Hypersonic flight vehicle control method based on adaptive dynamic programming

Abstract

The invention provides a hypersonic flight vehicle control method based on adaptive dynamic programming, and relates to the technical field of hypersonic flight vehicle control. The method specifically comprises the following steps: building an actual performance model of the hypersonic flight vehicle, and simplifying the actual performance model of the hypersonic flight vehicle; converting the simplified actual performance model of the hypersonic aircraft into a hypersonic aircraft model in a strict feedback form; designing a state feedback controller according to the thought of a backstepping method and a feedback linearization method, and then carrying out optimization compensation on the state feedback controller by utilizing a self-adaptive dynamic programming algorithm, namely, dynamically updating network weights on line by designing weight updating laws of an execution network and an evaluation network, so as to obtain a mathematical control surface angle control quantity; and converting the obtained mathematical control surface angle control quantity into an actual physical control surface angle control quantity, and inputting the actual physical control surface angle control quantity into an actual hypersonic aircraft model to realize a state tracking control closed loop of the whole hypersonic aircraft.

Description

Technical Field

[0001] The present invention relates to the technical field of hypersonic vehicle control, and particularly to a hypersonic vehicle control method based on adaptive dynamic programming. Background Art

[0002] Currently, countries with the ability to research high-performance aircraft technologies are focusing on breakthroughs in hypersonic vehicle-related technologies, because these technologies will have a profound impact on the international strategic pattern, military power comparison, and economic and social development. From the perspective of military strategy and tactics, hypersonic vehicle-related technologies will not only break through the performance scope of traditional weapons and have a subversive impact, but also promote the leapfrog development of new concepts of offense and defense. In the research on hypersonic vehicle-related technologies, one of the core technologies is the research on the control method of hypersonic vehicles. To ensure the normal flight of the vehicle in a harsh environment and achieve military objectives, special attention should be paid to the research on the state tracking control method of hypersonic vehicles.

[0003] In the early research process of the state tracking control method of hypersonic vehicles, the nonlinear dynamic inversion method that relies on a good mathematical model is usually used. The dynamic inversion method uses the model information of the hypersonic vehicle to construct a pseudo-inverse system to achieve input-output decoupling, and then uses linear system theory to design a controller. This method requires a high model accuracy, but there are still certain errors in the single model of the current stage of hypersonic vehicles, which may lead to a decrease in the control accuracy of the control law output by this method.

[0004] Using the adaptive control method to achieve the state tracking control of hypersonic vehicles is also one of the state tracking control methods that many researchers are currently concerned about. This method uses the Lyapunov stability principle to reasonably design the control law and parameters and the online update law to ensure the closed-loop stability of the state tracking control of hypersonic vehicles. However, single adaptive control is difficult to handle hypersonic vehicles with characteristics such as strong nonlinearity and strong disturbances. Therefore, existing research mostly combines the adaptive control method with other control methods.

[0005] Due to the strong nonlinear characteristics of hypersonic vehicles, the application of backstepping method in the control research of hypersonic vehicles has gradually attracted the attention of researchers. Backstepping is a recursive design method, and the main design process of this method is as follows: starting from the subsystem farthest from the actual control input, the virtual control laws of each subsystem are designed in turn to obtain the final actual control command. However, it is difficult to obtain good performance by only using the backstepping method to control hypersonic vehicles. Therefore, it is necessary to combine the backstepping method with technologies such as sliding mode control, adaptive control, and disturbance observer to achieve the expected tracking control effect. In the paper "Approximate backstepping fault-tolerant control of the flexible airbreathing hypersonic vehicle", An H et al. designed an anti-saturation controller based on the combination of backstepping method and sliding mode theory for a hypersonic vehicle model with uncertainties, external disturbances, and actuator constraints.

[0006] Currently, there are still certain technical defects and room for further optimization in the solutions for the state tracking control of hypersonic vehicles. The control methods that combine the backstepping method with technologies such as sliding mode, adaptive control, and disturbance observer all have their own technical defects. For example, the disturbance observer has tracking errors due to tracking lag; the adaptive control has the disadvantage of complex parameter estimator design, and there is a certain room for optimizing performance indicators due to its strong robustness; the sliding mode control will have a certain degree of frequent switching of the control output signal due to the characteristic of the control signal alternating between positive and negative values, thus increasing the failure rate of the physical actuators of hypersonic vehicles.

[0007] Due to the improvement of the computing power of hardware, the control method of hypersonic vehicles based on intelligent optimization algorithms has gradually attracted the attention of relevant researchers, among which neural networks with the ability to approximate any nonlinear function with specified accuracy have received high attention. There are several ideas for using neural networks to solve related problems in the field of hypersonic vehicle control: First, construct and train a specific neural network structure to estimate the impact brought by the nonlinear and uncertain parameters, external disturbances, etc. of hypersonic vehicles; Second, use the adaptive dynamic programming algorithm combining neural networks and dynamic programming theory to solve the approximate optimal controller and use it to estimate the optimal weights of the neural network online. However, there are still certain technical problems in applying neural networks to meet the control requirements of hypersonic vehicles. For example, there is an overfitting problem in the technical solution of using neural networks to approximate nonlinear control systems, and when the input quantity of the neural network model exceeds the training range of the model data, there will be a problem that the model approximation error is too large or even unable to accurately estimate the output of hypersonic vehicles. And using the adaptive dynamic programming algorithm to design the evaluation function and execution function to dynamically optimize the output command of the controller as one of the current key research methods also has certain technical problems in the actual simulation experiment process, that is, when the complexity of the hypersonic vehicle system model is relatively high, the order of the dynamic model in the system model is relatively high, and when using the adaptive dynamic programming algorithm to solve the optimal control law of the hypersonic vehicle system model, there will be a problem that the algorithm is difficult to converge, so that the approximate optimal control law cannot be obtained. Summary of the Invention

[0008] Aiming at the above deficiencies of the prior art, the present invention proposes a control method for hypersonic vehicles based on adaptive dynamic programming, aiming to meet the state tracking requirements of the longitudinal system and the lateral-directional system of hypersonic vehicles.

[0009] A control method for hypersonic vehicles based on adaptive dynamic programming proposed by the present invention includes the following steps:

[0010] Step 1: Build an actual performance model of a hypersonic vehicle;

[0011] Step 2: Simplify the actual performance model of the hypersonic vehicle;

[0012] Step 3: Convert the simplified actual performance model of the hypersonic vehicle into a hypersonic vehicle model in strict-feedback form; the hypersonic vehicle model in strict-feedback form includes a speed subsystem, a longitudinal altitude subsystem, and a lateral-directional subsystem;

[0013] Step 4: Use the backstepping method to design a state feedback controller for the hypersonic vehicle model in strict-feedback form to obtain the mathematical control amount of the rudder surface angle of the vehicle;

[0014] The state feedback controller of the hypersonic vehicle includes: a speed controller, a longitudinal backstepping controller, and a lateral backstepping controller;

[0015] The mathematical control amount of the rudder surface angle includes: the mathematical rudder surface input amount δ of the vehicle in the pitch direction z , the mathematical rudder surface input amount δ of the vehicle in the yaw direction x and the mathematical rudder surface input amount δ of the vehicle in the roll direction y ;

[0016] Step 5: Design an ADP optimization compensator using the adaptive dynamic programming ADP algorithm, and use the ADP optimization compensator to optimize and compensate the longitudinal backstepping controller of the hypersonic vehicle, and re-solve the mathematical rudder surface input amount δ of the vehicle in the pitch direction z , and update the mathematical control amount of the rudder surface angle of the vehicle obtained in Step 4;

[0017] Step 6: Convert the mathematical control amount of the rudder surface angle into a physical control amount of the rudder surface, and input the physical control amount of the rudder surface into the actual hypersonic vehicle model for state tracking control of the hypersonic vehicle;

[0018] Furthermore, the actual performance model of the hypersonic vehicle in Step 1 includes: a center-of-mass translational model and a rotation model about the center of mass; the center-of-mass translational model includes three translational degrees of freedom of the hypersonic vehicle - the distance x of the vehicle's center of mass along the X-axis direction, the distance y along the Y-axis direction, and the distance z along the Z-axis direction in the ground coordinate system; the rotation model about the center of mass includes three rotational degrees of freedom of the hypersonic vehicle, which are the pitch angle yaw angle ψ and roll angle γ of the vehicle's attitude in the ground coordinate system;

[0019] Furthermore, the process of simplifying the actual performance model of the hypersonic vehicle is: splitting the actual performance model of the hypersonic vehicle into a longitudinal model and a lateral-directional model;

[0020] The longitudinal model is:

[0021]

[0022]

[0023]

[0024]

[0025]

[0026] where θ is the flight path angle; is the derivative of the track angle θ; V is the vehicle speed; is the derivative of the vehicle speed V; P is the engine thrust; D is the vehicle drag; L is the vehicle lift; α is the angle of attack; is the derivative of the angle of attack α; m is the vehicle mass; g is the acceleration due to gravity; ω z is the vehicle pitch angular velocity; is the derivative of the vehicle pitch angular velocity ω z ; represents the derivative of the vehicle flight altitude h; M z represents the pitch moment of the vehicle; J z represents the moment of inertia of the vehicle about the z-axis of the body coordinate system;

[0027] The lateral-directional model is as follows:

[0028]

[0029]

[0030]

[0031]

[0032] where is the pitch angle of the vehicle; γ is the roll angle of the vehicle; is the derivative of the roll angle γ of the vehicle; β is the sideslip angle; is the derivative of the sideslip angle β of the vehicle; ω x is the roll angular velocity of the vehicle; is the derivative of the roll angular velocity ω of the vehicle x ; ω y is the roll angular velocity of the vehicle; is the derivative of the roll angular velocity ω of the vehicle y ; Z is the lateral force of the vehicle; J x represents the moment of inertia of the vehicle about the x-axis of the body coordinate system; J y represents the moment of inertia of the vehicle about the y-axis of the body coordinate system; is the moment of inertia of the vehicle about the x-axis in the body coordinate system; M x is the roll moment of the vehicle; M y is the yaw moment of the vehicle;

[0033] Furthermore, the process of transforming the simplified actual performance model of the hypersonic vehicle into a hypersonic vehicle model in strict feedback form in step 3 includes: transforming the longitudinal model into a model in strict feedback form and splitting it into a speed subsystem and a longitudinal altitude subsystem, and transforming the lateral-directional model into a lateral-directional subsystem in strict feedback form;

[0034] The speed subsystem is:

[0035]

[0036] where φ is the throttle opening; f V , g V are both intermediate variables, and:

[0037]

[0038]

[0039] where P1 and P2 are both known engine thrust parameters of the aircraft;

[0040] The longitudinal height subsystem is:

[0041]

[0042]

[0043]

[0044]

[0045] where y is the distance of the aircraft's center of mass along the Y-axis direction in the ground coordinate system; is the derivative of y; δ z is the mathematical rudder surface input of the aircraft in the pitch direction; f θ , g θ , f α , g α , are all intermediate variables, and:

[0046]

[0047]

[0048]

[0049] g α = 1 (27)

[0050]

[0051]

[0052] where W is the dynamic pressure, and W = 0.5Pv2; S is the characteristic area of the aircraft; is the coefficient of the lift coefficient that does not include the angle of attack; is the sum of the coefficients of the first-order term of the angle of attack in the lift coefficient; and there is Among them, C L is the lift coefficient of aerodynamic force; c is the longitudinal characteristic length; mz0 represents the coefficient sum in the pitching moment coefficient that does not include δ z ; m z1 represents the coefficient sum including δ z for the first-order term; and m z = m z0 + m z1 ; where m z is the pitching moment coefficient of aerodynamic moment;

[0053] The lateral-directional subsystem is as follows:

[0054]

[0055]

[0056] Among them, F1, G1, F2, and G2 are all intermediate variables; δ x , δ y are respectively the control input amounts of the aircraft, the roll rudder deflection angle and the pitch rudder deflection angle, and there are:

[0057]

[0058] Among them, F β is an intermediate variable, and there are:

[0059]

[0060]

[0061]

[0062]

[0063] Among them, M x0 represents the term in the roll moment that does not include δ x ; M y0 represents the term in the yaw moment that does not include δ y ; M x1x , M x1y represent the first-order terms of δ x and δ x in M y ; M y1x , M y1y represent the first-order terms of δ y and δ x in M y ;

[0064] Furthermore, the process of designing the state feedback controller of the hypersonic vehicle in step 4 includes three parts, which are respectively:

[0065] (1) Based on the velocity subsystem, a velocity controller is designed using feedback linearization control;

[0066] (2) According to the longitudinal height subsystem, a longitudinal backstepping controller is designed using backstepping method to solve the mathematical rudder surface input δ of the aircraft in the pitch direction z ;

[0067] (3) According to the lateral and directional subsystem, a lateral backstepping controller is designed using backstepping method, and the mathematical rudder surface input δ of the aircraft in the yaw direction and the mathematical rudder surface input δ of the aircraft in the roll direction are solved x and the mathematical rudder surface input δ of the aircraft in the roll direction y ;

[0068] Furthermore, the steps of designing the longitudinal backstepping controller include:

[0069] Step A1: Let the flight path angle θ be the virtual control variable, then the virtual control law of the flight path angle θ is:

[0070]

[0071] where kph is the height error feedback gain value; θ c is the virtual control law of the flight path angle θ; h r is the target height of the aircraft; is the derivative of the target height h r of the aircraft;

[0072] Step A2: Let the angle of attack α be the virtual control variable, then the virtual control law of the angle of attack α is:

[0073]

[0074] where kpθ is the flight path angle tracking error feedback gain value; α c is the virtual control law of the angle of attack α; is the derivative of θ c ;

[0075] Step A3: Let the pitch angular velocity ω z be the virtual control variable, then the virtual control law of the pitch angular velocity ω z is:

[0076]

[0077] where kpα is the angle of attack tracking error feedback gain value; is the virtual control law of the pitch angular velocity ω z ; isα The derivative of c;

[0078] Step A4: At the mathematical rudder surface input δ of the aircraft in the Z-axis pitch direction z is the actual control input of the aircraft model, and the actual control law of this input is:

[0079]

[0080] where kpω is the feedback gain value of the pitch angle rate tracking error; is the derivative of;

[0081] Furthermore, the said Step 5 includes:

[0082] Step 5.1: Design an ADP optimization compensator using the adaptive dynamic programming (ADP) algorithm. The ADP optimization compensator includes: an execution network and an evaluation network for the virtual control law of the flight path angle, an execution network and an evaluation network for the virtual control law of the angle of attack, an execution network and an evaluation network for the virtual control law of the pitch angular velocity, and an execution network and an evaluation network for the actual control law;

[0083] Step 5.2: Design the weight update laws for each execution network and evaluation network in Step 5.1, and update the network weights of the execution network and the network weights of the evaluation network according to the weight update laws;

[0084] Step 5.3: Apply the updated network weights of the execution network and the network weights of the evaluation network to each execution network and evaluation network designed in Step 5.1, solve the output of each execution network and compensate it into the longitudinal backstepping controller, and re-solve the mathematical rudder surface input δ of the aircraft in the pitch direction z ;

[0085] Furthermore, the weight update law of the execution network and the weight update law of the evaluation network in Step 5.2 are:

[0086]

[0087]

[0088] where is the derivative of the weight vector of the execution network; is the derivative of the weight vector of the evaluation network; γ a 、γ c respectively represent the weight update learning coefficients, which are used to control the weight update rates of the execution network and the evaluation network; is a vector function composed of radial basis functions with N different spike center coordinates, where N is the dimension of the weight vectors of the execution network and the evaluation network; zc represents the state error; when the output of the execution network in the adaptive dynamic programming is applied to the differential equation of a certain state, z c represents the tracking error of that state;

[0089] Furthermore, the formula for re-solving the mathematical rudder surface input quantity δ of the aircraft in the pitch direction is as follows: z The formula is:

[0090]

[0091]

[0092]

[0093]

[0094] where W a0 is the network weight vector of the execution network of the track angle virtual control law; W a1 is the network weight vector of the execution network of the angle of attack virtual control law; W a2 is the network weight vector of the execution network of the pitch angle virtual control law; W a3 is the mathematical rudder surface input quantity of the aircraft in the pitch direction, that is, the network weight vector of the execution network of the actual control law of the actual control input quantity of the aircraft model; is the vector function of the execution network in the track angle virtual control law; is the vector function of the execution network in the angle of attack virtual control law; is the vector function of the execution network in the pitch angle virtual control law; is the vector function of the execution network in the control law of the actual control input quantity of the aircraft model;

[0095] Furthermore, the physical rudder surface angle control quantity includes: the left elevator surface angle control quantity δ of the aircraft ec , the right elevator surface angle control quantity δ of the aircraft ac , and the rudder surface angle control quantity δ of the aircraft rc .

[0096] The beneficial effects of adopting the above technical solutions are as follows:

[0097] The method of the present invention designs a state feedback controller for a hypersonic vehicle by applying the backstepping method and the feedback linearization method, and avoids the problem of non-convergence of the adaptive dynamic programming algorithm caused by the complexity of the model of the hypersonic vehicle by adding an adaptive dynamic programming algorithm to optimize the compensation term for each order subsystem. To a certain extent, it solves the problem of difficult control design caused by the strong nonlinearity of the mathematical model in controlling the hypersonic vehicle; the designed state feedback controller of the hypersonic vehicle has a dynamic optimization effect on the state tracking effect, outputs a relatively stable control quantity, and realizes the state tracking control of the hypersonic vehicle.

[0098] The method of the present invention utilizes the adaptive dynamic programming algorithm to design an execution network and an evaluation network, and provides an update law for the network weights, dynamically learns and updates the weights online, and dynamically updates the optimization compensation of the execution network for the state feedback controller of the hypersonic vehicle, so as to further optimize the basic state tracking control of the hypersonic vehicle while meeting the state tracking requirements, avoiding the problem of difficult algorithm convergence caused by directly designing an ADP optimization compensator for a high-order hypersonic vehicle, making the state tracking speed of the hypersonic vehicle faster and the overshoot of the state smaller, improving the state tracking control effect of the hypersonic vehicle, and realizing dynamic optimization. BRIEF DESCRIPTION OF THE DRAWINGS

[0099] Figure 1 is a flowchart of a control method for a hypersonic vehicle based on adaptive dynamic programming in this embodiment;

[0100] Figure 2 is a schematic diagram of the principle of a control method for a hypersonic vehicle based on adaptive dynamic programming in this embodiment;

[0101] Figure 3 is a network structure diagram of a radial basis function neural network in this embodiment;

[0102] Figure 4 is a schematic diagram of the tracking effect of the flight altitude of the hypersonic vehicle after being controlled by the control method for the hypersonic vehicle based on adaptive dynamic programming in this embodiment;

[0103] Figure 5 is a schematic diagram of the tracking effect of the flight speed of the hypersonic vehicle after being controlled by the control method for the hypersonic vehicle based on adaptive dynamic programming in this embodiment;

[0104] Figure 6 is a schematic diagram of the holding effect of the lateral position of the hypersonic vehicle after being controlled by the control method for the hypersonic vehicle based on adaptive dynamic programming in this embodiment;

[0105] Figure 7 This is a schematic diagram showing the holding effect of the sideslip angle of a hypersonic vehicle after being controlled by the hypersonic vehicle control method based on adaptive dynamic programming in this embodiment. Specific implementation mode

[0106] To facilitate the understanding of this application, the specific implementation modes of the present invention will be further described in detail below in conjunction with the accompanying drawings and implementation modes. The following implementation modes are used to illustrate the present invention, but are not used to limit the scope of the present invention. On the contrary, the purpose of providing these implementation modes is to make the disclosure content of this application more thoroughly and comprehensively understood.

[0107] The core idea of the present invention: According to the hypersonic vehicle model introduced in "Gain Coordination Robust Parametric Control of Hypersonic Vehicles" written by Hou Mingzhe and Tan Feng, build a hypersonic vehicle actual performance model, including the center-of-mass translational model and the rotational model about the center of mass, with a total of 12 differential equations, simplify the hypersonic vehicle actual performance model to obtain the longitudinal model and the lateral-directional model of the hypersonic vehicle; convert the simplified hypersonic vehicle actual performance model into a hypersonic vehicle model in strict-feedback form, including splitting and converting the longitudinal model into a velocity subsystem and a longitudinal altitude subsystem, and converting the lateral-directional model into a lateral-directional subsystem; then design a state feedback controller for the hypersonic vehicle according to the idea of the backstepping method and the feedback linearization method to achieve the tracking control of the longitudinal velocity and altitude of the hypersonic vehicle and the stability control of the lateral direction; then use the adaptive dynamic programming algorithm to optimize and compensate the state feedback controller of the hypersonic vehicle, design the weight update laws of the execution network and the evaluation network to dynamically update the network weights online, so as to further optimize the tracking effect of the hypersonic vehicle for speed and altitude tracking, and obtain the final mathematical rudder surface angle control quantity; convert the obtained mathematical rudder surface angle control quantity into an actual physical rudder surface angle control quantity, including the left and right elevator angle control quantities and a longitudinal rudder angle control quantity, and input the obtained physical rudder surface angle control quantity into the actual hypersonic vehicle to realize the closed-loop of the entire hypersonic vehicle state tracking control.

[0108] A hypersonic vehicle control method based on adaptive dynamic programming in this embodiment is as Figure 1 shown, and this method includes the following steps:

[0109] Step 1: Build a hypersonic vehicle actual performance model;

[0110] The actual performance model of the hypersonic vehicle involves six degrees of freedom of the hypersonic vehicle, including three translational degrees of freedom, namely the distances x, y, and z of the vehicle's center of mass along the X-axis, Y-axis, and Z-axis in the ground coordinate system, respectively, and three rotational degrees of freedom, namely the pitch angle yaw angle ψ and roll angle γ of the vehicle's attitude in the ground coordinate system.

[0111] The actual performance model of the hypersonic vehicle includes: a center-of-mass translational model and a rotation model about the center of mass.

[0112] Among them, the center-of-mass translational model is shown in Formulas (1) and (2):

[0113]

[0114]

[0115] The rotation model about the center of mass is shown in Formulas (3) and (4):

[0116]

[0117]

[0118] Among them, θ is the track angle; ψ V is the ballistic deflection angle of the vehicle; γ V is the speed inclination angle of the vehicle; V is the vehicle speed; P is the engine thrust; D is the drag of the vehicle; L is the lift of the vehicle; Z is the lateral force of the vehicle; t is the time; α is the angle of attack; β is the sideslip angle; are the moments of inertia of the vehicle about each coordinate axis in the body coordinate system respectively; m is the mass of the vehicle; g is the acceleration due to gravity; are the components of the angular rate of rotation of the body coordinate system relative to the ground coordinate system on each coordinate axis in the body coordinate system respectively; are the components of the moment of all the resultant external forces acting on the vehicle about the center of mass on each coordinate axis in the body coordinate system respectively.

[0119] Step 2: Simplify the actual performance model of the hypersonic vehicle.

[0120] In this embodiment, since the actual performance model of a hypersonic vehicle involves 12 differential equations and is overall too complex, when studying problems in some specific scenario applications, appropriate and reasonable simplification is required while ensuring that the model does not suffer from serious distortion. When a hypersonic vehicle moves in a given vertical plane, since the longitudinal motion is symmetric, as long as the symmetry of the motion is not disrupted, that is, there is no lateral motion caused by the deflection of the yaw and roll control mechanisms and other interference factors, the longitudinal motion of the hypersonic vehicle can be achieved. Therefore, the actual performance model of the six-degree-of-freedom hypersonic vehicle is split into a longitudinal model and a lateral-directional model.

[0121] For the state of the vehicle, the angle of attack α and the sideslip angle β are two very important states during the flight of the vehicle. Therefore, the dynamic equations of the pitch angle and the yaw angle ψ in the six-degree-of-freedom model are replaced by the angle of attack α and the sideslip angle β.

[0122] The longitudinal model is as follows: When the hypersonic vehicle undergoes longitudinal motion, the flight path angle ψ V = 0, the velocity inclination angle β V = 0, the sideslip angle β = 0, and the lateral force Z of the vehicle = 0; at the same time, substituting the roll angle γ = 0, the yaw angle ψ = 0, the atmospheric density p at the center of mass of the vehicle = 0, the roll moment M x = 0, and the yaw moment M y = 0 into the actual performance model of the hypersonic vehicle to obtain the longitudinal model, as shown in Formulas (5) to (9):

[0123]

[0124]

[0125]

[0126]

[0127]

[0128] Where is the derivative of the vehicle velocity V; ω z is the pitch angular velocity of the vehicle; is the derivative of the pitch angular velocity ω z of the vehicle; represents the derivative of the flight altitude h of the vehicle; is the derivative of the angle of attack α; is the derivative of the track angle θ; M z represents the pitch moment of the vehicle; J z represents the moment of inertia of the vehicle about the Z-axis of the body coordinate system;

[0129] The lateral-directional model is composed of dynamic equations including the roll angle γ, sideslip angle β, roll angular velocity ω x and yaw angular velocity ω y and in the lateral-directional model, the input of the lateral-directional model includes the state quantities related to the longitudinal model.

[0130]

[0131]

[0132]

[0133]

[0134] where is the derivative of the roll angle γ; is the derivative of the sideslip angle β; is the derivative of the roll angular velocity ω x ; is the derivative of the roll angular velocity ω y ; J x represents the moment of inertia of the aircraft about the X-axis of the body coordinate system; J y represents the moment of inertia of the aircraft about the Y-axis of the body coordinate system.

[0135] In this embodiment, since thrust and aerodynamic forces are involved in the longitudinal model and the lateral-directional model, and the thrust and aerodynamic forces of the aircraft cannot be directly used as the input of the longitudinal model and the lateral-directional model, it is necessary to establish a thrust model and an aerodynamic force model, and use the established thrust model and aerodynamic force model as the input of the longitudinal model and the lateral-directional model.

[0136] The thrust model is expressed as:

[0137] P = P1 + P2·φ (14)

[0138] where P1 and P2 are both known engine thrust parameters of the aircraft; φ is the throttle opening.

[0139] The aerodynamic force model includes: decomposing the aerodynamic force of the aircraft along each coordinate axis in the velocity coordinate system to obtain the components of the aerodynamic force along each coordinate axis in the velocity coordinate system, which are the drag D, lift L, and side force Z of the aircraft, as shown in formula (15):

[0140]

[0141] where Q is the dynamic pressure, and C = 0.5Pv2; S is the characteristic area of the aircraft; C D 、CL , C N are respectively the drag coefficient, lift coefficient, and side force coefficient of the aerodynamic force.

[0142] Decompose the aerodynamic moment of the aircraft along each coordinate axis in the body coordinate system to obtain the components of the aerodynamic moment along each coordinate axis in the body coordinate system, which are respectively the roll moment M x of the aircraft, the yaw moment M y of the aircraft, and the pitch moment M z of the aircraft, as shown in formula (16):

[0143]

[0144] where c is the longitudinal characteristic length; b is the lateral characteristic length; m x , m y , m z are respectively the roll moment coefficient, yaw moment coefficient, and pitch moment coefficient of the aerodynamic moment.

[0145] Step 3: Convert the simplified actual performance model of the hypersonic aircraft into a hypersonic aircraft model in strict feedback form, and the hypersonic aircraft model in strict feedback form includes a speed subsystem, a longitudinal altitude subsystem, and a lateral-directional subsystem.

[0146] The speed subsystem is:

[0147]

[0148] where φ is the throttle opening; f V , g V are both intermediate variables, and:

[0149]

[0150]

[0151] where P1 and P2 are both known engine thrust parameters of the aircraft.

[0152] The longitudinal altitude subsystem is:

[0153]

[0154]

[0155]

[0156]

[0157] where is the longitudinal height of the aircraft's center of mass in the Y-axis direction of the ground coordinate system; is the derivative of y; δ z is the mathematical rudder surface input of the aircraft in the Z-axis, i.e., the pitch direction; f θ , g θ , f α , g α , are all intermediate variables, and:

[0158]

[0159]

[0160]

[0161] g α = 1 (27)

[0162]

[0163]

[0164] Among them is the coefficient of the lift coefficient that does not include the angle of attack; is the sum of the coefficients of the first-order term of the angle of attack in the lift coefficient; and there is mz0 represents the sum of the coefficients of the pitch moment coefficient that does not include δ z ; m z1 represents the sum of the coefficients that include the first-order term of δ z ; and m z = m z0 + m z1 ;.

[0165] The lateral-directional subsystem is:

[0166]

[0167]

[0168] Among them, F1, G1, F2, and G2 are all intermediate variables; δ x , δ y are the control input amounts of the aircraft, the roll rudder deflection angle and the pitch rudder deflection angle, respectively, and there are:

[0169]

[0170] Among them, F β is an intermediate variable, and there are:

[0171]

[0172]

[0173]

[0174]

[0175] Among them, M x0 represents the terms in the rolling moment that do not include δ x ; m y0 represents the terms in the yaw moment that do not include δ y ; M x1x , M x1y represent the first-order terms of δ x and δ x in M y ; m y1x , m y1y represent the first-order terms of δ y and δ x in m y .

[0176] Step 4: Use the backstepping method to design a state feedback controller for the hypersonic vehicle model in strict feedback form to obtain the mathematical control amount of the aircraft's rudder surface angle; wherein the state feedback controller of the hypersonic vehicle includes: a speed controller, a longitudinal backstepping controller, and a lateral backstepping controller; the mathematical control amount of the aircraft's rudder surface angle includes: the mathematical rudder surface input amount δ z in the pitch direction of the aircraft, the mathematical rudder surface input amount δ x in the yaw direction of the aircraft, and the mathematical rudder surface input amount δ y in the roll direction of the aircraft.

[0177] The process of designing the state feedback controller of the hypersonic vehicle includes three parts, which are respectively:

[0178] (1) According to the speed subsystem, use feedback linearization control to design a speed controller.

[0179] In this embodiment, since the speed subsystem only involves a differential equation, the feedback linearization method is directly used to solve the throttle opening φ.

[0180]

[0181] Among them, k V is the speed tracking error feedback gain; V d is the speed tracking target command; is the derivative of the speed tracking target command V d .

[0182] (2) According to the longitudinal height subsystem, use the backstepping method to design a longitudinal backstepping controller to solve the mathematical rudder surface input δ of the aircraft in the pitch direction. z .

[0183] For the simplified longitudinal height subsystem, it involves four differential equations and meets the requirements of the strict feedback form. Therefore, the backstepping method and the linear negative feedback method are used to solve the control problem of the longitudinal height subsystem and design a longitudinal backstepping controller.

[0184] The steps of designing the longitudinal backstepping controller include:

[0185] Step A1: Let the flight path angle θ be the virtual control variable, then the virtual control law of the flight path angle θ is:

[0186]

[0187] where kph is the height error feedback gain value; θ c is the virtual control law of the flight path angle θ; h r is the target height of the aircraft; is the derivative of the target height h r of the aircraft.

[0188] Step A2: Let the angle of attack α be the virtual control variable, then the virtual control law of the angle of attack α is:

[0189]

[0190] where kpθ is the flight path angle tracking error feedback gain value; α c is the virtual control law of the angle of attack α; is the derivative of θ c .

[0191] Step A3: Let the pitch angular velocity ω z in be the virtual control variable, then the virtual control law of the pitch angular velocity ω z is:

[0192]

[0193] where kpα is the angle of attack tracking error feedback gain value; is the virtual control law of the pitch angular velocity ω z ; is the derivative of α c .

[0194] Step A4: In the mathematical rudder surface input δ of the aircraft in the pitch direction on the Z-axis zis the actual control input of the aircraft model, and the actual control law of this input is as follows:

[0195]

[0196] where kpω is the feedback gain value of the pitch angle rate tracking error; is the derivative of.

[0197] (3) According to the lateral-directional subsystem, use the backstepping method to design the lateral backstepping controller, and solve the mathematical rudder surface input δ x of the aircraft in the yaw direction and the mathematical rudder surface input δ y of the aircraft in the roll direction.

[0198] The process of designing the lateral backstepping controller is as follows: Use the backstepping method to design the virtual control law ω xd with the roll angle rate as the virtual control quantity and the virtual control law ω yd with the yaw angle rate as the virtual control quantity for the formulas (30) and (31) in the lateral-directional subsystem, as shown in formula (42):

[0199]

[0200] where k ω is the feedback gain matrix of the roll angle and sideslip angle tracking errors, and where k ω1 and k ω2 are the feedback gain coefficients of the roll angle and sideslip angle, d ω represents the derivative of the tracking target value of the roll angle and sideslip angle, and Since only the longitudinal flight process of the hypersonic aircraft is studied, so d ψ is a zero vector, where and respectively represent the derivatives of the tracking target values of the roll angle and sideslip angle; z5 is the error vector between the actual roll angle and sideslip angle and the target value, and where γ c and β c respectively represent the tracking target values of the roll angle and sideslip angle.

[0201] Take the mathematical rudder surface input δ x of the aircraft in the X-axis, i.e., the yaw direction, and the mathematical rudder surface input δ y of the aircraft in the Y-axis, i.e., the roll direction, as the actual control inputs of the lateral-directional subsystem, and design the actual control law as follows:

[0202]

[0203] where k δis the feedback gain matrix of the roll angular rate and yaw angular rate tracking error, and where k δ1 and are the feedback gain coefficients of the roll angular rate and yaw angular rate tracking errors; d δ represents the derivative of the tracking target values of the roll angular rate and yaw angular rate, and is the derivative of the virtual control law ω xd with the roll angular rate as the virtual control variable; is the derivative of the virtual control law ω yd with the yaw angular rate as the virtual control variable; z6 is the error vector between the actual roll angular rate and yaw angular rate and the outputs of their respective virtual control laws, and

[0204] Step 5: Design an ADP optimization compensator using the adaptive dynamic programming ADP algorithm, and use the ADP optimization compensator to optimize and compensate the longitudinal backstepping controller of the hypersonic vehicle, and re-solve the mathematical rudder surface input δ z of the vehicle, and update the mathematical rudder surface angle control quantity of the vehicle obtained in Step 4.

[0205] In this embodiment, as Figure 2 shown, design an ADP optimization compensator using the policy iteration method in the adaptive dynamic programming algorithm: First, use a radial basis function neural network to design the execution network and evaluation network of each virtual control law and actual control law in the longitudinal backstepping controller respectively; Second, design the weight update law of each execution network and the weight update law a of each evaluation network c According to the designed weight update laws, online update the weight W a of the execution network and the weight W c of the evaluation network; Add the output of each execution network as a compensation term to each virtual control law and actual control law in the longitudinal backstepping controller of the hypersonic vehicle for optimization and compensation.

[0206] Step 5.1: Design an ADP optimization compensator using the adaptive dynamic programming ADP algorithm. The ADP optimization compensator includes: an execution network and an evaluation network of the virtual control law of the flight path angle, an execution network and an evaluation network of the virtual control law of the angle of attack, an execution network and an evaluation network of the virtual control law of the pitch angular velocity, and an execution network and an evaluation network of the actual control law;

[0207] In this embodiment, the adaptive dynamic programming algorithm is an optimal control method for continuous state spaces. Since the state space and action space of complex problems are often continuous, large in scale, and high in dimension, the traditional look-up table method cannot be used to obtain the performance function required in the adaptive dynamic programming algorithm. Therefore, a Radial Basis Function Neural Network (RBFNN) is used to approximate the performance function. The radial basis function neural network is independent of the space dimension and only depends on the distance between nodes. It consists of radial basis functions and network weights:

[0208] H out =W T *H(U in ) (44)

[0209] where W is the weight vector; H(·) is a vector function composed of radial basis functions; u in is the network input; U out is the network output; the structure of the radial basis function neural network is as Figure 3 shown. In the figure, x1, x2, and x3 all represent the network inputs of the radial basis function neural network, h1, h2, h3, h4, and h5 are all vector functions composed of radial basis functions, and w1, w2, w3, w4, and w5 are the weight vectors corresponding to h1, h2, h3, h4, and h5 respectively; out represents the network output of the radial basis function neural network;

[0210] The designed execution network is:

[0211]

[0212] where W a is the weight vector of the execution network; U ina is the input of the execution network function, including the state and state error quantity of the controlled model; U outa is the output of the execution network function;

[0213] The designed evaluation network is:

[0214]

[0215] where W c is the weight vector of the evaluation network; U inc is the input of the evaluation network; U outc is the output of the evaluation network;

[0216] In this embodiment, the radial basis function h(x) is selected as the Gaussian function, as shown in the following formula (45):

[0217]

[0218] where a g represents the peak height of the Gaussian function curve; b g represents the peak center coordinate; c g represents the standard variance of the Gaussian function; ‖·‖ represents taking the norm.

[0219] In this embodiment, the dimensions of W a and W c are both designed to be 11-dimensional, obtaining a vector function composed of 11 Gaussian radial basis functions with different peak center coordinates

[0220] Step 5.2: Design the weight update laws of each execution network and evaluation network in Step 5.1, and update the network weights of the execution network and the network weights of the evaluation network according to the weight update laws;

[0221] The weight update law of the execution network and the weight update law of the evaluation network are as follows:

[0222]

[0223]

[0224] where is the derivative of the weight vector of the execution network; is the derivative of the weight vector of the evaluation network; γ a and γ c respectively represent the weight update learning coefficients, used to control the weight update rates of the execution network and the evaluation network; is a vector function composed of radial basis functions with N different peak center coordinates, where N is the dimension of the weight vectors of the execution network and the evaluation network; z c represents the state error; when the output of the execution network in adaptive dynamic programming is applied to the differential equation of a certain state, z c represents the tracking error of that state.

[0225] Step 5.3: Apply the updated network weights of the execution network and the network weights of the evaluation network to each execution network and evaluation network designed in Step 5.1, solve the output of each execution network and compensate it into the longitudinal backstepping controller, and re-solve the mathematical rudder surface input δ z ;

[0226] In this embodiment, the compensation idea of the adaptive dynamic programming algorithm is applied to the control of each dynamic model in the altitude subsystem of the hypersonic vehicle, that is, the weight vector of the execution network is solved by using the weight vector of the evaluation network, and the output value of the execution network is added to each layer of the basic backstepping controller for controlling the altitude subsystem to perform online dynamic compensation on the virtual control quantity and the actual control quantity, that is, the mathematical rudder surface.

[0227] The formula for re-solving the input quantity δ of the mathematical rudder surface of the aircraft in the pitch direction is as follows: z is:

[0228]

[0229]

[0230]

[0231]

[0232] where W a0 is the network weight vector of the execution network of the virtual control law of the flight path angle; W a1 is the network weight vector of the execution network of the virtual control law of the angle of attack; W a2 is the network weight vector of the execution network of the virtual control law of the pitch angle; W a3 is the input quantity of the mathematical rudder surface of the aircraft in the pitch direction, that is, the network weight vector of the execution network of the actual control law of the actual control input quantity of the aircraft model; is the vector function of the execution network in the virtual control law of the flight path angle; is the vector function of the execution network in the virtual control law of the angle of attack; is the vector function of the execution network in the virtual control law of the pitch angle; is the vector function of the execution network in the control law of the actual control input quantity of the aircraft model; where the input quantity of each execution network is the state quantity and the tracking error to be tracked in each controller, including: altitude h and its corresponding tracking error, flight path angle θ and its corresponding tracking error, angle of attack α and its corresponding tracking error, pitch rate δ z and its corresponding tracking error.

[0233] Step 6: Convert the mathematical rudder surface angle control quantity into a physical rudder surface angle control quantity, and input the physical rudder surface angle control quantity into the actual hypersonic vehicle model for state tracking control of the hypersonic vehicle.

[0234] The mathematical rudder surface angle control quantity includes: the input quantity δ of the mathematical rudder surface of the aircraft in the yaw direction solved in Step 4 x and the input quantity δ of the mathematical rudder surface of the aircraft in the roll directiony and the mathematical rudder surface input δ in the pitch direction of the aircraft re-solved in step 5 z ;

[0235] The physical rudder surface angle control quantity includes: the left elevator surface angle control quantity δ of the aircraft ec , the right elevator surface angle control quantity δ of the aircraft ac , and the rudder surface angle control quantity δ of the aircraft rc ;

[0236] In this embodiment, the conversion formula for converting the mathematical rudder surface angle control quantity into a physical rudder surface angle control quantity with actual physical significance is as follows:

[0237] δ ec =δ z +δ x (54)

[0238] δ ac =δ z -δ x (55)

[0239] δ rc =δ y (56)

[0240] After obtaining the physical rudder surface angle control quantity, input the physical rudder surface angle control quantity into the actual hypersonic aircraft model for state tracking control of the hypersonic aircraft. The actual hypersonic aircraft model includes: a left elevator actuator, a right elevator actuator, and a rudder actuator.

[0241] The aircraft state quantities required in the speed controller, longitudinal backstepping controller, and lateral backstepping controller designed in this embodiment include: aircraft speed V, altitude h, flight path angle θ, angle of attack α, pitch rate, roll angle γ, and sideslip angle β. Input the above aircraft state quantities into the designed state feedback controller of the hypersonic aircraft to achieve the closed-loop of the entire hypersonic aircraft state tracking control. The specific control effects and optimization effects obtained include:

[0242] (1) Altitude tracking effect: As Figure 4 shown, the tracking effect of the flight altitude after applying the final control optimization algorithm designed to the hypersonic aircraft. The aircraft gives a 33 km tracking command at the 32.5 km altitude position and reaches stable tracking in 44 s.

[0243] (2) Speed tracking effect: Figure 5 shows the tracking effect of the flight speed of the hypersonic aircraft. The tracking command is 4570 m / s, and stable tracking is achieved in 16 s.

[0244] (3) Lateral position holding effect: Figure 6 The lateral position holding effect of the hypersonic vehicle is shown, and the maximum lateral offset is 1.5 m.

[0245] (4) Sideslip angle holding effect: Figure 7 The sideslip angle holding effect of the hypersonic vehicle is shown, and the maximum sideslip angle offset is 1.34°.

[0246] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than limiting them; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that they can still modify the technical solutions recorded in the foregoing embodiments, or perform equivalent replacements for some or all of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the scope defined by the claims of the present invention.

Claims

1. A control method for hypersonic vehicles based on adaptive dynamic programming, characterized in that The method includes the following steps: Step 1: Build a practical performance model of a hypersonic vehicle; Step 2: Simplify the practical performance model of the hypersonic vehicle; Step 3: Transform the simplified practical performance model of the hypersonic vehicle into a hypersonic vehicle model in strict-feedback form; the hypersonic vehicle model in strict-feedback form includes a velocity subsystem, a longitudinal altitude subsystem, and a lateral-directional subsystem; Step 4: Use the backstepping method to design a state-feedback controller for the hypersonic vehicle model in strict-feedback form to obtain the mathematical control quantity of the rudder surface angle of the vehicle; The state-feedback controller of the hypersonic vehicle includes: a velocity controller, a longitudinal backstepping controller, and a lateral-directional backstepping controller; The mathematical control quantity of the rudder surface includes: the mathematical rudder surface input quantity δ of the aircraft in the pitch direction z , the mathematical rudder surface input quantity δ of the aircraft in the yaw direction x and the mathematical rudder surface input quantity δ of the aircraft in the roll direction y ; Step 5: Design an ADP optimization compensator using the Adaptive Dynamic Programming (ADP) algorithm, and use the ADP optimization compensator to optimize and compensate the longitudinal backstepping controller of the hypersonic vehicle, and re-solve the mathematical rudder surface input δ of the vehicle in the pitch direction. z , and update the mathematical rudder surface angle control quantity of the vehicle obtained in Step 4; Step 6: Transform the mathematical control quantity of the rudder surface angle into a physical control quantity of the rudder surface angle, and input the physical control quantity of the rudder surface angle into the actual hypersonic vehicle model for state tracking control of the hypersonic vehicle.

2. The control method for a hypersonic vehicle based on adaptive dynamic programming according to claim 1, wherein The actual performance model of the hypersonic vehicle described in Step 1 includes: a center-of-mass translation model and a rotation model about the center of mass; the center-of-mass translation model includes three translational degrees of freedom of the hypersonic vehicle - the distance x of the center of mass of the vehicle along the X-axis direction, the distance y along the Y-axis direction, and the distance z along the Z-axis direction in the ground coordinate system; the rotation model about the center of mass includes three rotational degrees of freedom of the hypersonic vehicle, namely the pitch angle yaw angle ψ and roll angle γ of the attitude of the vehicle in the ground coordinate system.

3. A control method for a hypersonic vehicle based on adaptive dynamic programming according to claim 1, characterized in that The process of simplifying the practical performance model of the hypersonic vehicle is: splitting the practical performance model of the hypersonic vehicle into a longitudinal model and a lateral-directional model; The longitudinal model is: where θ is the track angle; is the derivative of the track angle θ; V is the aircraft speed; is the derivative of the aircraft speed V; P is the engine thrust; D is the aircraft drag; L is the aircraft lift; α is the angle of attack; is the derivative of the angle of attack α; m is the aircraft mass; g is the acceleration due to gravity; ω z is the pitch angular velocity of the aircraft; is the pitch angular velocity ω of the aircraft z derivative; represents the derivative of the aircraft flight altitude h; M z represents the pitch moment of the aircraft; J z represents the moment of inertia of the aircraft about the z-axis of the body coordinate system; The lateral-directional model is: where is the pitch angle of the aircraft; γ is the roll angle of the aircraft; is the derivative of the roll angle γ of the aircraft; β is the sideslip angle; is the derivative of the sideslip angle β of the aircraft; ω x is the roll angular velocity of the aircraft; is the roll angular velocity ω x of the aircraft; ω y is the roll angular velocity of the aircraft; is the roll angular velocity ω y of the aircraft; Z is the lateral force of the aircraft; J x represents the moment of inertia of the aircraft about the x-axis of the body coordinate system; J y represents the moment of inertia of the aircraft about the y-axis of the body coordinate system; is the moment of inertia of the aircraft about the x-axis in the body coordinate system; M x is the roll moment of the aircraft; M y is the yaw moment of the aircraft.

4. A control method for a hypersonic vehicle based on adaptive dynamic programming according to claim 3, characterized in that The process of transforming the simplified practical performance model of the hypersonic vehicle into a hypersonic vehicle model in strict-feedback form in Step 3 includes: transforming the longitudinal model into a model in strict-feedback form and splitting it into a velocity subsystem and a longitudinal altitude subsystem, and transforming the lateral-directional model into a lateral-directional subsystem in strict-feedback form; The velocity subsystem is: where φ is the throttle opening; f V , g V are both intermediate variables, and: where both P1 and P2 are known engine thrust parameters of the vehicle; The longitudinal altitude subsystem is: where y is the distance of the aircraft's center of mass along the Y-axis direction in the ground coordinate system; is the derivative of y; δ z is the mathematical rudder surface input of the aircraft in the pitch direction; f θ , g θ , f α , g α , are all intermediate variables, and: g α ＝1 (27) where Q is the dynamic pressure, and Q = 0.5Pv2; S is the characteristic area of the aircraft; is the coefficient of the lift coefficient that does not include the angle of attack; is the sum of the coefficients of the first-order term of the angle of attack in the lift coefficient; and there is where C L is the lift coefficient of the aerodynamic force; c is the longitudinal characteristic length; mz0 represents the sum of the coefficients of the pitching moment coefficient that does not include δ z ; m z1 represents the sum of the coefficients that include the first-order term of δ z ; and m z = m z0 + m z1 ; where m z is the pitching moment coefficient of the aerodynamic moment; The lateral-directional subsystem is: where F1, G1, F2, and G2 are all intermediate variables; δ x , δ y are the control input quantities of the aircraft, namely the roll rudder deflection angle and the pitch rudder deflection angle, respectively, and there are: where F β is an intermediate variable, and there is: Among which M x0 represents the terms in the rolling moment that do not include δ x ; M y0 represents the terms in the yawing moment that do not include δ y ; M x1x , M x1y represent the first-order terms of δ x and δ x in M y ; M y1x , M y1y represent the first-order terms of δ y and δ x in M y .

5. A control method for a hypersonic vehicle based on adaptive dynamic programming according to claim 4, characterized in that The process of designing the state-feedback controller of the hypersonic vehicle in Step 4 includes three parts, which are respectively: (1) According to the velocity subsystem, use feedback linearization control to design a velocity controller; (2) According to the longitudinal height subsystem, the longitudinal backstepping controller is designed by using the backstepping method to solve the mathematical rudder surface input δ of the aircraft in the pitch direction z ; (3) According to the lateral and directional subsystem, use the backstepping method to design a lateral backstepping controller, and solve the mathematical rudder input δ of the aircraft in the yaw direction x and the mathematical rudder input δ of the aircraft in the roll direction y .

6. A control method for a hypersonic vehicle based on adaptive dynamic programming according to claim 5, characterized in that, The steps of designing the longitudinal backstepping controller include: Step A1: Set The course angle θ is the virtual control variable, and the virtual control law for the course angle θ is: where kph is the height error feedback gain value; θ c is the virtual control law of the track angle θ; h r is the target height of the aircraft; is the target height h r of the derivative; Step A2: Set the angle of attack α in it as a virtual control variable, then the virtual control law of the angle of attack α is: where $k_{p\theta}$ is the feedback gain value of the track angle tracking error; $\alpha$ c is the virtual control law of the angle of attack $\alpha$; is the derivative of $\theta$ c ; Step A3: Set the pitch angular velocity ω z as the virtual control quantity, then the virtual control law of the pitch angular velocity ω z is: where $k_{p\alpha}$ is the feedback gain value of the angle of attack tracking error; is the pitch angular velocity $\omega$ z of the virtual control law; is the derivative of $\alpha$ c ; Step A4: At the mathematical rudder surface input δ of the aircraft in the Z-axis pitch direction z is the actual control input of the aircraft model, and the actual control law of this input is: where kpω is the feedback gain value of the pitch angle rate tracking error; is the derivative of.

7. A control method for a hypersonic vehicle based on adaptive dynamic programming according to claim 6, characterized in that, Step 5 includes: Step 5.1: Use the adaptive dynamic programming (ADP) algorithm to design an ADP optimization compensator. The ADP optimization compensator includes: an execution network and an evaluation network for the virtual control law of the flight path angle, an execution network and an evaluation network for the virtual control law of the angle of attack, an execution network and an evaluation network for the virtual control law of the pitch angular velocity, and an execution network and an evaluation network for the actual control law; Step 5.2: Design the weight update laws for each execution network and evaluation network in Step 5.1, and update the network weights of the execution network and the network weights of the evaluation network according to the weight update laws; Step 5.3: Apply the network weights of the updated execution network and the evaluation network to each execution network and evaluation network designed in Step 5.1, solve the output of each execution network and compensate it into the longitudinal backstepping controller, and re-solve the mathematical rudder surface input δ of the aircraft in the pitch direction z .

8. A control method for a hypersonic vehicle based on adaptive dynamic programming according to claim 7, characterized in that The weight update law of the execution network and the weight update law of the evaluation network in Step 5.2 are: wherein is the derivative of the weight vector of the execution network; is the derivative of the weight vector of the evaluation network; γ a , γ c respectively represent the weight update learning coefficients, which are used to control the weight update rates of the execution network and the evaluation network; is a vector function composed of radial basis functions of N different spike center coordinates, where N is the dimension of the weight vectors of the execution network and the evaluation network; z c represents the state error; when the output of the execution network in the adaptive dynamic programming is applied to the differential equation of a certain state, z c represents the tracking error of that state.

9. A hypersonic vehicle control method based on adaptive dynamic programming according to claim 8, characterized in that, The formula for re-solving the mathematical rudder surface input δ of the aircraft in the pitch direction z is as follows: Where W a0 is the network weight vector of the execution network of the track angle virtual control law; W a1 is the network weight vector of the execution network of the angle of attack virtual control law; W a2 is the network weight vector of the execution network of the pitch angle virtual control law; W a3 is the mathematical rudder surface input of the aircraft in the pitch direction, that is, the network weight vector of the execution network of the actual control law of the actual control input of the aircraft model; is the vector function of the execution network in the track angle virtual control law; is the vector function of the execution network in the angle of attack virtual control law; is the vector function of the execution network in the pitch angle virtual control law; is the vector function of the execution network in the control law of the actual control input of the aircraft model.

10. A control method for a hypersonic vehicle based on adaptive dynamic programming according to claim 1, characterized in that The physical control surface angle quantity includes: the left elevator control surface angle quantity δ of the aircraft ec , the right elevator control surface angle quantity δ of the aircraft ac , and the rudder control surface angle quantity δ of the aircraft rc .

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