An Online Prediction Method for the Maximum Lateral Maneuverability Boundary of a Gliding Hypersonic Vehicle

Abstract

This invention provides a method for predicting the maximum lateral maneuverability boundary of a hypersonic gliding vehicle. Based on a backpropagation (BP) neural network, this invention performs online prediction of the capability boundary. First, the flight state and corresponding reachable domain boundary data are used as the training database for the neural network. Second, a BP neural network model is established to map the vehicle's flight state to the terminal capability boundary, enabling rapid online prediction of the reachable domain. This further improves the calculation accuracy of the maximum lateral maneuverability boundary, providing accurate data for subsequent online assessment and decision-making regarding missile trajectory capabilities. In this prediction method, the process constraints of the vehicle trajectory are segmented and optimized according to its characteristics, isolating the more important trajectories that have a significant impact on calculations. This facilitates subsequent generation of trajectory data and construction of the neural network, improving calculation speed and meeting the needs of online assessment and decision-making for hypersonic gliding vehicles.

Description

Technical Field

[0001] This invention belongs to the field of trajectory planning and trajectory prediction for hypersonic gliding vehicles, and specifically relates to an online prediction method for the maximum lateral maneuverability boundary of a hypersonic gliding vehicle. Background Technology

[0002] The ballistic capability boundary of a gliding hypersonic vehicle refers to the range of lateral maneuvering capabilities that the vehicle can perform when reaching its terminal state, provided all constraints are met. During flight, a gliding hypersonic vehicle is affected by uncertainties in aerodynamics, thrust deviation, and penetration maneuvers, resulting in a monotonically decreasing energy characteristic. Influenced by flight conditions, the lateral maneuvering capability boundary of a gliding hypersonic vehicle also exhibits irregular changes, reflecting both longitudinal and lateral maneuvering capabilities, and comprehensively embodying the vehicle's overall maneuverability.

[0003] Because hypersonic gliding vehicles need to meet the requirements of multiple mission objectives, they must perform hop-glide flight according to certain patterns during both the active and passive phases of flight. Simultaneously, based on the current flight status, target location provided by the space-based data link, and air defense / missile launch sites, they must rapidly assess whether the missile can complete its given trajectory mission under the current conditions, and make decisions regarding whether to adjust the missile's target online or plan a penetration trajectory. To provide a basis for decision-making regarding online target adjustment and penetration trajectory planning for hypersonic gliding vehicles, an online prediction technology for the maximum lateral maneuverability boundary is required. This technology can calculate and predict whether the vehicle still possesses the margin for accurate target strike capability after adjusting its target or maneuvering to penetrate defenses.

[0004] Because the state of an aircraft changes rapidly under near-space flight conditions, accurately and quickly conducting online assessments and decisions on ballistic capabilities is an extremely challenging technical problem with significant practical implications. Summary of the Invention

[0005] During the actual engineering verification process, the applicant found that due to the influence of uncertain aerodynamics, thrust deviation and penetration maneuver during the gliding flight phase, the flight state of the gliding hypersonic vehicle changes drastically and is highly uncertain. As a result, the overall capability boundary of the vehicle changes irregularly due to the influence of the flight state, making it difficult to quickly conduct online assessment and decision-making on its ballistic capabilities.

[0006] Meanwhile, traditional reachability domain solving methods lack quantitative assessment of lateral maneuverability during flight, resulting in excessive lateral maneuverability in the early stages of flight and insufficient capability margin in the later stages. This makes it difficult to accurately describe the reachability domain of gliding hypersonic vehicles, which in turn affects the assessment and decision-making of ballistic capabilities, ultimately leading to poor practical engineering applicability of gliding hypersonic vehicles.

[0007] Therefore, this invention provides an online prediction method for the maximum lateral maneuverability boundary of a gliding hypersonic vehicle, which solves the problems of difficulty in predicting the reachable domain and poor solution accuracy of traditional gliding hypersonic vehicles, and has important practical significance.

[0008] To achieve the above objectives, the technical solution provided by this invention is:

[0009] A method for online prediction of the maximum lateral maneuverability boundary of a gliding hypersonic vehicle, characterized by the following steps:

[0010] Step 1: Establish the three-degree-of-freedom equations of motion for the gliding hypersonic vehicle;

[0011] Step 2: Set the constraints for the hypersonic vehicle during flight;

[0012] Step 3: Optimize the process constraints of the aircraft trajectory in segments;

[0013] The active phase and passive phase of the aircraft are divided into the following segments: active phase, lateral maneuver phase, and terminal phase.

[0014] Among them, the performance indicators of the active phase of the aircraft are to meet the latitude, longitude, speed and altitude requirements after the active phase ends; the performance indicators of the lateral maneuver phase of the aircraft are set to the farthest lateral boundary; and the performance indicators of the terminal phase of flight are set to the landing point and landing speed constraints and landing angle constraints.

[0015] Step 4: Solve the capability boundary problem within the same firing surface using the pseudospectral method to generate a ballistic dataset;

[0016] Step 5: Establish an offline BP neural network model;

[0017] Step 6: Collect the initial condition parameters of the current hypersonic vehicle, and use the BP neural network model from Step 5 to predict the maximum lateral boundary latitude and longitude of the gliding hypersonic vehicle online.

[0018] Furthermore,

[0019] The constraints in step 2 include initial state constraints, attitude constraints, process constraints, and terminal constraints.

[0020] The attitude constraints include attitude angle constraints and attitude angular velocity constraints;

[0021] The process constraints include dynamic pressure constraints, overload constraints, and heat flow constraints;

[0022] The terminal constraints include terminal angle constraints, terminal height constraints, terminal speed constraints, and terminal longitude and latitude constraints.

[0023] Furthermore,

[0024] Step 4 includes the following sub-steps:

[0025] Step 4.1: Design the performance indicators for the pseudospectral method;

[0026] The maximum longitude that the aircraft meets under different range constraints within the same firing surface during flight is used as the performance index.

[0027] Step 4.2: Generate ballistic dataset;

[0028] By sequentially changing the latitude, longitude, speed, and altitude of the aircraft after the active phase, multiple sets of initial conditions for different firing surfaces are generated. Within the same firing surface under these initial conditions, multiple sets of ranges corresponding to different latitudes are sequentially selected as terminal conditions in the ballistic data, which are then used as the ballistic dataset.

[0029] Step 4.3: For each set of ballistic data in Step 4.2, take its initial conditions and terminal conditions as constraints, take the angle of attack angular velocity and the tilt angle angular velocity as control quantities, change the terminal impact point constraints, use the pseudospectral method to solve for the latitude and longitude of the endpoint of the maximum lateral maneuverability boundary under different ranges in the firing surface, and generate the maximum flight lateral maneuverability boundary and the sequence of angle of attack and tilt angle control quantities required to reach the boundary in sequence;

[0030] Step 4.4: Connect the latitude and longitude of the endpoints of the maximum flight lateral maneuverability boundaries of all ranges within the same firing surface in Step 4.3 to form the reachability domain boundary data of the aircraft under various initial states for different ranges.

[0031] Furthermore,

[0032] Step 5.1: Referring to the ballistic data generation methods in Steps 4.2 to 4.4, establish a complete training database containing the current status and terminal capabilities of the gliding hypersonic vehicle;

[0033] Step 5.2: Randomly split the training database into a training set and a test set;

[0034] Step 5.3: Using the ballistic data in the training set as samples and the latitude and longitude of the endpoint of the maximum lateral maneuverability boundary as the output label, train the BP neural network model. By adjusting the input layer dimension, output layer dimension, number of hidden layers and learning rate, and verifying it using the test set in Step 5.2, finally establish the mapping function of the BP neural network model.

[0035] Furthermore,

[0036] Step 6.1: Collect the initial condition parameters of the current hypersonic vehicle, update the ballistic data in the training set, and perform backpropagation training on the BP neural network model in Step 5. Update the parameters of the neural network mapping function by taking derivatives layer by layer.

[0037] Step 6.2: Input the initial condition parameters into the updated BP neural network model in Step 6.1 to predict the latitude and longitude of the maximum flight lateral maneuverability boundary.

[0038] Furthermore,

[0039] The methods for adjusting the input layer dimension, output layer dimension, and number of hidden layers in step 5.3 include:

[0040] The input layer dimension is equal to the number of terms in the initial condition parameters;

[0041] The output layer dimension is the longitude dimension, and the output layer dimension is 2;

[0042] The number of hidden layers is dynamically adjusted during training, taking into account prediction accuracy and training time, with an adjustment range of 2 to 5 layers.

[0043] Furthermore,

[0044] The initial condition parameters include the time, altitude, speed, trajectory inclination angle, trajectory deviation angle, longitude, latitude, roll angle, angle of attack, and the longitude and latitude of the final landing point during the active phase and the lateral maneuver phase of the aircraft.

[0045] The input layer has a dimension of 11.

[0046] The concept and principle of this invention:

[0047] Currently, the maximum lateral maneuverability boundary under various constraints can be obtained by using the three-degree-of-freedom equations of motion of a gliding hypersonic vehicle through the pseudospectral method. However, this solution is time-consuming and has low accuracy, which cannot meet the needs of online calculation for the vehicle.

[0048] Therefore, this invention first solves the neural network model used for prediction offline, and then performs online prediction:

[0049] like Figure 1 As shown, this invention first uses the generated ballistic data to generate the maximum flight lateral maneuverability boundary of different firing surfaces and the sequence of angle of attack and roll control quantities required to reach the boundary through the Gaussian pseudospectral method. This is used as the ballistic dataset. Then, using the ballistic dataset as samples and the latitude and longitude of the maximum flight lateral maneuverability boundary as the output label, a BP neural network model is trained. By adjusting the number of hidden layers and learning rate and other network parameters, an offline BP neural network model is established to realize the mapping between the flight state of the aircraft and the terminal capability boundary.

[0050] During the online process, flight status at any time is collected and backpropagation training is performed on the pre-trained BP neural network model. The neural network is updated into an online fast prediction model of the reachability domain through layer-by-layer chain differentiation, further improving the prediction accuracy. Then, the initial condition parameters are input into the updated model to quickly predict the latitude and longitude of the maximum flight lateral maneuverability boundary, providing an accurate basis for the next evaluation and decision of the aircraft.

[0051] The advantages of this invention are:

[0052] 1. This invention uses the concept of reachability domain to reflect the boundary of the lateral maneuverability of a hypersonic glider under constrained conditions, thereby enabling offline flight capability assessment. Under process constraints such as thermal flux, dynamic pressure, and overload, as well as terminal constraints such as landing point and landing velocity, the Gaussian pseudospectral method is applied to generate the lateral maneuverability boundary of the aircraft. This yields an aircraft capability boundary that simultaneously satisfies the characteristics of "coverage" or "reachability," providing inspiration for applications and research in similar fields.

[0053] 2. This invention uses a backpropagation (BP) neural network for online prediction of capability boundaries. First, the flight state and corresponding reachable domain boundary data are used as the training database for the neural network. Then, a BP neural network model is established to map the aircraft's flight state to the terminal capability boundary, enabling rapid online prediction of the reachable domain. This further improves the calculation accuracy of the maximum lateral maneuverability boundary, providing an accurate basis for subsequent online assessment and decision-making regarding missile trajectory capabilities.

[0054] 3. In this prediction method, based on the characteristics of the aircraft trajectory, the process constraints of the aircraft trajectory are segmented and optimized, isolating the more important trajectories that have a greater impact on the calculation. This facilitates the subsequent generation of trajectory data and the construction of neural networks, improves the calculation speed, and meets the needs of online evaluation and decision-making for hypersonic gliding aircraft. Attached Figure Description

[0055] Figure 1 This is a flowchart of the offline solution and online prediction of the maximum lateral maneuverability boundary of an aircraft;

[0056] Figure 2 It is a graph showing how the aircraft's altitude changes over time;

[0057] Figure 3 It is a graph showing the change of the aircraft's latitude and longitude over time;

[0058] Figure 4 It is a two-dimensional planar trajectory curve of the aircraft;

[0059] Figure 5It is a three-dimensional planar trajectory curve of the aircraft;

[0060] Figure 6 It is a graph showing the change of the aircraft's trajectory deflection angle over time;

[0061] Figure 7 It is a graph showing the change of the trajectory inclination angle of an aircraft over time;

[0062] Figure 8 It is a graph of the predicted lateral boundary of the aircraft;

[0063] Figure 9 This is a graph showing the predicted results of the aircraft's longitudinal boundary. Detailed Implementation

[0064] The embodiments of the present invention are described in detail below with reference to the accompanying drawings. These embodiments are exemplary and intended to explain the present invention, but should not be construed as limiting the present invention.

[0065] A method for online prediction of the maximum lateral maneuverability boundary of a gliding hypersonic vehicle, comprising the following steps:

[0066] Step 1: Establish the three-degree-of-freedom equations of motion for the gliding hypersonic vehicle. When the vehicle enters the passive phase, the engine thrust P is zero. Ignore the Coriolis acceleration and entrainment acceleration caused by the Earth's rotation, and establish the following particle motion model:

[0067]

[0068] In the formula, g = g0(R0 / r) 2 Let g be the gravitational acceleration, and g0 = 9.81 m / s². 2 r is the distance from the Earth's center; λ is longitude, φ is latitude; V is the vehicle speed; θ is the trajectory inclination angle; σ is the roll angle; ψ v is the ballistic deflection angle, with counterclockwise rotation from north to south being positive; m is the mass.

[0069] L and D represent lift and drag, respectively, and the calculation formula is:

[0070] L = ρV 2 S ref C L / 2

[0071] D = ρV 2 S ref C D / 2

[0072] In the formula, S ref The reference area is ρ; atmospheric density is C. L and C D These are the lift coefficient and the drag coefficient, respectively.

[0073] Step 2: Set the constraints during the flight of the hypersonic vehicle and use the maximum longitude of the vehicle under different range constraints within the same firing surface as the performance index.

[0074] The constraints include initial state constraints, attitude angle constraints, attitude angular velocity constraints, overload constraints, heat flow constraints, process constraints, and terminal constraints.

[0075] Step 2.1: Terminal constraints include terminal angle constraints, terminal height constraints, terminal speed constraints, and terminal longitude and latitude constraints;

[0076]

[0077] In the formula, t f The terminal flight time of the aircraft; r f V f ,λ f ,φ f These are the corresponding terminal constraint values.

[0078] Step 2: Set the constraints for the hypersonic vehicle during flight;

[0079] Constraints include initial state constraints, attitude constraints, process constraints, and terminal constraints;

[0080] Attitude constraints include attitude angle constraints and attitude angular velocity constraints;

[0081] Process constraints include dynamic pressure constraints, overload constraints, and thermal flux constraints;

[0082] Dynamic pressure constraint, overload constraint, and thermal flux constraint are "hard constraints" that must be satisfied, expressed by formulas:

[0083]

[0084]

[0085]

[0086] In the formula: q, n, These represent the dynamic pressure, overload, and stagnation point heat flux of the aircraft, respectively; q max ,n max ,

[0087] These are the corresponding maximum constraint values; The heat transfer coefficient;

[0088] Terminal constraints include terminal angle constraints, terminal height constraints, terminal speed constraints, and terminal latitude and longitude constraints, which are expressed by formulas:

[0089]

[0090] In the formula: t f The terminal flight time of the aircraft; r f V f ,λ f ,φ f These are the corresponding terminal constraint values;

[0091] Step 2.3: To meet the actual ballistic requirements of the aircraft, the ballistic process constraints of the aircraft are optimized in segments, thereby transforming the aircraft ballistic optimization problem into a multi-segment trajectory optimization problem;

[0092] As shown in Table 1, the active phase and passive phase of the aircraft are divided into the following segments: active phase, lateral maneuver phase, and terminal phase.

[0093] Table 1. Ballistic segmentation and performance indicators of each segment

[0094]

[0095] Where, n 1min and n 1max For the minimum and maximum normal overload values ​​of the active segment, n 2min and n 2max The minimum and maximum values ​​of the normal overload of the passive segment; α min and β represents the minimum angle of attack and angular velocity at the angle of attack. min and α is the minimum value of the sideslip angle and the sideslip angular velocity. max and β represents the angle of attack and the maximum angular velocity at the angle of attack. max and These represent the sideslip angle and the maximum value of the sideslip angle angular velocity.

[0096] Step 4: Solve the capability boundary problem within the same firing surface using the Gauss pseudospectral method to generate a ballistic dataset;

[0097] Step 4.1: Design the performance indicators of the pseudospectral method;

[0098] The problem of solving the capability boundary within the same firing plane can be expressed as solving for the maximum longitude under different range constraints within the same firing plane. The longitude of the impact point is represented by latitude. Therefore, the performance index J used to evaluate the capability boundary is designed as follows:

[0099] J = cos(longtitude)

[0100] Step 4.2: Generate ballistic data;

[0101] Corresponding to the performance indicators of the active phase of the aircraft in step 3, by sequentially changing the latitude, longitude, speed and altitude of the aircraft after the active phase ends, multiple sets of initial conditions corresponding to different firing surfaces of the aircraft are generated. Within the same firing surface of the initial conditions, multiple sets of ranges corresponding to different latitudes are sequentially selected as terminal conditions in the ballistic data, which are used as ballistic datasets.

[0102] Step 4.3: For each set of ballistic data in Step 4.2, take its initial conditions and terminal conditions as constraints, take the angle of attack angular velocity and the tilt angle angular velocity as control quantities, change the terminal impact point constraints, use the pseudospectral method to solve for the latitude and longitude of the endpoint of the maximum lateral maneuverability boundary under different ranges in the firing surface, and generate the maximum flight lateral maneuverability boundary and the sequence of angle of attack and tilt angle control quantities required to reach the boundary in sequence;

[0103] Step 4.4: Connect the latitude and longitude of the endpoints of all the maximum flight lateral maneuverability boundaries within the same firing surface in Step 4.3 to form the reachability domain boundary data of the aircraft under various initial states for different ranges.

[0104] Step 5: Establish an offline BP neural network model;

[0105] Step 5.1: Referring to the ballistic data generation methods in Steps 4.2 to 4.4, establish a complete training database containing the current status and terminal capabilities of the gliding hypersonic vehicle;

[0106] Step 5.2: Randomly split the training database into a training set and a test set;

[0107] The test set is used to verify whether the error of the neural network has converged to a preset tolerance. In this embodiment, the preset tolerance is 1%.

[0108] Step 5.3: Using the ballistic data in the training set as samples and the latitude and longitude of the endpoint of the maximum lateral maneuverability boundary as the output label, train the BP neural network model. By adjusting the input layer dimension, output layer dimension, number of hidden layers and learning rate, and verifying it using the test set in Step 5.2, finally establish the mapping function of the BP neural network model to realize the mapping between the flight state of the aircraft and the terminal capability boundary.

[0109] in:

[0110] The input layer dimension is equal to the number of terms in the initial condition parameters;

[0111] Initial condition parameters include the time, altitude, speed, trajectory inclination angle, trajectory deflection angle, longitude, latitude, roll angle, angle of attack, and the longitude and latitude of the final impact point during the active phase and the lateral maneuver phase of the aircraft.

[0112] The output layer dimension is the longitude dimension; in this embodiment, the output layer has two dimensions.

[0113] The number of hidden layers needs to be dynamically adjusted during training, taking into account the prediction accuracy and the time required for training. The adjustment range is 2 to 5 layers.

[0114] In this embodiment, there are two hidden layers. On the one hand, the more hidden layers there are, the more parameters the neural network has, resulting in a smaller fitting error and better performance. On the other hand, the more network parameters there are, the longer the training and execution time becomes. Furthermore, since backpropagation requires chain-like differentiation to update network parameters, too many hidden layers can cause the derivative values ​​to approach zero, leading to gradient vanishing.

[0115] The learning rate in the neural network model of this embodiment is 0.01;

[0116] A learning rate that is too low makes training more reliable, but optimization takes longer because each step toward the minimum of the loss function is small. A learning rate that is too high may prevent training from converging at all, or even cause it to diverge, and the changes in weights may be so large that the optimization overshoots the minimum, worsening the loss function. Therefore, simulations of various learning rates are needed to determine the optimal learning rate, balancing the learning rate of the neural model with the loss function.

[0117] The neural network structure established in this embodiment is shown in Table 2;

[0118] Table 2. BP neural network structure trained based on ballistic samples

[0119]

[0120] Step 6: Using the BP neural network model from Step 5, predict the maximum lateral boundary latitude and longitude of the gliding hypersonic vehicle online;

[0121] Step 6.1: Backpropagation training is performed using ballistic data from the training set. The parameters of the neural network mapping function are updated by chain-like differentiation layer by layer, and an online fast prediction model for the reachable domain is established, which improves the accuracy of online prediction.

[0122] Step 6.2: Input the initial condition parameters (current time, altitude, speed, ballistic inclination angle, ballistic deflection angle, longitude, latitude, bank angle, angle of attack, and longitude and latitude of the final landing point) into the updated BP neural network model in Step 6.1, and predict the longitude and latitude of the maximum flight lateral maneuverability boundary.

[0123] The optimization curve of the maximum lateral boundary of the aircraft used in the simulation experiment in this embodiment is shown in the figure below. Figures 2-7 As shown:

[0124] Simulation results show that during the boost phase, the aircraft's trajectory angle decreases while its speed increases, resulting in a continuous climb. After the boost phase ends, the angle of attack gradually increases to reach and maintain its maximum value, allowing for deceleration to meet the landing speed requirements. The aircraft reaches its highest point in approximately 150 seconds, then performs a jump maneuver, adjusting its trajectory angle to meet the landing speed requirements. Within the same firing plane, the aircraft's lateral capability boundary exhibits a negative correlation with the firing range; the closer the range, the higher the aircraft's energy margin, and the farther the maximum lateral capability boundary.

[0125] Figure 8 , Figure 9 The simulation results show that the predicted values ​​during the active phase (0s-47.2s) fluctuate within a small range, with an average difference of 4.87 km between the predicted and actual values, indicating poor prediction accuracy. However, during the passive phase (300s) from the end of the active phase to the prediction cutoff, the flight parameters change slowly and have a stronger linear correlation with the predicted values, resulting in higher prediction accuracy. The prediction errors are all within 3 km, and the prediction accuracy is within 1%.

[0126] The simulation results show that this method trains an offline neural network using the state information during flight as input, which can fit the mapping function from "current state" to "prediction capability boundary". A neural network with "current state" as input and "prediction capability boundary" as output is established, and the prediction is initially realized. During the online process, this method can update the neural network in real time according to the flight state parameters collected online, and realize the online rapid prediction of the maximum lateral boundary.

[0127] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any person skilled in the art can easily conceive of various equivalent modifications or substitutions within the scope of the technology disclosed in the present invention, and such modifications or substitutions should all be covered within the scope of protection of the present invention.

Claims

1. A method for online prediction of the maximum lateral maneuverability boundary of a gliding hypersonic vehicle, characterized in that, Includes the following steps: Step 1: Establish the three-degree-of-freedom equations of motion for the gliding hypersonic vehicle; Step 2: Set the constraints for the hypersonic vehicle during flight; the constraints include initial state constraints, attitude constraints, process constraints, and terminal constraints. The attitude constraints include attitude angle constraints and attitude angular velocity constraints; The process constraints include dynamic pressure constraints, overload constraints, and heat flow constraints; The terminal constraints include terminal angle constraints, terminal height constraints, terminal speed constraints, and terminal longitude and latitude constraints; Step 3: Optimize the process constraints of the aircraft trajectory in segments; The active phase and passive phase of the aircraft are divided into the following segments: active phase, lateral maneuver phase, and terminal phase. Among them, the performance indicators of the active phase of the aircraft are to meet the latitude, longitude, speed and altitude requirements after the active phase ends; the performance indicators of the lateral maneuver phase of the aircraft are set to the farthest lateral boundary; and the performance indicators of the terminal phase of flight are set to the landing point and landing speed constraints and landing angle constraints. Step 4: Solve the capability boundary problem within the same firing surface using the pseudospectral method to generate a ballistic dataset; this includes the following sub-steps: Step 4.1: Design the performance indicators for the pseudospectral method; The maximum longitude that the aircraft can achieve under different range constraints within the same firing surface during flight is used as the performance index. Step 4.2: Generate ballistic dataset; By sequentially changing the latitude, longitude, speed, and altitude of the aircraft after the active phase, multiple sets of initial conditions for different firing surfaces are generated. Within the same firing surface under these initial conditions, multiple sets of ranges corresponding to different latitudes are sequentially selected as terminal conditions in the ballistic data, which are then used as the ballistic dataset. Step 4.3: For each set of ballistic data in Step 4.2, take its initial conditions and terminal conditions as constraints, take the angle of attack angular velocity and the tilt angle angular velocity as control quantities, change the terminal impact point constraints, use the pseudospectral method to solve for the latitude and longitude of the endpoint of the maximum lateral maneuverability boundary under different ranges in the firing surface, and generate the maximum flight lateral maneuverability boundary and the sequence of angle of attack and tilt angle control quantities required to reach the boundary in sequence; Step 4.4: Connect the latitude and longitude of the endpoints of the maximum flight lateral maneuverability boundaries of all ranges within the same firing surface in Step 4.3 to form the reachability domain boundary data of the aircraft under various initial states for different ranges. Step 5: Establish an offline BP neural network model; Step 6: Collect the initial condition parameters of the current hypersonic vehicle, and use the BP neural network model from Step 5 to predict the maximum lateral boundary latitude and longitude of the gliding hypersonic vehicle online.

2. The method for online prediction of the maximum lateral maneuverability boundary of a gliding hypersonic vehicle according to claim 1, characterized in that: Step 5.1: Referring to the ballistic data generation methods in Steps 4.2 to 4.4, establish a complete training database containing the current status and terminal capabilities of the gliding hypersonic vehicle; Step 5.2: Randomly split the training database into a training set and a test set; Step 5.3: Using the ballistic data in the training set as samples and the latitude and longitude of the endpoint of the maximum lateral maneuverability boundary as the output label, train the BP neural network model. By adjusting the input layer dimension, output layer dimension, number of hidden layers and learning rate, and verifying it using the test set in Step 5.2, finally establish the mapping function of the BP neural network model.

3. The method for online prediction of the maximum lateral maneuverability boundary of a gliding hypersonic vehicle according to claim 2, characterized in that: Step 6.1: Collect the initial condition parameters of the current hypersonic vehicle, update the ballistic data in the training set, and perform backpropagation training on the BP neural network model in Step 5. Update the parameters of the neural network mapping function by taking derivatives layer by layer. Step 6.2: Input the initial condition parameters into the updated BP neural network model in Step 6.1 to predict the latitude and longitude of the maximum flight lateral maneuverability boundary.

4. The method for online prediction of the maximum lateral maneuverability boundary of a gliding hypersonic vehicle according to claim 2, characterized in that: The methods for adjusting the input layer dimension, output layer dimension, and number of hidden layers in step 5.3 include: The input layer dimension is equal to the number of terms in the initial condition parameters; The output layer dimension is the longitude dimension, and the output layer dimension is 2; The number of hidden layers is dynamically adjusted during training, taking into account prediction accuracy and training time, with an adjustment range of 2 to 5 layers.

5. The online prediction method for the maximum lateral maneuverability boundary of a gliding hypersonic vehicle according to claim 4, characterized in that: The initial condition parameters include the time, altitude, speed, trajectory inclination angle, trajectory deviation angle, longitude, latitude, roll angle, angle of attack, and the longitude and latitude of the final landing point during the active phase and the lateral maneuver phase of the aircraft. The input layer has a dimension of 11.

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