Model predictive control method for high-speed aircraft based on physical information neural network

Abstract

This invention belongs to the field of hypersonic aircraft control technology and relates to a model predictive control method for high-speed aircraft based on a physical information neural network. This method includes constructing a hypersonic aircraft attitude dynamics model, designing and training a physical information neural network, performing control-oriented hypersonic aircraft model conversion, and implementing model predictive control that considers input and output constraints. This method demonstrates greater accuracy and adaptability in addressing aircraft control issues, providing a more efficient and practical solution to the complexities and uncertainties inherent in aircraft design and control.

Description

Technical Field

[0001] The present invention belongs to the technical field of hypersonic aircraft control, and relates to a high-speed aircraft model predictive control method based on physical information neural network. Background Art

[0002] Hypersonic vehicles, with their long range, high maneuverability, and mission flexibility, are crucial for meeting future long-range combat requirements, overcoming missile defense systems, and achieving precise and rapid strikes. As the benefits of hypersonic vehicles gradually become apparent, enhancing their flight performance has become a worthy research topic. Introducing deformation technology into hypersonic vehicles, integrating deformation as a controllable parameter into the vehicle design process, allows them to operate over a wider range of airspace and speed ranges, thereby improving flight performance and achieving greater mission flexibility and environmental adaptability. In current research, numerous advanced control strategies have been gradually applied to the design of hypersonic vehicle control systems.

[0003] Model predictive control (MPC) methods predict the system state and derive control commands in a rolling optimization format that satisfies state constraints. As can be seen, MPCs can achieve good control performance under strong parameter perturbations. Therefore, using MPC as a baseline attitude controller, by constructing an optimization model that incorporates control performance and state constraints, it is possible to achieve fast system tracking with strong robustness while satisfying state constraints. However, it is worth noting that MPC-based approaches ignore the impact of noise interference, which is inevitable in practical applications. Physically informed neural networks have become a transformative approach at the intersection of machine learning and physical science, offering a new paradigm for solving complex problems governed by the laws of physics. By integrating principles from both fields, physics-informed neural networks enable researchers to leverage the expressive power of neural networks while adhering to fundamental physical constraints. Traditionally, machine learning and physics have operated independently, each addressing distinct challenges. Machine learning excels at uncovering complex patterns in data but often struggles to integrate prior knowledge or enforce physical constraints. In contrast, physics-based modeling, such as the finite element method or computational fluid dynamics, relies on explicit physical equations but can suffer from scalability and generalization issues in complex real-world scenarios. Physics-informed neural networks bridge this gap by combining the flexibility of neural networks with the rigor of physical principles. By embedding the laws of physics into the learning process, physics-informed neural networks provide a powerful framework for solving both forward and inverse problems in various fields, including fluid dynamics, materials science, and quantum mechanics. This integration improves predictive accuracy, provides insights into physical phenomena, and facilitates the discovery of new scientific principles.

[0004] The patent "Neural Network Learning Control Method for Hypersonic Aircraft Based on Predictive Modeling" (patent, Northwestern Polytechnical University, CN 201710789199.4, 20191018) proposes a neural network learning control method for hypersonic aircraft based on predictive modeling, aiming to address the poor stability of existing hypersonic aircraft control methods. However, this method is relatively complex in its design process. The neural network control system must complete complex calculations in a very short time to ensure real-time control commands. Furthermore, it relies on the accuracy of predictive modeling, which is not conducive to engineering implementation and affects the operational safety and control accuracy of the aircraft.

[0005] The patent "A Robust Attitude Control Method for Hypersonic Aircraft Based on Predictive Sliding Mode" (Nanjing University of Information Science and Technology, CN111290278B, 20220503) designs an attitude control method based on predictive sliding mode. This method ensures the stability of the attitude closed-loop control system and enables it to accurately track attitude command signals under parameter uncertainty, improving the system's control accuracy and performance. However, the system is also highly sensitive to noise, further affecting the accuracy and stability of the control system. The design process of this method is cumbersome, and the control scheme requires a high level of modeling accuracy, which is not conducive to engineering implementation.

[0006] The paper "Ge Jianhao, Guo Jie, Wang Haoning, et al. Adaptive Model Predictive Control for Hypersonic Variable-Shape Vehicles [J]. Journal of Beijing University of Aeronautics and Astronautics, 2025, 1-19" proposes a parameter-adaptive model predictive control method based on reinforcement learning to address the high-precision control of hypersonic variable-shape vehicles under state constraints. While the method presented in the paper can improve control accuracy under vehicle constraints, its adaptability and robustness to complex or extreme fault conditions may be insufficient. Furthermore, in practical engineering, some uncertainty and noise continue to degrade the performance of model predictive control. To overcome these limitations, new methods are needed to achieve interference-resistant control of hypersonic vehicles.

[0007] The paper "He Tao, Chen Zhong, Cen Lihui, et al. Data-driven predictive control of hypersonic morphing vehicles based on a composite observer [J]. Control Theory and Applications, 2025, 1-9" proposes a data-driven model predictive control approach based on a composite observer for the attitude control of hypersonic morphing vehicles subject to parameter uncertainty and external disturbances. However, the proposed approach relies on parameter tuning of the composite observer, and its ability to handle high-quality control under the combined influence of noise and disturbances has not yet been demonstrated.

[0008] The paper "Mi Hanpeng, Hu Chaofang, Yang Xiaohe, et al. Adjustable Tube-MPC Fault-Tolerant Control for Elastic Hypersonic Vehicles [J]. Aeronautical Science and Technology, 2022, 33(08):88-94" proposes a predictive control fault-tolerant control method for elastic hypersonic vehicles with state-dependent input saturation after feedback linearization. However, the adopted model predictive control scheme ignores the influence of noise interference that is inevitable in practical applications, and its engineering application remains to be verified.

[0009] Existing control methods are often relatively conservative in their handling of uncertainty and noise, which can lead to inflexible and poorly adaptable control strategies in practical applications. This can lead to poor performance when dealing with unforeseen aircraft behavior or environmental changes. In current technological developments, intelligent technologies driven by a hybrid of data and models play a crucial role in improving system performance and adaptability. However, existing technologies fail to leverage these advanced technologies to enhance control systems' resilience to noise interference, particularly in complex and highly dynamic flight environments, lacking effective and robust adaptive mechanisms. Summary of the Invention

[0010] To solve the above problems, the present invention provides a high-speed aircraft model predictive control method based on physical information neural network to achieve stable tracking control of hypersonic aircraft.

[0011] The technical solutions of the present invention are as follows:

[0012] The model predictive control method for high-speed aircraft based on physical information neural network includes: constructing the attitude dynamics model of hypersonic aircraft, designing and training the physical information neural network, control-oriented hypersonic aircraft model conversion, and model predictive control considering input and output constraints. The details are as follows:

[0013] Step (1) Constructing the attitude dynamics model of the hypersonic vehicle

[0014] (1)

[0015] in, is the angle of attack, is the sideslip angle, is the roll angle, is the roll angular velocity, is the yaw angular velocity, is the pitch angular velocity, is the moment of inertia of the object around the x-axis, is the moment of inertia of the object around the y-axis, is the moment of inertia of the object around the z-axis, represents the product of inertia about the x-axis and y-axis, is the rolling moment on the aircraft, is the yaw moment on the aircraft, is the pitching aerodynamic moment of the aircraft, which is expressed as

[0016] (2)

[0017] in, It is dynamic pressure, is the reference area, is the reference length; is the rolling moment coefficient, is the yaw moment coefficient, is the pitching moment coefficient, and the relationship is expressed as

[0018] (3)

[0019] in, It is the aerodynamic coefficient related to the rolling moment of the aircraft in the zero rudder deflection state. is the aerodynamic increment related to the rolling moment of the aircraft under the influence of the right elevator, is the aerodynamic increment related to the rolling moment of the aircraft under the influence of the left elevator, It is the aerodynamic increment related to the rolling moment of the aircraft under the influence of the rudder; It is the aerodynamic coefficient related to the yaw moment of the aircraft in the zero rudder deflection state. is the aerodynamic increment related to the yaw moment of the aircraft under the influence of the right elevator, is the aerodynamic increment related to the yaw moment of the aircraft under the influence of the left elevator, It is the aerodynamic increment related to the yaw moment of the aircraft under the influence of the rudder; is the aerodynamic coefficient related to the pitch moment of the aircraft in the zero rudder deflection state, is the aerodynamic increment related to the pitch moment of the aircraft under the influence of the right elevator, is the aerodynamic increment related to the pitch moment of the aircraft under the influence of the left elevator, It is the aerodynamic increment related to the pitching moment of the aircraft under the influence of the rudder;

[0020] Step (2) Design and training of physical information neural network

[0021] The state value and state change value of the aircraft attitude are predicted through the physical information neural network PINN; the loss function Expressed as

[0022] (4)

[0023] in, is the data loss function, is the physical information loss function; and To balance the weights of data loss function and physical information loss function;

[0024] Data loss function The expression is as follows:

[0025] (5)

[0026] in, Indicates the number of data for calculating the data-driven loss function, It represents the real state value obtained by solving the hypersonic aircraft attitude dynamics equation (1) by numerical method, which specifically includes the state quantity ,and It is the predicted value of PINN, which specifically includes the state quantity ;

[0027] Physical Information Loss Function The expression is as follows:

[0028] (6)

[0029] in, Indicates the number of data for calculating physical constraint loss, represents the difference between the actual state change and the predicted state change, where The result obtained by calculating the kinetic equation (1) is , that is, the actual state change value, Indicates the predicted state change value obtained by PINN prediction;

[0030] Step (3) Control-oriented hypersonic vehicle model conversion

[0031] Select the three-channel aerodynamic torque of the aircraft 、 、 As the control input, the attitude angle vector Ω is the control output, and the nonlinear attitude dynamics for control is written as

[0032] (7)

[0033] Where: is the system state vector, obtained through the PINN network prediction in step (2), is the control vector, For output, , d is the external interference term of the system;

[0034] , ;

[0035] After differentiating the output vector y twice, the control input u is expressed as follows;

[0036] (8)

[0037] Where: is the aggregate uncertainty; K and B are respectively expressed as

[0038] (9)

[0039] (10)

[0040] in: is the output function right 、 Lie derivative of ; is the output function right The second-order Lie derivative of , i = 1, 2 or 3, j = 1, 2 or 3;

[0041] Through feedback linearization, the original control input aerodynamic torque 、 、 The corresponding control vector is converted into a virtual control quantity v; the following feedback control law is designed:

[0042] (11)

[0043] Where: , 、 and Represent the virtual control quantities corresponding to the x, y and z axes respectively; and Expressed as

[0044] (12)

[0045] (13)

[0046] Through exact feedback linearization, the original nonlinear system is transformed into Brunovsky standard form, which is expressed as follows:

[0047] (14)

[0048] Where: is the state of the aircraft; A is the state matrix, and C is the output matrix, which are expressed as follows:

[0049]

[0050] Step (4) Model predictive control considering input and output constraints

[0051] After the feedback is linearized, the system is s Discretize and get the prediction model:

[0052] (15)

[0053] Where: and is the state of the aircraft at the kth and k+1th moments, is the virtual control quantity of the aircraft at the kth moment, , 、 is the system matrix of matrices A and B at the kth moment, expressed as

[0054] (16)

[0055] Where: I is the unit matrix, T s is the sampling time; combined with the output of PINN, the discrete state matrix is ​​updated according to formula (16) and ;

[0056] Set the prediction time domain to N p , the control time domain is N c , predict the system state quantity in the time domain Calculated by the following formula:

[0057] (17)

[0058] Where: is the control matrix; F and is the recursive matrix of the system, expressed as

[0059] (18)

[0060] (19)

[0061] Design the following objective function:

[0062] (20)

[0063] Where: is the reference output trajectory; and are system output and control quantity respectively; is the diagonal matrix of control weights;

[0064] Considering the performance of the servo, the actuator rudder deflection angle constraint and rudder deflection angle rate constraint are introduced. is the angular velocity vector, is the rudder deflection vector, is the rudder angular velocity vector, and each constraint is expressed as

[0065] (twenty one)

[0066] Where: and are the minimum and maximum values ​​of the angular velocity constraints, and are the minimum and maximum values ​​of the rudder angle vector constraint, and The minimum and maximum values ​​of the rudder angular velocity vector constraints respectively;

[0067] Arrange through matrix operations and write into standard quadratic programming form:

[0068] (twenty two)

[0069] By solving the quadratic programming problem under inequality constraints, the control quantity corresponding to the control time domain in the current state can be obtained. The model prediction control quantity solution is repeated in the next control cycle, and the optimal control of the hypersonic aircraft attitude is achieved through rolling optimization.

[0070] Beneficial effects of the present invention:

[0071] This invention, by incorporating a model predictive control approach based on a physical information neural network, not only overcomes the limitations of traditional model predictive control strategies but also enables more precise and dynamic control of hypersonic vehicles. By integrating the physical information neural network into the learning process and utilizing differential equations that incorporate physical process information, this technology effectively addresses the issue of hypersonic vehicle attitude control and enhances the online control system's adaptability to uncertainties and changing conditions.

[0072] Unlike traditional neural networks that rely solely on data, this approach is driven by physics information and incorporates domain-specific knowledge and physical laws to enhance its predictive capabilities. Specifically in the context of hypersonic vehicle engineering, this approach combines data-driven learning with physics-based constraints, providing a powerful framework for solving complex problems posed by complex partial and ordinary differential equations. Physical terms are incorporated into the loss function. By incorporating equation-based constraints into the loss function, the network outputs results that satisfy the laws of physics. First, it reduces the reliance on large datasets because the laws of physics provide prior knowledge to guide the learning process. Second, it enhances the robustness and reliability of the model, ensuring that predictions conform to physical laws even in areas with sparse data. Third, the goal is to infer unknown parameters or inputs from observed outputs. This is achieved by combining data and physical laws, providing a greater information reserve. This ensures that the resulting model is not only data-driven but also physically consistent and interpretable. Data augmentation using physics-based simulations also involves incorporating physical laws into neural networks. When synthetic data obtained through simulation is fed into the network for generalization, the neural network is trained on a "rich" dataset, thereby improving its robustness. In this way, the physics-informed neural network ensures that the learned solution not only conforms to the data, but also satisfies the physical constraints imposed by the partial differential equations. This approach reduces the reliance on large datasets and combines the advantages of physics-based modeling and data-driven learning, resulting in more accurate models with better generalization and interpretability. Traditional methods are less suitable when applied to large and complex datasets for hypersonic vehicles. Physics-driven neural networks improve the accuracy and reliability of diagnostic and control algorithms by incorporating the laws of physics into the learning process.

[0073] The comparative analysis between traditional neural networks and physical information neural networks is shown in the following table.

[0074]

[0075] Overall, this method shows higher accuracy and adaptability in dealing with aircraft control problems, especially when facing the complex and uncertain factors in aircraft design and control, providing a more efficient and practical solution. BRIEF DESCRIPTION OF THE DRAWINGS

[0076] Figure 1 It is a model predictive control flow chart based on physical information neural network;

[0077] Figure 2 It is a model predictive control method and system technology block diagram based on physical information neural network

[0078] Figure 3This is a simulation curve diagram of the angle of attack tracking of a hypersonic aircraft;

[0079] Figure 4 It is a simulation curve diagram of sideslip angle tracking of hypersonic aircraft;

[0080] Figure 5 It is a graph of the time curve of the hypersonic vehicle's bank angle tracking;

[0081] Figure 6 It is a time curve of the left elevator deflection angle of the hypersonic aircraft;

[0082] Figure 7 It is a time curve of the right elevator deflection angle of the hypersonic aircraft;

[0083] Figure 8 It is a time curve of the rudder deflection angle of a hypersonic aircraft. DETAILED DESCRIPTION

[0084] The following further illustrates the embodiments of the present invention in conjunction with the accompanying drawings and technical solutions.

[0085] like Figure 1 and Figure 2 As shown, a high-speed aircraft model predictive control method based on physical information neural network includes:

[0086] Step (1) Constructing the attitude dynamics model of the hypersonic vehicle

[0087] (1)

[0088] in, is the angle of attack, is the sideslip angle, is the roll angle, is the roll angular velocity, is the yaw angular velocity, is the pitch angular velocity, is the moment of inertia of the object around the x-axis, is the moment of inertia of the object around the y-axis, is the moment of inertia of the object around the z-axis, represents the product of inertia about the x-axis and y-axis, is the rolling moment on the aircraft, is the yaw moment on the aircraft, is the pitching aerodynamic moment of the aircraft, which is expressed as

[0089] (2)

[0090] in, It is dynamic pressure, is the reference area, is the reference length. is the rolling moment coefficient, is the yaw moment coefficient, is the pitching moment coefficient, which is related to the speed Ma, angle of attack α, sideslip angle β, and roll angle , right elevator angle , left elevator angle and rudder angle is closely related, and its polynomial function relationship can be expressed as

[0091] (3)

[0092] in, It is the aerodynamic coefficient related to the rolling moment of the aircraft in the zero rudder deflection state. is the aerodynamic increment related to the rolling moment of the aircraft under the influence of the right elevator, is the aerodynamic increment related to the rolling moment of the aircraft under the influence of the left elevator, It is the aerodynamic increment related to the rolling moment of the aircraft under the influence of the rudder; It is the aerodynamic coefficient related to the yaw moment of the aircraft in the zero rudder deflection state. is the aerodynamic increment related to the yaw moment of the aircraft under the influence of the right elevator, is the aerodynamic increment related to the yaw moment of the aircraft under the influence of the left elevator, It is the aerodynamic increment related to the yaw moment of the aircraft under the influence of the rudder; is the aerodynamic coefficient related to the pitch moment of the aircraft in the zero rudder deflection state, is the aerodynamic increment related to the pitch moment of the aircraft under the influence of the right elevator, is the aerodynamic increment related to the pitch moment of the aircraft under the influence of the left elevator, It is the aerodynamic increment related to the pitch moment of the aircraft under the influence of the rudder.

[0093] Step (2) Design and training of physical information neural network

[0094] Physical Information Neural Network (PINN) can significantly improve the robustness of hypersonic vehicle attitude control by integrating flight data with rigid body dynamics equations. The physical information neural network PINN is used to predict the state value and state change value of the aircraft attitude. In the field of applying physical information neural network to hypersonic vehicle control, the construction and optimization of loss function is key. The loss function is denoted as A data loss function that combines data measurements and physical information loss function . Among them, the data loss function Ensure that the network accurately fits the flight measured data, and the physical information loss function The network is then forced to satisfy the vehicle attitude dynamics equation shown in Equation (1). The trained PINN will be embedded in the model predictive control (MPC) as the core prediction module. By learning the hypersonic vehicle attitude dynamics model through the PINN, it replaces the numerical model in the traditional MPC, thereby accelerating the optimization process and improving the model accuracy.

[0095] During online optimization, tracking accuracy and physical feasibility are taken into account, especially for highly nonlinear conditions at hypersonic speeds. It can be expressed as

[0096] (4)

[0097] in, and To balance the weights of the data loss function and the physical information loss function, these weights are adjusted to ensure that both empirical data and physical laws are adequately represented during training.

[0098] Data loss function is the mean square error between the network's predicted value and the actual observed value, expressed as

[0099] (5)

[0100] in, Indicates the number of data for calculating the data-driven loss function, It represents the real state value obtained by solving the hypersonic aircraft attitude dynamics equation (1) by numerical method, which specifically includes the state quantity ,and It is the predicted value of PINN, which specifically includes the state quantity .

[0101] Physical Information Loss Function A set of sample points is generated in the state space of the hypersonic vehicle, ensuring a comprehensive and evenly distributed set of points for evaluating the physics-based loss aspects. The mean square error is then calculated based on the difference between the predicted state change and the actual state change of the hypersonic vehicle's physical dynamic control:

[0102] (6)

[0103] in, Indicates the number of data for calculating physical constraint loss, represents the difference between the actual state change and the predicted state change, where The result obtained by calculating the kinetic equation (1) is , that is, the actual state change value, Indicates the predicted state change value obtained by PINN prediction.

[0104] Step (3) Control-oriented hypersonic vehicle model conversion

[0105] The core of MPC is to optimize the future control sequence through the prediction model. Its efficiency depends on the simplicity and predictability of the model. MPC requires the model to be in the form of discrete state space. Therefore, it is necessary to transform the attitude dynamics model of the hypersonic aircraft (Equation (1)) into a simplified model suitable for MPC solution. 、 、 As the control input, the attitude angle vector Ω is the control output, and the control-oriented nonlinear attitude dynamics can be written as

[0106] (7)

[0107] Where: is the system state vector, obtained through the PINN network prediction in step (2), is the control vector, For output, , d is the external interference term of the system;

[0108] , .

[0109] After differentiating the output vector y twice, the control input u can be expressed explicitly.

[0110] (8)

[0111] Where: is the aggregate uncertainty; K and B can be expressed as

[0112] (9)

[0113] (10)

[0114] in: is the output function right 、 Lie derivative of ; is the output function right The second-order Lie derivative of , i = 1, 2 or 3, j = 1, 2 or 3. Since the aircraft adopts the tilting and turning maneuvering flight mode, when the sideslip angle Enough hours, assuming , we know that the matrix Not strange.

[0115] Through feedback linearization, the original control input aerodynamic torque 、 、 The corresponding control vector is converted into a virtual control quantity v. The following feedback control law can be designed:

[0116] (11)

[0117] Where: , 、 and Represent the virtual control quantities corresponding to the x, y and z axes respectively; and Expressed as

[0118] (12)

[0119] (13)

[0120] Through exact feedback linearization, the original nonlinear system is transformed into Brunovsky standard form, which is expressed as follows:

[0121] (14)

[0122] Where: is the state of the aircraft; A is the state matrix, and C is the output matrix, which are expressed as follows:

[0123]

[0124] Step (4) Model predictive control considering input and output constraints

[0125] After the feedback is linearized, the system is s Discretize and get the prediction model:

[0126] (15)

[0127] Where: and is the state of the aircraft at the kth and k+1th moments, is the virtual control quantity of the aircraft at the kth moment, , 、 is the system matrix of matrices A and B at the kth moment, which can be expressed as

[0128] (16)

[0129] Where: I is the unit matrix, T s is the sampling time. Combined with the output of PINN, the discrete state matrix is ​​updated according to formula (16): and , in order to solve optimization problems with physical constraints.

[0130] In order to reduce computing resources, the controller is designed using the limited prediction horizon control concept. By designing an appropriate prediction horizon, the stability and robustness of the control system can be guaranteed. Set the prediction horizon to N p , the control time domain is N c , predict the system state quantity in the time domain It can be calculated by the following formula:

[0131] (17)

[0132] Where: is the control matrix; F and is the recursive matrix of the system, which can be expressed as

[0133] (18)

[0134] (19)

[0135] In order to achieve accurate tracking of the aircraft's attitude and introduce control variables into the objective function to reduce the burden on the actuator, the following objective function is designed:

[0136] (20)

[0137] Where: is the reference output trajectory; and are system output and control quantity respectively; is the diagonal matrix of control weights.

[0138] During the flight, the elastic effect of the slender body, the saturation problem of the measuring element, and the angular velocity constraint introduced by the mission requirements need to be considered; the actuator rudder deflection angle constraint and rudder deflection angle rate constraint are introduced considering the performance of the servo. is the angular velocity vector, is the rudder deflection vector, is the rudder angular velocity vector, and the various constraints can be expressed as

[0139] (twenty one)

[0140] Where: and are the minimum and maximum values ​​of the angular velocity constraints, and are the minimum and maximum values ​​of the rudder angle vector constraint, and The minimum and maximum values ​​of the rudder angular velocity vector constraints respectively.

[0141] Arrange through matrix operations and write into standard quadratic programming form:

[0142] (twenty two)

[0143] By solving the quadratic programming problem under inequality constraints, the control quantity corresponding to the control time domain in the current state can be obtained. The model prediction control quantity solution is repeated in the next control cycle, and the optimal control of the hypersonic aircraft attitude is achieved through rolling optimization.

[0144] In order to verify the effectiveness of the proposed high-speed aircraft model predictive control method based on physical information neural network, simulation verification was carried out under typical flight conditions. The initial conditions of the simulation were set to an altitude of 30 km and a speed of 2500 m / s. The initial attitude angle and angular velocity were both zero, and the desired angle was deg. The controller needs to be disturbed by external

[0145]

[0146] The existence of _ ... , , the angular velocity constraint is , ensuring that the dynamic performance of the servo meets the actual hardware limitations. The model predictive controller uses the prediction time domain and control time domain , with sampling time Perform rolling optimization. The control input weight matrix is ​​set to To balance the priority of each channel torque. The loss function of the physical information neural network consists of data-driven terms and physical constraint terms, and the weights are set as and , balancing historical data fitting with dynamic equation constraints. The training data includes 10,000 sets of historical flight states, with 5,000 points uniformly sampled in the state space for physical consistency assessment. The network adopts a four-layer fully connected structure (256 neurons per layer) and is trained through 1,000 Adam optimization iterations. It is ultimately embedded in the MPC framework to provide high-precision state prediction. The total simulation duration is 10 seconds. MPC uses quadratic programming to solve the control variables in real time, combined with the physical constraint prediction of PINN, to ensure attitude tracking accuracy while strictly meeting the control surface and angular velocity constraints. This parameter set achieves a balance between dynamic performance and robustness in hypersonic environments.

[0147] in, Figure 3 The angle of attack change curve of the hypersonic aircraft is given. It can be seen that the angle of attack converges to 3 degrees after a period of attitude adjustment. Figure 4 This is the sideslip angle simulation curve. It can be seen that the sideslip angle is greatly disturbed, but its angle adjustment range remains within 0.5 degrees and converges to near 0 after a period of time. Figure 5 is the roll angle tracking curve, and the roll angle converges to near 0 after adjustment. Figure 6-Figure 8 The corresponding control input curves are presented, including left elevator commands, right elevator commands, and rudder commands. The control surface deflection angles are all within reasonable constraints. In summary, the proposed model predictive control method for hypersonic aircraft based on physical information neural networks can achieve satisfactory tracking results.

Claims

1. A high-speed aircraft model predictive control method based on a physical information neural network, characterized in that: The specific steps are as follows: Step (1) Constructing the attitude dynamics model of the hypersonic vehicle (1) , where is the angle of attack, is the sideslip angle, is the roll angle, is the roll angular velocity, is the yaw angular velocity, is the pitch angular velocity, is the moment of inertia of the object around the x-axis, is the moment of inertia of the object around the y-axis, is the moment of inertia of the object around the z-axis, represents the product of inertia about the x-axis and y-axis, is the rolling moment on the aircraft, is the yaw moment on the aircraft, is the pitching aerodynamic moment of the aircraft, which is expressed as (2) , where It is dynamic pressure, is the reference area, is the reference length; is the rolling moment coefficient, is the yaw moment coefficient, is the pitching moment coefficient, and the relationship is expressed as (3) , where It is the aerodynamic coefficient related to the rolling moment of the aircraft in the zero rudder deflection state. is the aerodynamic increment related to the rolling moment of the aircraft under the influence of the right elevator, is the aerodynamic increment related to the rolling moment of the aircraft under the influence of the left elevator, It is the aerodynamic increment related to the rolling moment of the aircraft under the influence of the rudder; It is the aerodynamic coefficient related to the yaw moment of the aircraft in the zero rudder deflection state. is the aerodynamic increment related to the yaw moment of the aircraft under the influence of the right elevator, is the aerodynamic increment related to the yaw moment of the aircraft under the influence of the left elevator, It is the aerodynamic increment related to the yaw moment of the aircraft under the influence of the rudder; is the aerodynamic coefficient related to the pitch moment of the aircraft in the zero rudder deflection state, is the aerodynamic increment related to the pitch moment of the aircraft under the influence of the right elevator, is the aerodynamic increment related to the pitch moment of the aircraft under the influence of the left elevator, It is the aerodynamic increment related to the pitching moment of the aircraft under the influence of the rudder; Step (2) Design and training of physical information neural network The state value and state change value of the aircraft attitude are predicted through the physical information neural network PINN; the loss function Expressed as (4) , where is the data loss function, is the physical information loss function; and To balance the weights of data loss function and physical information loss function; Data loss function The expression is as follows: (5) , where Indicates the number of data for calculating the data-driven loss function, It represents the real state value obtained by solving the hypersonic aircraft attitude dynamics equation (1) by numerical method, which specifically includes the state quantity ,and It is the predicted value of PINN, which includes the state quantity ; Physical Information Loss Function The expression is as follows: (6) , where Indicates the number of data for calculating physical constraint loss, represents the difference between the actual state change and the predicted state change, where The result obtained by calculating the kinetic equation (1) is , that is, the actual state change value, Indicates the predicted state change value obtained by PINN prediction; Step (3) Control-oriented hypersonic vehicle model conversion Select the three-channel aerodynamic torque of the aircraft 、 、 As the control input, the attitude angle vector Ω is the control output, and the control-oriented nonlinear attitude dynamics is written as (7) , where: is the system state vector, obtained through the PINN network prediction in step (2), is the control vector, For output, , d is the external interference term of the system; ， ； After differentiating the output vector y twice, the control input u is expressed as follows; (8) , where: is the aggregate uncertainty; K and B are respectively expressed as (9) ， (10) , where: is the output function right 、 Lie derivative of ; is the output function right The second-order Lie derivative of , i = 1, 2 or 3, j = 1, 2 or 3; Through feedback linearization, the original control input aerodynamic torque 、 、 The corresponding control vector is converted into a virtual control quantity v; the following feedback control law is designed: (11) , where: , 、 and Represent the virtual control quantities corresponding to the x, y and z axes respectively; and Expressed as (12) ， (13) , through exact feedback linearization, the original nonlinear system is transformed into Brunovsky standard form, which is expressed as follows: (14) , where: is the state of the aircraft; A is the state matrix, and C is the output matrix, which are expressed as follows: ， Step (4) Model predictive control considering input and output constraints After the feedback is linearized, the system is s Discretize and get the prediction model: (15) , where: and is the state of the aircraft at the kth and k+1th moments, is the virtual control quantity of the aircraft at the kth moment, , 、 is the system matrix of matrices A and B at the kth moment, expressed as (16) , where I is the unit matrix, T s is the sampling time; combined with the output of PINN, the discrete state matrix is ​​updated according to formula (16) and ; Set the prediction time domain to N p , the control time domain is N c , predict the system state quantity in the time domain Calculated by the following formula: (17) , where: is the control matrix; F and is the recursive matrix of the system, expressed as (18) ， (19) ， Design the following objective function: (20) , where: is the reference output trajectory; and are system output and control quantity respectively; is the diagonal matrix of control weights; Considering the performance of the servo, the actuator rudder deflection angle constraint and rudder deflection angle rate constraint are introduced. is the angular velocity vector, is the rudder deflection vector, is the rudder angular velocity vector, and each constraint is expressed as (21) , where: and are the minimum and maximum values ​​of the angular velocity constraints, and are the minimum and maximum values ​​of the rudder angle vector constraint, and The minimum and maximum values ​​of the rudder angular velocity vector constraints respectively; Arrange through matrix operations and write into standard quadratic programming form: (22) ， By solving the quadratic programming problem under inequality constraints, the control quantity corresponding to the control time domain in the current state can be obtained. The model prediction control quantity solution is repeated in the next control cycle, and the optimal control of the hypersonic aircraft attitude is achieved through rolling optimization.

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