High-speed aircraft climbing trajectory multi-target control method based on protopigeon heuristic intelligence
Through a multi-objective control method inspired by the intelligence of Yuanbi, the climbing trajectory of high-speed aircraft is optimized, and the control problem of high-speed aircraft under multiple constraints during the climbing stage is solved, achieving a fast, stable and fuel-efficient climbing effect.
Patent Information
- Application Number
- CN202411371509.7
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2024-09-29
- Publication Date
- 2025-02-14
AI Technical Summary
High-speed aircraft faces control problems under multiple constraints during the climbing stage. How to quickly complete the climb while ensuring flight speed, stability and fuel efficiency.
A multi-objective control method based on the inspiration of the Yuanbi, through the construction of an integrated flight/push system model and a longitudinal channel control law strategy, combined with multiple constraints, the pigeon flock optimization algorithm is used to optimize the climbing trajectory of the high-speed aircraft.
It improves the control effect of high-speed aircraft during climbing, enhances climbing efficiency, and achieves rapid, stable and fuel-efficient climbing under multi-constraint conditions.
Smart Images
Figure CN119440082A_ABST
Abstract
Description
Technical Field
[0001] The invention discloses a multi-objective control method for a high-speed aircraft climbing trajectory based on pigeon-inspired intelligence, and belongs to the field of autonomous control of unmanned aerial vehicles. Background Art
[0002] Generally, aircraft that can reach a maximum flight speed of more than Mach 5 and a maximum flight altitude greater than 20, that is, aircraft operating in near space, are classified as high-speed aircraft. They have the advantages of high speed, strong penetration capability, and flexibility, and have the ability to perform tasks in the aerospace field. Since the operating speed range of high-speed aircraft is relatively wide, and different engines have different operating speed ranges, high-speed aircraft usually use combined power engines to cope with the working environment in a wide speed range, and the climb phase is the key stage for the aircraft to switch power. High-speed aircraft face a drastically changing environment during the climb phase. How to ensure that the aircraft can complete the climb quickly, stably, and save fuel under multiple constraints is of great research significance.
[0003] The present invention proposes a multi-objective control method based on pigeon-inspired intelligence to optimize the climbing trajectory of high-speed aircraft. First, a flight / thrust integrated system model is constructed for high-speed aircraft, and a corresponding longitudinal channel control law strategy is established for the model. Secondly, a variety of constraints are constructed for the process of high-speed aircraft in the climbing phase to calculate the aircraft's climbing time and fuel consumption. Finally, for the optimization problem of the climbing trajectory of high-speed aircraft, the pigeon flock optimization algorithm is used to optimize it. Summary of the invention
[0004] The purpose of the present invention is to propose a multi-objective control method for the climbing trajectory of a high-speed aircraft based on pigeon-inspired intelligence, which is used to optimize the climbing trajectory of the high-speed aircraft, aiming to improve the control effect of the high-speed aircraft when climbing and enhance the climbing efficiency of the high-speed aircraft.
[0005] The present invention is a multi-objective control method for high-speed aircraft climbing trajectory based on pigeon-inspired intelligence, and the specific implementation steps are as follows:
[0006] Step 1: Create an environment model and a high-speed aircraft model
[0007] The flight mission of high-speed aircraft involves a large altitude span. In order to meet the authenticity and accuracy of control simulation, the atmospheric parameters at different altitudes are first modeled and solved, aiming to find out the atmospheric parameters at different flight altitudes, including temperature, speed of sound, gravity acceleration, atmospheric static pressure and air density. The modeling is based on the American standard atmospheric altitude variation table. The temperature, gravity acceleration, atmospheric static pressure and air density can be calculated by interpolation based on the input altitude.
[0008] The sound velocity data is calculated according to the following formula:
[0009]
[0010] Among them, T e is the ambient temperature calculated by the above interpolation, in which the Kelvin temperature scale is required; R is the universal gas constant, which is 2.87 J / (kg·K); k is the specific heat ratio of the gas, which is approximately 1.4.
[0011] Considering the aircraft as a rigid body and ignoring elastic coupling and mass changes, considering its longitudinal kinematics and dynamics equations, we have:
[0012]
[0013] Where T is the thrust of the engine, L is the lift of the aircraft, D is the drag of the aircraft, M is the pitch moment of the aircraft; V is the flight speed of the aircraft, h is the flight altitude of the aircraft, γ is the track angle, θ is the pitch angle, q is the pitch angular velocity, α is the flight angle of attack; m is the mass of the aircraft, I yy is the moment of inertia.
[0014] The calculation of the flight angle of attack α is:
[0015] α=θ-γ
[0016] The calculation formulas for lift L, drag D, and pitching moment M are as follows:
[0017]
[0018] in, is the dynamic pressure, S is the reference wing area, is the average aerodynamic chord length; C L , C D , C M is the aircraft aerodynamic derivative, and the specific calculation formula is as follows:
[0019]
[0020] Among them, δ e is the elevator deflection angle.
[0021] The aircraft inertial parameters, geometric parameters, and aerodynamic parameters are obtained by consulting the literature. The aircraft thrust is provided by the engine model. The one-dimensional simplified engine model consists of an inlet, a combustion chamber, and a tail nozzle. The calculation formulas for the inlet, combustion chamber, and tail nozzle characteristics are as follows:
[0022]
[0023]
[0024] Where: is the temperature, P is the atmospheric static pressure, Ma is the aircraft flight Mach number, k is the air specific heat ratio, R is the universal gas constant, n is the component working efficiency, f is the air-fuel ratio, and u is the air flow velocity. The engine thrust calculation formula is:
[0025] T=((1+f)u s -u d )·m ar =T mar ·m ar
[0026] Among them, m ar Indicates equivalent gas mass.
[0027] Step 2: Design of Longitudinal Control Law for High-Speed Aircraft
[0028] Simplifying the kinematic and dynamic equations, we get the following equations:
[0029]
[0030] Among them, the expression of the coefficient term is:
[0031]
[0032] In the longitudinal channel, the elevator is the control loop where the control quantity is located, generating a pitch moment, thereby generating a pitch angular velocity, and then changing the longitudinal attitude, and finally achieving the purpose of changing the flight altitude. The control loops involved include the innermost pitch angular velocity control loop, the second innermost pitch angle control loop, and the outermost altitude control loop. The pitch angular velocity control loop tracks the pitch angular velocity command, and the specific control law is:
[0033]
[0034] Among them, k Q is the parameter to be adjusted, q des is the pitch angle velocity command, which is obtained by the pitch angle control loop. The specific control law of the pitch angle control loop is:
[0035]
[0036] Among them, θ des is the pitch angle command, which is obtained by the track angle control loop. The specific control law of the track angle control loop is:
[0037] θ des =γ des +α
[0038] Among them, γ des is the pitch angle command, which is obtained by the altitude control loop. The specific control law of the altitude control loop is:
[0039]
[0040] Among them, h ref Enter the command for the altitude.
[0041] The longitudinal channel thrust control law is further designed. The dynamic principle of thrust channel control is to change the longitudinal axis force of the aircraft, thereby generating axial acceleration and finally realizing the control of flight speed. Usually, the required thrust is determined by the speed control law, which is equivalent to directly controlling the thrust as a set value. The speed control law is designed as:
[0042] The engine thrust control law is designed as:
[0043]
[0044] The speed command value is the control input of the entire thrust channel, and the speed control law is designed as:
[0045]
[0046] The thrust control law is further obtained:
[0047]
[0048] When the engine mode is switched, the ramjet engine starts from the 0 thrust state to the thrust command obtained by fully assuming speed control. The first-order inertia link is used to smooth the transition process. The thrust command is set as:
[0049]
[0050] in, is the thrust command change rate of the ramjet engine. When entering the power mode 3, its initial value is 0; t ram is the time constant of the inertia link, and the selection principle is to ensure that the mode conversion can be completed completely and smoothly before the end of the transition process.
[0051] The thrust command obtained when the turbine engine starts from the 0 thrust state to the full speed control is also smoothed by the first-order inertia link. The thrust command is set as:
[0052]
[0053] in, is the change rate of the thrust command of the turbine engine. When entering the fourth power mode, its initial value is 0; t tur is the time constant of the inertia link, and the selection principle is also to ensure that the mode conversion can be completed completely and smoothly before the end of the transition process.
[0054] The final high-speed aircraft longitudinal control law is as followsFigure 1 shown.
[0055] Step 3: Design of high-speed aircraft climb constraint model
[0056] During the climbing process of a high-speed aircraft, in order to simplify the optimization problem, it is assumed that the aircraft first climbs to a certain altitude and then switches the acceleration power mode, thereby avoiding complex control problems during the climbing phase and engine failure problems caused by drastic environmental changes.
[0057] Considering the main requirements of the climb phase, it is hoped that high-speed aircraft can save fuel and complete the climb quickly. Therefore, the main performance index examination includes the following indicators:
[0058] (1) Maximum range performance indicators
[0059] The maximum range problem is mainly used to calculate the maximum flight distance of an aircraft under a given fuel load, so it can be established
[0060] The maximum range performance indicators are as follows:
[0061]
[0062] (2) Most fuel-efficient performance index
[0063] During the high-speed aircraft climb, it is hoped that the aircraft can complete the climb with the most fuel-efficient method. Therefore, the following fuel-efficient performance index can be established:
[0064]
[0065] (3) Shortest time performance index
[0066] During the high-speed aircraft climb, it is hoped that the aircraft can complete the climb as quickly as possible, so the following shortest
[0067] Time performance indicators:
[0068]
[0069] In the actual flight process, the above performance indicators need to be considered comprehensively, and the actual emphasis on different indicators should be considered.
[0070] Different indicators are weighted, so the following comprehensive performance indicators are established:
[0071]
[0072] Among them, ω k is the weight corresponding to each performance indicator. The higher the demand, the greater the weight.
[0073] Step 4: Optimization of high-speed aircraft climbing trajectory based on original pigeon intelligence
[0074] In D-dimensional space, set the number of pigeons to N and the initial position of the pigeons to X. i =[X i1 , X i2 , X i3 , ..., X iD ], speed is V i =[V i1 , V i2 , V i3 , ..., V iD ], where i = 1, 2, 3, ..., N, and the position of the pigeon represents the independent variable of the fitness function to be solved, that is, the control quantity of the control system.
[0075] In the initialization phase, the state of the pigeon flock is randomly initialized in the search space. In the first phase, each pigeon updates its position and velocity according to the following formula:
[0076]
[0077] Where R represents the map and guide factor, X gbest represents the global best position of the pigeon after t-1 cycles, V i (t) represents the speed of the i-th individual at the t-th iteration, X i (t) represents the position of the i-th individual at the t-th iteration.
[0078] Set the exploration group of pigeons to search the new area. The exploration group of pigeons updates the position and speed according to the following formula:
[0079]
[0080] Among them, R e represents the map factor of the exploration group, which is affected by the results of the previous iteration; X m is the average of the two best individuals in each round of iteration. e Update according to the following formula:
[0081]
[0082] Among them, R min Represents the minimum value set for the exploration group map factor, R max represents the maximum value of the exploration group map factor; p i is the fitness value of the ith individual, p max is the maximum value of the fitness value; ζ is the iteration index, which is set to 1 at the end of each iteration when the global optimal solution is updated, and is set to 0 when the global optimal solution is not updated.
[0083] The average value of the best two individuals is X m The update formula is as follows:
[0084]
[0085] Among them, τ1 and τ2 represent the two individuals with the best global fitness value, X pbest (τ1) and X pbest (τ2)) represents the historical optimal position of these two individuals.
[0086] In the second stage, the landmark operator stage, the pigeon flock uses landmark navigation, and the update strategy is as follows:
[0087]
[0088] Among them, N N (t) is the number of individuals in the pigeon group at the tth iteration, X center (t) is the center position of the pigeon group at the tth iteration, fitness(X i ) is the fitness value of the i-th individual. After the number of iterations reaches the maximum, the loop ends and the optimal solution X is obtained. best , which is the optimal control quantity of the control system. The above optimization steps are shown in Figure 2 .
[0089] The optimization steps for the final high-speed aircraft climbing trajectory are as follows:
[0090] S41. Complete state balancing according to the initial flight conditions of the aircraft to obtain state quantities and control quantities of the aircraft during stable flight.
[0091] S42. Initialize the specific control input of the system to ensure that the aircraft is stable in the process of following the control signal input.
[0092] S43, calculate and obtain the adaptation value of the initial control amount of the aircraft, and complete the initialization of the pigeon flock.
[0093] S44. The pigeon flock updates the exploration map factor and further updates the speed and position.
[0094] S45. Complete the landmark operator iteration and output the optimization result.
[0095] Finally, the optimization of the high-speed aircraft climbing trajectory is completed. The specific results are shown in Figure 3 .
[0096] The invention discloses a multi-objective control method for a high-speed aircraft climbing trajectory based on pigeon-inspired intelligence, which has the advantages and effects of: when optimizing the climbing trajectory of a high-speed aircraft, after comprehensively considering multiple indicators such as climbing speed and climbing fuel consumption, the control effect of the high-speed aircraft during climbing is improved through an optimization algorithm, thereby enhancing the climbing efficiency of the high-speed aircraft. BRIEF DESCRIPTION OF THE DRAWINGS
[0097] Figure 1 is the longitudinal control strategy z of the high-speed aircraft.
[0098] Figure 2 This is the flow chart of the climbing trajectory optimized by YuanGe intelligent algorithm.
[0099] Figure 3 This is a comparison chart of trajectory optimization results. DETAILED DESCRIPTION
[0100] The effectiveness of the high-speed aircraft flight / thrust integrated parameter optimization method provided by the present invention is verified by a specific example below. In this example, the initial flight conditions and initial control parameters are given, and the original pigeon grouping optimization algorithm is used for optimization. The simulation environment of this example is configured with an Intel i7-9750 processor, 2.60GHz main frequency, 8G memory, and the software is MATLAB 2019b version.
[0101] The multi-objective control method of high-speed aircraft climbing trajectory based on pigeon-inspired intelligence is implemented as follows: Figure 3 As shown, the specific practical steps of this example are as follows:
[0102] Step 1: Create an environment model and a high-speed aircraft model
[0103] The modeling is based on the U.S. standard atmospheric variation with altitude table. The temperature, gravitational acceleration, atmospheric static pressure and air density can be interpolated and calculated according to the input altitude. The ambient temperature is Kelvin temperature scale; R is, the universal gas constant is 2·87J / (kg·K); the gas specific heat ratio is taken as 1.4 approximate value; the gravitational constant is 6.67×10 -11 N·m 2 / kg 2 ; The mass of the Earth is 5.965×10 24 kg; the radius of the earth is taken as the average radius of 6371km.
[0104] The results of the atmospheric model constructed are basically consistent with those of the atmospheric parameter module in Simulink. The relative error of air density is the largest, with a relative error of about 1.7% at an altitude of 12.8 km; the relative errors of ambient temperature and atmospheric static pressure are second, with a maximum value of about 1.0%; the relative error of ambient sound speed is relatively small, with a maximum value of about 0.5%; the relative error of gravity acceleration is the smallest, about 0.05%. Through numerical analysis, the atmospheric parameter values obtained by the constructed atmospheric model have a small relative error with the recognized standard values, and the model can be used to calculate the atmospheric parameters at the altitude where the aircraft is located.
[0105] Step 2: Design of Longitudinal Control Law for High-Speed Aircraft
[0106] Aircraft control is based on a constant speed level flight state. The dynamic principle of elevator control is to change the pitch moment of the aircraft, thereby generating pitch angular velocity, and then changing the longitudinal attitude, and finally achieving the purpose of changing the flight altitude. The multi-loop altitude control of the elevator channel is in the order of the innermost loop pitch angular velocity control, the second inner loop pitch angle control, the second outer loop track angle control, and the outermost loop altitude control.
[0107] Aircraft control is based on a constant speed level flight state. The dynamic principle of thrust channel control is to change the axial force of the aircraft's longitudinal axis, thereby generating axial acceleration and ultimately achieving flight speed control. The required thrust is determined by the speed control law, and the thrust expression directly includes the throttle opening, which is equivalent to controlling the thrust directly as a set value. In addition to speed control, the thrust channel also includes an engine thrust control loop, which is represented by two loops.
[0108] The control system parameters are adjusted, and the selected parameters and initial value ranges are set as shown in Table 1.
[0109] Table 1 Range of control system parameters to be optimized
[0110]
[0111] Step 3: Design of high-speed aircraft climb constraint model
[0112] During the climbing process of a high-speed aircraft, in order to simplify the optimization problem, it is assumed that the aircraft first climbs to a certain altitude and then switches the acceleration power mode, thereby avoiding complex control problems during the climbing phase and engine failure problems caused by drastic environmental changes.
[0113] Considering the main requirements of the climb phase, it is hoped that high-speed aircraft can save fuel and complete the climb quickly. Therefore, the main performance index examination includes the following indicators:
[0114] (1) Maximum range performance indicators
[0115] The maximum range problem is mainly used to calculate the maximum flight distance of an aircraft under a given fuel load. The range calculation within each simulation step is completed by coordinate system transformation.
[0116] (2) Most fuel-efficient performance index
[0117] During the climb of a high-speed aircraft, it is hoped that the aircraft can complete the climb in the most fuel-efficient way. The fuel consumption in each simulation step is completed by interpolation calculation.
[0118] (3) Shortest time performance index
[0119] During the climb of a high-speed aircraft, it is hoped that the aircraft can complete the climb as quickly as possible, and the flight time is obtained by the time it takes to reach the specified altitude during simulation.
[0120] In the actual flight process, the above performance indicators need to be considered comprehensively, and different indicators should be given weights according to the actual importance they attach to different indicators. Since high-speed aircraft consume more fuel during the climb phase, a greater weight is given to the fuel consumption performance indicator.
[0121] Step 4: Optimization of high-speed aircraft climbing trajectory based on original pigeon intelligence
[0122] Set the number of pigeons to N and the initial position of the pigeons to X i =[X i1 , X i2 , X i3 , ..., X iD ], speed is V i =[V i1 , V i2 , V i3 , ..., V iD ], where i = 1, 2, 3, ..., N, and the position of the pigeon represents the independent variable of the fitness function to be solved, that is, the control quantity of the control system.
[0123] In the initialization phase, the state of the pigeon flock is randomly initialized in the search space. In the first phase, each pigeon searches the new area and updates its position and speed. In the second phase, the pigeon flock uses landmark navigation to perform updates.
[0124] After the number of iterations reaches the maximum, the loop ends and the optimal solution is obtained, which is the optimal control quantity of the desired control system.
[0125] The optimization steps for the final high-speed aircraft climbing trajectory are as follows:
[0126] S41. Complete state balancing according to the initial flight conditions of the aircraft to obtain state quantities and control quantities of the aircraft during stable flight.
[0127] S42. Initialize the specific control input of the system to ensure that the aircraft is stable in the process of following the control signal input.
[0128] S43, calculate and obtain the adaptation value of the initial control amount of the aircraft, and complete the initialization of the pigeon flock.
[0129] S44, Pigeon flock updates exploration map factors and further updates speed and position
[0130] S45. Complete the landmark operator iteration and output the optimization results
[0131] Finally, the optimization of the high-speed aircraft climbing trajectory is completed. The specific results are shown in Figure 3 .
Claims
1. A multi-objective control method for high-speed aircraft climbing trajectory based on pigeon-inspired intelligence, characterized by: The steps of this method are as follows: Step 1: Create an environment model and a high-speed aircraft model First, the atmospheric parameters at different altitudes are modeled and solved to obtain the atmospheric parameters at different flight altitudes, including temperature, speed of sound, gravitational acceleration, atmospheric static pressure and air density; The sound velocity data is calculated according to the following formula: Among them, T e is the ambient temperature calculated by the above interpolation, where the Kelvin temperature scale is required; R is the universal gas constant, which is 2.87 J / (kg·K); k is the specific heat ratio of the gas; Considering the aircraft as a rigid body and ignoring elastic coupling and mass changes, considering its longitudinal kinematics and dynamics equations, we have: Where T is the thrust of the engine, L is the lift of the aircraft, D is the drag of the aircraft, M is the pitch moment of the aircraft; V is the flight speed of the aircraft, h is the flight altitude of the aircraft, γ is the track angle, θ is the pitch angle, q is the pitch angular velocity, α is the flight angle of attack; m is the mass of the aircraft, I yy is the moment of inertia; The calculation of the flight angle of attack α is: α=θ-γ The calculation formulas for lift L, drag D, and pitching moment M are as follows: in, is the dynamic pressure, S is the reference wing area, is the average aerodynamic chord length; C L , C D , C M is the aircraft aerodynamic derivative, and the specific calculation formula is as follows: Among them, δ e is the elevator deflection angle; The aircraft thrust is provided by the engine model. The one-dimensional simplified engine model consists of an inlet duct, a combustion chamber, and a tail nozzle. The calculation formulas for the inlet duct, combustion chamber, and tail nozzle characteristics are as follows: Where: is the temperature, P is the atmospheric static pressure, Ma is the aircraft flight Mach number, k is the air specific heat ratio, R is the universal gas constant, n is the component working efficiency, f is the air-fuel ratio, and u is the air flow velocity; the engine thrust calculation formula is: T=((1+f)u s -u d )·m ar =T mar· m ar Among them, m ar Indicates equivalent gas mass; Step 2: Design of Longitudinal Control Law for High-Speed Aircraft Simplifying the kinematic and dynamic equations, we get the following equations: Among them, the expression of the coefficient term is: In the longitudinal channel, the elevator is used as the control quantity in the control loop, which generates a pitch moment, thereby generating a pitch angular velocity, and then changing the longitudinal attitude, and finally achieving the purpose of changing the flight altitude. The control loops involved include the innermost pitch angular velocity control loop, the second inner pitch angle control loop and the outermost altitude control loop; the pitch angular velocity control loop tracks the pitch angular velocity command, and the specific control law is: Among them, k Q is the parameter to be adjusted, q des is the pitch angle velocity command, which is obtained by the pitch angle control loop. The specific control law of the pitch angle control loop is: Among them, θ des is the pitch angle command, which is obtained by the track angle control loop. The specific control law of the track angle control loop is: i des =c des +a Among them, γ des is the pitch angle command, which is obtained by the altitude control loop. The specific control law of the altitude control loop is: Among them, h ref Enter the command for altitude; The thrust control law of the longitudinal channel is further designed, and the required thrust is determined by the speed control law, which is equivalent to directly controlling the thrust as the set value; the speed control law is designed as: The engine thrust control law is designed as: The speed command value is the control input of the entire thrust channel, and the speed control law is designed as: The thrust control law is further obtained: When the engine mode is switched, the ramjet engine starts from the 0 thrust state to the thrust command obtained by fully assuming speed control. The first-order inertia link is used to smooth the transition process. The thrust command is set as: in, is the thrust command change rate of the ramjet engine. When entering the power mode 3, its initial value is 0; t ram is the time constant of the inertia link, and the selection principle is to ensure that the mode conversion can be completed completely and smoothly before the end of the transition process; The thrust command obtained when the turbine engine starts from the 0 thrust state to the full speed control is also smoothed by the first-order inertia link. The thrust command is set as: in, is the change rate of the thrust command of the turbine engine. When entering the fourth power mode, its initial value is 0; t tur is the time constant of the inertia link, and the selection principle is also to ensure that the mode conversion can be completed completely and smoothly before the end of the transition process; Step 3: Design of high-speed aircraft climb constraint model Considering the requirements of the climb phase, it is hoped that high-speed aircraft can save fuel and complete the climb quickly. Therefore, the performance index examination includes the following indicators: (1) Maximum range performance indicators The maximum range problem is used to calculate the maximum flight distance of an aircraft under a given fuel load and establish the following maximum range performance index: (2) Most fuel-efficient performance index During the high-speed aircraft climb, it is hoped that the aircraft can complete the climb with the most fuel efficiency. The following fuel efficiency performance indicators are established: (3) Shortest time performance index During the high-speed aircraft climb, it is hoped that the aircraft can complete the climb as quickly as possible, and the following minimum time performance indicators are established: In the actual flight process, the above performance indicators need to be comprehensively considered, and different indicators are weighted according to the actual degree of importance attached to different indicators. Therefore, the following comprehensive performance indicators are established: Among them, ω k is the weight corresponding to each performance indicator. The higher the demand, the greater the weight. Step 4: Optimization of high-speed aircraft climbing trajectory based on original pigeon intelligence S41, completing state balancing according to the initial flight conditions of the aircraft, and obtaining state quantities and control quantities of the aircraft during stable flight; S42, initializing the specific control input of the system to ensure that the aircraft is stable in the process of following the control signal input; S43, calculating and obtaining the adaptation value of the initial control amount of the aircraft, and completing the initialization of the pigeon flock; S44, the pigeon flock updates the exploration map factor, and further updates the speed and position; S45. Complete the landmark operator iteration and output the optimization result.
2. The method according to claim 1, characterized in that: Step 4: In the D-dimensional space, the number of pigeons is set to N, and the initial position of the pigeons is set to X. i =[X i1 , X i2 , X i3 , ..., X iD ], speed is V i =[V i1 , V i2 , V i3 , ..., V iD ], where i = 1, 2, 3, ..., N, and the position of the pigeon represents the independent variable of the fitness function to be solved, that is, the control quantity of the control system; In the initialization phase, the state of the pigeon flock is randomly initialized in the search space; in the first phase, each pigeon updates its position and speed according to the following formula: Where R represents the map and guide factor, X gbest represents the global best position of the pigeon after t-1 cycles, V i (t) represents the speed of the i-th individual at the t-th iteration, X i (t) represents the position of the i-th individual at the t-th iteration; Set the exploration group of pigeons to search the new area. The exploration group of pigeons updates the position and speed according to the following formula: Among them, R e represents the map factor of the exploration group, which is affected by the results of the previous iteration; X m is the average of the two best individuals in each iteration; R e Update according to the following formula: Among them, R min Represents the minimum value set for the exploration group map factor, R max represents the maximum value of the exploration group map factor; p i is the fitness value of the ith individual, p max is the maximum value of the fitness value; ζ is the set iteration index, which is set to 1 at the end of each iteration when the global optimal solution is updated, and is set to 0 when the global optimal solution is not updated; The average value of the best two individuals is X m The update formula is as follows: Among them, τ1 and τ2 represent the two individuals with the best global fitness value, X pbest (τ1) and X pbest (τ2)) represents the historical optimal position of these two individuals; In the second stage, the landmark operator stage, the pigeon flock uses landmark navigation, and the update strategy is as follows: Among them, N N (t) is the number of individuals in the pigeon group at the tth iteration, X center (t) is the center position of the pigeon group at the tth iteration, fitness(X i ) is the fitness value of the i-th individual; after the number of iterations reaches the maximum, the loop ends and the optimal solution X is obtained. best , which is the optimal control quantity of the control system.