An optimal robust fault-tolerant control method for quadrotor unmanned aerial vehicles considering external disturbances

Abstract

The application discloses a kind of optimal robust fault-tolerant control methods of quadrotor unmanned aerial vehicle considering external disturbance, determine the attitude dynamics equation of final quadrotor unmanned aerial vehicle, and the augmented equation consisting of tracking error equation and reference equation;According to augmented equation, design a performance index function considering actuator failure and external disturbance, and determine Hamilton equation;Optimal robust fault-tolerant controller is constructed, and Hamilton-Jacobi-Isaacs equation is established;Optimal performance index function is approximated using single evaluation structure neural network, and optimal control input approximation and optimal disturbance input approximation are obtained, which are solved by gradient descent method, to obtain the approximate optimal weight update rate of evaluation neural network;The approximate optimal weight of evaluation neural network is solved, and the final approximate optimal robust fault-tolerant controller is obtained by integrating with optimal robust fault-tolerant controller, to complete the optimal robust fault-tolerant control of quadrotor unmanned aerial vehicle.The application can not only ensure that the system is optimal, but also improve the fault-tolerant capability and robustness of quadrotor unmanned aerial vehicle.

Description

Technical Field

[0001] This invention relates to the field of fault-tolerant attitude control design for quadrotor unmanned aerial vehicles (UAVs), and specifically to an optimal robust fault-tolerant control method for quadrotor UAVs that takes into account external disturbances. Background Technology

[0002] Attitude control of quadcopter drones is a challenging task involving multiple difficulties and complexities. First, the nonlinear dynamics of quadcopter drones make attitude control more complex, requiring appropriate nonlinear control methods to handle the nonlinear characteristics of the system dynamics. Second, drones face varying operating conditions during flight, necessitating adaptability and robustness of the controller to ensure flight stability under different conditions. Furthermore, actuators are responsible for providing thrust and controlling the aircraft's attitude during flight; therefore, any actuator-related failures can lead to flight anomalies or even accidents. Fault-tolerant control techniques for actuator failures are essential to improve the reliability and safety of drones. Finally, the attitude control system needs to possess rapid response and stability to meet the requirements of fast and precise control. To overcome these challenges in attitude control, it is necessary to integrate traditional control theory with advanced control technologies to improve the performance and stability of the attitude control system.

[0003] Chinese patent application CN202110038758.4 proposes an anti-interference fault-tolerant control method for a quadcopter. This method designs a nonlinear adaptive state observer to estimate the efficiency loss coefficient, then designs a disturbance observer to estimate external disturbances, and finally designs a composite controller based on the estimates. While this method increases the robustness of the quadcopter, it cannot guarantee the stability of the quadcopter in the event of a serious fault. Chinese patent application CN202210563595.6 proposes an attitude fault-tolerant control method for a quadcopter considering unknown wind disturbances. This method designs a non-singular fast terminal sliding surface, a failure factor compensator, and a disturbance compensator. However, the controller designed using this method cannot guarantee that the quadcopter is in an optimal state. Summary of the Invention

[0004] The purpose of this invention is to propose an optimal robust fault-tolerant control method for quadrotor UAVs that takes into account external disturbances, aiming to solve the problems of partial actuator failure and unknown time-varying external disturbances encountered by quadrotor UAVs in complex flight missions.

[0005] The technical solution to achieve the purpose of this invention is as follows: an optimal robust fault-tolerant control method for a quadcopter UAV considering external disturbances, comprising the following steps:

[0006] Step 1: Establish an attitude control model for a quadrotor UAV with unknown time-varying disturbances and partial actuator failures using the Newton-Euler method. Determine the final attitude dynamics equations of the quadrotor UAV by defining attitude parameters.

[0007] Step 2: Introduce the reference equation and determine the augmented equation consisting of the tracking error equation and the reference equation;

[0008] Step 3: Based on the augmented equation, design a performance index function that considers actuator failure and external disturbances, and determine the Hamilton equation;

[0009] Step 4: By solving the partial derivatives of the Hamilton equation, the optimal control input and the optimal disturbance input are obtained. Then, the optimal robust fault-tolerant controller is constructed, and the Hamilton-Jacobi-Isaacs equation is established.

[0010] Step 5: Use a neural network with a single evaluation structure to approximate the optimal performance index function, obtain the approximate values ​​of the optimal control input and the optimal disturbance input, and solve for the approximate optimal weight update rate of the evaluation neural network by gradient descent method;

[0011] Step 6: Based on the approximate optimal weight update rate of the evaluation neural network in Step 5, solve for the approximate optimal weight of the evaluation neural network, and integrate it with the optimal robust fault-tolerant controller in Step 4 to obtain the final approximate optimal robust fault-tolerant controller, thus completing the optimal robust fault-tolerant control of the quadcopter UAV.

[0012] Furthermore, in step 1, an attitude control model for a quadcopter UAV with unknown time-varying disturbances and partial actuator failures is established using the Newton-Euler method. By defining attitude parameters, the final attitude dynamics equations of the quadcopter UAV are determined. The specific method is as follows:

[0013] (1) An attitude control model for a quadcopter UAV with unknown disturbances and actuator failures is established using the Newton-Euler method, and the expression is as follows:

[0014]

[0015] The variables in equation (1) are defined as follows: The attitude angles of the UAV are represented by φ, where φ is the roll angle, θ is the pitch angle, and ψ is the yaw angle. The attitude angular velocities of the UAV are represented by roll rate, pitch rate, and yaw rate. The attitude angular accelerations of the UAV are represented by roll acceleration, pitch acceleration, and yaw acceleration; J = diag{J φ J θ J ψ} represents the inertia matrix; Represents the Coriolis term of coupling; This represents the control input torque, where τ ψ =k l k w u φ τ represents the roll angle channel control input torque. θ =k l k w u θ τ represents the input torque for the pitch angle channel control. ψ =k τ u ψ Indicates the yaw angle channel control input torque, k l k is the distance from the motor to the center of mass of the machine body. w and k τ This represents the proportionality coefficient. The input signals represent the roll angle input signal, pitch angle input signal, and yaw angle input signal, respectively. υ1, υ2, υ3, and υ4 represent the rotational speeds of the four motors of the quadcopter drone. These represent the external uncertainty disturbances of roll angle, pitch angle, and yaw angle, respectively; Λ=diag{Λ φ Λ θ Λ ψ} represent the unknown actuator failure factors for roll angle, pitch angle, and yaw angle, respectively. in Indicates the upper bound of Λ;

[0016] (2) Define B = diag{k l k w k l k w k τ Equation (1) can be rewritten as follows:

[0017]

[0018] where u=[u φ u θ u ψ ] T This indicates a control input.

[0019] (3) Definition Let the attitude parameters of the UAV be represented. Equation (2) can be rewritten as follows, and the final attitude dynamics equation of the quadcopter UAV can be obtained, as shown in the following expression:

[0020]

[0021] The meanings of each variable are as follows:

[0022] This indicates a disturbance input.

[0023] Furthermore, in step 2, a reference equation is introduced, and the augmented equation consisting of the tracking error equation and the reference equation is determined. The specific method is as follows:

[0024] The introduced reference equation is as follows:

[0025]

[0026] in This represents the expected value of X; Let φ represent the expected attitude angle of the UAV. d Let θ be the expected roll angle. d Let ψ be the desired pitch angle. d This represents the expected value of the yaw angle. These represent the expected values ​​of the UAV's attitude angular velocities, namely the expected values ​​of roll angular velocity, pitch angular velocity, and yaw angular velocity;

[0027] The tracking error equation is defined as E = XX d Then the derivative of the tracking error equation is as follows:

[0028]

[0029] The augmented equation, composed of the tracking error equation and the reference equation, is expressed as follows:

[0030]

[0031] in In the following text, for the sake of simplicity, we will use... ω represents ω(Z).

[0032] Furthermore, in step 3, based on the augmented equation, a performance index function considering actuator failure and external disturbances is designed, and the Hamilton equation is determined. The specific method is as follows:

[0033] Design a performance index function that considers actuator failure and external interference:

[0034]

[0035] Where γ is the discount factor of the performance index function, t represents time, and Q T =diag{Q,0 6×6}, K > 0 is a diagonal matrix, and and All are positive definite symmetric matrices;

[0036] And the coefficient β satisfies For simplicity, V is used to represent V(Z);

[0037] Taking the derivative of equation (7), we obtain the derivative of the performance index function as follows:

[0038]

[0039] If the first term on the right side of equation (8) equals γV, then equation (8) can be rewritten as:

[0040]

[0041] According to equation (9), the Hamilton equation is determined to be of the following form:

[0042]

[0043] in This represents the partial derivative of the performance index function V with respect to Z.

[0044] Furthermore, in step 4, by solving the partial derivatives of the Hamilton equation, the optimal control input and optimal disturbance input are obtained. Then, the optimal robust fault-tolerant controller is constructed, and the Hamilton-Jacobi-Isaacs equation is established. The specific method is as follows:

[0045] The optimal control input, optimal disturbance input, and optimal performance index function satisfy the following equation:

[0046]

[0047] Where u * ω represents the optimal control input. * V represents the optimal perturbation input. * This represents the optimal performance index function. The optimal performance index function V represents * Take the partial derivative with respect to Z;

[0048] Optimal control input u * The solution can be obtained using the following formula:

[0049]

[0050] Optimal perturbation input ω * The solution can be obtained using the following formula:

[0051]

[0052] By solving equations (12) and (13), the optimal control input u can be obtained. * Optimal perturbation input ω * as follows:

[0053]

[0054]

[0055] It is worth noting that the optimal control input u * The dynamic equations are optimal only if there are no actuator failures. Therefore, the optimal control input u obtained by solving the equations is... * Construct the optimal robust fault-tolerant controller This enables attitude control of a quadcopter UAV with actuator failure, and constructs an optimal robust fault-tolerant controller. As shown in the following formula:

[0056]

[0057] Substituting equations (14) and (15) into equation (11), we obtain the Hamilton-Jacobi-Isaacs equation as follows:

[0058]

[0059] Furthermore, in step 5, an approximate optimal performance index function is obtained using a neural network with a single evaluation structure. The approximate values ​​of the optimal control input and the optimal disturbance input are then obtained. The approximate optimal weight update rate of the evaluation neural network is obtained by solving the gradient descent method. The specific method is as follows:

[0060] The equivalent form of the optimal performance index function and its derivative is as follows:

[0061] V * =W c T Φ(Z)+ξ(Z) (18)

[0062]

[0063] Among them, W c Let Φ(Z) represent the weights of the evaluation neural network, Φ(Z) represent the activation function of the evaluation neural network, and ξ(Z) represent the approximation error of the evaluation neural network. This indicates that Φ(Z) is differentiated with respect to Z. This indicates that ξ(Z) is differentiated with respect to Z;

[0064] Substituting equation (19) into equations (14) and (15), we obtain the equivalent forms of the optimal control input and the optimal disturbance input as follows:

[0065]

[0066]

[0067] in,

[0068] The optimal performance index function V is approximated by a neural network with a single evaluation structure. * As shown in the following formula:

[0069]

[0070] in V represents * The approximate optimal value, W c The approximate optimal value, express Take the partial derivative with respect to Z;

[0071] Therefore, the approximate values ​​of the optimal control input and the optimal disturbance input are as follows:

[0072]

[0073]

[0074] in is u * Approximate value, It is ω * Approximate value;

[0075] Since the Hamilton-Jacobi-Isaacs equations cannot be solved directly, they can be approximated by the following equation:

[0076]

[0077] The error of the neural network is evaluated using the following formula:

[0078]

[0079] According to the gradient descent method, the approximate optimal weight update rate of the evaluation neural network is obtained as follows:

[0080]

[0081] Where ρ > 0 represents the learning rate used to evaluate the neural network.

[0082] An optimal robust fault-tolerant control system for a quadrotor unmanned aerial vehicle (UAV) considering external disturbances is characterized by achieving optimal robust fault-tolerant control of the quadrotor UAV considering external disturbances based on the aforementioned optimal robust fault-tolerant control method for a quadrotor UAV.

[0083] A computer device includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements optimal robust fault-tolerant control of a quadcopter drone considering external disturbances based on the aforementioned optimal robust fault-tolerant control method for quadcopter drones considering external disturbances.

[0084] A computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements optimal robust fault-tolerant control of a quadcopter drone considering external disturbances, based on the aforementioned optimal robust fault-tolerant control method for quadcopter drones considering external disturbances.

[0085] Compared with the prior art, the present invention has the following significant advantages: (1) It adopts a single-evaluation structure neural network of reinforcement learning, thereby avoiding the direct solution of the numerical solution of the Hamilton-Jacobi-Isaacs equation and obtaining an approximately optimal robust fault-tolerant controller. (2) It combines fault-tolerant control theory and reinforcement learning theory. Therefore, when the quadcopter UAV experiences actuator failure, the method of the present invention has extremely strong adaptive and learning capabilities, continuously optimizing the controller to adapt to different flight conditions, and improving the anti-interference capability and fault tolerance capability of the quadcopter UAV. Attached Figure Description

[0086] Figure 1 This is a flowchart of the control algorithm of the method of the present invention.

[0087] Figure 2 It is the basic structure and coordinate system of a quadcopter drone.

[0088] Figure 3 This is a structural block diagram of the method of the present invention. Detailed Implementation

[0089] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0090] To address the failure of some actuators, an improved performance index function is introduced to overcome the adverse effects of the failure on the UAV. In order to cope with the unknown time-varying external disturbance problem, a robust control design is adopted for the attitude controller.

[0091] like Figure 1 As shown, the specific implementation steps of the present invention are as follows:

[0092] Step 1: Establish an attitude control model for a quadrotor UAV with unknown time-varying disturbances and partial actuator failures using the Newton-Euler method. Determine the final attitude dynamics equations of the quadrotor UAV by defining attitude parameters.

[0093] (1) An attitude control model for a quadcopter UAV with unknown disturbances and actuator failures is established using the Newton-Euler method, and the expression is as follows:

[0094]

[0095] The variables in equation (1) are defined as follows: The attitude angles of the UAV are represented by φ, where φ is the roll angle, θ is the pitch angle, and ψ is the yaw angle. The attitude angular velocities of the UAV are represented by roll rate, pitch rate, and yaw rate. The attitude angular accelerations of the UAV are represented by roll acceleration, pitch acceleration, and yaw acceleration; J = diag{J φ J θ J ψ} represents the inertia matrix; Represents the Coriolis term of coupling; This represents the control input torque, where τ ψ =k l k w u φ τ represents the roll angle channel control input torque. θ =k l k w u θ τ represents the input torque for the pitch angle channel control. ψ =k τ u ψ Indicates the yaw angle channel control input torque, k l k is the distance from the motor to the center of mass of the machine body. w and k τ This represents the proportionality coefficient. The input signals represent the roll angle input signal, pitch angle input signal, and yaw angle input signal, respectively. υ1, υ2, υ3, and υ4 represent the rotational speeds of the four motors of the quadcopter drone. These represent the external uncertainty disturbances of roll angle, pitch angle, and yaw angle, respectively; Λ=diag{Λ φ Λ θ Λ ψ} represent the unknown actuator failure factors for roll angle, pitch angle, and yaw angle, respectively. in This represents the upper bound of Λ.

[0096] (2) Define B = diag{k l k w k l k w k τ Equation (1) can be rewritten as follows:

[0097]

[0098] where u=[u φ u θ u ψ ] T This indicates a control input.

[0099] (3) Definition Let the attitude parameters of the UAV be represented. Equation (2) can be rewritten as follows, and the final attitude dynamics equation of the quadcopter UAV can be obtained, as shown in the following expression:

[0100]

[0101] The meanings of each variable are as follows:

[0102] This indicates a disturbance input.

[0103] Step 2: Introduce the reference equation and determine the augmented equation consisting of the tracking error equation and the reference equation;

[0104] The introduced reference equation is as follows:

[0105]

[0106] in This represents the expected value of X; Let φ represent the expected attitude angle of the UAV. d Let θ be the expected roll angle. d Let ψ be the desired pitch angle. d This represents the expected value of the yaw angle. These represent the expected values ​​of the UAV's attitude angular velocities, namely the expected values ​​of roll angular velocity, pitch angular velocity, and yaw angular velocity.

[0107] The tracking error equation is defined as E = XX d Then the derivative of the tracking error equation is as follows:

[0108]

[0109] The augmented equation, composed of the tracking error equation and the reference equation, is expressed as follows:

[0110]

[0111] in In the following text, for the sake of simplicity, we will use... ω represents ω(Z).

[0112] Step 3: Based on the augmented equation, design a performance index function that considers actuator failure and external disturbances, and determine the Hamilton equation;

[0113] Design a performance index function that considers actuator failure and external interference:

[0114]

[0115] Where γ is the discount factor of the performance index function, t represents time, and Q T =diag{Q,0 6×6}, K > 0 is a diagonal matrix, and and All are positive definite symmetric matrices;

[0116] And the coefficient β satisfies For the sake of simplicity, V will be used to represent V(Z) in the following text.

[0117] Taking the derivative of equation (7), we obtain the derivative of the performance index function as follows:

[0118]

[0119] If the first term on the right side of equation (8) equals γV, then equation (8) can be rewritten as:

[0120]

[0121] According to equation (9), the Hamilton equation is determined to be of the following form:

[0122]

[0123] in This represents the partial derivative of the performance index function V with respect to Z.

[0124] Step 4: By solving the partial derivatives of the Hamilton equation, the optimal control input and the optimal disturbance input are obtained. Then, the optimal robust fault-tolerant controller is constructed, and the Hamilton-Jacobi-Isaacs equation is established.

[0125] The optimal control input, optimal disturbance input, and optimal performance index function satisfy the following equation:

[0126]

[0127] Where u* ω represents the optimal control input. * V represents the optimal perturbation input. * This represents the optimal performance index function. The optimal performance index function V represents * Take the partial derivative with respect to Z.

[0128] Optimal control input u * The solution can be obtained using the following formula:

[0129]

[0130] Optimal perturbation input ω * The solution can be obtained using the following formula:

[0131]

[0132] By solving equations (12) and (13), the optimal control input u can be obtained. * Optimal perturbation input ω * as follows:

[0133]

[0134]

[0135] It is worth noting that the optimal control input u * The dynamic equations are optimal only if there are no actuator failures. Therefore, the optimal control input u obtained by solving the equations is... * Construct the optimal robust fault-tolerant controller This enables attitude control of a quadcopter UAV with actuator failure, and constructs an optimal robust fault-tolerant controller. As shown in the following formula:

[0136]

[0137] Substituting equations (14) and (15) into equation (11), we obtain the Hamilton-Jacobi-Isaacs equation as follows:

[0138]

[0139] Because equation (17) is a high-order partial differential equation, it is difficult to obtain an analytical solution by directly solving the equation. Therefore, this specification uses a neural network with a single evaluation structure to approximate the optimal performance index function and solves the equation through reinforcement learning.

[0140] Step 5: Use a neural network with a single evaluation structure to approximate the optimal performance index function, obtain the approximate values ​​of the optimal control input and the optimal disturbance input, and solve for the approximate optimal weight update rate of the evaluation neural network by gradient descent.

[0141] The equivalent form of the optimal performance index function and its derivative is as follows:

[0142]

[0143]

[0144] Among them, W c Let Φ(Z) represent the weights of the evaluation neural network, Φ(Z) represent the activation function of the evaluation neural network, and ξ(Z) represent the approximation error of the evaluation neural network. This indicates that Φ(Z) is differentiated with respect to Z. This indicates that ξ(Z) is differentiated with respect to Z.

[0145] Substituting equation (19) into equations (14) and (15), we obtain the equivalent forms of the optimal control input and the optimal disturbance input as follows:

[0146]

[0147]

[0148] in,

[0149] The optimal performance index function V is approximated by a neural network with a single evaluation structure. * As shown in the following formula:

[0150]

[0151] in V represents * The approximate optimal value, W c The approximate optimal value, express Take the partial derivative with respect to Z.

[0152] Therefore, the approximate values ​​of the optimal control input and the optimal disturbance input are as follows:

[0153]

[0154]

[0155] in is u * Approximate value, It is ω * Approximate value.

[0156] Since the Hamilton-Jacobi-Isaacs equations cannot be solved directly, they can be approximated by the following equation:

[0157]

[0158] The error of the neural network is evaluated using the following formula:

[0159]

[0160] According to the gradient descent method, the approximate optimal weight update rate of the evaluation neural network is obtained as follows:

[0161]

[0162] Where ρ > 0 represents the learning rate used to evaluate the neural network.

[0163] The Lyapunov function is designed as follows:

[0164]

[0165] in To evaluate the weight error of a neural network, the following formula can be solved:

[0166]

[0167] in

[0168] Differentiating equation (28) yields:

[0169]

[0170] Substituting equations (11), (14), and (15) into equation (30), we get:

[0171]

[0172] In equation (31) It can be simplified to the following formula:

[0173]

[0174] in It is a constant and greater than zero. It is a positive number.

[0175] 2β in equation (31) 2 ||ω * || 2It can be simplified to the following formula:

[0176]

[0177] in It is a constant and greater than zero. It is a positive number.

[0178] In equation (31) It can be simplified to the following formula:

[0179]

[0180] in It is a positive number.

[0181] In equation (31) Satisfy the following formula:

[0182]

[0183] Where ||ξ e ||≤η3 is a positive constant.

[0184] Substituting equations (32)-(35) into equation (31), and Z T Q T Z = E T QE, can be obtained

[0185] The derivative of the Lyapunov function is less than zero when equation (36) satisfies the following conditions:

[0186]

[0187]

[0188] in It is a constant and greater than zero.

[0189] Substituting equations (37) and (38) into equation (36), we get

[0190]

[0191] Equation (39) shows that the tracking error E and the weight error of the evaluation neural network are known. It is uniformly bounded.

[0192] Step 6: Solve for the approximate optimal weight update rate of the evaluation neural network in Step 5, obtain the approximate optimal weight of the evaluation neural network, and integrate it with the optimal robust fault-tolerant controller in Step 4 to obtain the final approximate optimal robust fault-tolerant controller.

[0193] Given a set of initial values ​​for the approximate optimal weights of the evaluation neural network, and substituting them into equation (27), by iteratively solving equation (27), the approximate optimal weights of the evaluation neural network can be obtained. Substituting the obtained approximate optimal weights of the evaluation neural network into equation (23) yields the approximate value of the optimal control input. Then, substituting the approximate value of the optimal control input into equation (16), the approximate optimal robust fault-tolerant controller is obtained as follows:

[0194]

[0195] Under the action of the near-optimal robust fault-tolerant controller, the quadcopter drone can effectively suppress the adverse effects of actuator failure and external disturbances, ensuring that the quadcopter drone can fly stably.

[0196] This invention also proposes an optimal robust fault-tolerant control system for quadrotor UAVs that considers external disturbances. The system is characterized by achieving optimal robust fault-tolerant control of quadrotor UAVs that considers external disturbances based on the aforementioned optimal robust fault-tolerant control method for quadrotor UAVs.

[0197] A computer device includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements optimal robust fault-tolerant control of a quadcopter drone considering external disturbances based on the aforementioned optimal robust fault-tolerant control method for quadcopter drones considering external disturbances.

[0198] A computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements optimal robust fault-tolerant control of a quadcopter drone considering external disturbances, based on the aforementioned optimal robust fault-tolerant control method for quadcopter drones considering external disturbances.

[0199] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0200] The embodiments described above are merely illustrative of several implementation methods of this application, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of this application. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these modifications and improvements all fall within the protection scope of this application. Therefore, the protection scope of this application should be determined by the appended claims.

Claims

1. An optimal robust fault-tolerant control method for a quadcopter unmanned aerial vehicle considering external disturbances, characterized in that, The steps are as follows: Step 1: Establish an attitude control model for a quadrotor UAV with unknown time-varying disturbances and partial actuator failures using the Newton-Euler method. Determine the final attitude dynamics equations of the quadrotor UAV by defining attitude parameters. Step 2: Introduce the reference equation and determine the augmented equation consisting of the tracking error equation and the reference equation; Step 3: Based on the augmented equation, design a performance index function that considers actuator failure and external disturbances, and determine the Hamilton equation; Step 4: By solving the partial derivatives of the Hamilton equation, the optimal control input and the optimal disturbance input are obtained. Then, the optimal robust fault-tolerant controller is constructed, and the Hamilton-Jacobi-Isaacs equation is established. Step 5: Use a neural network with a single evaluation structure to approximate the optimal performance index function, obtain the approximate values ​​of the optimal control input and the optimal disturbance input, and solve for the approximate optimal weight update rate of the evaluation neural network by gradient descent method; Step 6: Based on the approximate optimal weight update rate of the evaluation neural network in Step 5, solve for the approximate optimal weight of the evaluation neural network, and integrate it with the optimal robust fault-tolerant controller in Step 4 to obtain the final approximate optimal robust fault-tolerant controller, thus completing the optimal robust fault-tolerant control of the quadcopter UAV.

2. The optimal robust fault-tolerant control method for a quadcopter UAV considering external disturbances according to claim 1, characterized in that, Step 1: Establish an attitude control model for a quadrotor UAV with unknown time-varying disturbances and partial actuator failures using the Newton-Euler method. Define attitude parameters to determine the final attitude dynamics equations of the quadrotor UAV. The specific method is as follows: (1) An attitude control model for a quadcopter UAV with unknown disturbances and actuator failures is established using the Newton-Euler method, and the expression is as follows: (1)； The variables in equation (1) are defined as follows: This represents the attitude angle of the drone, where This is the roll angle. The pitch angle, Yaw angle; The attitude angular velocities of the UAV are represented by roll rate, pitch rate, and yaw rate. The attitude angular accelerations of the UAV are represented by roll acceleration, pitch acceleration, and yaw acceleration. Represents the inertia matrix; Represents the Coriolis term of coupling; This indicates the control input torque, where This indicates the input torque for the roll angle channel control. This indicates the input torque for the pitch angle channel control. This indicates the yaw angle channel control input torque. This is the distance from the motor to the center of mass of the machine body. and This represents the proportionality coefficient. , , The input signals represent the roll angle input signal, pitch angle input signal, and yaw angle input signal, respectively. , , and This indicates the rotational speed of the four motors in a quadcopter drone; These represent external uncertainty disturbances in roll angle, pitch angle, and yaw angle, respectively. These represent the unknown actuator failure factors for roll angle, pitch angle, and yaw angle, respectively. ,in express The upper bound; (2) Definition Equation (1) can be rewritten as follows: (2)； in Indicates control input; (3) Definition Let the attitude parameters of the UAV be represented. Equation (2) can be rewritten as follows, and the final attitude dynamics equation of the quadcopter UAV can be obtained, as shown in the following expression: (3)； The meanings of each variable are as follows: , , , This indicates a disturbance input.

3. The optimal robust fault-tolerant control method for a quadcopter UAV considering external disturbances according to claim 2, characterized in that, Step 2: Introduce the reference equation and determine the augmented equation composed of the tracking error equation and the reference equation. The specific method is as follows: The introduced reference equation is as follows: (4)； in express Expected value; This represents the expected attitude angle of the UAV, where This is the expected value of the roll angle. The expected value of the pitch angle. This represents the expected value of the yaw angle. These represent the expected values ​​of the UAV's attitude angular velocities, namely the expected values ​​of roll angular velocity, pitch angular velocity, and yaw angular velocity; The tracking error equation is defined as follows: Then the derivative of the tracking error equation is as follows: (5)； The augmented equation, composed of the tracking error equation and the reference equation, is expressed as follows: (6)； in , , , In the following text, for the sake of simplicity, we will use... , They represent , .

4. The optimal robust fault-tolerant control method for a quadcopter UAV considering external disturbances according to claim 3, characterized in that, Step 3: Based on the augmented equation, design a performance index function that considers actuator failure and external disturbances, and determine the Hamilton equation. The specific method is as follows: Design a performance index function that considers actuator failure and external interference: (7)； in Here, t represents the discount factor for the performance index function. , K>0 is a diagonal matrix, and and All are positive definite symmetric matrices; And coefficient satisfy For simplicity, V is used to represent V(Z); Taking the derivative of equation (7), we obtain the derivative of the performance index function as follows: (8)； The first term on the right side of equation (8) equals Then equation (8) can be rewritten as: (9)； According to equation (9), the Hamilton equation is determined to be of the following form: (10)； in This represents the partial derivative of the performance index function V with respect to Z.

5. The optimal robust fault-tolerant control method for a quadcopter UAV considering external disturbances according to claim 4, characterized in that, Step 4: By solving the partial derivatives of the Hamilton equation, the optimal control input and optimal disturbance input are obtained. Then, the optimal robust fault-tolerant controller is constructed, and the Hamilton-Jacobi-Isaacs equation is established. The specific method is as follows: The optimal control input, optimal disturbance input, and optimal performance index function satisfy the following equation: (11)； Where u* represents the optimal control input. V* represents the optimal perturbation input, and V* represents the optimal performance index function. This represents the partial derivative of the optimal performance index function V* with respect to Z; The optimal control input u* can be solved by the following formula: (12)； Optimal perturbation input The solution can be obtained using the following formula: (13)； By solving equations (12) and (13), the optimal control input u* and the optimal disturbance input can be obtained. as follows: (14)； (15)； It is worth noting that the optimal control input u* only guarantees that the dynamic equations are optimal when there are no actuator failures. Therefore, the optimal robust fault-tolerant controller is constructed by solving for the optimal control input u*. This enables attitude control of a quadcopter UAV with actuator failure, and constructs an optimal robust fault-tolerant controller. As shown in the following formula: (16)； Substituting equations (14) and (15) into equation (11), we obtain the Hamilton-Jacobi-Isaacs equation as follows: (17)。 6. The optimal robust fault-tolerant control method for a quadcopter UAV considering external disturbances according to claim 5, characterized in that, Step 5: Using a neural network with a single evaluation structure to approximate the optimal performance index function, obtain the approximate values ​​of the optimal control input and the optimal disturbance input. Solve using the gradient descent method to obtain the approximate optimal weight update rate of the evaluation neural network. The specific method is as follows: The equivalent form of the optimal performance index function and its derivative is as follows: (18)； (19)； Among them, W c The weights represent the evaluation values ​​of the neural network. This represents the activation function for evaluating a neural network. This represents the approximation error used to evaluate the neural network. express right Differentiate, express right Differentiate; Substituting equation (19) into equations (14) and (15), we obtain the equivalent forms of the optimal control input and the optimal disturbance input as follows: (20)； (21)； in, , ; The optimal performance index function V* is approximated by a neural network with a single evaluation structure as follows: (22)； in This represents the approximate optimal value of V*. express The approximate optimal value, express right Find the partial derivative; Therefore, the approximate values ​​of the optimal control input and the optimal disturbance input are as follows: (23)； (24)； in yes Approximate value, yes Approximate value; Since the Hamilton-Jacobi-Isaacs equations cannot be solved directly, they can be approximated by the following equation: (25)； The error of the neural network is evaluated using the following formula: (26)； According to the gradient descent method, the approximate optimal weight update rate of the evaluation neural network is obtained as follows: (27)； in The learning rate is used to evaluate the neural network. .

7. An optimal robust fault-tolerant control system for a quadcopter unmanned aerial vehicle considering external disturbances, characterized in that, Based on the optimal robust fault-tolerant control method for quadrotor UAVs considering external disturbances as described in any one of claims 1-6, optimal robust fault-tolerant control of quadrotor UAVs considering external disturbances is achieved.

8. A computer device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein when the processor executes the computer program, it implements optimal robust fault-tolerant control of a quadcopter drone considering external disturbances based on the optimal robust fault-tolerant control method for a quadcopter drone considering external disturbances as described in any one of claims 1-6.

9. A computer-readable storage medium having a computer program stored thereon, wherein when the computer program is executed by a processor, it implements optimal robust fault-tolerant control of a quadcopter drone considering external disturbances based on the optimal robust fault-tolerant control method for a quadcopter drone considering external disturbances as described in any one of claims 1-6.

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