An Adaptive Parameter Optimization Method for L1 UAV Based on an Improved Multi-Objective Particle Swarm Optimization Algorithm

Abstract

This invention belongs to the field of UAV flight control technology, and particularly relates to a method for optimizing L1 adaptive parameters of UAVs based on an improved multi-objective particle swarm optimization algorithm. The method includes the following steps: S1, establishing a six-degree-of-freedom nonlinear dynamic model of the UAV, and constructing a desired maneuver mission model based on this model; S2, designing longitudinal and lateral channel attitude controllers for the aircraft based on an L1 adaptive controller, and selecting core parameters that have a critical impact on control performance to form a set of parameters to be optimized; S3, setting multiple conflicting optimization objectives for the maneuver mission, and establishing corresponding performance index functions to form a multi-objective optimization problem; S4, using an improved multi-objective particle swarm optimization algorithm to optimize the parameters. This scheme can efficiently optimize L1 controller parameters and significantly improve the trajectory tracking accuracy, response speed, and anti-disturbance capability of the UAV under high-maneuver conditions.

Description

Technical Field

[0001] This invention belongs to the field of UAV flight control technology, and particularly relates to a method for optimizing L1 adaptive parameters of UAVs based on an improved multi-objective particle swarm optimization algorithm. Background Technology

[0002] When UAVs perform high-maneuver missions (such as high angle-of-attack climbs, rapid rolls, and Herbst maneuvers) near the boundary of their flight envelope, they face severe challenges such as deteriorated stability, insufficient control torque, and severe coupling between climb and roll control. To ensure flight stability and improve mission adaptability, their maneuver control systems need to have higher robustness and dynamic response capabilities.

[0003] L1 adaptive technology estimates the total internal and external disturbances in real time through a state observer, generates a compensation signal by an adaptive compensation controller, and filters out high-frequency components in the compensation signal through a low-pass filter. This effectively compensates for system uncertainties while avoiding the excitation of unmodeled high-frequency dynamics by high-gain control. Therefore, L1 adaptive control has significant advantages over traditional adaptive control methods in high-dynamic, strongly coupled, and highly uncertain UAV high-maneuver flight scenarios.

[0004] However, the L1 adaptive controller has many parameters to be tuned, and these parameters are tightly coupled and mutually restrictive. For example, increasing the bandwidth can enhance the disturbance suppression capability, but may reduce robust stability; increasing the adaptive gain can speed up the compensation response, but may easily induce oscillations. The multi-parameter, strongly coupled, and conflicting control objectives make parameter tuning extremely complex. Existing engineering practices mostly rely on empirical trial and error or simple cyclic tuning, making it difficult to obtain the globally optimal parameter configuration among multiple conflicting objectives, thus limiting the performance potential of the L1 controller under complex maneuvering conditions.

[0005] In the existing technology, attempts have been made to use intelligent optimization algorithms such as genetic algorithms and particle swarm optimization to address the above-mentioned parameter tuning problem. However, traditional single-objective optimization methods can usually only optimize a single performance index and cannot take into account multiple control objectives. Typical multi-objective optimization algorithms (such as NSGA-II) have problems such as slow convergence speed and parameter sensitivity when dealing with continuous space optimization. Particle swarm optimization has advantages such as fast convergence and fewer parameters, but its direct extension to multi-objective scenarios still needs improvement. Its selection of excellent individuals requires a certain degree of random selection from individuals in the Pareto front, which is particularly disadvantageous in applications such as flight control where reliability and robustness requirements are extremely high.

[0006] Therefore, there is an urgent need for an L1 adaptive controller parameter optimization method based on multi-objective particle swarm optimization to obtain the optimal parameter set that can take into account multiple conflicting performance indicators, so as to give full play to the comprehensive control performance of L1 adaptive control under the high maneuvering conditions of UAVs. Summary of the Invention

[0007] In view of this, the present invention aims to provide an L1 adaptive parameter optimization method for UAVs based on an improved multi-objective particle swarm optimization algorithm, so as to solve the problem that it is difficult to efficiently and stably obtain the global optimal parameter set under multi-parameter and multi-objective conflicts in the L1 adaptive controller during high-maneuver flight of UAVs.

[0008] To achieve the above objectives, the technical solution created by this invention is implemented as follows: An adaptive parameter optimization method for L1 drones based on an improved multi-objective particle swarm optimization algorithm includes the following steps: S1. Establish a six-degree-of-freedom nonlinear dynamic model of the UAV, and construct the desired maneuver mission model based on this model; S2. Design the longitudinal and lateral channel attitude controllers for the aircraft based on the L1 adaptive controller, and select the core parameters that have a key impact on the control performance to form a set of parameters to be optimized. S3. For maneuver missions, set multiple conflicting optimization objectives and establish corresponding performance index functions to form a multi-objective optimization problem; S4. Parameter optimization is performed using an improved multi-objective particle swarm optimization algorithm; S4 includes the following sub-steps: S401. Initialize controller parameters; wherein, population initialization is performed using parameter encoding. S402. Initialize external archive; S403. Determine the Pareto dominance relationship and perform non-dominated sorting on the population in S401 and the individuals in the external archive in S402 to divide different non-dominated layers. S404. Perform congestion calculation; S405. A weighted fitness-based hybrid selection strategy is adopted as the globally optimal selection strategy. S406. Update the velocity and position of each particle according to the standard particle swarm algorithm; S407. Based on the Pareto dominance relationship, perform individual optimal updates on the position of each particle; S408. Update and trim external archives; S409. Perform mutation operation; apply polynomial mutation to some particles in each iteration; S410, Iteration Termination and Optimal Parameter Output.

[0009] Furthermore, in S2, for the longitudinal channel attitude controller, Introducing a state observer: ; Define state estimation error ,but: ; set up ,but ; Introducing the projection operator as an adaptive law: ; The pitch rate control law is designed as follows: ; The low-pass filter is of first-order form. ; in, For pitch angular velocity, For pitch angular velocity state estimation error, The derivative of the pitch angular velocity state estimation error, For pitch acceleration, For the state observer to observe pitch angular velocity values, The derivative of the pitch angular velocity value observed by the state observer, For reference model bandwidth, For nominal rudder efficiency, For elevator deflection commands, For system lumped disturbances, For the total disturbance of the state observer, The derivative of the total perturbation of the state observer, For adaptive gain, For low-pass filters, For filter bandwidth, s For the Laplace operator.

[0010] Furthermore, in S2, for the lateral channel attitude controller, Introducing a state observer: ; Define state estimation error ,but: ; remember ,but ; Introducing the projection operator as an adaptive law: ; The pitch rate control law is designed as follows: ; The low-pass filter is of first-order form. ; in, For roll angular velocity, For the roll angular velocity state estimation error, The derivative of the roll angular velocity state estimation error, For roll angular acceleration, For the state observer to observe the roll angular velocity value, The derivative of the roll angular velocity value observed by the state observer, For reference model bandwidth, For nominal rudder efficiency, For aileron deflection commands, For system lumped disturbances, For the total disturbance of the state observer, The derivative of the total perturbation of the state observer, For adaptive gain, For low-pass filters, Let be the filter bandwidth and s be the Laplace operator.

[0011] Furthermore, in S2, the parameters that the L1 adaptive controller needs to optimize include: , , The parameters are expressed as a linear relationship with dynamic pressure, specifically: ; in, For dynamic pressure, The slope term for the linear relationship between adaptive gain and dynamic pressure. The intercept term for the linear relationship between adaptive gain and dynamic pressure. The slope term for linearly relating the bandwidth and dynamic pressure of the reference model. The intercept term for the linear relationship between the bandwidth and dynamic pressure of the reference model. The slope term for linearly relating the low-pass filter to dynamic voltage. This is the intercept term for the linear correlation between the low-pass filter and dynamic voltage; At this point, there are six parameters to be optimized, namely... , , , , , .

[0012] Furthermore, in S3, settings , , , Four optimization objectives, among which, and Corresponding to longitudinal maneuvering, and Corresponding to lateral maneuvers; In S405, the initial basic weight vectors for the four optimization objectives are set according to engineering preferences: ; in, for Optimize the weight values ​​of the target. for Optimize the weight values ​​of the target. for Optimize the weight values ​​of the target. for Optimize the weight values ​​of the target; For each non-dominated solution in the external archive Calculate its weighted fitness: ; in, For the first The normalized values ​​of the targets; The weights for the r-th optimization objective; The normalization method is as follows: ; in, and These are the current external archives, number 1 and 2 respectively. The minimum and maximum values ​​of each target.

[0013] Furthermore, in S405, when a hybrid probability selection strategy is adopted: With probability The individual with the lowest weighted fitness in the external archive is selected as the global optimal guide for the current particle. ; With probability Randomly select one individual from the top 20% of those with the highest crowding levels as... .

[0014] Furthermore, in S401, the six controller parameters to be optimized constitute the position vector of a particle, using a real number encoding method, and the position of each particle is composed of the physical values ​​of the six parameters to be optimized; Let the first The positions of the particles are: ; in, The basic value of adaptive gain, The basic value of the low-pass filter bandwidth, The basic value of the reference model bandwidth, The slope term when adaptive gain is linearly correlated with dynamic pressure. The slope term when the bandwidth of a low-pass filter is linearly correlated with dynamic pressure. This is the slope term when the bandwidth of the reference model is linearly correlated with dynamic pressure; Initialize the particle's velocity to a zero vector, i.e. Population size set to .

[0015] Furthermore, in S402, when initializing the external archive, the fitness value of each particle in the population on the four optimization objectives is calculated. Then, based on the Pareto dominance relationship, all non-dominated solutions are filtered out and stored in an external archive; the initial maximum capacity of the archive is set to... Mmax =50.

[0016] Furthermore, in S406, the velocity update formula is: ; in, For inertial weights, Let be the particle velocity at time t+1. Let be the particle velocity at time t. Let be the particle position at time t; For the first The optimal position of each particle The globally optimal leader selected according to step S405; , As the learning factor, take c 1= c 2 = 1.5; for A random number that is uniformly distributed within an interval; Using a linear decreasing strategy, take , ;but: ;in, t For the current iteration number, This represents the maximum number of iterations. The position update formula is: ; in, The particle position at time t+1 The particle position at time t Let t be the particle velocity at time t+1.

[0017] Furthermore, in S409, the mutation probability of the polynomial mutation applied to the particle is set to... For the selected particle, its first... Each parameter is variable according to the following formula: ;in, For the mutated first New values ​​for each parameter For the selected particle's first The current value of each parameter For the first The upper bound of the search range for each parameter For the first The lower bound of the search range for each parameter These are the polynomial variation perturbation coefficients; in, It is generated by the following multinomial distribution: ; in, for Uniform random numbers; Pm is the distribution index. .

[0018] Compared with the prior art, the present invention can achieve the following beneficial effects: 1. This invention solves the problem that traditional parameter tuning methods are difficult to obtain the global optimal solution under multi-objective conflict by constructing a multi-objective particle swarm optimization framework and combining external archiving and adaptive selection strategies. This allows for the efficient acquisition of optimal L1 controller parameters and improves the trajectory tracking accuracy, response speed, anti-disturbance capability and stability of UAVs during maneuvers.

[0019] 2. This invention improves the global optimization capability under multi-objective conflict: by constructing a multi-objective particle swarm optimization framework and introducing a weighted fitness optimal selection strategy, it overcomes the problems of unclear convergence direction and poor reliability caused by the random selection of individuals at the Pareto front in traditional multi-objective particle swarm algorithms, and can stably converge to the global optimal parameter solution of the multi-conflict control objective.

[0020] 3. This invention can balance convergence speed and population diversity: By adopting a hybrid probability selection mechanism, it maintains population diversity while ensuring fast convergence, effectively avoiding premature convergence. It solves the defects of slow convergence and premature convergence of algorithms such as NSGA-II in continuous space optimization. Compared with traditional empirical trial and error or simple cyclic tuning methods, this invention realizes automated and efficient optimization of multiple parameters of L1 controller, reduces manual debugging costs, and improves the feasibility of engineering applications.

[0021] 4. This invention can significantly improve the high-maneuver control performance of UAVs and enhance the robustness and reliability of the controller: By deeply integrating the improved algorithm with the L1 adaptive controller, the trajectory tracking accuracy, response speed and anti-disturbance capability of the UAV are significantly improved when performing high-maneuver tasks close to the boundary of the flight envelope, ensuring stability and mission adaptability. At the same time, by optimizing the obtained parameter set, the L1 adaptive controller can effectively compensate for the total disturbance inside and outside the system without exciting high-frequency dynamics, especially under the maneuver conditions with severe lift-roll coupling, it exhibits higher robustness and flight reliability. Attached Figure Description

[0022] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments and descriptions of the invention are used to explain the invention and do not constitute an undue limitation of the invention. In the drawings: Figure 1 A block diagram of the longitudinal channel L1 adaptive controller architecture in the optimization method described in the embodiments of the present invention; Figure 2 A block diagram of the lateral channel L1 adaptive controller architecture in the optimization method described in the embodiments of the present invention; Figure 3 The flowchart of the improved multi-objective particle swarm optimization algorithm in the optimization method described in the embodiments of the present invention is shown. Detailed Implementation

[0023] To make the purpose, technical solution, and advantages of this invention clearer, the following description is provided in conjunction with the appendix. Figure 1-3 The present invention will be further described in detail below with reference to specific embodiments. It should be understood that the specific embodiments described herein are only for explaining the present invention and do not constitute a limitation thereof.

[0024] It should be noted that, unless otherwise specified, the embodiments and features described in the present invention can be combined with each other.

[0025] In the description of this invention, it should be understood that the terms "center," "longitudinal," "lateral," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," and "outer," etc., indicating orientations or positional relationships based on the orientations or positional relationships shown in the accompanying drawings, are only for the convenience of describing this 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 on this invention. Furthermore, the terms "first," "second," etc., are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of indicated technical features. Thus, features defined with "first," "second," etc., may explicitly or implicitly include one or more of that feature. In the description of this invention, unless otherwise stated, "a plurality of" means two or more.

[0026] In the description of this invention, it should be noted that, unless otherwise explicitly specified and limited, the terms "installation," "connection," and "linking" 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 will understand the specific meaning of the above terms in this invention based on the specific circumstances.

[0027] The following will refer to the appendix. Figure 1-3 The invention will be described in detail with reference to the embodiments.

[0028] An adaptive parameter optimization method for L1 drones based on an improved multi-objective particle swarm optimization algorithm includes the following steps: S1. Establish a six-degree-of-freedom nonlinear dynamic model of the UAV, and build the desired maneuver mission model based on the model, which will serve as a simulation verification environment for subsequent controller parameter optimization.

[0029] First, a twelve-state, six-degree-of-freedom nonlinear dynamic model of the supersonic UAV is established. In this embodiment, the North-East-Earth (NED) coordinate system is used as the navigation coordinate system, and the azimuth angle of the UAV is set as follows. The pitch angle is The roll angle is The coordinate transformation matrix from the ground coordinate system to the body coordinate system is: .

[0030] The transformation between the airflow coordinate system and the body coordinate system is determined by the flight angle of attack. and sideslip angle The transformation matrix is ​​determined as follows: .

[0031] The translational dynamics equations of the UAV are derived from the coordinate transformation matrix: .

[0032] Similarly, the rotational dynamics equations of the UAV can be derived: .

[0033] in, for External torque in the axial direction; for External torque in the axial direction; for External torque in the axial direction; The acceleration component in the x-axis (vertical axis, forward) direction of the body coordinate system; The acceleration component in the y-axis (horizontal axis, to the right) of the body coordinate system; This represents the acceleration component along the z-axis (vertical axis, downward) of the body coordinate system. m This refers to the total mass of the drone; g This refers to the local gravitational acceleration. v The linear velocity component in the y-axis (horizontal axis, to the right) of the body coordinate system; r The angular velocity component (yaw rate) in the z-axis (yaw axis) direction of the body coordinate system; This refers to the angular acceleration component (yaw acceleration) along the z-axis of the body coordinate system. w The linear velocity component along the z-axis (vertical axis, downward) of the body coordinate system; q The angular velocity component (pitch angular velocity) in the y-axis (pitch axis) direction of the body coordinate system. This refers to the angular acceleration component (pitch acceleration) along the y-axis of the body coordinate system. p The angular velocity component (roll angular velocity) in the x-axis (roll axis) direction of the body coordinate system. This refers to the angular acceleration component (roll angular acceleration) along the x-axis of the body coordinate system. u The linear velocity component in the x-axis (vertical axis, forward) direction of the body coordinate system; T The thrust generated by the engine is along the positive x-axis of the airframe coordinate system; D This represents aerodynamic drag, along the negative x-axis of the airflow coordinate system (opposite to the airspeed vector). L It is the aerodynamic lift force, along the negative z-axis of the airflow coordinate system (perpendicular to the airspeed vector upwards). Z This is the aerodynamic lateral force, along the positive y-axis of the airflow coordinate system; to The inertia coefficient; Inertia coefficient ; Inertia coefficient ; Inertia coefficient ; Inertia coefficient ; Inertia coefficient ; Inertia coefficient ; Inertia coefficient ; Inertia coefficient ; Inertia coefficient ; ; Let x be the moment of inertia of the machine body about the x-axis; Let y be the moment of inertia of the machine body about the y-axis; The moment of inertia of the machine body about the z-axis; It is the product of inertia in the xz plane; This is the applied torque (rolling torque) acting on the center of mass along the x-axis of the machine body. The pitching moment is the external torque (pitching moment) acting on the center of mass along the y-axis of the aircraft. This is the external torque (yawing torque) acting on the center of mass along the z-axis of the aircraft.

[0034] Based on the coordinate system transformation relationship, the kinematic equations for translation and rotation are supplemented as follows: .

[0035] .

[0036] in, The linear velocity component (northward ground speed) of the x-axis in the NED navigation coordinate system. The linear velocity component (eastward ground speed) of the y-axis in the NED navigation coordinate system. The linear velocity component (ground velocity) of the z-axis (ground direction) in the NED navigation coordinate system. The linear velocity components along the x-axis (vertical axis, forward) of the body coordinate system. The linear velocity component along the y-axis (horizontal axis, to the right) of the body coordinate system. The linear velocity component along the z-axis (vertical axis, downward) of the body coordinate system. For the roll angular velocity of the ground coordinate system, For the pitch angular velocity in the ground coordinate system, Yaw angular velocity in ground coordinate system The angular velocity component (roll angular velocity) in the x-axis (roll axis) direction of the body coordinate system. The angular velocity component (pitch angular velocity) in the y-axis (pitch axis) direction of the body coordinate system. The angular velocity component (yaw rate) in the z-axis (yaw axis) direction of the body coordinate system.

[0037] In this embodiment, the above equations are numerically solved using the 6DOFECEF module in the MATLAB / Simulink platform, and the aerodynamic coefficients are obtained through a pre-calculated three-dimensional interpolation table. In this embodiment, it is preferred to use the Simulink platform.

[0038] Next, maneuver commands are generated. To verify the UAV's response to control signals, this embodiment uses rapid longitudinal altitude switching and lateral S-turn maneuvers as verification tasks. The core of the rapid longitudinal altitude switching maneuver is the multiple step switching of pitch angle commands. The core objective of the S-turn maneuver is to make continuous bidirectional rolls and heading adjustments. The conditions for maneuvering start are set as follows: the indicated airspeed is stable above 100m / s to ensure that the rudder effect is insufficient at low speeds, which may cause the maneuver to fail. At the same time, the average sea level height is above 3000m to avoid low-altitude airflow disturbances and terrain limitations.

[0039] During maneuver execution, the command generator controls the pitch and roll angles by controlling the normal overload. The roll angle command is derived from the normal overload and the gravity component. ;in, This is the roll angle command. For the overload of Dharma image, A constant with a value of 1 or -1, indicating whether the aircraft is rolling left or right.

[0040] S2. Design the longitudinal and lateral channel attitude controllers of the aircraft based on the L1 adaptive controller, and select the core parameters that have a key impact on the control performance to form a set of parameters to be optimized. In this embodiment, the inner loop attitude controller of the UAV is designed using L1 adaptive control technology. The design process of the controller is as follows.

[0041] For the longitudinal channel attitude controller, the kinematic equation for the pitch angle is: ;in, pitch angular velocity in the ground coordinate system Pitch angular velocity in body coordinate system, This refers to the yaw rate in the body coordinate system.

[0042] The equations of motion for rotation, after simplification, are as follows: ;in, Pitch acceleration in body coordinate system, for External torque in the axial direction For the roll angular velocity in the body coordinate system, Yaw angular velocity in the body coordinate system The moment of inertia of the body about the x-axis, The moment of inertia of the body about the y-axis, Let be the moment of inertia of the machine body about the z-axis.

[0043] The general expression for the pitching moment M is: ;in, Zero-lift pitch moment coefficient, For longitudinal static stability derivative, To improve elevator control efficiency, For elevator deflection commands, For pitch damping derivative, For dimensionless pitch angular velocity, For wing reference area, It is the average aerodynamic chord length of the wing.

[0044] Combining and rearranging the above formulas, we get: .

[0045] in, Let the angle of attack be the flight angle. From the above equation, it can be seen that... It is not only directly controlled by the elevator, but also by... , , To simplify control design, the nonlinear coupling terms caused by factors such as [various factors] are treated as a total disturbance and estimated and compensated by the controller. The above equation can be rewritten as: .

[0046] make: .

[0047] but: ;in, This represents the total system disturbance term.

[0048] The state-space equation of the object required for L1 adaptation is: ;in, For system state variables, The first derivative of the state variable, Output variables for the system For input matrix coefficients, To output matrix coefficients, For reference model bandwidth, For equivalent control gain coefficient, For system control input, State coupling coefficient, This is the total disturbance term.

[0049] Furthermore, suppose , , and order , .

[0050] The system can then be written as: ;in, For pitch angular velocity, For elevator control gain, For elevator deflection commands, This is the lumped disturbance of the system.

[0051] Introducing a state observer: .

[0052] Define state estimation error ,but: ; set up ,but .

[0053] Introducing the projection operator as an adaptive law: .

[0054] The pitch rate control law is designed as follows: .

[0055] The low-pass filter is of first-order form. .

[0056] in, For pitch angular velocity, For pitch angular velocity state estimation error, The derivative of the pitch angular velocity state estimation error, For pitch acceleration, For the state observer to observe pitch angular velocity values, The derivative of the pitch angular velocity value observed by the state observer, For reference model bandwidth, For nominal rudder efficiency, For elevator deflection commands, For system lumped disturbances, For the total disturbance of the state observer, The derivative of the total perturbation of the state observer, For adaptive gain, For low-pass filters, Let be the filter bandwidth and s be the Laplacian operator; where, t represents time. The total perturbation of the state observer in the time domain. The total disturbance of the state observer in the time-frequency domain is transformed into the frequency domain, which is a common expression in the control field.

[0057] The system block diagram of the longitudinal channel attitude controller is as follows: Figure 1 As shown: Among them, To determine the proportional gain between pitch angular velocity control values ​​based on pitch angle error.

[0058] For the lateral channel attitude controller, the kinematic equation for the roll angle is: ;in, For the roll angular velocity in the ground coordinate system, For the roll angular velocity in the body coordinate system, Yaw angular velocity in the body coordinate system The pitch angular velocity is given in the body coordinate system.

[0059] The equations of motion for rotation, after simplification, are as follows: ;in, For the roll acceleration in the body coordinate system, For rolling torque, Pitch angular velocity in body coordinate system, Yaw angular velocity in the body coordinate system The moment of inertia of the body about the x-axis, The moment of inertia of the body about the y-axis, Let be the moment of inertia of the body about the y-axis.

[0060] The general expression for the rolling torque L is: ;in, Sideslip angle, The derivative of the rolling torque with respect to the sideslip angle, The derivative of the rolling moment with respect to the aileron deflection angle, The derivative of the rolling moment with respect to the rudder deflection angle, The derivative of the rolling torque with respect to the dimensionless rolling angular velocity, The derivative of the rolling torque with respect to the dimensionless yaw rate, For aileron deflection commands, For rudder deflection command, For dimensionless roll angular velocity, For dimensionless pitch angular velocity, For dimensionless yaw rate, For wing reference area, For wingspan.

[0061] Combining and rearranging the above formulas, we get: .

[0062] in, Let the sideslip angle be the angle between the two sideslip angles. As can be seen from the above formula, It is not only directly controlled by the ailerons, but also coupled with the rudder, and by... , , To simplify control design, the nonlinear coupling terms caused by factors such as [variable name] are treated as a total disturbance and estimated and compensated by the controller. The above equation can be rewritten as: .

[0063] make: .

[0064] but: ;in, This represents the total system disturbance term.

[0065] The form of the state-space equation of the object required by L1 adaptation: ;in, For system state variables, The first derivative of the state variable, Output variables for the system For input matrix coefficients, To output matrix coefficients, For reference model bandwidth, For equivalent control gain coefficient, For system control input, State coupling coefficient, This is the total disturbance term.

[0066] Furthermore, suppose , , and order , .

[0067] The system can then be written as: ;in, For roll angular velocity, For aileron control gain, For aileron deflection commands, This is the lumped disturbance of the system.

[0068] Introducing a state observer: .

[0069] Define state estimation error ,but: .

[0070] remember ,but .

[0071] Introducing the projection operator as an adaptive law: .

[0072] The pitch rate control law is designed as follows: ; The low-pass filter is of first-order form. .

[0073] in, For roll angular velocity, For the roll angular velocity state estimation error, The derivative of the roll angular velocity state estimation error, For roll angular acceleration, For the state observer to observe the roll angular velocity value, The derivative of the roll angular velocity value observed by the state observer, For reference model bandwidth, For nominal rudder efficiency, For aileron deflection commands, For system lumped disturbances, For the total disturbance of the state observer, The derivative of the total perturbation of the state observer, For adaptive gain, For low-pass filters, Let be the filter bandwidth and s be the Laplacian operator; where, t represents time. The total perturbation of the state observer in the time domain. The total disturbance of the state observer in the time-frequency domain is transformed into the frequency domain, which is a common expression in the control field.

[0074] The system block diagram of the lateral channel attitude controller is as follows: Figure 2 As shown, where, To determine the proportional gain between roll angular velocity control values ​​based on roll angle error.

[0075] The parameters that need to be optimized for the L1 adaptive controller include: , , The parameters are expressed as a linear relationship with dynamic pressure, specifically: .

[0076] in, For dynamic pressure, The slope term for the linear relationship between adaptive gain and dynamic pressure. The intercept term for the linear relationship between adaptive gain and dynamic pressure. The slope term for linearly relating the bandwidth and dynamic pressure of the reference model. The intercept term for the linear relationship between the bandwidth and dynamic pressure of the reference model. The slope term for linearly relating the low-pass filter to dynamic voltage. This is the intercept term for the linear correlation between the low-pass filter and the dynamic voltage.

[0077] At this point, there are six parameters to be optimized, namely... , , , , , .

[0078] S3. For the maneuver mission, multiple conflicting optimization objectives are set, and corresponding performance index functions are established, forming a multi-objective optimization problem. In this embodiment, the following is set: , , , Four optimization objectives, among which, and Corresponding to longitudinal maneuvering, and Corresponding to lateral maneuvers.

[0079] The maximum response speed is defined as the time required for the pitch angle to rise from 10% to 90% of the steady-state value, reflecting the controller's response speed. Its calculation formula is as follows: ;in, The moment when the pitch angle first reaches 10% of the target value. The moment when the pitch angle first reaches 90% of the target value. The smaller the value, the faster the controller response speed.

[0080] Minimizing pitch oscillation is defined as the sum of the distances from the average pitch response to the actual pitch response at the current time point within the time interval during which the pitch response catches up with the constant pitch angle command. This is done across all time intervals to remove the influence of the monotonically rising and falling phases of the pitch response following the pitch signal on the calculation of oscillation. The quantification formula is as follows: ;in, for The actual pitch angle at all times, To ensure the pitch response catches up with the start time of the constant pitch angle command phase, The point in time at which the pitch angle response remains constant is the end of the constant pitch angle response period. The smaller the value, the smoother the pitch motion.

[0081] Maximizing roll tracking accuracy is defined as the root mean square error of the difference between the actual roll angle and the desired roll angle during maneuvering. The quantification formula is as follows: ;in, for The actual roll angle at all times, for The expected roll angle for a maneuver in an S-curve at any given moment. The number of target simulations. The smaller the value, the higher the roll tracking accuracy.

[0082] The roll oscillation degree is defined similarly to the pitch oscillation degree, and the formula is: ;in, for The actual roll angle at all times, The initial sampling time at which the roll response first catches up with the command and enters the stable phase, The final sampling time is when the roll response first catches up with the instruction and enters the stable phase.

[0083] The initial base weight vector is set in the program as follows: ;in, for Optimize the weight values ​​of the target. for Optimize the weight values ​​of the target. for Optimize the weight values ​​of the target. for Optimize the weight values ​​of the target.

[0084] S4. An improved multi-objective particle swarm optimization algorithm is used for parameter optimization. The overall framework of the algorithm is as follows: Figure 3 As shown.

[0085] S4 includes the following sub-steps: S401. Initialize controller parameters.

[0086] The six controller parameters to be optimized constitute the position vector of a particle. In this embodiment, the real number encoding method is used for population initialization. With the real number encoding method, the position of each particle is composed of the physical values ​​of the six parameters to be optimized, without the need for binary conversion.

[0087] Let the first The positions of the particles are: ; in, The basic value of adaptive gain, The basic value of the low-pass filter bandwidth, The basic value of the reference model bandwidth, The slope term when adaptive gain is linearly correlated with dynamic pressure. The slope term when the bandwidth of a low-pass filter is linearly correlated with dynamic pressure. This is the slope term when the bandwidth of the reference model is linearly related to the dynamic pressure.

[0088] Initialize the particle's velocity to a zero vector, i.e. Population size set to .

[0089] S402, Initialize external archive.

[0090] The external archive is used to store all non-dominated solutions (Pareto optimal solutions) found during the algorithm's iterations. When initializing the external archive, the fitness value of each particle in the population on the four optimization objectives is calculated. Then, based on the Pareto dominance relationship, all non-dominated solutions are filtered out and stored in an external archive; the initial maximum capacity of the archive is set to... Mmax =50.

[0091] S403. Determine the Pareto dominance relationship and perform non-dominated sorting on the population in S401 and the individuals in the external archive in S402 to divide different non-dominated layers. A solution that is not dominated by any other solution is called a non-dominated solution.

[0092] For two solutions and If the conditions are met: Then it is called Dominate .

[0093] In this algorithm, after each iteration, individuals in the current population and the external archive need to be sorted in a non-dominated manner to divide different non-dominated layers, namely the Pareto front layers.

[0094] S404. Perform congestion calculation.

[0095] To maintain the diversity of solutions in the external archive, crowding density is used to measure the distribution density of individuals within the same non-dominated layer. A higher crowding density indicates a sparser environment around the individual, and therefore, it should be preferentially retained. The formula for calculating crowding density is: ;in, For the first The degree of crowding of individuals and They were respectively in the second The fitness values ​​of the two adjacent individuals on a given target. and These are the first and second layers of the non-dominated layer. The maximum and minimum values ​​of each target are determined, and the crowding degree of the boundary individuals is set to infinity.

[0096] S405. Traditional multi-objective particle swarm optimization algorithms typically select a globally optimal leader randomly from an external archive or based on crowding. This approach lacks a clear objective preference, leading to random convergence direction and algorithm instability. To address this issue, this embodiment employs a weighted fitness-based hybrid selection strategy as the globally optimal selection strategy. This strategy ensures that the algorithm converges towards the region with the best overall performance while retaining a certain degree of random exploration capability, avoiding premature entrapment in local optima. This significantly improves the convergence direction and stability of the algorithm, avoiding the inefficiency caused by random search. Specifically: Based on engineering preferences, the initial basic weight vectors for the four optimization objectives are set: ; in, for Optimize the weight values ​​of the target. for Optimize the weight values ​​of the target. for Optimize the weight values ​​of the target. for Optimize the weight values ​​of the target.

[0097] For each non-dominated solution in the external archive Calculate its weighted fitness: ; in, For the first The normalized values ​​of the targets; Let r be the weight of the r-th optimization objective.

[0098] The normalization method is as follows: ; in, and These are the current external archives, number 1 and 2 respectively. The minimum and maximum values ​​of each target.

[0099] To balance convergence speed and population diversity, a hybrid probabilistic selection strategy is adopted: With probability The individual with the smallest weighted fitness (for minimization problems) in the external archive is selected as the global optimal guide for the current particle. ; With probability Randomly select one individual from the top 20% of those with the highest crowding levels as... .

[0100] In this embodiment, the optimal combination of 70% weighted fitness and 30% sparse region randomization ensures both convergence speed and population diversity, effectively preventing premature convergence.

[0101] S406. Update the velocity and position of each particle according to the standard particle swarm algorithm.

[0102] The speed update formula is: ; in, For inertial weights, The particle velocity at time t+1 Let be the particle velocity at time t. Let t be the particle position at time t; For the first The optimal position of each particle The globally optimal leader selected according to step S405; , As the learning factor, take c 1= c 2 = 1.5; for A random number that is uniformly distributed within an interval.

[0103] Using a linear decreasing strategy, take , ;but: ;in, t For the current iteration number, This represents the maximum number of iterations. The position update formula is: ; in, The particle position at time t+1 The particle position at time t Let t be the particle velocity at time t+1.

[0104] After the update, it is necessary to check whether each parameter exceeds its current search range (dynamically updated by the parameter range adaptive mechanism). If it does, it is clamped to the boundary value.

[0105] S407. Based on the Pareto dominance relationship, perform individual optimal updates on the position of each particle.

[0106] For each particle, the new position Its individual historical best position The comparison is based on Pareto dominance rules: That is, if Dominate ,but ;like Dominate Then retain the original If neither can control the other, then one of them is randomly selected as the new one. .

[0107] S408. Update and trim external archives.

[0108] Add all non-dominated solutions from the current population to an external archive, then remove individuals from the archive that are dominated by other solutions. If the archive size exceeds the preset capacity... Then, based on the crowding level, pruning is performed, prioritizing the deletion of individuals with the lowest crowding level (i.e., solutions in dense regions) until the archive size meets the requirements.

[0109] S409, Perform mutation operation; apply polynomial mutation to some particles in each iteration.

[0110] Let the mutation probability of the polynomial mutation applied to the particle be set as For the selected particle, its first... Each parameter is variable according to the following formula: ;in, For the mutated first New values ​​for each parameter For the selected particle's first The current value of each parameter For the first The upper bound of the search range for each parameter For the first The lower bound of the search range for each parameter is the polynomial variation perturbation coefficient.

[0111] in, It is generated by the following multinomial distribution: ; in, for Uniform random numbers; ; Pm The distribution index, .

[0112] S410, Iteration Termination and Optimal Parameter Output.

[0113] Repeat sub-steps S404 to S409 until the multi-objective genetic algorithm iterates to the preset termination condition, i.e., until the preset maximum number of iterations is reached. After that, the iteration ends. At this point, the individual with the best overall performance is selected from the final Pareto optimal solution set. The six parameter values ​​corresponding to this individual are the optimized L1 adaptive controller parameters.

[0114] It should be understood that the various forms of processes shown above can be used to reorder, add, or delete steps. For example, the steps described in this invention disclosure can be executed in parallel, sequentially, or in different orders, as long as the desired result of the technical solution disclosed in this invention can be achieved, and this is not limited herein.

[0115] The specific embodiments described above do not constitute a limitation on the scope of protection of this invention. Those skilled in the art should understand that various modifications, combinations, sub-combinations, and substitutions can be made according to design requirements and other factors. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of this invention should be included within the scope of protection of this invention.

Claims

1. A method for L1 adaptive parameter optimization of unmanned aerial vehicles based on an improved multi-objective particle swarm optimization algorithm, characterized in that: Includes the following steps: S1. Establish a six-degree-of-freedom nonlinear dynamic model of the UAV, and construct the desired maneuver mission model based on this model; S2. Design the longitudinal and lateral channel attitude controllers for the aircraft based on the L1 adaptive controller, and select the core parameters that have a key impact on the control performance to form a set of parameters to be optimized. S3. For maneuver missions, set multiple conflicting optimization objectives and establish corresponding performance index functions to form a multi-objective optimization problem; S4. Parameter optimization is performed using an improved multi-objective particle swarm optimization algorithm; S4 includes the following sub-steps: S401. Initialize controller parameters; wherein, population initialization is performed using parameter encoding. S402. Initialize external archive; S403. Determine the Pareto dominance relationship and perform non-dominated sorting on the population in S401 and the individuals in the external archive in S402 to divide different non-dominated layers. S404. Perform congestion calculation; S405. A weighted fitness-based hybrid selection strategy is adopted as the globally optimal selection strategy. S406. Update the velocity and position of each particle according to the standard particle swarm algorithm; S407. Based on the Pareto dominance relationship, perform individual optimal updates on the position of each particle; S408. Update and trim external archives; S409. Perform mutation operation; apply polynomial mutation to some particles in each iteration; S410, Iteration Termination and Optimal Parameter Output.

2. The UAV L1 adaptive parameter optimization method based on the improved multi-objective particle swarm optimization algorithm according to claim 1, characterized in that: In S2, for the longitudinal channel attitude controller, Introducing a state observer: ; Define state estimation error ,but: ； set up ,but ; Introducing the projection operator as an adaptive law: ; The pitch rate control law is designed as follows: ; The low-pass filter is of first-order form. ; in, For pitch angular velocity, For pitch angular velocity state estimation error, The derivative of the pitch angular velocity state estimation error, For pitch acceleration, For the state observer to observe pitch angular velocity values, The derivative of the pitch angular velocity value observed by the state observer, For reference model bandwidth, For nominal rudder efficiency, For elevator deflection commands, For system lumped disturbances, For the total disturbance of the state observer, The derivative of the total perturbation of the state observer, For adaptive gain, For low-pass filters, For filter bandwidth, s For the Laplace operator.

3. The UAV L1 adaptive parameter optimization method based on the improved multi-objective particle swarm optimization algorithm according to claim 2, characterized in that: In S2, for the lateral channel attitude controller, Introducing a state observer: ; Define state estimation error ,but: ； remember ,but ; Introducing the projection operator as an adaptive law: ; The pitch rate control law is designed as follows: ; The low-pass filter is of first-order form. ; in, For roll angular velocity, For the roll angular velocity state estimation error, The derivative of the roll angular velocity state estimation error, For roll angular acceleration, For the state observer to observe the roll angular velocity value, The derivative of the roll angular velocity value observed by the state observer, For reference model bandwidth, For nominal rudder efficiency, For aileron deflection commands, For system lumped disturbances, For the total disturbance of the state observer, The derivative of the total perturbation of the state observer, For adaptive gain, For low-pass filters, Let be the filter bandwidth and s be the Laplace operator.

4. The UAV L1 adaptive parameter optimization method based on the improved multi-objective particle swarm optimization algorithm according to claim 3, characterized in that: In S2, the parameters that the L1 adaptive controller needs to optimize include: , , The parameters are expressed as a linear relationship with dynamic pressure, specifically: ； in, For dynamic pressure, The slope term for the linear relationship between adaptive gain and dynamic pressure. The intercept term for the linear relationship between adaptive gain and dynamic pressure. The slope term for linearly relating the bandwidth and dynamic pressure of the reference model. The intercept term for the linear relationship between the bandwidth and dynamic pressure of the reference model. The slope term for linearly relating the low-pass filter to dynamic voltage. This is the intercept term for the linear correlation between the low-pass filter and dynamic voltage; At this point, there are six parameters to be optimized, namely... , , , , , .

5. The UAV L1 adaptive parameter optimization method based on the improved multi-objective particle swarm optimization algorithm according to claim 4, characterized in that: In S3, the settings , , , Four optimization objectives, among which, and Corresponding to longitudinal maneuvering, and Corresponding to lateral maneuvers; In S405, the initial basic weight vectors for the four optimization objectives are set according to engineering preferences: ； in, for Optimize the weight values ​​of the target. for Optimize the weight values ​​of the target. for Optimize the weight values ​​of the target. for Optimize the weight values ​​of the target; For each non-dominated solution in the external archive Calculate its weighted fitness: ； in, For the first The normalized values ​​of the targets; The weights for the r-th optimization objective; The normalization method is as follows: ； in, and These are the current external archives, number 1 and 2 respectively. The minimum and maximum values ​​of each target.

6. The UAV L1 adaptive parameter optimization method based on the improved multi-objective particle swarm optimization algorithm according to claim 5, characterized in that: In S405, when a hybrid probability selection strategy is used: With probability The individual with the lowest weighted fitness in the external archive is selected as the global optimal guide for the current particle. ; With probability Randomly select one individual from the top 20% of those with the highest crowding levels as... .

7. The UAV L1 adaptive parameter optimization method based on the improved multi-objective particle swarm optimization algorithm according to claim 5, characterized in that: In S401, the six controller parameters to be optimized constitute the position vector of a particle. The real number encoding method is used, and the position of each particle is composed of the physical values ​​of the six parameters to be optimized. Let the first The positions of the particles are: ; in, The basic value of adaptive gain, The basic value of the low-pass filter bandwidth, The basic value of the reference model bandwidth, The slope term when adaptive gain is linearly correlated with dynamic pressure. The slope term when the bandwidth of a low-pass filter is linearly correlated with dynamic pressure. This is the slope term when the bandwidth of the reference model is linearly correlated with dynamic pressure; Initialize the particle's velocity to a zero vector, i.e. Population size set to .

8. The UAV L1 adaptive parameter optimization method based on the improved multi-objective particle swarm optimization algorithm according to claim 5, characterized in that: In S402, when initializing the external archive, the fitness value of each particle in the population on the four optimization objectives is calculated. Then, based on the Pareto dominance relation, all non-dominated solutions are filtered out and stored in an external archive. The initial maximum size of the archive is set to Mmax =50.

9. The UAV L1 adaptive parameter optimization method based on the improved multi-objective particle swarm optimization algorithm according to claim 5, characterized in that: In S406, the speed update formula is: ； in, For inertial weights, The particle velocity at time t+1 Let be the particle velocity at time t. Let be the particle position at time t; For the first The optimal position of each particle The globally optimal leader selected according to step S405; , Let c1 = c2 = 1.5 be the learning factor; for A random number that is uniformly distributed within an interval; Using a linear decreasing strategy, take , ;but: Where t is the current iteration number, This represents the maximum number of iterations. The position update formula is: ； in, The particle position at time t+1 The particle position at time t Let t be the particle velocity at time t+1.

10. The UAV L1 adaptive parameter optimization method based on the improved multi-objective particle swarm optimization algorithm according to claim 5, characterized in that: In S409, the mutation probability of the polynomial mutation applied to the particle is set to For the selected particle, its first... Each parameter is variable according to the following formula: ;in, For the mutated first New values ​​for each parameter For the selected particle's first The current value of each parameter For the first The upper bound of the search range for each parameter For the first The lower bound of the search range for each parameter These are the polynomial variation perturbation coefficients; in, It is generated by the following multinomial distribution: ； in, for Uniform random numbers; Pm is the distribution index. .

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