A method for controlling the landing point and speed of an aircraft based on optimal control theory

Abstract

The present invention provides a method for controlling the landing point and speed of an aircraft based on optimal control theory, and belongs to the technical field of aircraft landing point and speed control. The method for precise control of the landing point and speed of an aircraft based on the optimal control theory provided by the present invention has the actual input conditions of the current flight time t0 and position velocity vector x0 of the aircraft provided by an external device, and utilizes the initial instruction sequence u0 and the real-time instructions that meet the terminal landing point and speed capability obtained by the variational method, and solves the new instruction angle according to the target point parameters and the reference instructions, so as to form an instruction update closed-loop format, and the solution process has the characteristics of rapidity, strong real-time performance, and is suitable for online applications. The present invention solves the problem that the landing point and speed are difficult to accurately control during the reentry of an aircraft.

Description

Technical Field

[0001] The present invention belongs to the technical field of aircraft landing point and speed control, and in particular, relates to an aircraft landing point and speed control method based on optimal control theory. Background Art

[0002] The main research idea of ​​the existing methods for precise control of the landing point and speed of aircraft in China is to control the landing point and speed in accordance with the combination of the pre-designed ideal flight profile and the real-time deviation correction during the flight. Since the aircraft will be affected by complex constraints such as overload, dynamic pressure, and heat flow during the reentry process, it is difficult to accurately control the landing point and speed. The existing methods mainly focus on the following points: First, the combination of multiple guidance laws is used to give full play to their respective advantages to achieve precise control; second, the combination of offline trajectory planning and online trajectory planning, first track the standard trajectory, and when the flight deviation is large, plan the flight trajectory through the online planning method; third, through the good design of the mid-guidance trajectory, guide the aircraft to the appropriate handover point, and then use algorithms such as proportional guidance with constraints to accurately control the landing point and speed. However, these methods all have some limitations, poor adaptability, and the control accuracy sometimes cannot meet the established requirements. Therefore, it is necessary to propose a new guidance method to achieve precise control of the landing point and speed. Summary of the invention

[0003] In view of the above-mentioned deficiencies in the prior art, the present invention provides a method for controlling the landing point and speed of an aircraft based on optimal control theory, which solves the problem that the landing point and speed of an aircraft is difficult to accurately control during the re-entry process.

[0004] In order to achieve the above purpose, the technical solution adopted by the present invention is:

[0005] This solution provides a method for controlling the landing point and speed of an aircraft based on optimal control theory, comprising the following steps:

[0006] S1. Determine the current flight parameters: obtain the current flight time and position velocity vector according to the output of the navigation device;

[0007] S2. Determine the terminal output under the current state: use the initial instruction sequence and the flight parameters at the current moment to calculate all state parameters from the current moment to the end of the flight;

[0008] S3, determine whether to output the guidance instruction: determine whether the module value between the terminal output and the expected output meets the preset index requirements, if so, output the guidance instruction and end the process, otherwise, enter step S4;

[0009] S4. Determine the state equations satisfied during the flight and the problem transformation: According to the current flight time and position velocity vector, obtain the state equation of the time-varying system, and construct a two-point boundary value problem through the continuous state equation;

[0010] S5. Determine the augmented performance index: According to the minimum setting of the overall control amount, the performance index of the optimization problem is set, and combined with the equality constraints in the two-point boundary value problem, the Lagrange multiplier is introduced to combine the equality constraints with the performance index to obtain the augmented performance index;

[0011] S6. Determine the control equation and adjoint equation: According to the augmented performance index, introduce Hamiltonian function and variational optimal control theory to obtain the control equation and adjoint equation;

[0012] S7, determining the optimal control instruction: according to the control equation and the adjoint equation, the optimal control instruction is obtained by eliminating the co-state vector through discretization;

[0013] S8. Output guidance instructions: Approximate the optimal control instruction sequence according to the fitting function, and calculate and output the guidance instructions that meet the terminal's multi-constraint conditions through the current flight time to complete the control of the aircraft's landing point and speed.

[0014] The beneficial effects of the present invention are as follows: the method for precise control of the landing point and speed of an aircraft based on the optimal control theory provided by the present invention has the actual input conditions of the current flight time t0 and position velocity vector x0 of the aircraft provided by an external device, and uses the initial instruction sequence u0 and the real-time instructions that meet the terminal landing point and speed capability obtained by the variational method, and solves the new instruction angle according to the target point parameters and the reference instructions, so as to form an instruction update closed-loop format, and the solution process has the characteristics of rapidity, strong real-time performance, and is suitable for online applications. The present invention solves the problem that the landing point and speed are difficult to accurately control during the reentry of an aircraft.

[0015] Furthermore, the expression of the terminal output in the current state is as follows:

[0016]

[0017] Where Output represents the terminal output in the current state, x(t) represents the state of the time-varying system, u(t) represents the control quantity of the time-varying system, t represents the flight time of the time-varying system, F[·] represents the differential equation satisfied by the state quantity of the aircraft, t0 represents the current flight time, t f represents the end time of the flight, dt represents the differential with respect to time t, and ∫ represents the integral sign.

[0018] The beneficial effect of the above further scheme is that the terminal output parameter Output during the flight of the aircraft is obtained through numerical integration calculation, which provides a basis for the subsequent calculation of the terminal deviation.

[0019] Furthermore, the expression of the modulus between the terminal output and the expected output is as follows:

[0020] d Output =x desire -x true

[0021] Among them, d Output Represents the modulus between the terminal output and the expected output, x desire represents the terminal's desired position velocity vector, x true Represents the actual position velocity vector.

[0022] The beneficial effect of the above further solution is that the terminal deviation vector modulus d is obtained by subtracting the preset expected terminal output from the actual terminal output. Output , providing a basis for subsequent instruction updates.

[0023] Furthermore, the state equation of the time-varying system is expressed as follows:

[0024]

[0025] in, represents the state equation of the time-varying system, x represents the state quantity of the system, which includes the position vector r and velocity vector v of the aircraft, and u represents the control quantity of the system;

[0026] The expression for constructing the two-point boundary value problem is as follows:

[0027] r(t0)=r0,v(t0)=v0

[0028] r(t f )=r f ,v(t f )=v f

[0029] Among them, r(t0) represents the position of the aircraft at time t0, r0 represents the initial position of the aircraft, v(t0) represents the speed of the aircraft at time t0, v0 represents the initial speed of the aircraft, r(t f ) indicates that the aircraft is at t f The position at the moment, r f represents the terminal position of the aircraft, v(t f ) indicates that the aircraft is at t f The speed at the moment, v f Indicates the aircraft terminal velocity.

[0030] The beneficial effect of the above further scheme is that a two-point boundary value problem is obtained by construction, which provides a basis for determining the augmented performance index.

[0031] Furthermore, the expression of the performance indicator is as follows:

[0032]

[0033] Among them, J represents the performance index, K(t) represents the time-varying weight coefficient, and T represents transposition;

[0034] The expression of the augmented performance index is as follows:

[0035]

[0036] λ x =[λ r λ v ]

[0037] in, represents the augmented performance index, λ x represents the co-state vector corresponding to the state quantity, λ r , v denote the co-state vectors corresponding to the position and velocity vectors, respectively. represents the derivative of the aircraft state quantity, and F(x,u,t) represents the differential equation satisfied by the aircraft state quantity.

[0038] The beneficial effect of the above further scheme is that through the performance index and the boundary value problem obtained by construction, the augmented performance index is finally determined, which provides a basis for the subsequent solution of the equation satisfied by the optimal control quantity.

[0039] Furthermore, the expressions of the control equation and the adjoint equation are as follows:

[0040]

[0041]

[0042] in, represents the governing equation, and represents the adjoint equation, H represents the Hamiltonian function, represents the optimal first-order necessary condition.

[0043] The beneficial effect of the above further scheme is: based on the augmented performance index, combined with the Hamiltonian function and the first-order necessary conditions, the relationship satisfied by the control quantity is obtained, which provides a basis for the subsequent solution of the updated optimal instruction analytical expression.

[0044] Furthermore, the expression of the optimal control instruction is as follows:

[0045]

[0046]

[0047] Among them, u n represents the optimal control command, u0 represents the benchmark command, D n It represents the Jacobian matrix related to the position vector r, velocity vector v of the aircraft and the control quantity u of the system, N represents the number of discrete nodes, and n represents the parameter of the nth discrete node.

[0048] The beneficial effect of the above further scheme is that by solving the relationship satisfied by the optimal instruction, the optimal instruction at each discrete node is obtained, which provides a basis for the fitting output of the guidance instruction.

[0049] Furthermore, the expression of the guidance instruction is as follows:

[0050] u now =Polyfit(u n )

[0051] Among them, u now represents the guidance instruction, and Polyfit(·) represents the fitting function. BRIEF DESCRIPTION OF THE DRAWINGS

[0052] Figure 1 The figure is a flow chart of the method of the present invention.

[0053] Figure 2 Schematic diagram of the flight instruction approximation curve in this embodiment.

[0054] Figure 3 Schematic diagram of Jacobian matrix analysis verification curve in this embodiment.

[0055] Figure 4 Schematic diagram of the Monte Carlo target position accuracy and flight time deviation statistical curve in this embodiment.

[0056] Figure 5 Schematic diagram of the Monte Carlo target shooting speed inclination angle and speed deviation angle statistical curve in this embodiment. DETAILED DESCRIPTION

[0057] The specific implementation modes of the present invention are described below so that those skilled in the art can understand the present invention. However, it should be clear that the present invention is not limited to the scope of the specific implementation modes. For those of ordinary skill in the art, as long as various changes are within the spirit and scope of the present invention as defined and determined by the attached claims, these changes are obvious, and all inventions and creations utilizing the concept of the present invention are protected.

[0058] Example

[0059] As can be seen from the above description, the main purpose of the present invention is to solve the problem that the landing point and speed are difficult to be accurately controlled during the re-entry of the aircraft. Due to some shortcomings of the existing guidance methods, such as when considering the maneuvering deceleration and the stability of the control system at the same time, it is impossible to complete the ballistic downward pressure and achieve directional strikes within a limited time; and for the method of tracking the ideal flight profile such as the speed and altitude profile, the accuracy of the landing speed control is difficult to guarantee due to the low accuracy of the model; the method of guiding the aircraft to a suitable handover point has the problem that the handover point is difficult to obtain and the instructions before and after the handover may have a large mutation, making it difficult to achieve the established task. Therefore, in order to improve the precise control of the landing point and speed during the re-entry of the aircraft, the present invention, based on the optimal control theory and the variational method, transforms the original terminal constraint problem into a two-point boundary value problem for solution, and obtains the analytical form solution of the instruction update, which has a strong adaptability and can achieve precise control of the landing point and speed.

[0060] like Figure 1 As shown, the present invention provides a method for controlling the landing point and speed of an aircraft based on optimal control theory, and the implementation method thereof is as follows:

[0061] S1. Determine the current flight parameters: obtain the current flight time and position velocity vector according to the output of the navigation device;

[0062] S2. Determine the terminal output under the current state: Calculate all state parameters from the current moment to the end of the flight using the initial instruction sequence and the current flight parameters, and provide data support for solving the subsequent optimal control problem;

[0063] In this embodiment, the expression of the terminal output in the current state is as follows:

[0064]

[0065] Where Output represents the terminal output in the current state, x(t) represents the state of the time-varying system, u(t) represents the control quantity of the time-varying system, t represents the flight time of the time-varying system, F[·] represents the differential equation satisfied by the state quantity of the aircraft, t0 represents the current flight time, t f represents the end time of the flight, dt represents the differential with respect to time t, and ∫ represents the integral sign;

[0066] S3, determine whether to output the guidance instruction: determine whether the module value between the terminal output and the expected output meets the preset index requirements, if so, output the guidance instruction and end the process, otherwise, enter step S4;

[0067] In this embodiment, the calculated modulus d between the terminal output and the expected output Output Make a judgment, where d Outputis the terminal desired position velocity vector x desire With the actual position velocity vector x true Deviation value, and d Output =x desire -x true , if the predetermined index ε is met desire If the requirement is met, the guidance instruction is output and the process ends; if it is not met, the next step is entered to transform the original problem into an optimal control problem for solution. The judgment logic is as follows;

[0068] if||d Output ||≤ε desire : Directly output guidance instructions

[0069] if||d Output ||>ε desire : Solving the optimal control problem

[0070] S4. Determine the state equations satisfied during the flight and the problem transformation: According to the current flight time and position velocity vector, obtain the state equation of the time-varying system, and construct a two-point boundary value problem through the continuous state equation;

[0071] In this embodiment, the dynamic model of the aircraft belongs to a group of nonlinear time-varying differential equations, which can be expressed as:

[0072]

[0073]

[0074] Where r is the position vector, v is the velocity vector, g is the gravitational acceleration, and u is the acceleration generated by the thrust and aerodynamic force other than gravity. The present invention regards u as the control quantity. Based on the above description, the center of mass dynamics equation of the aircraft can be simplified to the state equation of the time-varying system:

[0075]

[0076] in, The state equation of the time-varying system represents the relationship between the state and control quantities of the time-varying system.

[0077] In order to achieve precise control of the landing point and speed, that is, precise control of the terminal position velocity vector, the current position vector and velocity vector are combined to form a typical two-point boundary value problem:

[0078] r(t0)=r0,v(t0)=v0

[0079] r(t f )=rf ,v(t f )=v f

[0080] Among them, r(t0) represents the position of the aircraft at time t0, r0 represents the initial position of the aircraft, v(t0) represents the speed of the aircraft at time t0, v0 represents the initial speed of the aircraft, r(t f ) indicates that the aircraft is at t f The position at the moment, r f represents the terminal position of the aircraft, v(t f ) indicates that the aircraft is at t f The speed at the moment, v f Indicates the aircraft terminal velocity.

[0081] Designing the minimum overall control energy with time-varying weights as the performance indicator can effectively reduce the overall overload, as shown in the following formula:

[0082]

[0083] Among them, J represents the performance index, K(t) represents the time-varying weight coefficient, T represents the transposition, and n is the time-varying weight coefficient, which is usually 1. When n=1, the performance index is the minimum control energy of the time-varying weight, which effectively reduces the required overload while taking into account the convergence of the overload. So far, the dynamic model, constraint conditions and index function of the optimal control problem have been constructed, and the problem will be solved by the variational method.

[0084] S5. Determine the augmented performance index: According to the minimum setting of the overall control amount, the performance index of the optimization problem is set, and combined with the equality constraints in the two-point boundary value problem, the Lagrange multiplier is introduced to combine the equality constraints with the performance index to obtain the augmented performance index;

[0085] In this embodiment, the performance index J of the optimization problem is set according to the minimum overall control amount, and then the terminal constraint is combined with the performance index according to the Lagrange multiplier to obtain the augmented performance index J, which lays the foundation for solving the subsequent optimal control problem.

[0086] S6. Determine the control equation and adjoint equation: According to the augmented performance index, introduce Hamiltonian function and variational optimal control theory to obtain the control equation and adjoint equation;

[0087] S7, determining the optimal control instruction: according to the control equation and the adjoint equation, the optimal control instruction is obtained by eliminating the co-state vector through discretization;

[0088] S8. Output guidance instructions: Approximate the optimal control instruction sequence according to the fitting function, and calculate and output the guidance instructions that meet the terminal's multi-constraint conditions through the current flight time to complete the control of the aircraft's landing point and speed.

[0089] In this embodiment, the precise control method of the landing point and speed of the aircraft based on the variational method theory, when n=1, the control energy of the time-varying weight is minimized as the performance index to reduce the whole-stage overload and ensure the overload convergence. At this time, the performance index form becomes:

[0090]

[0091] Among them, J represents the performance index, t0 represents the current flight time, u represents the control amount, t f represents the end time of the flight, K(t) represents the time-varying weight coefficient, and T represents the transpose.

[0092] The guidance law can be obtained by solving the two-point boundary value problem. The Lagrange multiplier is introduced to combine the terminal constraint with the performance index, which is:

[0093]

[0094] λ x =[λ r λ v ]

[0095] in, represents the augmented performance index, λ x represents the co-state vector corresponding to the state quantity, λ r , v denote the co-state vectors corresponding to the position and velocity vectors, respectively. represents the derivative of the aircraft state quantity, and F(x,u,t) represents the differential equation satisfied by the aircraft state quantity.

[0096] The Hamiltonian function corresponding to this performance indicator is:

[0097]

[0098] Where: x =[λ r λ v ] and r , v are the co-state vectors corresponding to the position and velocity vectors, respectively, and K(t) is the time-varying weight coefficient. By solving the optimal control problem by the variational method, we can obtain the control equation and the adjoint equation:

[0099]

[0100] in, represents the governing equation, and represents the adjoint equation, H represents the Hamiltonian function, represents the optimal first-order necessary condition.

[0101] By discretizing and eliminating the co-variable λ r and λ v , the solution of the optimal control instruction is:

[0102]

[0103] D n The calculation is as follows:

[0104]

[0105] Among them, u n represents the optimal control command, u0 represents the benchmark command, D n represents the Jacobian matrix related to the position vector r, velocity vector v of the aircraft and the control quantity u of the system, N represents the number of discrete nodes, and n represents the parameter of the nth discrete node. The right side of the equation is the Jacobian matrix between the trajectory parameters, which can be solved by the trajectory difference method or the analytical recursive method. One solution method is:

[0106]

[0107]

[0108] Output guidance instructions u that satisfy the terminal's multiple constraints now , to meet the terminal's multi-constraint requirements: The instruction is calculated as follows, where Polyfit is the specified fitting function, such as polynomial fitting.

[0109] u now =Polyfit(u n )

[0110] Among them, u now represents the guidance instruction, and Polyfit(·) represents the fitting function.

[0111] In this embodiment, the actual input conditions of the method for precise control of the landing point and speed of an aircraft based on optimal control theory are the current flight time t0 and position velocity vector x0 of the aircraft provided by external devices. The initial instruction sequence u0 and the real-time instructions that meet the terminal landing point and speed capabilities are obtained according to the variational method, and the new instruction angle is solved according to the target point parameters and the benchmark instructions. This can form a closed-loop format for instruction update. The solution process is characterized by rapidity and strong real-time performance, making it suitable for online applications.

[0112] The present invention is verified below, and the implementation examples of the present invention are:

[0113] (1) Flight command approach effect verification

[0114] like Figure 2As shown, for instructions in different fitting time intervals, as the number of the highest term increases, the instruction approximation effect becomes better and better, which means that the instruction output can be performed with high precision, where φ is the instruction. Figure 2 (a) is the curve of the instruction fitting result changing with the fitting order N, where the fitting time interval is [228s, 631s], N = 5, 10, 15, 20. It can be seen that with the increase of the fitting order, the fitting accuracy gradually improves; Figure 2 (b) is the fitting result of the fitting order N = 60, where the fitting time interval is [228s, 631s], the maximum absolute error is only 0.01°, and the relative error is only 1e-4, and the fitting accuracy is very high; Figure 2 (c) is the curve of the instruction fitting result changing with the fitting order N, where the fitting time interval is [0s, 682s], N = 5, 10, 15, 20. It can be seen that with the increase of the fitting order, the fitting accuracy gradually improves; Figure 2 (d) is the fitting result with the fitting order N=60, where the fitting time interval is [0s, 682s], the maximum absolute error is only 0.001°, and the relative error is only on the order of 1e-5, and the fitting accuracy is very high.

[0115] (2) Jacobian matrix analytical solution verification

[0116] like Figure 3 As shown in Figure 1, some Jacobian matrix components were verified by analytical difference, and the relative deviation between the analytical solution accuracy and the true value was only one thousandth. Figure 3 (a) is a comparative verification of the partial derivative of atmospheric density with respect to height. The ordinate is the partial derivative of atmospheric density with respect to height, the abscissa is height, the solid line is the difference solution result, and the dotted line is the analytical solution result. It can be seen that the analytical solution is very consistent with the numerical solution. Figure 3 (b) is a comparative verification of the partial derivative of the speed of sound with respect to height. The ordinate is the partial derivative of the speed of sound with respect to height, the abscissa is height, the solid line is the analytical solution result, and the dotted line is the differential solution result. It can be seen that the analytical solution is very consistent with the numerical solution.

[0117] (3) Statistics of parameters related to position and speed control under Monte Carlo shooting conditions

[0118] As shown in Table 2, Table 2 is the statistical results of the Monte Carlo simulation of the fixed-point flight mission under deviation conditions. The dispersion of the landing point position and speed deviation is relatively small. The proposed landing point and speed control method based on the optimal control theory achieves the purpose of high-precision position and speed control. Figure 4 As shown, the landing point miss is less than 1m and the flight time deviation is only in milliseconds, which shows that the mission accuracy is guaranteed. Figure 4(a) shows the statistical results of the aircraft's landing point miss distance and the number of target shots. The mean miss distance is 0.34m and the standard deviation is 0.0402m, which shows that the landing point accuracy is very high. Figure 4 (b) shows the statistical results of the aircraft flight time deviation and the number of target shots. The mean of the flight time deviation is 0.00364s, and the standard deviation is 0.117s. The flight time deviation is very small.

[0119] Table 1

[0120]

[0121] The deviations at all levels are randomly selected according to the normal distribution, where the mean of the normal distribution is the standard value of each parameter. The deviations at all levels are treated as interference at the same time. 1000 target shooting simulation experiments are carried out, and the terminal constraint velocity inclination angle and velocity deviation angle of 1000 simulations are statistically analyzed. Figure 5 (a) is the curve of the aircraft velocity inclination angle theta changing with time. The terminal velocity inclination angle theta is around 2.3°, which meets the flight requirements. Figure 5 (b) is the curve of the aircraft velocity angle sigma changing with time. The terminal velocity angle sigma is around -0.5°, which meets the flight requirements.

Claims

1. A method for controlling the landing point and speed of an aircraft based on optimal control theory, characterized in that: The following steps are involved: S1. Determine the current flight parameters: obtain the current flight time and position velocity vector according to the output of the navigation device; S2. Determine the terminal output under the current state: use the initial instruction sequence and the flight parameters at the current moment to calculate all state parameters from the current moment to the end of the flight; The expression of the terminal output in the current state is as follows: in, Indicates the terminal output in the current state. represents the state of a time-varying system, represents the control quantity of the time-varying system, represents the flight time of the time-varying system, Represents the differential equation satisfied by the aircraft state quantity, Indicates the current flight time. Indicates the end time of the flight. Indicates time The differential of represents the integral symbol; S3, determine whether to output the guidance instruction: determine whether the module value between the terminal output and the expected output meets the preset index requirements, if so, output the guidance instruction and end the process, otherwise, enter step S4; The expression of the modulus between the terminal output and the expected output is as follows: in, Indicates the modulus between the terminal output and the expected output. represents the terminal's expected position velocity vector, Represents the actual position velocity vector; S4. Determine the state equations satisfied during the flight and the problem transformation: According to the current flight time and position velocity vector, obtain the state equation of the time-varying system, and construct a two-point boundary value problem through the continuous state equation; The state equation of the time-varying system is expressed as follows: in, represents the state equation of the time-varying system, Represents the state of the system, which includes the position vector of the aircraft With velocity vector , Indicates the control quantity of the system; The expression for constructing the two-point boundary value problem is as follows: in, Indicates that the aircraft is The location at the moment, represents the initial position of the aircraft, Indicates that the aircraft is The speed of time, represents the initial velocity of the aircraft, Indicates that the aircraft is The location at the moment, Indicates the aircraft terminal position, Indicates that the aircraft is The speed of time, Indicates the terminal velocity of the aircraft; S5. Determine the augmented performance index: According to the minimum setting of the overall control amount, the performance index of the optimization problem is set, and combined with the equality constraints in the two-point boundary value problem, the Lagrange multiplier is introduced to combine the equality constraints with the performance index to obtain the augmented performance index; The expression of the performance index is as follows: in, Represents performance indicators, represents the time-varying weight coefficient, represents transpose; The expression of the augmented performance index is as follows: in, represents the augmented performance index, represents the co-state vector corresponding to the state quantity, , denote the co-state vectors corresponding to the position and velocity vectors, respectively. represents the derivative of the aircraft state quantity, The differential equations satisfied by the aircraft state quantities are expressed; S6. Determine the control equation and adjoint equation: According to the augmented performance index, introduce Hamiltonian function and variational optimal control theory to obtain the control equation and adjoint equation; S7, determining the optimal control instruction: according to the control equation and the adjoint equation, the optimal control instruction is obtained by eliminating the co-state vector through discretization; S8. Output guidance instructions: Approximate the optimal control instruction sequence according to the fitting function, and calculate and output the guidance instructions that meet the terminal's multi-constraint conditions through the current flight time to complete the control of the aircraft's landing point and speed.

2. The method for controlling the landing point and speed of an aircraft based on optimal control theory according to claim 1, characterized in that: The expressions of the control equation and adjoint equation are as follows: in, represents the governing equation, and represents the adjoint equation, represents the Hamiltonian function, represents the optimal first-order necessary condition.

3. The method for controlling the landing point and speed of an aircraft based on optimal control theory according to claim 2, characterized in that: The expression of the optimal control instruction is as follows: in, represents the optimal control instruction, Indicates the base instruction, Represents the position vector with respect to the aircraft , velocity vector and the control quantity of the system The associated Jacobian matrix, represents the number of discrete nodes, Indicates Discrete node parameters.

4. The method for controlling the landing point and speed of an aircraft based on optimal control theory according to claim 3, characterized in that: The expression of the guidance instruction is as follows: in, Indicates guidance instructions, represents the fitting function.

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