Proportional guidance method based on neural network

Abstract

The invention provides a proportional guidance method based on a neural network. The method comprises the following steps: for the current moment, acquiring position and attitude information of a target and an aircraft; based on the position and attitude information of the target and the aircraft, respectively using a neural network and a proportional guidance law to generate control quantities; performing weighted summation on the control quantity generated by using the neural network and the proportional guidance law to obtain the control quantity required at the current moment; wherein the weighting coefficient is at least related to the height of the aircraft. Compared with an existing proportional guidance method with angle constraint, the method gives consideration to the ballistic end velocity, planning real-time performance and impact angle satisfaction under the condition of considering high dynamic.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of aircraft terminal guidance law design, in particular to a proportional navigation guidance method based on neural network. More specifically, the method relates to a terminal guidance method combining hp adaptive pseudospectral method, neural network, quasi-Newton iteration method and Lyapunov-based proportional navigation guidance law. BACKGROUND

[0002] As the last and most important link of various aircraft (especially hypersonic aircraft) attacking the ground, the design of accurate terminal guidance law has an important influence on the guidance accuracy of the aircraft and the damage effect on the target. For example, the objects of hypersonic aircraft attacking the ground are mainly missile launchers, large building groups and hidden defense works, etc. The aircraft not only needs to have high precision and large falling speed, but also needs to hit the target at a nearly vertical angle, so as to exert the maximum damage effect.

[0003] Proportional navigation guidance law (PNG law) is an effective homing guidance law applied to aircraft (for example, tactical missiles), which is simple in form, easy to implement in technology, and does not need too much information, and the main purpose is to improve the attack precision on the target, but the trajectory generated by the algorithm is relatively flat, and there are problems of low real-time performance, inability to well meet the large falling speed and expected falling angle, etc., which restrict the application of the algorithm. The guidance law based on biased proportional navigation adds a bias term to compensate the command, so that the flight trajectory satisfies the terminal angle constraint, but its derivation process depends on the small angle linearization assumption of the initial line-of-sight angle, and the guidance performance decreases when the initial line-of-sight angle is large. Lyapunov-based angle constraint guidance (LIACG) is suitable for nonlinear cases with large heading deviation, but does not consider the falling speed index.

[0004] Therefore, it is necessary to improve the guidance law. SUMMARY

[0005] In order to solve the problem that the proportional navigation guidance law cannot simultaneously satisfy the real-time performance, large falling speed and expected falling angle, the present application proposes a multi-constraint online iterative proportional navigation guidance method based on neural network, so as to improve the ability of the aircraft attacking the ground.

[0006] One aspect of the present invention provides a proportional guidance method based on a neural network. The method includes: acquiring, for the current moment, the position and attitude information of a target and an aircraft; generating control quantities using a neural network and a proportional guidance law based on the position and attitude information of the target and the aircraft; and performing a weighted summation of the control quantities generated by the neural network and the proportional guidance law to obtain the control quantity required for the current moment; wherein the weighting coefficients are at least related to the altitude of the aircraft.

[0007] In an exemplary embodiment of the present invention, the neural network is an iterative guidance network; the proportional guidance law is based on Lyapunov's angle-constrained proportional guidance law; and the weighted summation formula is as follows: a = ρa cx +(1-ρ)a PN Where, the weight coefficient ρ∈[0,1], a cx a represents the control quantity given by the iterative guidance network. PN The control quantity is given by the proportional guidance law based on the landing angle constraint of Lyapunov; the weighting coefficient ρ is designed in the following form: So that: if the altitude difference between the aircraft and the target is hh mid As ρ increases, it also increases to approach 1, and the weights of the control quantities given by the iterative guidance network increase accordingly; if the altitude difference hh between the aircraft and the target... mid As the value decreases, ρ decreases accordingly to approach 0, and the weight of the control quantity given by the Lyapunov-based angle constraint proportional guidance law increases.

[0008] In an exemplary embodiment of the present invention, the control quantities include the roll angle and the angle of attack; wherein generating the control quantities from the proportional guidance law includes: calculating the lateral guidance command based on the position and attitude information of the target and the aircraft. Where K is the proportional guidance coefficient; V is the vehicle velocity vector; It is the ballistic deflection acceleration of the aircraft; The lateral line-of-sight angle change rate is used; based on the target and the aircraft's position and attitude information, the longitudinal guidance command is calculated: Where K is the proportional guidance coefficient; V is the vehicle velocity vector; The longitudinal line-of-sight angle change rate; based at least on the lateral guidance command and the longitudinal guidance command, the tilt angle is calculated as: σ n =atan2(-n y ·cosγ,n z +g cosγ) where atan is the arctangent function, γ is the aircraft trajectory tilt angle, and g is the gravitational acceleration; at least based on the tilt angle, the lift coefficient C is calculated through the dynamic equations.L Based on the lift coefficient C L The angle of attack is obtained based on the correspondence between lift coefficient, Mach number, and angle of attack in the aerodynamic database; wherein the aerodynamic database is the CAV-L aerodynamic database.

[0009] In an exemplary embodiment of the present invention, the training process of the neural network includes:

[0010] Step 1.1: For multiple given initial states of the aircraft, the HP adaptive pseudospectral method is used to find control variables that minimize the cost function, obtaining data for multiple optimal trajectories that guide the aircraft to the target position while satisfying the constraints. The minimum sum of squares of the control variables is selected as the performance index of the cost function. The constraints of the aircraft's terminal state variables are also selected as the performance index of the cost function. Step 1.2: For each of the multiple initial states of the aircraft, a polynomial curve is fitted to the optimal trajectory and the corresponding control variables. The fitting of the angle of attack in the control variables and the altitude data in the trajectory is as follows: α cx =c3H 3 +c2H 2 In the formula: +c1H+c0, α cx c0, c1, c2, c3 are fitting coefficients; H is the height.

[0011] Step 2.1: For each of the multiple initial states of the aircraft, establish a data pair between the aircraft's state variable set and the fitting coefficients; wherein the state variable set includes at least: range error and terminal ballistic tilt angle error; Step 2.2: Use multiple data pairs corresponding to the multiple initial states of the aircraft as standard samples to train the neural network; wherein the structure of the neural network is set to 1 input layer, 4 hidden layers, and 1 output layer; the input layer contains 6 neurons for receiving the aircraft's state variable set, each hidden layer contains 64 neurons; the output layer contains 4 neurons for outputting the fitting coefficients; the input layer and hidden layers, and the hidden layers and output layers are connected by linear weights, and each hidden layer is connected by linear weights, with a hyperbolic tangent tanh function added as the activation function; wherein the loss function is MSE, and the Adam method is used to train the neural network.

[0012] In the example embodiment of the present application, generating the control quantity using the neural network comprises: generating a state variable group of the aircraft at the current time based on the target and position and attitude information of the aircraft; inputting the state variable group of the aircraft at the current time into the neural network to obtain a fitting coefficient at the current time; optimizing the fitting coefficient at the current time output by the neural network using a quasi-Newton iteration method; and calculating an angle of attack in the control quantity based on at least the optimized fitting coefficient at the current time and the height of the aircraft.

[0013] The present application has the advantages that:

[0014] 1. In the embodiment of the present application, the control quantities generated using the neural network and the proportional guidance law respectively are weighted and summed to obtain the required control quantity at the current time. In addition, the weighting coefficients are related to at least the height of the aircraft. In this way, the aircraft can achieve accurate attack on the target position and more easily meet the relevant constraints of the terminal state (e.g., ballistic inclination angle, etc.).

[0015] 2. More specifically, the present application proposes a three-order angle of attack height polynomial reference profile that takes into account both the form simplicity and the ease of guidance and tracking implementation based on the hp adaptive pseudospectral method, the neural network, the quasi-Newton iteration method and the Lyapunov-based impact angle constraint proportional guidance law, and fits the reference profile of different ballistic states and angles of attack to improve the algorithm efficiency.

[0016] 3. The present application optimizes and corrects the initial value of the polynomial reference profile predicted by the neural network using the quasi-Newton method based on the hp adaptive pseudospectral method, the neural network, the quasi-Newton iteration method and the Lyapunov-based impact angle constraint proportional guidance law, taking into account the requirements of the impact point constraint and the impact velocity constraint.

[0017] 4. The present application proposes a method that can switch from the polynomial profile predicted and corrected by the neural network to the Lyapunov-based impact angle constraint proportional guidance law based on the hp adaptive pseudospectral method, the neural network, the quasi-Newton iteration method and the Lyapunov-based impact angle constraint proportional guidance law, while meeting the large impact angle control guidance and real-time requirements, and also has good guidance accuracy and reliability in the presence of uncertain factors. BRIEF DESCRIPTION OF DRAWINGS

[0018] Figure 1 The present application is based on the hp adaptive pseudospectral method, the neural network, the quasi-Newton iteration method and the Lyapunov-based impact angle constraint proportional guidance law flowchart.

[0019] Figure 2 The present application is based on the hp adaptive pseudospectral method, the neural network, the quasi-Newton iteration method and the Lyapunov-based impact angle constraint proportional guidance law flowchart.

[0020] Figure 3Trajectory design related parameters.

[0021] Figure 4 Trajectory design related parameters. Figure 5 State normalization method table.

[0022] Figure 6 Constraint parameter setting table. Figure 7 Trajectory design problem structure parameter table.

[0023] Figure 8 Trajectory initial conditions at different altitudes. Figure 9 Terminal state constraints at different altitudes.

[0024] Figure 10A Nominal space trajectory at different initial altitudes. Figure 10B Example of data related to one of the nominal space trajectories.

[0025] Figure 11 Nominal trajectory inclination angle curves at different initial altitudes. Figure 12 Angle of attack curves at different initial altitudes. Figure 13 Angle of attack-altitude fitting profile at different initial altitudes.

[0026] Figure 14 Polynomial coefficient distribution at different initial altitudes.

[0027] Figure 15A Picture showing root mean square error RMSE and loss function MSE after neural network training. Figure 15B Neural network generated data parameter table.

[0028] Figure 16 Coordinate system and geometric relationship of Lyapunov-based impact angle constraint proportional guidance law.

[0029] Figure 17 Three-dimensional space trajectories under different lateral distances. Figure 18 Control variable curves under different lateral distances. Figure 19 Trajectory state variable curves under different lateral distances. Figure 20 Terminal state deviations under different lateral distances.

[0030] Figure 21 Three-dimensional space trajectories under different ranges. Figure 22 Control variable curves under different ranges. Figure 23 Trajectory state variable curves under different ranges.

[0031] Figure 24 Three-dimensional space trajectories under different terminal trajectory inclination angle constraints.Figure 25 Control quantity curves for different terminal ballistic inclination angle constraints. Figure 26 Each ballistic state quantity curve for different terminal ballistic inclination angle constraints.

[0032] Figure 27 Monte Carlo shooting deflection distribution diagram. Figure 28 Monte Carlo shooting x-direction error probability distribution diagram. Figure 29 Monte Carlo shooting y-direction error probability distribution diagram. Figure 30 Monte Carlo shooting terminal ballistic inclination angle error probability distribution diagram. Figure 31 Monte Carlo shooting terminal velocity distribution diagram.

[0033] Figure 32 Monte Carlo shooting three-dimensional space ballistic diagram. Figure 33 Monte Carlo shooting velocity curve. Figure 34 Monte Carlo shooting attack angle curve. Figure 35 Monte Carlo shooting roll angle curve. Figure 36 Monte Carlo shooting ballistic inclination angle curve. DETAILED DESCRIPTION

[0034] The present application will be further described in detail below with examples.

[0035] The present application is based on hp adaptive pseudospectral method, neural network, quasi-Newton iteration method and Lyapunov-based impact angle constraint proportional guidance law, as shown in Figure 1

[0036] First, the aircraft control process is described.

[0037] In the process of guiding the aircraft to fly towards the target, with the help of the aircraft's own sensors or guidance information from the outside world, the aircraft first obtains the position and attitude information of the target and itself at the current time.

[0038] These information are input to the interception geometry configuration, which refers to the geometric shape formed by the relative position and attitude relationship between the interceptor (for example, the aircraft here) and the target in the interception process. For example, in the present application, direct impact on the target is expected to be achieved.

[0039] The relevant information in the interception geometry configuration (i.e. the position, attitude, etc. of the target and the aircraft itself) are output to the guidance neural network and the proportional guidance law (for example, the proportional guidance law with impact angle constraint) respectively.

[0040] The outputs (i.e. control quantities) of the guidance neural network and the proportional guidance law are combined. In the embodiments of the present application, a weighted manner can be used for combination. As described in the specific embodiments below, the weights can also vary.​

[0041] The combined control quantity is output to the aircraft, i.e. the control of the aircraft is completed, and the state of the aircraft is changed. The control process at one time is completed. When using the dynamic equation instead of the controller directly output to the aircraft, the process of prediction, simulation, etc. for the aircraft control process can be realized.

[0042] Before using the guidance neural network, the guidance neural network needs to be trained. The generation of the data set required for training, i.e. a plurality of standard input, output data pairs, will be described further below. Generally, the aircraft attitude information is taken as input, and the guidance parameter is taken as output. The guidance parameter is a parameter used to calculate the control quantity according to the current (relative to the target) attitude position information of the aircraft.

[0043] The parameter output by the guidance neural network can be further optimized before being used for guidance, and the optimization method will be described below.

[0044] The specific steps of how to obtain the final required combined guidance law are described in detail as follows:

[0045] Step 1: For a given plurality of initial states of the aircraft, the hp adaptive pseudospectral method is used to obtain optimal trajectory data reaching the target position satisfying the constraint conditions;

[0046] Solving the optimal flight trajectory problem of the hypersonic aircraft in the terminal phase is actually an optimal control problem. Solving this optimal control problem is to find the control variable under the condition of satisfying the path constraint and boundary constraint, so that the cost function is minimized. The hypersonic aircraft terminal trajectory optimization can be generally summarized as the following optimal control problem:

[0047]

[0048]

[0049] Φ(X(t0),t0,X(t f ),t f )=0

[0050] C(X(t),u(t),t)≤0

[0051] In the formula, s.t. represents the condition limited thereafter;

[0052] t0 is the initial time, and t f is the termination time;

[0053] is the dynamic equation of the aircraft; u(t) = [u1(t), u2(t)] is the control variable, which can be, for example, the attack angle and the roll angle of the aircraft;

[0054] Path constraints are C(X(t),u(t),t)≤0, for example, this can represent state path constraints: directly limit the value range or trajectory of system state variables. For example, one or more of the aircraft's altitude, speed, attitude angle, etc. state variables can be required to change within a certain range, which can also represent control path constraints: limit the value range or change mode of control variables (for example, the above-mentioned aircraft angle of attack, roll angle);

[0055] The boundary function is Φ(X(t0),t0,X(t f ),t f )=0, which can limit the state of the aircraft at the initial and terminal time, for example, specify the initial position, speed, and target state desired to be reached at the terminal time, etc., so as to guide the system to find the optimal control strategy that satisfies the performance index under the premise of meeting these boundary conditions;

[0056] The integral cost function is g(X(t),u(t),t), which can represent the difference between the current state of the aircraft, the control amount and the ideal state, the control amount, for example, the difference in various aspects such as flight altitude, speed, overload, control amount change rate.

[0057] For example, in an embodiment of the present application, in order to make the optimized angle of attack and roll angle smooth enough, the sum of squares of each control amount is selected as the performance index. At the same time, in order to enhance the robustness of the guidance algorithm, the constraint of the terminal state quantity is added to the performance index, and the specific form is:

[0058]

[0059] In the formula: K is a weighting coefficient. The optimal control makes the J minimum (min).

[0060] The pseudospectral method has great advantages in solving trajectory optimization problems. In this paper, the hp adaptive pseudospectral method is used as the trajectory optimization method. The hp adaptive pseudospectral method discretizes the optimal control problem into a sparse nonlinear programming (NLP) problem on a series of nodes, and then uses a nonlinear programming solver software to solve the optimal solution.

[0061] Therefore, the optimal trajectory, in essence, is to design a nominal state x * (t) and nominal input u * (t), that is, (x * (t), u *(t)), satisfying the impact requirements on the target. From a mathematical point of view, the trajectory optimization design problem is essentially a nonlinear optimal control problem with differential-algebraic constraints and inequality constraints, and its solution method can be divided into indirect method and direct method. The hp-adaptive pseudospectral method is a kind of direct method, and the GPOPSII software package based on the Radau pseudospectral method is used as a tool to design the optimal trajectory. The following is the definition of each element of the optimal trajectory obtained by the application under the constraint condition.

[0062] ①Dynamics equation

[0063] The aircraft angle and coordinate system definition is shown in Figure 2 . Considering that the atmosphere is relatively stationary relative to the earth, a three-dimensional coordinate system (x, y, z) of the plane earth is constructed, and it is assumed that the position of the initial point is (0, 0, h), the ballistic inclination angle γ is defined as the angle between the velocity vector V and the horizontal plane (the plane in which the x and y axes are located), and the upward direction is positive; the ballistic deflection angle is defined as the angle between the y axis and the horizontal component of the velocity, and the clockwise rotation is positive; the lift is L (F L ), the upward direction is positive, the drag is D (F D ), the backward direction is positive, and g is the gravity; the attack angle α (not shown) is the angle between the velocity direction and the longitudinal axis of the aircraft, and the upward direction is positive; X (V direction), Y, Z is the body coordinate system, L is the lift direction, and σ is the angle between the Z axis due to the roll motion of the aircraft, i.e. the roll angle of the aircraft, the direction is defined as the roll angle is positive when looking at the tail of the aircraft in the counterclockwise direction, then the dynamics equation of the downward segment of the aircraft can be written as:

[0064]

[0065] wherein, is the velocity of the aircraft in the x direction, is the velocity of the aircraft in the y direction, is the velocity of the aircraft in the z direction, is the linear acceleration of the aircraft, is the roll angle acceleration of the aircraft, is the ballistic deflection angle acceleration of the aircraft, is the attack angle acceleration of the aircraft, is the control variable, is the roll angle acceleration of the aircraft, is another control variable; ( is the rate of change of the attack angle of the aircraft, which ensures the continuity and smoothness of the change of the control variable and the roll angle. In the optimization process of generating the nominal trajectory by using the hp-adaptive pseudospectral method, u1 and u2 are control variables. But in the subsequent design of the terminal guidance law, the attack angle and the roll angle can be used as control variables) The reference area of the aircraft is S, the air density is ρ, the dynamic pressure is q, the Mach number is Ma, the lift coefficient (Coefficient of Lift) is CL The drag coefficient is C. D The flight altitude during the down-pressure phase is set at 30 km. An exponential atmospheric model is used to represent the variation in air density. All physical quantities used are expressed in SI units and their derived units, and angles are expressed in radians. The widely applicable hypersonic vehicle model CAV-L is used. For example, for a vehicle mass m = 816.47 kg, S = 0.3226 m... 2 (Aerodynamic reference area of ​​the CAV-L general aviation aircraft) Air density, dynamic pressure, and Mach number are:

[0066]

[0067] In the formula, e is the natural constant.

[0068] because Figure 3 The lift and drag coefficients shown are discretized for angle of attack and Mach number; that is, for the specific combinations of angle of attack and Mach number listed in the table, the available coefficients are given. However, for other combinations of angle of attack and Mach number not listed, corresponding calculations are required. For example, MATLAB functions can be used for... Figure 3 The data in the dataset were fitted using MATLAB's poly function to obtain coefficients that best suit the current aircraft condition (especially specific angles of attack and Mach numbers).

[0069] CAV-L's aerodynamic data are as follows Figure 3 As shown, the aerodynamic coefficient fitting formula for an aircraft in the lower dense atmosphere can be generally expressed as:

[0070]

[0071] The coefficients in the given formula (which can be determined based on the current practical application, for example, through computational simulation or experimental verification)

[0072] C L =0.05109-0.006128.*Ma+1.666.*alpha+0.0003574.*Ma.*Ma-0.03671.*alpha.*Ma

[0073] +1.628.*alpha.*alpha;

[0074] C D =0.1045-0.009765.*Ma+0.1643.*alpha+0.0003315.*Ma.*Ma-0.006391.*alpha.*Ma+2.31.*alpha.*alpha;

[0075] In the formula, for example, C L0 = 0.05109, C L1 = -0.006128…, the CL coefficient has a positive or negative sign.

[0076] Then, the lift and drag are:

[0077] L = qC L S

[0078] D = qC D S

[0079] In addition, for the sake of uniformity, the related parameters of trajectory design are set as shown in Figure 4 In order to control the change of dynamics equation caused by different dimensions, make the dynamics equation more uniform in form, and make the design of guidance law have stronger universality, the normalization parameter and method are adopted to normalize the dynamics equation. Figure 5 The state quantity normalization method diagram is shown in Figure 5 After the state quantity is normalized, the normalized dynamics equation is obtained as follows:

[0080]

[0081] In the formula, subscript 1 indicates that the parameter is a normalized parameter, R E is the radius of the earth, and r is the distance from the aircraft to the center of the earth. The parameter t refers to time, and the parameter R0 is the distance from the aircraft at the initial position to the center of the earth, and g0 is the initial position gravity acceleration.

[0082] The normalized dynamics can reduce each state quantity to a similar order of magnitude, which is beneficial to reduce calculation error and make the program optimization converge faster.

[0083] 2. Constraint conditions

[0084] Considering the heat protection and structural strength, the overload n N and the dynamic pressure q are constrained during flight:

[0085]

[0086] In the formula: q max and are selected according to the specific aircraft. Considering the harsh environment of the hypersonic aircraft during the final flight process, in addition to the requirement that the attack angle α and the roll angle σ should be kept within a certain range, the rate of change must also be kept within a certain range, i.e.:

[0087]

[0088] The landing point constraint is established considering the distance between the landing point and the target:

[0089]

[0090] where x diff ,y diff ,z diff are the three-axis distances between the landing point and the target. The impact angle constraint is established considering the impact effect on the target:

[0091] γ constrain-min ≤γ end ≤γ constrain-max

[0092] where γ constrain-min ,γ constrain-max are the minimum and maximum values of the terminal trajectory inclination angle. The greater the terminal velocity, the stronger the impact effect, and the landing velocity constraint is established:

[0093] v constrain-min ≤v end ≤v constrain-max

[0094] where v constrain-min ,v constrain-max are the minimum and maximum constraint values of the terminal velocity. The related parameter settings for the constraint conditions are shown in Table 1. Figure 6 The parameters of the trajectory design problem structure are shown in Table 2. Figure 7 The nominal trajectory of the aircraft is required to meet the following terminal constraint conditions under the initial and process pull-off conditions:

[0095]

[0096] where t f is the terminal landing time.

[0097] The variation ranges of the attack angle, the roll angle, and the control amount are as follows:

[0098]

[0099] It should be understood that the above specific steps, numerical values, etc. are only for illustrating examples of the present application, and are not limited, and other different steps, numerical values, etc. can also be applied.

[0100] ③ Attack angle-height polynomial profile fitting

[0101] For the optimal flight trajectory and the corresponding optimal guidance command data, further processing. For the angle of attack law analysis, extract the angle of attack-height, angle of attack trajectory inclination profile, through the third order polynomial curve fitting, obtain the angle of attack-height, angle of attack trajectory inclination benchmark profile analytical model. Because the third order polynomial form is simple, the curvature changes slowly, it is convenient for guidance tracking to realize, so the third order polynomial curve is used to fit the profile of the above state quantity, among them, the fitting consistency of the angle of attack-height profile is higher. The benchmark profile model expression is as follows:

[0102] α cx =c3H 3 +c2H 2 +c1H+c0

[0103] In the formula: α cx is the benchmark angle of attack profile; c0, c1, c2, c3 are fitting coefficients.

[0104] It should be understood that if the fitting consistency of other profiles is also high, the model of other profiles can also be used.

[0105] For the initial conditions listed in table 1 and the initial conditions based on Lyapunov's landing angle constraint proportional guidance law, Figure 8 The terminal state constraint of Figure 9 , the initial speed is 1870 m / s, the initial angle of attack is released, the space trajectory of Figure 10A ( Figure 10B is an example of a nominal trajectory), Figure 11 The trajectory inclination curve of Figure 12 The angle of attack-height curve of

[0106] The angle of attack in each case is not much different in the later period of flight, and the adjustment of the trajectory is mainly concentrated in the early stage, and finally all can meet the constraint condition that the terminal angle of attack is 0°. Because the initial speed is equal, as the initial height becomes higher and higher, the energy of the missile also becomes larger, and when reaching the terminal position, the energy needed to be consumed is also larger, and the time spent is also longer. For the missile with higher height, it needs to start with a larger angle of attack to decelerate, so that the trajectory is quickly pressed down, so the value of the initial angle of attack is also larger and larger. The angle of attack-height profile of Figure 12 is fitted by a polynomial curve, and the third order angle of attack-height benchmark profile analytical model of Figure 13 is obtained, Figure 14 is the distribution of each polynomial coefficient under different initial heights.

[0107] Therefore, for a given set of initial states of the aircraft, the fitting relationship between the angle of attack and the altitude (characterized by the above equations and coefficients) can be applied to directly calculate the required control quantity (angle of attack) at different altitudes of the aircraft through the processing of step 1.

[0108] In addition, after calculating the above polynomial coefficients for a plurality of initial states of the aircraft, a plurality of standard sample data sets are obtained, which can be used to train the neural network.

[0109] Step 2: Training the neural network

[0110] The terminal guided aircraft is affected by environmental disturbances, and the initial altitude is difficult to control accurately. The angle of attack altitude reference profile is sensitive to the initial point height deviation, so the reference profile is corrected. The purpose of using the neural network is to provide the initial value (c0, c1, c2, c3) for the optimal control numerical method to promote the solving efficiency and speed.

[0111] To improve the training effect of the neural network, define the range error e x and the terminal trajectory inclination error e γ :

[0112]

[0113] Therefore, the state variable group that is, the three-dimensional coordinates x, y, z of the aircraft in the plane, the trajectory inclination angle θ, and the trajectory deflection angle , etc. can be equivalently changed according to the position (for example, a coordinate value x f ) and attitude error (for example, an angle value γ f ) when reaching the target. For example, the equivalent transformation is and it is used as the input of the neural network, and the output of the neural network is the polynomial coefficients (c0, c1, c2, c3) of the angle of attack-altitude profile of the aircraft. That is, the standard sample data set here is a plurality of transformed state variables and the pairing of the polynomial coefficients.

[0114] Considering the fitting accuracy and calculation efficiency of the neural network, the structure of the neural network is set to 1 input layer, 4 hidden layers, and 1 output layer. The input layer includes 6 neurons for receiving the state variable group The hidden layers each contain 64 neurons. The output layer contains 4 neurons for outputting the polynomial coefficients (c0, c1, c2, c3) of the aircraft angle of attack-altitude profile. Linear weight connections are used between the input layer and the hidden layers, between the hidden layers and the output layer, and between the individual hidden layers, and a tanh (hyperbolic tangent) function is added as an activation function. It should be understood that the specific neural network structure, the functions used, etc. are examples, and other structures or functions can also be used.

[0115] Figure 15A Pictures of the root mean square error RMSE and the loss function MSE after the neural network training are shown. The loss function is MSE, i.e. Mean Squared Error, and the neural network is trained using the Adam method, with a data batch size of 512 for each learning, a learning rate of 0.0001, and the training is stopped when the loss function is less than 0.01.

[0116] During the neural network training process, the gradual decrease of the loss function is the core indicator of model optimization, and the smaller the value is, the closer the prediction results (predicted polynomial coefficients) of the model are to the true data (in the initial training stage, for example, the polynomial coefficients provided in the above standard samples). The mean squared error MSE refers to the squared difference between the predicted value and the true value, and the training process is essentially a process of constantly approaching the target value, so when the loss function is less than a certain value, the training network can be stopped.

[0117] During guidance, after the trained neural network receives the attitude data of the aircraft, it can output the above-mentioned polynomial coefficients for guidance.

[0118] In order to make the application scenarios of the trained neural network general, during the above-mentioned trajectory (sample) generation process, the GPOPSII software package is used to generate a nominal trajectory according to the parameters shown in Figure 15B , i.e. a certain number of nominal samples with a certain distribution are provided. Figure 15B The case of generating 7*5*20*3 training samples is shown in the above-mentioned table, and it should be understood that other quantities are also possible.

[0119] Then, as described before, the structure of the neural network is set to 1 input layer, 4 hidden layers, and 1 output layer using the trainNetwork function provided by matlab. The input layer contains 6 neurons for receiving the state variable group The hidden layer contains 64 neurons per layer. The output layer contains 4 neurons for outputting the polynomial coefficients (c0, c1, c2, c3) of the aircraft angle of attack-altitude profile. Linear weight connections are used between the input layer and the hidden layer, between the hidden layers and the output layer, and between each hidden layer, and a tanh function is added as the activation function.

[0120] The loss function is MSE, and the neural network is trained using the Adam method. The data batch size for each learning is 512, the learning rate is 0.0001, and the training is stopped when the loss function is less than 0.01.

[0121] Step 3: Use the quasi-Newton iterative method to optimize the profile initial value output by the neural network.

[0122] Neural networks have certain advantages in solving nonlinear problems and computing real-time performance, but fitting errors can affect the accuracy of the aircraft hitting the target. Therefore, the quasi-Newton iterative method is used to further optimize the angle of attack-altitude profile initial value output by the neural network.

[0123] The quasi-Newton method updates the positive definite matrix by iteration to approximate the inverse of the Hessian matrix, thereby avoiding the high cost of directly calculating the inverse of the Hessian matrix. For the objective function F(x k ), the general format of the quasi-Newton method is:

[0124] x k+1 =x k +λ k p k

[0125] p k =-C k -1 g k

[0126] where: λ k is the step size, usually determined by some line search method; p k is the search direction; is the gradient of the objective function; the quasi-Newton method has different correction formulas, which are reflected in different C k , common ones include the DFP algorithm and the BFGS algorithm:

[0127]

[0128] where: s k =x k+1 -x k , y k =g k+1 -g k .

[0129] Ck of DFP algorithm is H matrix, and Ck of BFGS is B matrix.

[0130] For example, in the embodiment of the application, the optimization process applying the quasi-Newton method is as follows:

[0131] 1) Let x=(c0, c1, c2, c3), and initialize the matrix B as an identity matrix;

[0132] 2) Calculate the objective function f(x) as follows:

[0133] f(x) = (L(c0, c1, c2, c3) - L goal ) 2

[0134] wherein L(c0, c1, c2, c3) is the range obtained by area division, i.e. the final position of the aircraft after applying the set of coefficients for flight guidance. L goal is the target range, i.e. the desired position;

[0135] 3) Obtain the gradient g(x) of each coefficient with respect to the objective function f(x), i.e. the ratio of the change of the objective function value to the change of the above-mentioned coefficients. The calculation method is as follows:

[0136]

[0137] If g(x)≤ε, the current optimal solution x opt =x is obtained. Wherein ε is the gradient tolerance value.

[0138] 4) Calculate the search direction p = -B×g(x);

[0139] 5) Obtain the line search step size α using the Armijo rule, which can make the function value of the objective function have sufficient decrease; the specific implementation of the Armijo rule can be determined according to the application scenario or the function tool that can be called, and need not be limited.

[0140] 6) Update the optimal solution x new =x+α×p, and obtain the updated gradient g(x new )

[0141] 7) Update the matrix B, and the calculation method is as follows:

[0142]

[0143] wherein the operators s=x new -x, and y=g(x new )-g(x);

[0144] 8) Judge g(x new) whether it is less than or equal to the allowable value ε, if yes, the optimal solution x opt = x new ; if no, return to step 4).

[0145] 9) Repeat steps 4) to 8) until the final optimal solution is found. For example, the termination condition can be the gradient judgment: when the modulus of the gradient is less than a certain preset threshold value ε1, it is considered that the optimal solution has been approached, and the iteration is stopped. Because at the optimal solution, the gradient is theoretically a zero vector. It can also be the iteration point change judgment: when the distance of the adjacent two iteration points ||x k+1 - x k || is less than a certain preset threshold value ε2, the iteration is stopped. This indicates that the change of the iteration point has been very small, and it is possible to converge to the optimal solution. It can also be the function value change judgment: when the difference of the objective function values of the adjacent two iterations |f(x k+1 )-f(x k )| is less than a certain preset threshold value ε3, the iteration is stopped. This means that the change of the objective function value has been very small, and it is possible to have reached the optimal.

[0146] After the complete updating process, the polynomial coefficients of the aircraft angle of attack-altitude profile that can be applied to actual guidance can be obtained.

[0147] Step 4: Switch to the Lyapunov-based impact angle constraint proportional guidance law using adaptive switching logic.

[0148] The coordinate system and geometric relationship of the target and the aircraft are shown in Figure 16 . This coordinate system takes the position of the aircraft as the origin and takes the east, north and vertically upward direction of the position of the aircraft as the coordinate axis direction. Combining the respective advantages of the iterative guidance network and the proportional guidance law, a combined attack angle constraint guidance law is designed:

[0149] a = ρa cx +(1-ρ)a PN

[0150] wherein the weight coefficient ρ in the formula ∈ [0, 1], a cx represents the guidance instruction (control quantity) calculated using the coefficients given by the iterative guidance network and after optimization, and a PN is the guidance quality (control quantity) obtained based on the Lyapunov-based impact angle constraint proportional guidance law.

[0151] The weight coefficient ρ can be designed as follows to realize the continuous transition of the guidance instruction:

[0152]

[0153] When the distance is far and the trajectory height is high (i.e. the height of the aircraft h - the height of the target h mid When the trajectory height is low, the main task of the guidance law is to satisfy the terminal trajectory angle constraint, and the main guidance law is the angle-proportional guidance law. At this time, p is close to 0.

[0154] For example, referring to the previous embodiment, a cx = c3H 3 + c2H 2 + c1H + c0.

[0155] In addition, various angle-of-descent constraint proportional guidance laws can be used, such as the guidance law described in “Du Zehong, Tang Shuo, Pan Bin. High-speed reentry aircraft with angle-of-descent constraint terminal guidance law [J]. Flight dynamics, 2013 (2): 139-142”.

[0156] First, the relationship between the guidance command (such as the longitudinal, lateral acceleration or overload required by the aircraft, etc.) and the controllable quantity (such as the angle of attack of the aircraft, the roll angle, etc.) is derived.

[0157] For example, the Lyapunov-based angle-of-descent constraint proportional guidance law is first decomposed into the longitudinal and lateral planes, and the lateral guidance law uses a simple proportional guidance law, and the guidance command can be:

[0158]

[0159] Where K is the proportional guidance coefficient; its role is to determine how much control action the aircraft needs to generate according to the size of the line-of-sight angular velocity, so that the aircraft can fly towards the target along the desired trajectory. When the proportional coefficient is large, the attitude of the aircraft can be changed quickly, however, the guidance accuracy may be reduced. The performance parameters of the aircraft (such as maximum maneuverability, speed, etc.), the motion characteristics of the target (such as speed, maneuverability, etc.), and the requirements of the guidance system (such as accuracy, stability, etc.) can be considered to determine, optimize and adjust the proportional guidance coefficient.

[0160] Where V is the velocity vector of the aircraft; is the trajectory bank angle acceleration of the aircraft; is the lateral line-of-sight angular rate

[0161]

[0162] Where V ⊥ is the component of the velocity vector of the aircraft perpendicular to the vertical plane in which the vector r from the aircraft points to the target; d is the horizontal distance between the aircraft and the target; x m , ym x represents the coordinates of the aircraft's horizontal plane; t y t V represents the coordinates of the target horizontal plane; c Let Vc and V be the projections of the aircraft's velocity vector onto the vertical plane containing the vector r that the aircraft points towards the target. ⊥ The sum of the two vectors gives the aircraft's velocity vector.

[0163] For the longitudinal plane guidance law, firstly, calculate the rate of change of the longitudinal line-of-sight angle:

[0164]

[0165] Where C1 and C2 are positive numbers (given constants, for example, C1 = 1, C2 = 0.4, used for regulation and control). Calculate the weights of the two terms on the right-hand side of the expression. η is the estimated remaining flight time; η is the lead angle of the aircraft in the vertical plane containing r, and q is the lead angle of the aircraft in the vertical plane containing r. vd The desired terminal trajectory inclination angle (q) v q represents the line-of-sight angle in the longitudinal plane. h This indicates the lateral line-of-sight angle; the subscript 'd' indicates the desired value. The final longitudinal guidance command is:

[0166]

[0167] This yields the relationships between relative position deviation, velocity deviation, and trajectory tilt angle deviation, as well as lateral and longitudinal guidance commands, and finally, the angle of attack and the tilt angle.

[0168] Upon receiving the lateral guidance command n y and longitudinal guidance command n z Then, the inverse solution is obtained from the kinetic equations:

[0169]

[0170] We can obtain:

[0171]

[0172] Right now:

[0173]

[0174] The required tilt angle is:

[0175] σ n =atan2(-n y ·cosγ,n + +g cosγ)

[0176] Guidance command ny , n z have been given, the rest are all known quantities related to the current flight attitude, thus the required control quantity, the roll angle, can be obtained.

[0177] Substitute the required roll angle into the dynamic equation, we get:

[0178]

[0179] where we can get,

[0180] Since other parameters are known, we can calculate C L . Then, according to the aerodynamic data Figure 3 table, we can get the required angle of attack value by bisection method. That is, use the C L of the aircraft, compare the Mach number with the coefficient Mach number in the table, and get the angle of attack value according to the related AOA data in the table.

[0181] In the actual guidance of the aircraft, the angle of attack and roll angle at this time can be used to control the motion of the aircraft.

[0182] In the process of trajectory prediction or verification, after obtaining the angle of attack and roll angle, we can get the trajectory curve by using the fourth-order Runge-Kutta integration.

[0183] In order to verify the effect of the algorithm, the performance of the guidance law under different initial lateral distances with fixed angle constraints is simulated, as shown in Figure 17 to Figure 20 . Record the terminal state deviation of the trajectory under different lateral distances, and the final terminal trajectory angle deviation can be guaranteed within the order of magnitude of 0.001, and the terminal velocity deviation meets the requirements.

[0184] Furthermore, the performance of the guidance law under different ranges with fixed angle constraints and different terminal trajectory angle constraints with fixed range is also simulated, and the experimental results are shown in Figure 21 to Figure 26 .

[0185] In order to further illustrate the effectiveness and robustness of the guidance algorithm, 500 Monte Carlo targeting experiments are carried out. For the flight environment, a drag bias model is established for the atmospheric density change with height:

[0186] ρ = ρ st + ρ(H)Δρ

[0187] where ρ(H) is a function of atmospheric density change with height, and ρ(H) can reach 0.05ρ st at most, and Δρ is a [-100%, 100%] drag bias coefficient.

[0188] For the aerodynamic pull-off model of an aircraft, a deviation is added to the standard aerodynamic coefficients:

[0189]

[0190] Where, ΔC L ,ΔC D C is the pull coefficient of the lift coefficient and drag coefficient. L,st C D,st The standard aerodynamic coefficients are given. The initial pull term and aerodynamic pull are as follows: Figure 27 As shown, velocity is quite sensitive to initial altitude and trajectory inclination, and velocity control capability is limited. Therefore, the initial altitude deviation and trajectory inclination deviation are relatively small.

[0191] Error P of terminal position in the x and y directions Δx ,P Δy probability distribution as Figure 28 , Figure 29 As shown, the error in each direction is within 0.1m. Figure 30 and Figure 31 The probability distribution of terminal ballistic inclination angle error P Δγ and terminal velocity distribution P v Most of them are distributed within the constraint range and satisfy the constraint conditions. Figure 32 to Figure 3 7 represents the ballistic cluster from the Monte Carlo firing experiment. Simulation results show that even under uncertainty conditions, the algorithm has advantages in terms of terminal velocity and impact angle satisfaction, and can achieve the expected results under different calculation conditions.

[0192] In summary, specific embodiments of the present invention can combine multiple guidance methods to solve the problem that proportional guidance laws cannot simultaneously satisfy real-time performance, high drop velocity, and desired drop angle. A multi-constraint online iterative proportional guidance method based on neural networks is proposed to improve the ground attack capability of aircraft.

[0193] Any appropriate steps, methods, features, functions, or benefits disclosed herein may be performed by one or more functional units or modules of one or more computing devices (especially aircraft control devices).

[0194] For example, an aircraft control device may include a processor and a memory storing instructions that can be executed by the processor. When the processor executes the relevant instructions, the aircraft control device performs the embodiments described above.

[0195] Furthermore, each computing device can include multiple such functional units. The functional units can be implemented via processing circuitry that can include one or more microprocessors or microcontrollers, as well as other digital hardware, which can include digital signal processors (DSPs), special-purpose computer chips, etc. The processing circuitry can be configured to execute program code stored in memory, which can include one or several types of memory such as read-only memory (ROM), random-access memory (RAM), cache memory, flash memory devices, optical storage, etc. The program code stored in memory includes program instructions for implementing telecommunication and / or data communication protocols and instructions for carrying out one or more of the techniques described herein. In some embodiments, the processing circuitry can be used to cause the corresponding functional unit(s) to perform corresponding functions according to one or more embodiments of the present disclosure.

[0196] The term "unit" can have the conventional meaning in the field of electronic, electrical, and / or computer hardware and can include, for example, electrical and / or electronic circuitry, devices, modules, processors, memories, logic solid-state and / or discrete devices, computer programs or instructions for carrying out respective tasks, procedures, computations, outputs, and / or displays, and so on, as those terms are conventionally used in the fields of electronic, electrical, and / or computer hardware.

Claims

1. A proportional guidance method based on neural networks, characterized in that, The method includes: At the current moment, obtain the position and attitude information of the target and the aircraft; Based on the target and the position and attitude information of the aircraft, control quantities are generated using neural networks and proportional guidance laws, respectively; and The control quantities generated using neural networks and proportional guidance laws are weighted and summed to obtain the control quantity required at the current moment. The weighting coefficients are at least related to the altitude of the aircraft.

2. The method according to claim 1, characterized in that: in, The neural network is an iterative guidance network; wherein the proportional guidance law is based on Lyapunov's angle-constrained proportional guidance law; and wherein the weighted summation formula is as follows: a=ρa cx +(1-p)a PN Where, the weight coefficient ρ∈[0,1], a cx a represents the control quantity given by the iterative guidance network. PN The control quantity is given by the proportional guidance law based on the landing angle constraint of Lyapunov; the weighting coefficient ρ is designed in the following form: So that: if the altitude difference between the aircraft and the target is hh mid As ρ increases, it also increases to approach 1, and the weights of the control quantities given by the iterative guidance network increase accordingly; if the altitude difference hh between the aircraft and the target... mid As the value decreases, ρ decreases accordingly to approach 0, and the weight of the control quantity given by the Lyapunov-based angle constraint proportional guidance law increases.

3. The method as described in claim 2, characterized in that, in, Control parameters include tilt angle and angle of attack; The control quantities generated by the proportional guidance law include: Based on the target and the position and attitude information of the aircraft, calculate the lateral guidance command: Where K is the proportional guidance coefficient; V is the vehicle velocity vector; It is the ballistic deflection acceleration of the aircraft; This represents the rate of change of the lateral line-of-sight angle. Based on the target and the position and attitude information of the aircraft, the longitudinal guidance command is calculated: Where K is the proportional guidance coefficient; V is the vehicle velocity vector; This represents the rate of change of the longitudinal line of sight angle; Based at least on the lateral guidance command and the longitudinal guidance command, the roll angle is calculated as follows: s n =atan2(-n y ·cosγ,n z +g cosγ) Where atan is the arctangent function, γ is the trajectory inclination angle of the aircraft, and g is the gravitational acceleration; Based at least on the roll angle, the lift coefficient C is calculated using the dynamic equations. L ; Based on the lift coefficient C L The angle of attack is obtained based on the correspondence between lift coefficient, Mach number, and angle of attack in the aerodynamic database. The pneumatic database is the CAV-L pneumatic database.

4. The method as described in claim 1, characterized in that, The training process of the neural network includes: Step 1.1: For a given set of multiple initial states of the aircraft, use the HP adaptive pseudospectral method to find the control variables that minimize the cost function, and obtain data on multiple optimal trajectories that satisfy the constraints to guide the aircraft to the target position. Among them, the minimum sum of squares of the control variables is selected as the performance index of the cost function; Among them, the constraints of the terminal state variables of the aircraft are selected as the performance index of the cost function; Step 1.2: For each of the multiple initial states of the aircraft, calculate the optimal trajectory and corresponding control variables, and perform polynomial curve fitting. The fitting of the angle of attack in the control variables and the height data in the trajectory is as follows: a cx =c3H 3 +c2H 2 +c1H+c1 In the formula: α cx c0, c1, c2, c3 are fitting coefficients; H is the height. Step 2.1: For each of the multiple initial states of the aircraft, establish a data pair between the set of state variables of the aircraft and the fitting coefficients; The state variable group includes at least: range error and terminal ballistic tilt angle error; Step 2.2: Use multiple data pairs corresponding to the initial states of the multiple aircraft as standard samples to train the neural network; The neural network is structured as follows: one input layer, four hidden layers, and one output layer. The input layer contains six neurons to receive the state variables of the aircraft. Each hidden layer contains 64 neurons. The output layer contains four neurons to output the fitting coefficients. The input layer and hidden layers, and the hidden layers and output layers are connected by linear weights. The hidden layers are also connected by linear weights, and a hyperbolic tangent tanh function is added as the activation function. The loss function is MSE, and the Adam method is used to train the neural network.

5. The method as described in claim 4, characterized in that, Generating control quantities using the neural network includes: Based on the target and the position and attitude information of the aircraft, generate the current state variable set of the aircraft; The current state variables of the aircraft are input into the neural network to obtain the fitting coefficients at the current moment; The fitting coefficients of the neural network output at the current time are optimized using a quasi-Newton iterative method; and The angle of attack in the control variables is calculated based at least on the optimized fitting coefficients and the aircraft altitude at the current moment.

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