the first error variable attacked, The first attack signal The estimated value of is the compensation variable, represents the fuzzy basis function vector, as well as is the positive control gain to be designed, is the weight vector estimated value.

[0010] The integral concurrent learning parameter update law Designed to: in, is a positive definite diagonal learning matrix, is the output signal of the first-order filter, is the second error variable under attack, The second attack signal The estimated value of represents the fuzzy basis function vector, is the positive control gain to be designed, l and Δt i are the size of the integral concurrent learning history stack and the integral window, The cumulative sum of The cumulative sum of The second error variable is The value at the moment.

[0011] The parameter update law and parameter update law for in, is the control gain to be designed, and is the positive control gain to be designed, is the filtering error, is the output signal of the first-order filter, For virtual controllers, Unknown The estimated value of is a positive definite diagonal matrix, represents the fuzzy basis function vector, is the weight vector estimated value.

[0012] The attack compensator for in, and is the positive control gain to be designed, Second attack signal estimated value.

[0013] The memory event-triggered interval type-2 fuzzy integral concurrent learning safety consistency controller for in, is the intermediate control signal, and is the positive control gain to be designed, is the memory interval, satisfy is a small positive constant, is the trigger time interval, Weight vector estimated value.

[0014] Compared with the prior art, the present invention has the following beneficial effects: (1) This paper proposes an adaptive integral concurrent learning consistency control method for UAV swarms, achieving leaderless attitude consistency control under spoofing attacks. This scheme introduces a compensation variable into the coordinate transformation equation and designs a novel attack compensator to achieve online recognition and real-time compensation for spoofing attacks, thereby effectively ensuring the attitude stability and network security of the UAV swarm system. (2) Unlike existing adaptive estimation schemes that update parameters based on instantaneous data convergence, this paper designs a parameter update law based on an integral concurrent learning strategy. This approach relaxes the traditional continuous excitation condition to a limited excitation condition, significantly reducing the dependence on the excitation condition and bringing the theoretical results closer to practical engineering needs. (3) The present invention further proposes a concurrent learning safety consistency controller based on type-II fuzzy integral of memory event trigger interval. Compared with the traditional relative threshold event trigger mechanism controller, the controller extends the average trigger interval by introducing a memory item containing historical information of dynamic variables, realizes non-periodic intermittent update of control signals, thereby effectively reducing the continuous occupation of limited airborne communication bandwidth and significantly improving the utilization of communication resources. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] Figure 1 This is a flow chart of a method for controlling the safety consistency of an adaptive integral concurrent learning of a UAV cluster according to the present invention; Figure 2 The communication topology diagram of the drone cluster; Figure 3 The rolling angle trajectory diagram of the drone cluster followers F1-F4; Figure 4 This is the pitch angle trajectory diagram of the drone cluster followers F1-F4; Figure 5 The yaw angle trajectory diagram of the drone cluster followers F1-F4; Figure 6 This is the trajectory diagram of the rolling angle consistency tracking error of the UAV follower; Figure 7This is the trajectory diagram of the pitch angle consistency tracking error of the UAV follower; Figure 8 The yaw angle consistency tracking error trajectory diagram of the UAV follower; Figure 9 The weight norm trajectory graph for integral concurrent learning; Figure 10 This is the control input curve and trigger interval diagram of follower F1 in the UAV cluster; Figure 11 This is the control input curve and trigger interval diagram of follower F2 in the drone cluster; Figure 12 This is the control input curve and trigger interval diagram of follower F3 in the drone cluster; Figure 13 This is the control input curve and trigger interval diagram of follower F4 in the drone cluster. DETAILED DESCRIPTION

[0016] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments.

[0017] Please refer to Figure 1 The present invention provides a method for controlling the safety consistency of an adaptive integral concurrent learning of a UAV cluster, comprising the following steps: Step S1: Obtain a state space equation based on the deformation of the UAV attitude dynamics model, and define the state signal of the UAV under deception attack through the state space equation. Specifically, it includes: Construct the following attitude dynamics model of the i-th UAV: Where i = 1, 2, ..., n, n is the number of followers in the drone cluster, φ i ,θ i and ψ i are the roll angle, pitch angle and yaw angle of the i-th UAV respectively; as well as are the angular velocities of the roll angle, pitch angle, and yaw angle of the i-th UAV respectively; as well as are the angular accelerations of the roll angle, pitch angle, and yaw angle of the i-th UAV; χ iφ , χ iθ and χ iψ is the control torque of the i-th UAV; as well as is the inertia coefficient of the i-th UAV, as well as is the aerodynamic damping coefficient of the i-th UAV, as well as is an external unknown disturbance and satisfies is an unknown positive constant, Δ ＝ φ,θ,ψ.

[0018] According to the attitude dynamics model (1) of the i-th UAV, the state space equation is defined as: in,

[0019] Assume that the i-th drone suffers a deception attack as follows: in, and The drone is under attack. and are the first attack signal and the second attack signal respectively. Step S2: Establish a topological communication network and use the topological communication network to design compensation variables Design based on adaptive dynamic surface control technology includes adaptive parameters A first-order filter, combined with compensation variables First-order filter and state space equations are used to construct coordinate transformation equations. Based on the state signal of the drone being attacked by deception, the coordinate transformation equations including the attack state are constructed. Specifically, it includes: Using directed graph represents the topological communication network between drone clusters, and denote point sets and edge sets respectively; represents the neighbor set of the i-th drone, is the adjacency matrix; when When the i-th UAV can receive the information of the j-th UAV, it is recorded as a ij =1; otherwise, a ij =0; is the in-degree matrix, and

[0020] Directed Graph The Laplace matrix of Defined as If there is a directed path between any two different nodes, then the directed graph is strongly connected. Compensation variable design for: in, and are the attitude output signals of the i-th UAV and the j-th UAV respectively.

[0021] The first-order filter is designed as: in, is the positive control gain to be designed, is the filtering error, is a time-varying bounded function, is the output signal of the first-order filter, is the derivative of the output signal of the first-order filter, is the input signal of the first-order filter, For the unknown top estimated value.

[0022] According to the compensation variable design And a first-order filter, the state transition equation is constructed as: in, and are the first error variable and the second error variable respectively.

[0023] Since the original system state cannot be measured when the drone is under deception attack, the coordinate transformation equation of the attacked state is constructed: in, and are the first and second error variables attacked.

[0024] Step S3: Construct the first Lyapunov function according to the first error variable of the coordinate transformation equation And the derivative is Define auxiliary variables in conjunction with the coordinate transformation equation of the attacked state Through auxiliary variables Design attack compensator Parameter update law Combined auxiliary variables Attack Compensator and parameter update law Get virtual controller Specifically include: According to the coordinate transformation equation, the first Lyapunov function is constructed for: in, is a positive definite diagonal matrix, are the unknown weight vectors and the first attack signal estimated value.

[0025] For the first Lyapunov function Taking the derivative, we can get: in, and is the positive control gain to be designed.

[0026] definition for The upper bound of and They are and The lower and upper bounds of is a time-varying bounded function. Using interval type-2 fuzzy logic system Estimating composite terms We can get: in, is the unknown weight vector, Indicates that the input is The fuzzy basis function vector, is the estimation error.

[0027] Defining auxiliary variables Further calculations yield: in, Through auxiliary variables Design parameter update law and Attack Compensator for: in, Indicates that the input is The fuzzy basis function vector, as well as is the positive control gain to be designed.

[0028] Combined auxiliary variables Attack Compensator and parameter update law Get virtual controller Designed to: Attack Compensator Parameter update law and virtual controllers Substituting into formula (11) and simplifying it using Young's inequality, we can obtain: Step S4: Obtain the derivative of the second error variable using the unknown function approximately defined by the interval type-2 model logic system Based on the integral concurrent learning strategy, design the integral concurrent learning parameter update law According to the second error variable of the coordinate transformation equation, the second Lyapunov function is constructed And the derivative is Define auxiliary variables in conjunction with the coordinate transformation equation of the attacked state Through auxiliary variables Design parameter update law Parameter update law and Attack Compensator Combined auxiliary variables Parameter update law and Attack Compensator A concurrent learning safety consistency controller based on memory event-triggered interval type-2 fuzzy integral is obtained. Specifically include: According to the state transition equation (6), Taking the derivative, we can get: Defining unknown functions Interval Type-2 Fuzzy Logic System Approximate unknown function We can get: in, is the unknown weight vector, and are the fuzzy basis function vector and approximation error respectively,

[0029] Furthermore, formula (16) can be rewritten as: in, Constructing the parameter update law for integral concurrent learning for: in, is a positive definite diagonal learning matrix, is the output signal of the first-order filter, is the positive control gain to be designed, l and Δt i are the size of the integral concurrent learning history stack and the integral window, and For vehicle dynamics in [t i -Δt i ,t i ] output and input data, 0 q×1 is a column vector with all elements equal to 0, and is the size of the k-th history stack. The second error variable is The upper bound of formula (18) is t i The next Integral to find out.

[0030] for Integrating both sides of equation (18) yields: Then, further simplification yields: According to the state space equation obtained in step S2, the second Lyapunov function is constructed for: in, is a positive definite diagonal matrix, as well as They are as well as estimated value.

[0031] For the second Lyapunov function Taking the derivative, we can get: in, and is the positive control gain to be designed.

[0032] definition for The upper bound of and They are and The lower and upper bounds of . Using interval type-2 fuzzy logic system Online approximation of composite functions We can get: definition Substituting formula (24) into formula (23) yields: in,

[0033] Design parameter update law and parameter update law for: in, and is the positive control gain to be designed.

[0034] Attack Compensator Designed to: in, and is the positive control gain to be designed.

[0035] In order to reduce unnecessary usage of communication bandwidth and implement non-periodic intermittent updating of control signals, the following memory event triggering mechanism is designed: According to formula (29), for definition: in, is the actual controller, which is denoted as a concurrent learning safety consistency controller based on memory event-triggered interval type-II fuzzy integral. as well as is the positive control gain to be designed, is the memory interval, satisfy is a small positive constant. The designed integral concurrent learning parameter update law Parameter update law Parameter update law Attack Compensator And concurrent learning safety consistency controller based on memory event triggered interval type-2 fuzzy integral Simplifying formula (25) we can get: in, for The upper bound of .

[0036] Step S5: According to the first Lyapunov function and the second Lyapunov function Constructing a global Lyapunov function Based on Lyapunov stability theory, the stability of the closed-loop attitude control system is analyzed, the controller gains of the virtual controller and the safety consistency controller are determined, and the leaderless attitude consistency safety control of the UAV swarm under deception attacks is realized. Specifically, it includes: According to step S3 and step S4, construct the overall Lyapunov function for: Combining Equation (15) and Equation (32), the overall Lyapunov function Taking the derivative, we can get: in, Since the controlled drone is fully motivated within a limited interval, Existence of λ * >0 and T i >Δt i Make Established. We can get: As a result, equations (35) to (37) can be calculated to obtain: in,

[0037] Integrating both sides of equation (38) yields: Based on formula (39), when t→∞, It can be further deduced that all signals of the closed-loop system are bounded. According to Barbalat's lemma, we can get definition as well as Combining formula (6), we can get: Directed Graph is strongly connected, so There is a zero eigenvalue, and its corresponding eigenvector is 1 n , the other eigenvectors lie on the open right half plane. Therefore, in It is the standard type of Jordan. The column is The right eigenvector of . Definition So because The first line of is a zero vector, so P1(t)=P1(0), where P1 is the first term of P. Definition N=diag{ν}, we can get Given that N>0 and is bounded, so ||P|| is bounded. Choose the Lyapunov function is the identity matrix. For the Lyapunov function Taking the derivative, we can get: because There is a boundary, so Further available Bounded. Based on Barbalat's lemma, because The first column is 1 n , so in, for The first line of .

[0038] According to the above analysis, the attitude output trajectory of the UAV cluster system can achieve leaderless asymptotic consistency, that is,

[0039] According to formula (29), for The following inequality holds: Based on formula (31), we can get is differentiable, and its derivative is bounded, so there exists a positive constant satisfy Therefore, the minimum trigger interval satisfies Zeno's phenomenon will not occur.

[0040] The following simulation experiments are conducted in the simulation software MATLAB R2020a / SIMULINK to illustrate the effectiveness and feasibility of the adaptive integral concurrent learning safety consistency control method designed by the present invention. Assume that the drone cluster system contains four followers, labeled "F1-F4", and its communication topology network is as follows Figure 2 As shown, 1 represents drone communication.

[0041] The parameters of the UAV attitude dynamics system and the external disturbance are selected as follows:

[0042] The initial conditions of the UAV are selected as: [φ1(0),θ1(0),ψ1(0)]=[1,0.9,0.5], [φ2(0),θ2(0),ψ2(0)]=[0.1,0.75,-0.4], [φ3(0),θ3(0),ψ3(0)]=[-0.4,-0.3,0.6], [φ4(0),θ4(0),ψ4(0)]=[0.3,0.6,-0.5].

[0043] The controller parameters are selected as follows:

[0044] The fuzzy membership function is selected as:

[0045] The spoof attack signal is designed to: Assume injection at t=5s.

[0046] The size of the history stack l and the integration window Δt i They are designed as follows: l=25, Δt i =0.25.

[0047] The simulation results are plotted on Figures 3 to 6 . Figures 3 to 5 The roll angle, pitch angle and yaw angle trajectory diagrams of followers F1-F4 in the drone cluster are plotted respectively. Figures 6 to 8 The following are the trajectory diagrams of the roll, pitch, and yaw angle consistency tracking errors of the UAV cluster. The simulation results show that the designed adaptive integral concurrent learning security consistency control method ensures the asymptotic consistency of the leaderless attitude control when the UAV cluster is subjected to a deception attack. Figure 9 Graph of weight norm trajectories for concurrent learning of integrals. Figure 10-13 The control input curves and trigger interval diagrams of followers F1-F4 are plotted respectively.The simulation results show that the designed memory event trigger mechanism realizes the non-periodic intermittent update of the control signal and effectively avoids the Zeno phenomenon.

[0048] The simulation experimental results prove that the memory event-triggered interval type-2 fuzzy integral concurrent learning adaptive consistency control strategy designed in the present invention solves the leaderless asymptotic consistency problem of drone clusters under deception attacks, and relaxes the continuous excitation conditions required by traditional adaptive estimation schemes to milder finite excitation conditions to ensure the convergence of parameter estimation.

[0049] The foregoing description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Those skilled in the art will readily appreciate that various modifications and variations of the present invention are possible. Any modifications, equivalent substitutions, or improvements made within the spirit and principles of the present invention are intended to be within the scope of protection of the present invention.

Claims

1. An adaptive integral concurrent learning consistency control method for UAV swarms, characterized by: The following steps are involved: Step 1: Obtain a state-space equation based on the deformation of the UAV attitude dynamics model, and define the state signal of the UAV under deception attack through the state-space equation; Step 2: Establish a topological communication network and use it to design compensation variables Design based on adaptive dynamic surface control technology includes adaptive parameters A first-order filter, combined with compensation variables First-order filter and state space equation are used to construct coordinate transformation equations. Based on the state signal of the drone being attacked by deception, the coordinate transformation equations including the attack state are constructed. Step 3: Construct the first Lyapunov function based on the first error variable of the coordinate transformation equation And the derivative is Define auxiliary variables in conjunction with the coordinate transformation equation of the attacked state Through auxiliary variables Design attack compensator Parameter update law Combined auxiliary variables Attack Compensator and parameter update law Get virtual controller Step 4: Use the interval type-2 model logic system to approximate the defined unknown function and obtain the derivative of the second error variable Based on the integral concurrent learning strategy, design the integral concurrent learning parameter update law According to the second error variable of the coordinate transformation equation, the second Lyapunov function is constructed And the derivative is Define auxiliary variables in conjunction with the coordinate transformation equation of the attacked state Through auxiliary variables Design parameter update law Parameter update law and Attack Compensator Combined auxiliary variables Parameter update law and Attack Compensator A concurrent learning safety consistency controller based on memory event-triggered interval type-2 fuzzy integral is obtained. Step 5: According to the first Lyapunov function and the second Lyapunov function Constructing a global Lyapunov function Based on Lyapunov stability theory, the stability of the closed-loop attitude control system is analyzed, the controller gains of the virtual controller and the safety consistency controller are determined, and the leaderless attitude consistency safety control of the UAV swarm under deception attack is realized.

2. The adaptive integral concurrent learning consistency control method for a UAV swarm according to claim 1, characterized in that: The compensation variable for in, The i-th UAV can receive the information of the j-th UAV, denoted as a ij =1; otherwise, a ij =0; It is the first attack signal; and are the attitude output signals of the i-th UAV and the j-th UAV respectively.

3. The adaptive integral concurrent learning consistency control method for a UAV swarm according to claim 1, characterized in that: The first-order filter is in, is the positive control gain to be designed, is the filtering error, is a time-varying bounded function, is the output signal of the first-order filter, is the derivative of the output signal of the first-order filter, is the input signal of the first-order filter, Unknown estimated value.

4. The adaptive integral concurrent learning consistency control method for a UAV swarm according to claim 1, characterized in that: The virtual controller for in, and is the positive control gain to be designed, is the first error variable attacked, First attack signal The estimated value of is the compensation variable, represents the fuzzy basis function vector, is the weight vector estimated value.

5. The adaptive integral concurrent learning consistency control method for a UAV swarm according to claim 1, characterized in that: The attack compensator and parameter update law for in, is a positive definite diagonal matrix, is the first error variable attacked, The first attack signal The estimated value of is the compensation variable, represents the fuzzy basis function vector, k ih1 、 as well as is the positive control gain to be designed, is the weight vector estimated value.

6. The adaptive integral concurrent learning consistency control method for a UAV swarm according to claim 1, characterized in that: The integral concurrent learning parameter update law Designed to: in, is a positive definite diagonal learning matrix, is the output signal of the first-order filter, is the second error variable under attack, The second attack signal The estimated value of represents the fuzzy basis function vector, is the positive control gain to be designed, l and Δt i are the size of the integral concurrent learning history stack and the integral window, The second error variable is The value at the moment.

7. The adaptive integral concurrent learning consistency control method for a UAV swarm according to claim 1, characterized in that: The parameter update law and parameter update law for in, is the control gain to be designed, and is the positive control gain to be designed, is the filtering error, is the output signal of the first-order filter, For virtual controllers, Unknown The estimated value of is a positive definite diagonal matrix, represents the fuzzy basis function vector, is the weight vector estimated value.

8. The adaptive integral concurrent learning consistency control method for a UAV swarm as claimed in claim 1, characterized in that: The attack compensator for in, and is the positive control gain to be designed, Second attack signal estimated value.

9. The method for adaptive integral concurrent learning consistency control of a UAV swarm as claimed in claim 1, characterized in that: The memory event-triggered interval type-2 fuzzy integral concurrent learning safety consistency controller for in, is the intermediate control signal, and is the positive control gain to be designed, is the memory interval, satisfy is a small positive constant, is the trigger time interval, is the weight vector estimated value.

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