Safe attitude control method and system for quad-rotor unmanned aerial vehicle system under hidden attack

Abstract

The invention discloses a safe attitude control method and system for a quad-rotor unmanned aerial vehicle system under hidden attacks, and the method comprises the steps: building a nonlinear model of the unmanned aerial vehicle attitude control system under hidden attacks, constructing a convex optimization problem based on a Lyapunov function and a linear matrix inequality, solving the gain of a controller, and carrying out the calculation of the safety attitude of the quad-rotor unmanned aerial vehicle system. According to the method, the attitude safety and stability of the quad-rotor unmanned aerial vehicle system under the hidden false data injection attack are ensured, the limitation caused by model linearization is avoided in the solving process of the method, the attitude safety and stability of the unmanned aerial vehicle under the complex nonlinear condition are ensured, and the hidden attack resistance of the quad-rotor unmanned aerial vehicle system is improved.

Description

Technical Field

[0001] This invention belongs to the field of unmanned aerial vehicle (UAV) attack technology, and relates to a method and system for safe attitude control of a quadcopter UAV system under covert attack. Background Technology

[0002] With the widespread application of drones in the civilian sector, as a typical cyber-physical system, they face increasingly severe cybersecurity threats. Among these threats, covert fictitious data injection (FDI) attacks, by tampering with or injecting false data, cause deviations in drone status monitoring and control, potentially leading to system instability or mission failure. However, existing attack detection mechanisms often have limitations in coverage, making it difficult to guarantee 100% accuracy against highly covert attacks. Therefore, it is necessary to develop proactive defense or security control strategies against covert attacks.

[0003] Chinese invention patent "Safety Control Method for Multi-rate Heavy Medium Coal Mine Separation System under Covert Attack" (Publication No. CN115970880A). This invention designs an output feedback controller for multi-rate heavy medium coal mine separation systems subjected to covert attacks, ensuring that the density of the heavy medium suspension remains within a safe range. However, this method is applicable to systems for which relatively mature linear or approximate linear models can be established for analysis and control. Quadrotor UAV systems, with their highly nonlinear, multivariable, and strongly coupled dynamic characteristics, are no longer suitable for this method. Therefore, developing a control method capable of actively defending against covert FDI attacks and ensuring the safe and stable operation of nonlinear UAV systems under attack is of significant practical importance.

[0004] Chinese invention patent "Method for Detection and Security Control of Covert Fake Data Injection Attacks on Quadrotor UAVs" (Publication No. CN119363432A). This method linearizes the quadrotor UAV model before performing attack detection to resist covert attacks. However, the linearization assumption of this method has certain limitations: although linearization can simplify analysis and controller design near certain operating points, quadrotor UAVs often operate in nonlinear, large attitude angle, and high-speed motion states during actual flight. In these scenarios, the linearized model will fail to accurately describe the dynamic behavior of the UAV, leading to decreased detection and control accuracy, or even failure.

[0005] The Chinese invention patent "Safety Control Method and System for Unmanned Vehicles Resisting Covert Fake Data Injection Attacks" (Publication No. CN119937635A) constructs a robust controller through a differential closed-loop system and an escapeless set, but mainly designs the control law based on a linear or linearized model.

[0006] Chinese invention patent titled "A Detection and Security Control Defense Method for UAV Hidden False Information Injection Attacks" (Publication No. CN117938487A). This method uses an end-to-end encryption / decryption method for attack detection, and activates a backup secure communication channel after an attack is detected, thereby introducing additional communication resources and computational overhead. Summary of the Invention

[0007] The purpose of this invention is to address the limitations of existing attack detection mechanisms, which often suffer from incomplete coverage and cannot guarantee 100% accuracy for highly covert attacks, thus affecting the stable operation of unmanned aerial vehicle (UAV) systems under covert attacks. This invention provides a safe attitude control method and system for quadcopter UAV systems under covert attacks.

[0008] To achieve the above objectives, the present invention employs the following technical solution: A method for safe attitude control of a quadcopter unmanned aerial vehicle system under covert attack includes the following steps: Construct a nonlinear model of the UAV attitude control system under covert attack conditions; Obtaining Nonlinear Terms Based on Nonlinear Model of UAV Attitude Control System Based on nonlinear terms Calculate and obtain the Lipschitz constant ; Based on Lipschitz constant Lyapunov functions and linear matrix inequalities are constructed using nonlinear models. Based on these, a convex optimization problem is established. The convex optimization problem is solved to obtain the controller gain, thus yielding a safe attitude control method for a quadrotor UAV system.

[0009] A further improvement of the present invention is that: The construction of the nonlinear model for the UAV attitude control system under covert attack conditions includes:

[0010]

[0011] in, Here is the system state vector; k represents time. This is the attitude angle error vector of the quadcopter UAV. These represent the actual roll attitude Euler angles, pitch attitude Euler angles, and yaw attitude Euler angles of the UAV, respectively. All are constants, representing the expected values ​​of the UAV's roll attitude Euler angles, pitch attitude Euler angles, and yaw attitude Euler angles, respectively; Let p be the first derivative of e, q be the roll rate, r be the pitch rate, and A be the system matrix and B be the input matrix. A and B are... Based on the parameters discretized using the Euler method , ; This represents the moment of inertia of the UAV in the body coordinate system. These are the moments of inertia along the x, y, and z axes, respectively. Indicates control input, This indicates a sequence of covert attacks targeting the executor. Let T be the system nonlinear term and T be the sampling time.

[0012] Define detector residuals:

[0013] in, This represents the nonlinear term of the system at the previous time step; This represents the system state vector at the previous moment.

[0014] The detector works as follows: when When the value is ≤1, the detector will not alarm; When the value is greater than 1, the detector will sound an alarm; among which, satisfy: ; The nonlinear term is obtained from the nonlinear model based on the UAV attitude control system. Based on nonlinear terms Calculate and obtain the Lipschitz constant ,include: Define nonlinear terms With Lipschitz constant The following conditions must be met: ,

[0015] Wherein, the domain D The range of angular velocity of the drone was limited. , and It is a constant; , Representing vectors respectively ,vector 2-norm; Let p, q, and r represent the absolute values ​​of p, q, and r, respectively. definition , Combining the above formula, The maximum value is defined as the Lipschitz constant. :

[0016] In the formula, , Indicates the roll angular velocity; , Indicates pitch angular velocity; , This indicates the yaw rate.

[0017] The construction of the convex optimization problem includes: Build a state feedback controller:

[0018] The convex optimization problem is expressed by the following formula:

[0019] Where 0 < α < 1, matrix P 0, M=PBL, It is a 6×6 identity matrix. It is a 6×6 zero matrix. It is a 6×3 zero matrix. It is a 3×6 zero matrix; Solving for P and The controller gain L is obtained according to the following formula: L=

[0020] in, Represents the Moore-Penrose generalized inverse of PB; Optimal control is obtained by combining the controller gain L and the state feedback controller.

[0021] The construction of the convex optimization problem includes: Define augmented state vector ; Construct constraints: According to Lyapunov functions For consecutive 0 < α < 1, if there exist β > 0 and matrix P If 0, then the following inequality holds: , in, , The constraints that covert attacks must satisfy; get:

[0022] in, , Given a 6th-order identity matrix, applying Schur's complement theory yields: 0 in, It is a 6×6 zero matrix. It is a 6×3 zero matrix. It is a 3×6 zero matrix; By introducing the variable M=PBL, we obtain the linear inequality for the convex optimization problem.

[0023] A safe attitude control system for a quadcopter unmanned aerial vehicle system under covert attack includes: The nonlinear model building module is used to build a nonlinear model of the UAV attitude control system under covert attack conditions. The nonlinear term solving module is used to obtain nonlinear terms from the nonlinear model of the UAV attitude control system. Based on nonlinear terms Calculate and obtain the Lipschitz constant ; Based on Lipschitz constant Lyapunov functions and linear matrix inequalities are constructed using nonlinear models. A convex optimization problem is then constructed based on the Lyapunov functions and linear matrix inequalities. The convex optimization problem is solved to obtain a control gain acquisition module, which is used for controller gain, thus obtaining a safe attitude control method for a quadrotor UAV system.

[0024] A terminal device includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor, when executing the computer program, implements the steps of any of the methods described above.

[0025] A computer-readable storage medium storing a computer program that, when executed by a processor, performs any of the steps of the method described above.

[0026] A computer program product includes a computer program that, when executed by a processor, implements any one of the methods described.

[0027] Compared with the prior art, the present invention has the following beneficial effects: This invention discloses a safe attitude control method for a quadrotor unmanned aerial vehicle (UAV) system under covert attacks. By establishing a nonlinear model of the UAV attitude control system under covert attacks, a convex optimization problem is constructed based on Lyapunov functions and linear matrix inequalities to obtain the controller gain. This ensures the safe and stable attitude of the quadrotor UAV system under covert false data injection attacks. The solution process of this method avoids the limitations caused by model linearization, ensures the safe and stable attitude of the UAV under complex nonlinear conditions, and improves the ability of the quadrotor UAV system to resist covert attacks. Attached Figure Description

[0028] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the embodiments will be briefly introduced below. It should be understood that the following drawings only show some embodiments of the present invention and should not be regarded as a limitation on the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort.

[0029] Figure 1 A flowchart of a security control method for covert false data injection attacks in a quadcopter unmanned aerial vehicle system according to the present invention; Figure 2 The convergence characteristics of attitude angle error of a quadcopter UAV under a covert false data injection attack according to an embodiment of the present invention; Figure 3 The attitude angular velocity convergence characteristics of a quadcopter drone under a covert false data injection attack according to an embodiment of the present invention; Figure 4 The present invention describes the time response of a quadcopter drone to various attitude angle errors under a covert false data injection attack. Figure 5 The present invention relates to the time response of a quadcopter drone at various attitudes and angular velocities under a covert false data injection attack according to an embodiment of the present invention. Detailed Implementation

[0030] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations.

[0031] Therefore, the following detailed description of the embodiments of the invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the invention without inventive effort are within the scope of protection of the invention.

[0032] It should be noted that similar labels and letters in the following figures indicate similar items. Therefore, once an item is defined in one figure, it does not need to be further defined and explained in subsequent figures.

[0033] In the description of the embodiments of the present invention, it should be noted that if terms such as "upper," "lower," "horizontal," or "inner" indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings, or the orientation or positional relationship commonly used when the product of the invention is in use, they are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation of the present invention. Furthermore, terms such as "first" and "second" are only used to distinguish descriptions and should not be construed as indicating or implying relative importance.

[0034] Furthermore, the use of the term "horizontal" does not imply that the component must be absolutely horizontal, but rather that it can be slightly tilted. For example, "horizontal" simply means that its direction is more horizontal than "vertical," and does not mean that the structure must be completely horizontal, but can be slightly tilted.

[0035] In the description of the embodiments of the present invention, it should also be noted that, unless otherwise explicitly specified and limited, the terms "set," "install," "connect," and "link" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal connection of two components. Those skilled in the art can understand the specific meaning of the above terms in the present invention according to the specific circumstances.

[0036] The present invention will now be described in further detail with reference to the accompanying drawings: See Figure 1 This invention discloses a safe attitude control method for a quadrotor unmanned aerial vehicle (UAV) system under covert attacks, aiming to ensure the safe attitude control of the quadrotor UAV system under covert spoofing data injection attacks and to stabilize the system state within an invariant reachable set { The following steps are included within the scope of this document: Step 1: Establish a model of a nonlinear unmanned aerial vehicle system subjected to covert actuator attacks: The specific derivation is as follows: Based on Euler's formula Establish a mathematical model of the UAV in the body coordinate system:

[0037] in, This represents the torque acting on the drone; This represents the moment of inertia of the UAV in the body coordinate system. These are the moments of inertia along the x, y, and z axes, respectively. Let be the attitude angular velocity of the UAV, p be the roll angular velocity, q be the pitch angular velocity, and r be the yaw angular velocity. They are respectively The first derivative of ; x represents the cross product.

[0038] Take the attitude angle error of the UAV and its first derivative: ,

[0039] Where Ф, θ, and ψ represent the actual roll attitude Euler angle, pitch attitude Euler angle, and yaw attitude Euler angle of the UAV, respectively; All are constants, representing the expected values ​​of the UAV's roll attitude Euler angle, pitch attitude Euler angle, and yaw attitude Euler angle, respectively.

[0040] Furthermore, take the second derivative of the UAV attitude angle error:

[0041] Furthermore, take the system state variables. Then we have: ,Right now:

[0042] Right now:

[0043] in, , , It is a 3×3 identity matrix. It is a 3×3 zero matrix. , .

[0044] Furthermore, based on the sampling time T of the UAV, after discretization using the Euler method, the state equation of the nonlinear UAV system under the condition of not being subjected to covert attacks is:

[0045] Among them, A and B are Based on the parameters discretized using the Euler method, k represents time. Indicates the system status. Indicates control input, Indicates control input, Indicates belonging to, Let represent n-dimensional Euclidean space.

[0046] Furthermore, under a covert attack on the actuator, the state equation of the nonlinear unmanned aerial vehicle system is:

[0047] Furthermore, define the detector residual: ; Furthermore, define the detection logic: ≤1, that is When the value is ≤1, the detector will not alarm; When the value is greater than 1, the detector will sound an alarm; among which, satisfy: .

[0048] Step 2: Find the Lipschitz constant for the nonlinear term. : Specifically, the following steps are included: It is easy to see the nonlinear term Lipschitz continuity, meaning there exists a Lipschitz constant. , making any They all ; Wherein, the domain D The range of the UAV's angular velocity is limited, with l, m, and n being constants; , Representing vectors respectively ,vector 2-norm; Let p, q, and r represent the absolute values ​​of p, q, and r, respectively.

[0049] Furthermore, take , , ,in For the roll angular velocity, The pitch angular velocity, This is the yaw rate.

[0050] because It can be achieved by seeking If the maximum value is achieved, then find the Lipschitz constant. That is to seek The maximum value.

[0051] Step 3: Construct a convex optimization problem based on Lyapunov functions and linear matrix inequalities. Solve the convex optimization problem to obtain the controller gain: Specifically, the following steps are included: Easy to launch, covert attack fulfills the following requirements: ,in .

[0052] Get Lyapunov function For consecutive 0 < α < 1, if there exists β > 0, matrix P 0, making ; in, , { } is an invariant reachable set of the system, which guarantees the stability of the system.

[0053] Furthermore, design a state feedback controller: .

[0054] Furthermore, we define the augmented state vector. ; Then the inequality It can be represented as:

[0055] in, , It is a 6th-order identity matrix.

[0056] Furthermore, applying Schur's complement theory to the above equation yields: 0 in, It is a 6×6 zero matrix. It is a 6×3 zero matrix. It is a 3×6 zero matrix.

[0057] Furthermore, introducing the variable M=PBL, the solution is as follows, using matrices P, M, and scalars... Convex optimization problem with variables:

[0058] Solving the above convex optimization problem yields P and M; From L= The controller gain L can be obtained.

[0059] in, Represents the Moore-Penrose generalized inverse of PB.

[0060] The present invention also discloses specific embodiments: This invention employs a safe attitude control method for a nonlinear quadrotor unmanned aerial vehicle (UAV) system under covert spoofing attacks. Considering covert attacks targeting the actuators, the method designs a controller gain to ensure the quadrotor UAV system's attitude remains stable within a certain safe range. The specific implementation method is as follows: Step 1: The status of the quadcopter UAV system subjected to a covert actuator attack and the designed controller are as follows:

[0061] Discretization with a time step of T=0.01s yields the following parameter matrix: ,

[0062] Furthermore, the parameters of the quadcopter drone model are as follows: , , .

[0063] Step 2: Set the drone's angular velocity The range is ; Right now Domain D is ; The nonlinear term is obtained according to step 2. Lipschitz constant .

[0064] Solving step 3 using matrices P, M, and scalars Convex optimization problem with variables:

[0065] Pick ,when We obtain: scalar , matrix , matrix Therefore, the attainable set of states of a quadcopter UAV system under covert attack is an ellipsoid { }

[0066] From L= We obtain: matrix

[0067] Based on the invariant reachability set matrix P and controller gain L obtained by solving a convex optimization problem in this invention, a Monte Carlo simulation was performed to verify the quadrotor unmanned aerial vehicle system. like Figure 2 and Figure 3 As shown, after 50 Monte Carlo simulations, under the controller designed in this invention (blue dashed line), the simulated trajectories of the quadcopter UAV system's attitude angle error and angular velocity quickly converge to the invariant reachable set (light gray ellipsoidal projection) described by the P matrix in the state space. This strongly proves that the designed controller can ensure that the system state is within a safe range under covert attacks and nonlinear disturbances. However, without the controller (red dashed line), the simulated trajectories of the quadcopter UAV system's attitude angle error and attitude angular velocity show a divergent trend, exceeding the invariant reachable set, and the system is in an unstable state.

[0068] like Figure 4As shown, under the controller designed in this invention (thick solid line), the roll attitude angle error of the quadcopter UAV system is... pitch attitude angle error Yaw attitude angle error The roll attitude angle error of the quadcopter UAV system converges rapidly to a very small neighborhood of 0 over time; however, without a controller (thin solid line), the roll attitude angle error... pitch attitude angle error The yaw attitude angle errors all showed a divergent trend, and the error magnitudes deviated significantly from the safe range.

[0069] like Figure 5 As shown, under the controller designed in this invention (thick solid line), the roll angular velocity p, pitch angular velocity q, and yaw angular velocity r of the quadcopter UAV system remain stable within a small fluctuation range around 0 rad; while without the controller (thin solid line), the angular velocity fluctuates violently and with a large amplitude, and the system state shows a divergent trend.

[0070] Simulation results clearly demonstrate that the controller gain designed in this invention can ensure rapid convergence and sustained stability of the attitude of a non-quadrotor UAV system under covert attacks, greatly improving the system's ability to resist covert attacks.

[0071] The method disclosed in this invention directly establishes a nonlinear model for quadcopter UAV systems and obtains the controller gain by solving a convex optimization problem based on LMI. This method avoids the limitations caused by model linearization and better ensures the attitude safety and stability of the UAV under complex nonlinear conditions.

[0072] The method disclosed in this invention designs an algorithm-level security control method that does not rely on additional encryption / decryption operations or the activation of backup communication channels, thereby saving network and computing resources and efficiently ensuring the stable operation of the UAV system under covert attacks.

[0073] This invention presents a method for secure attitude control of a quadrotor unmanned aerial vehicle (UAV) system under covert false data injection attacks. This method establishes a nonlinear model of the UAV attitude control system under covert attacks, constructs a convex optimization problem based on Lyapunov functions and linear matrix inequalities, and obtains the controller gain. This ensures the attitude security and stability of the quadrotor UAV system under covert false data injection attacks, thereby improving the quadrotor UAV system's resistance to covert attacks.

[0074] An embodiment of the present invention provides a safe attitude control system for a quadcopter unmanned aerial vehicle system under covert attack, comprising: The nonlinear model building module is used to build a nonlinear model of the UAV attitude control system under covert attack conditions. The nonlinear term solving module is used to obtain nonlinear terms from the nonlinear model of the UAV attitude control system. Based on nonlinear terms Calculate and obtain the Lipschitz constant ; Based on Lipschitz constant Lyapunov functions and linear matrix inequalities are constructed using nonlinear models. A convex optimization problem is then constructed based on the Lyapunov functions and linear matrix inequalities. The convex optimization problem is solved to obtain a control gain acquisition module, which is used for controller gain, thus obtaining a safe attitude control method for a quadrotor UAV system.

[0075] A schematic diagram of a terminal device according to an embodiment of the present invention. The terminal device of this embodiment includes: a processor, a memory, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements the steps in the various method embodiments described above. Alternatively, when the processor executes the computer program, it implements the functions of each module / unit in the various device embodiments described above.

[0076] The computer program can be divided into one or more modules / units, which are stored in the memory and executed by the processor to complete the present invention.

[0077] The terminal device can be a desktop computer, laptop computer, cloud server, or other device with strong computing power. The terminal device may include, but is not limited to, a processor and memory.

[0078] The optimal choice for the processor is a multi-core high-speed central processing unit (CPU).

[0079] The memory can be used to store the computer program and / or module. The processor implements various functions of the terminal device by running or executing the computer program and / or module stored in the memory and calling the data stored in the memory.

[0080] If the modules / units integrated in the terminal device are implemented as software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, all or part of the processes in the methods of the above embodiments can also be implemented by a computer program instructing related hardware. The computer program can be stored in a computer-readable storage medium, and when executed by a processor, it can implement the steps of the various method embodiments described above. The computer program includes computer program code, which can be in the form of source code, object code, executable files, or certain intermediate forms. The computer-readable medium can include: any entity or device capable of carrying the computer program code, recording media, USB flash drives, portable hard drives, magnetic disks, optical disks, computer memory, read-only memory (ROM), random access memory (RAM), electrical carrier signals, telecommunication signals, and software distribution media, etc. It should be noted that the content included in the computer-readable medium can be appropriately added or removed according to the requirements of legislation and patent practice in the jurisdiction. For example, in some jurisdictions, according to legislation and patent practice, computer-readable media do not include electrical carrier signals and telecommunication signals. The above are merely preferred embodiments of the present invention and are not intended to limit the present invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for safe attitude control of a quadcopter unmanned aerial vehicle system under covert attack, characterized in that, Includes the following steps: Construct a nonlinear model of the UAV attitude control system under covert attack conditions; Obtaining Nonlinear Terms Based on Nonlinear Model of UAV Attitude Control System Based on nonlinear terms Calculate and obtain the Lipschitz constant ; Based on Lipschitz constant Lyapunov functions and linear matrix inequalities are constructed using nonlinear models. Based on these, a convex optimization problem is established. The convex optimization problem is solved to obtain the controller gain, thus yielding a safe attitude control method for a quadrotor UAV system.

2. The safe attitude control method for a quadcopter unmanned aerial vehicle system under covert attack as described in claim 1, characterized in that, The construction of the nonlinear model for the UAV attitude control system under covert attack conditions includes: in, Here is the system state vector; k represents time. This is the attitude angle error vector of the quadcopter UAV. These represent the actual roll attitude Euler angles, pitch attitude Euler angles, and yaw attitude Euler angles of the UAV, respectively. All are constants, representing the expected values ​​of the UAV's roll attitude Euler angles, pitch attitude Euler angles, and yaw attitude Euler angles, respectively; Let p be the first derivative of e, q be the roll rate, r be the pitch rate, and A be the system matrix and B be the input matrix. A and B are... Based on the parameters discretized using the Euler method , ; This represents the moment of inertia of the UAV in the body coordinate system. Represents a diagonal matrix. These are the moments of inertia along the x, y, and z axes, respectively. Indicates control input, This indicates a sequence of covert attacks targeting the executor. Here, T represents the system's nonlinear term, and T is the sampling time.

3. The safe attitude control method for a quadcopter unmanned aerial vehicle system under covert attack as described in claim 2, characterized in that, It also includes defining the detector residuals based on the nonlinear model of the X UAV attitude control system: in, This represents the nonlinear term of the system at the previous time step; This represents the system state vector at the previous moment; The detector works as follows: when When the value is ≤1, the detector will not alarm; When the value is greater than 1, the detector will sound an alarm; among which, satisfy: .

4. The safe attitude control method for a quadcopter unmanned aerial vehicle system under covert attack as described in claim 2, characterized in that, The nonlinear term is obtained from the nonlinear model based on the UAV attitude control system. Based on nonlinear terms Calculate and obtain the Lipschitz constant ,include: Define nonlinear terms With Lipschitz constant The following conditions must be met: ， Wherein, the domain D The range of angular velocity of the drone was limited. , and It is a constant; , Representing vectors respectively ,vector 2-norm; Let p, q, and r represent the absolute values ​​of p, q, and r, respectively. definition , In the formula, and Let be any two values ​​of the UAV's angular velocity within the domain D; By solving The maximum value yields the Lipschitz constant: 。 5. A method for safe attitude control of a quadcopter unmanned aerial vehicle system under covert attack as described in claim 2, characterized in that, The construction of the convex optimization problem includes: Build a state feedback controller: The convex optimization problem is expressed by the following formula: Where 0 < α < 1, matrix P 0, M=PBL, It is a 6×6 identity matrix. It is a 6×6 zero matrix. It is a 6×3 zero matrix. It is a 3×6 zero matrix; Solving for P and The controller gain L is obtained according to the following formula: L= in, Represents the Moore-Penrose generalized inverse of PB; Optimal control is obtained by combining the controller gain L and the state feedback controller.

6. The safe attitude control method for a quadcopter unmanned aerial vehicle system under covert attack as described in claim 5, characterized in that, The construction of the convex optimization problem includes: Define augmented state vector ; Construct constraints: According to Lyapunov functions For consecutive 0 < α < 1, if there exist β > 0 and matrix P If 0 makes the following inequality true, then the unmanned aerial vehicle (UAV) system is stable: ， in, , The constraints that must be satisfied for covert attacks; get: in, , Given a 6th-order identity matrix, applying Schur's complement theory yields: 0 in, It is a 6×6 zero matrix. It is a 6×3 zero matrix. It is a 3×6 zero matrix; By introducing the variable M=PBL, we obtain the linear inequality for the convex optimization problem.

7. A safe attitude control system for a quadcopter unmanned aerial vehicle system under covert attack, characterized in that, include: The nonlinear model building module is used to build a nonlinear model of the UAV attitude control system under covert attack conditions. The nonlinear term solving module is used to obtain nonlinear terms from the nonlinear model of the UAV attitude control system. Based on nonlinear terms Calculate and obtain the Lipschitz constant ; Based on Lipschitz constant Lyapunov functions and linear matrix inequalities are constructed using nonlinear models. A convex optimization problem is then constructed based on the Lyapunov functions and linear matrix inequalities. The convex optimization problem is solved to obtain a control gain acquisition module, which is used for controller gain, thus obtaining a safe attitude control method for a quadrotor UAV system.

8. A terminal device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements the steps of the method as described in any one of claims 1-6.

9. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by a processor, it implements the steps of the method as described in any one of claims 1-6.

10. A computer program product, comprising a computer program, characterized in that, When the computer program is executed by a processor, it implements the method as described in any one of claims 1-6.

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