An Adaptive Regulation Control Method for a Nonlinear Parameterized Hypersonic Vehicle

Abstract

The present invention discloses a non - linear parametric modeling and its adaptive regulation control method for a hypersonic vehicle in cruise mode, including: using data fitting for comparative analysis to compare the fitting indexes and fitting curves under polynomial function and trigonometric function curve fitting methods; decomposing the longitudinal model of the non - linear parametric hypersonic vehicle with engine dynamics into two interconnected non - linear parametric velocity subsystems and flight path angle subsystems; when the system parameters are known, using the backstepping method to complete the design of the nominal controller; when the system parameters are unknown, using adaptive technology and the backstepping method for the design of the adaptive controller, and globally asymptotically regulating the state variables of the system to non - zero equilibrium points; giving a robust control simulation experiment for the non - linear parametric hypersonic vehicle system with disturbances. The present invention can effectively improve the safety and reliability of the system and ensure the flight stability of the hypersonic vehicle.

Description

Technical Field

[0001] The present invention belongs to the technical field of automatic control of aircraft, and relates to an adaptive regulation control method for a non-linear parameterized hypersonic aircraft. Background Art

[0002] As a new type of aircraft with a large airspace, ultra-high speed, long distance and high precision, the structural characteristics, dynamic characteristics, flight characteristics and environmental characteristics of a hypersonic aircraft are more complex than those of general aircraft. Its main characteristics include a large working range, a complex system dynamic range, and many components. Therefore, it has strong non-linear characteristics and there are significant uncertainties in parameters and structures. These factors make the research on aircraft modeling and control highly scientific and challenging, and face many unknown frontier scientific problems. At the same time, this type of aircraft performs flight missions in the near space (the airspace 20-100 km from the ground), having both the advantages of aviation technology and advantages that cannot be compared with spacecraft. It can not only cruise at hypersonic speed within the atmosphere, but also re-enter the orbit by crossing the atmosphere. The supersonic ramjet engine it uses is considered the third power revolution after the propeller and jet propulsion, and has significant military and civilian value.

[0003] The actual dynamic model of hypersonic aircraft is particularly complex, with characteristics such as high nonlinearity, strong coupling and fast time variation. In addition, its complex flight environment makes the system dynamic function uncertain. Especially when the hypersonic aircraft has uncertain factors such as actuator failure, structural damage, sensor failure, etc., the uncertainty of the system dynamic function is more significant, which leads to the uncertainty of the system structure. This change may make the system unable to be linearly parameterized. At this time, the unknown parameters of the system are characterized in a nonlinear form. Therefore, for nonlinear parameterized uncertain multivariable systems, especially nonlinear systems with non-minimum phase characteristics and non-controllable and observable linearization characteristics, it is particularly important to develop adaptive stabilization, regulation and output tracking strategies for nonlinear parameterized systems. More serious function uncertainty will also cause the system to transform from a parameterizable system to a non-parameterizable system, and from a minimum phase system to a non-minimum phase system. At present, the methods for nonlinear parameterized uncertain systems are mainly limited to single-input single-output systems and approximate systems. However, many actual system models are multi-input and multi-output systems and are non-minimum phase, such as flight control systems with strong nonlinearity, large working range, large-scale parameter and structural uncertainty, non-minimum phase and other characteristics. Therefore, how to utilize the existing flight test data and the experience gained from the verification aircraft test flights, conduct in-depth basic theoretical research, establish a more accurate aerodynamic coefficient model and torque coefficient model for hypersonic aircraft, and develop adaptive control technology for nonlinear parameterized uncertain nonlinear multivariable systems, so as to promote the research and development of a new generation of higher-performance hypersonic verification aircraft and the development of hypersonic technology, is a difficult problem that needs to be solved urgently. Summary of the invention

[0004] The purpose of the present invention is to overcome the defects of the prior art and provide an adaptive adjustment control method for a nonlinear parameterized hypersonic aircraft, which can improve the safety and reliability of a type of nonlinear parameterized hypersonic aircraft control system and ensure the control stability of the aircraft during operation.

[0005] In order to solve the above technical problems, the present invention adopts the following technical solutions.

[0006] An adaptive regulation control method for a nonlinear parameterized hypersonic aircraft comprises the following steps:

[0007] Step 1: Use data fitting method to conduct comparative analysis, perform polynomial function curve fitting and trigonometric function curve fitting on the existing publicly processed flight data, obtain the expression of aerodynamic force and aerodynamic moment coefficient of the longitudinal model of the hypersonic aircraft, and provide a fitting curve graph;

[0008] Step 2: By comparing the fitting metrics and fitting curves of two different function curve fitting methods, namely polynomial functions and trigonometric functions, it is shown that the trigonometric function curve fitting method is more accurate;

[0009] Step 3: Transfer the non-zero equilibrium point of the hypersonic vehicle to the origin through coordinate transformation. After designing the virtual control signal and the actual control signal, the design of the nominal controller is completed, and a Lyapunov function is selected to analyze the stability of the nonlinear parametric hypersonic vehicle model system with engine dynamics;

[0010] Step 4: For the more accurate nonlinear parametric hypersonic vehicle model, by analyzing the influence of the two control inputs of the vehicle on the vehicle system, the longitudinal model of the nonlinear parametric hypersonic vehicle with engine dynamics is decomposed into two interconnected nonlinear parametric subsystems: the velocity subsystem and the flight path angle subsystem; for the velocity subsystem and the flight path angle subsystem, the backstepping method is used to design the adaptive controller to ensure that all signals of the closed-loop system are globally bounded and the state variables of the system are globally asymptotically regulated to the non-zero equilibrium point;

[0011] Step 5: For other flight phases of the hypersonic vehicle, based on the above design method, a nonlinear parametric hypersonic vehicle system with disturbances is given, and the robust performance of the proposed adaptive controller under wind disturbances is studied.

[0012] Specifically, the process of Step 1 includes:

[0013] Step 1-1: Establish a nonlinear parametric aerodynamic model of the hypersonic vehicle based on known flight data, indicating that the nonlinear parametric aerodynamic model in expressions (5)-(8) has higher accuracy than the existing linear parametric aerodynamic model:

[0014] The longitudinal dynamics model of the hypersonic vehicle is

[0015]

[0016]

[0017]

[0018]

[0019] where the engine thrust T, drag D, lift L, and pitching moment M yy are

[0020]

[0021]

[0022]

[0023]

[0024] The aerodynamic coefficients and moment coefficients in the above formula are as follows:

[0025]

[0026]

[0027]

[0028]

[0029]

[0030]

[0031] And the engine throttle dynamics model is represented by the following second-order system:

[0032]

[0033] Wherein, the aircraft state includes speed V, flight path angle γ, angle of attack α, pitch rate q, engine throttle opening Φ and engine throttle opening derivative The aircraft control inputs include elevator deflection angle δ and engine throttle opening control command Φ c , and the physical constants include gravitational acceleration g, aircraft mass m, moment of inertia I yy , air density ρ, wing reference area S, mean aerodynamic chord Natural frequency ω n and damping ratio ∈;

[0034] A hypersonic aircraft with engine dynamics has two basic control actions, namely, increasing and decreasing the flight path angle and increasing and decreasing the speed during horizontal flight. Among them, the flight path angle is determined by the elevator deflection angle δ in (8), and the speed during horizontal flight is mainly determined by the engine throttle opening control command Φ in (15) c ; Specifically, the six state variables of a hypersonic aircraft with engine dynamics and the two control inputs [δ, Φ c T affect the dynamic changes in formulas (1)-(4) through thrust T, drag D, lift L and pitching moment M yy ; Due to changes in the aircraft payload or component aging, in the aerodynamic models (9)-(14) and ​System parameters that are all unknowns, and all states of the hypersonic vehicle are measurable;

[0035] Step 1-2: Perform data fitting, that is, find a suitable non-linear continuous function to approximate discrete data points, including: obtaining discrete data, fitting existing data and processing discrete data in different forms into a standard form; determining the fitting function, setting the basic function form according to the specific influence relationship of the data and the mechanism model of the research object, and then using an optimization algorithm to solve the specific parameters in the function to obtain a continuous form of the fitting function model; calculating fitting indicators to test the fitting effect;

[0036] Step 1-3: Use the sum of squared errors SSE and the correlation coefficient CD to evaluate the fitting effect and accuracy;

[0037] A data set has n values, labeled as y 1 ,…,y n , which are associated with the fitting values f 1 ,…,f n Define an error e i =y i -f i , i = 1,…,n, representing the difference between the actual data and the fitting value; the sum of squared errors SSE is defined as

[0038]

[0039] The correlation coefficient CD is defined as

[0040]

[0041] where is the mean of a discrete data

[0042] The closer the sum of squared errors SSE is to 0, the better the model selection and the more accurate the data prediction result; if the square of the correlation coefficient CD is closer to 1, it means that the model fitting effect is better and the coefficient will be more persuasive;

[0043] Step 1-4: Longitudinal dynamics model data fitting: On the basis of existing data, re-fit the drag coefficient C D (α), lift coefficient C L (α) and moment coefficient C M (α), and plot the discrete aerodynamic data points as a fitting curve graph according to different angles of attack α;

[0044] Step 1-4-1, Trigonometric function fitting: Based on the aerodynamic data in existing literature, analyze the variation law of the aerodynamic data. It can be found that the expression obtained by trigonometric function fitting is more accurate than that obtained by polynomial fitting. Then, use the new expression to re-establish the drag coefficient C D (α), lift coefficient C L (α) and moment coefficient C M (α) of the dynamic equations are

[0045] C D (α) = 1.631 - 0.8702cos(0.04987α) + 0.1957sin(0.04987α) (18)

[0046] C L (α) = 0.08289sin(0.03914α - 0.02531) (19)

[0047] C M (α) = -0.1461 + 0.1645cos(0.05314α) - 0.08719sin(0.05314α) (20)

[0048] Their corresponding sum of squared errors SSE are 1.99×10 -4 , 2.26×10 -5 and 4.16×10 -7 , and the corresponding correlation coefficients CD are 0.9999, 0.9960 and 0.9990; According to the determined trigonometric function form, plot the curves of the drag coefficient C D (α), lift coefficient C L (α) and moment coefficient C M (α) versus the angle of attack α;

[0049] Step 1-4-2, Polynomial function fitting: The hypersonic vehicle uses the same data for polynomial function fitting, and the obtained drag coefficient C D (α), lift coefficient C L (α) and moment coefficient C M (α) of the dynamic equations are

[0050] C D (α) = 3.493×10 -4 α 2 + 0.02216α + 0.7421 (21)

[0051] C L (α) = 1.653×10 -3 α + 0.01206 (22)

[0052] C M (α) = -4.871×10 -6 α 2 -0.008197α + 0.02365 (23)

[0053] The corresponding sum of squared errors SSEs are 4.01×10 -3 and 8.74×10 -4 and 2.71×10 -3 respectively, and the corresponding correlation coefficients CD are 0.9970, 0.8454 and 0.9962.

[0054] Specifically, the process of step 2 includes:

[0055] Step 2-1, Comparison between polynomial function fitting and trigonometric function fitting: According to the definition of the fitting index, the sum of squared errors obtained by trigonometric function fitting is closer to 0, and the obtained correlation coefficient is closer to 1. Therefore, according to the longitudinal dynamics model data fitting process, it can be known that the aerodynamic coefficients obtained by trigonometric function fitting are more accurate than those obtained by polynomial function fitting;

[0056] Step 2-2, Explanation of non-linear parametric aerodynamic coefficients: Through the trigonometric function fitting method, a hypersonic vehicle aerodynamic model with aerodynamic force coefficients and moment coefficients in trigonometric function form can be obtained. The characteristics of this model are:

[0057] Step 2-2-1, Considering the uncertainty of the aerodynamic coefficients and ensuring the accuracy of curve fitting, the aerodynamic coefficient expressions of the dynamic equations of the drag coefficient, lift coefficient and moment coefficient in the gliding state are characterized as aerodynamic coefficient functions with unknown parameters:

[0058]

[0059]

[0060]

[0061] For C L (α), C D (α) and C M (α) in equations (24)-(26), the unknown aerodynamic coefficients themselves contain serious uncertainties of aerodynamic coefficients, including structural uncertainties and parameter uncertainties. These specific non-linear parametric functions are only some representative examples, and more general or different non-linear parametric fitting functions can also be considered within the framework of the proposed adaptive control scheme;

[0062] Step 2-2-2: According to the dominant control input idea, the speed state is mainly affected by the engine throttle opening Φ, and the engine throttle opening control command Φ c controls the engine throttle opening Φ through the engine second-order dynamic equation (15); the flight attitude is controlled by the elevator deflection angle δ; therefore, the longitudinal dynamics model of the hypersonic vehicle with engine dynamics is divided into two interrelated subsystems: the speed subsystem and the flight path angle subsystem, and models are established for these two interrelated subsystems respectively;

[0063] So far, a complete longitudinal dynamics model of a non-linear parameterized hypersonic vehicle with engine dynamics has been established

[0064]

[0065]

[0066]

[0067]

[0068] Among them, the engine thrust T, drag D, lift L, and pitching moment M yy are

[0069]

[0070]

[0071]

[0072]

[0073] The aerodynamic coefficients and moment coefficients in the above formula are as follows:

[0074]

[0075]

[0076]

[0077]

[0078]

[0079]

[0080] And the engine throttle opening dynamics model is expressed as:

[0081]

[0082] Specifically, the process of step 3 includes:

[0083] Step 3-1: Under the cruise phase of the hypersonic vehicle, the non-zero equilibrium points of the hypersonic vehicle dynamic models (1)-(12), (15), and (27)-(28) with engine throttle dynamics are expressed as

[0084]

[0085] The non-zero equilibrium points are transformed into the coordinate origin by defining the following coordinate transformation:

[0086] x 1 = γ x 2 = α - α * x 3 = q (30)

[0087]

[0088] Based on this, the dynamic models of the improved hypersonic vehicle (1)-(4) and engine throttle opening (15) can be expressed as

[0089]

[0090]

[0091]

[0092]

[0093]

[0094]

[0095] where u 1 = δ - δ * , δ * and respectively represent their ideal values under cruise conditions, and the functions g 1 (z 1 ), g 3 (z 1 ), k 1 (z 1 , x 2 ) and k 3 are

[0096]

[0097]

[0098]

[0099]

[0100] Among them, the uncertain non - linear functions f i and h i , where i = 1, 2, 3 and j = 1, 3 are expressed as

[0101]

[0102]

[0103]

[0104]

[0105]

[0106] Since both f i and h j are continuous functions and f i (0)=0, h j (0)=0, the upper bounds of the non - linear functions f i and h j are obtained

[0107]

[0108]

[0109]

[0110]

[0111]

[0112] Among them, β 1 (z 1 )≥1, β 2 (z 1 )≥1, β 3 (x 2 ,x 3 ,z 1 )≥1 and λ 1 (z 1 ,x 2 )≥1 are all known functions, and are all unknown parameters, and their specific expressions are as follows:

[0113]

[0114]

[0115]

[0116]

[0117]

[0118]

[0119]

[0120]

[0121]

[0122] Step 3-2: Conduct nominal control design for the transformed aircraft dynamics model control system (32)-(37) without unknown parameters; introduce the following coordinate transformation:

[0123] ξ 1 = x 1 - α 0 α 0 = 0 (61)

[0124]

[0125]

[0126] η 1 = z 1 - β 0 β 0 = 0 (64)

[0127]

[0128]

[0129] where α i , β i are virtual control signals, ξ j , η j are the errors between the state variables of the aircraft dynamics model control system and the virtual control signals, is a positive function to be determined;

[0130] Step 3-3: Nominal system control design: For the transformed aircraft dynamics model control system (32)-(37) with a relative degree of {3,3}, the improved backstepping control process includes:

[0131] Step 3-3-1, a) Design the nominal virtual signal α 1 ; For the track angle subsystem (32)-(34), select the first positive definite function

[0132]

[0133] Positive definite function The time derivative of is

[0134]

[0135] where is a combined value of the track angle subsystem constant and the track angle subsystem parameters, defined as

[0136]

[0137] Select the virtual control signal α 1

[0138]

[0139] where p 1 is a constant to be determined, thus obtaining

[0140]

[0141] b) Design the nominal virtual control signal β 1 ; For the speed subsystem (35)-(37), select the first positive definite function

[0142]

[0143] Positive definite function The time derivative of is

[0144]

[0145] where is a combined value of the speed subsystem constant and the speed subsystem parameters, defined as

[0146]

[0147] Select the virtual control signal β 1

[0148]

[0149] where q 1 is a constant to be determined, thus obtaining

[0150]

[0151] Step 3-3-2, a) Design the nominal virtual control signal α 2 ; For the track angle subsystem (32)-(34), select the second positive definite function

[0152]

[0153] Positive definite function The time derivative of

[0154]

[0155] where

[0156] and is a combined value of the track angle subsystem constants and track angle subsystem parameters, defined as

[0157]

[0158] Select the virtual control signal α 2

[0159]

[0160] where p 2 is a constant to be determined, thus obtaining

[0161]

[0162] b) Design the nominal virtual control signal β 2 ; For the speed subsystem (35)-(37), select the second positive definite function

[0163]

[0164] Positive definite function The time derivative of

[0165]

[0166] where

[0167] and is a combined value of the speed subsystem constants and speed subsystem parameters, defined as

[0168]

[0169] Select the virtual control signal β 2

[0170]

[0171] where q 2 is a constant to be determined, so as to obtain

[0172]

[0173] Step 3-3-3, a) Design the nominal actual control μ 1 ; Select the third positive definite function for the track angle subsystem (32)-(34)

[0174]

[0175] The positive definite function The time derivative of is

[0176]

[0177] where

[0178] and is a combined value of the track angle subsystem constant and the track angle subsystem parameter, defined as

[0179]

[0180] Select the actual control signal μ 1

[0181]

[0182] where p 3 is a constant to be determined, so as to obtain

[0183]

[0184] b) Design the nominal actual control signal μ 2 ; Select the third positive definite function for the speed subsystem (35)-(37)

[0185]

[0186] The positive definite function The time derivative of is

[0187]

[0188] where

[0189] and is a combined value of the speed subsystem constant and the speed subsystem parameter, defined as

[0190]

[0191] Select the actual control signal μ 2

[0192]

[0193] where q 3 is a constant to be determined, thus obtaining

[0194]

[0195] Step 3-4, Stability analysis: For the converted nonlinear parametric hypersonic vehicle dynamics model control system (32)-(37), select the Lyapunov function

[0196]

[0197] From the above nominal control design process, the designed nominal control signals μ 1 (90) and μ 2 (95) make the derivative of the Lyapunov function be

[0198]

[0199] By selecting p 1 = 9, p 2 = 11 / 2, p 3 = 3 / 2, q 1 = 13 / 2, q 2 = 3 and q 3 = 1, the derivative

[0200]

[0201] Therefore, by adopting the above nominal controller design, the stability analysis of the nonlinear parametric hypersonic vehicle model system with engine dynamics is carried out, and the conclusion is:

[0202] For the nonlinear parametric vehicle longitudinal model (1)-(4) and the engine throttle opening dynamics (15) that meet the assumption conditions, the designed nominal control signals (90) and (95) ensure the stability of the closed-loop system and achieve the global exponential convergence of the vehicle state;

[0203] Proof: Define the state variable of the closed-loop system Υ(t) = [ξ(t), η(t)] T , where ξ(t) = [ξ 1 (t), ξ 2 (t), ξ 3 (t)] T , and η(t) = [η 1 (t), η 2 (t), η 3 (t)] T ; It can be obtained from (99) that Therefore is a monotonically non-increasing function; for any initial state ξ(t 0 ), η(t 0 ), it can be obtained that Therefore, the nominal control signals (90) and (95) ensure that the closed-loop system is globally bounded;

[0204] Define According to the definition of the Lyapunov function , it is obtained that

[0205]

[0206] Inequalities (98) and (99) show that satisfies the differential inequality

[0207]

[0208] According to inequality (101), it can be obtained that

[0209]

[0210] According to (100) and (102), it is further obtained that

[0211]

[0212] Therefore, for any γ(t 0 ) ∈ R 6 , the origin is globally exponentially stable; according to (61)-(66), it can be obtained that x i and z i globally exponentially converge to the origin; according to (30) and (31), the state variables of the hypersonic vehicle system globally exponentially converge to the non-zero equilibrium point in (29)

[0213] Specifically, the process of step 4 includes:

[0214] Step 4-1. The adaptive control signal in the nonlinear systems (32)-(37) can be expressed as

[0215]

[0216]

[0217]

[0218] where x = [x 1 , x 2 , x 3 T , z = [z 1 , z 2 , z 3 T , and is the estimated value of the nominal parameter :

[0219]

[0220]

[0221]

[0222]

[0223]

[0224]

[0225] For the control system (32)-(37) of the aircraft dynamics model with unknown parameters, based on the improved backstepping control strategy and the adaptive control method, an adaptive control signal is designed to ensure the global stability of all system states;

[0226] Coordinate transformation: For the flight path angle subsystem (32)-(34) representing the aircraft attitude and the velocity subsystem (35)-(37) representing the aircraft velocity, the following state errors and virtual control signals are defined:

[0227] ξ 1 = x 1 - α 0 α 0 = 0 (107)

[0228]

[0229]

[0230] η 1 ​​= z 1 -β 0 β 0 = 0 (110)

[0231]

[0232]

[0233] where α i and β i , i = 0, 1, 2 are virtual control signals to be designed in the following, a 10 , a 20 , b 10 , b 20 are all positive definite functions;

[0234] Step 4-2, Adaptive design under unknown parameters, including the adaptive control design of the path angle subsystem (32)-(34) and the speed subsystem (35)-(37):

[0235] Step 4-2-1, a) Design the virtual control signal α 1 and the parameter update law For the path angle subsystem (32)-(34), select the following positive definite function

[0236]

[0237] where is the parameter estimation error; Combining equations (32), (38), (47), (69), (107), (108) and the Young inequality, the derivative of the function V 1 is as follows:

[0238]

[0239] Select the virtual control signal α 1 and the parameter update law in the following form

[0240]

[0241]

[0242] where and p 1 is a parameter to be designed, thus obtaining

[0243]

[0244] b) Design the virtual control signal β 1 and the parameter update law For the velocity subsystems (35)-(37), select the following positive definite function

[0245]

[0246] where is the parameter estimation error; combining equations (35), (40), (50), (74), (110), (111) and Young's inequality, the derivative of the function W 1 is as follows:

[0247]

[0248] Select the virtual control signal β in the following form 1 and the parameter update law as

[0249]

[0250]

[0251] where and b 11 = q 1 ; q 1 is the parameter to be designed, thus obtaining

[0252]

[0253] Step 4-2-2, a) Design the virtual control signal α 2 and the parameter update law For the course angle subsystems (32)-(34), select the following positive definite function

[0254]

[0255] where is the parameter estimation error; combining equations (33), (108), (109), (117) and Young's inequality, the derivative of the function V 2 is as follows:

[0256]

[0257] Select the virtual control signal α in the following form 2 and the parameter update law as

[0258]

[0259]

[0260] Among them, a 22 = π 11 +

[0261] π 12 + π 13 , and

[0262] p 2 is a parameter to be designed. Furthermore,

[0263]

[0264] b) Design the virtual control signal β 2 and the parameter update law For the velocity subsystem (35)-(37), select the following positive definite function

[0265]

[0266] Among them, is the parameter estimation error; Combining equations (111) and (112), the derivative of the function W 2 is as follows:

[0267]

[0268] Select the virtual control signal β with the following form 2 and the parameter update law as

[0269]

[0270]

[0271] Among them,

[0272] and

[0273] q 2 is a parameter to be designed. Furthermore,

[0274]

[0275] Step 4-2-3, a) Design the actual control μ 1 and the parameter update law For the course angle subsystem (32)-(34), select the following positive definite function

[0276]

[0277] wherein, is the parameter estimation error; combining equations (107)-(109), the derivative of the function V 3 is as follows:

[0278]

[0279]

[0280] Select the actual control signal μ 1 and the parameter update law as

[0281]

[0282]

[0283] wherein, and

[0284]

[0285] p 3 is a parameter to be designed, and then

[0286]

[0287] b) Design the virtual control signal μ 2 and the parameter update law For the velocity subsystem (35)-(37), select the following positive definite function

[0288]

[0289] wherein, is the parameter estimation error; combining equations (110)-(112), the derivative of W 3 is

[0290]

[0291] Select the actual control signal μ 2 and the parameter update law as

[0292]

[0293]

[0294] Among them, b 31 = q 3 + 1,

[0295] and

[0296]

[0297]

[0298] q 3 is a parameter to be designed. Furthermore, we can obtain

[0299]

[0300] Step 4-3, Stability analysis: Based on the above design steps, for the non-linear parameterized system (32)-(37) after coordinate transformation, define the following Lyapunov function:

[0301]

[0302] It is easy to obtain that the Lyapunov function defined in (143) is positive definite and radially unbounded;

[0303] The above-designed control signals (135) and (140) and parameter update laws (116), (121), (126), (131), (136) and (141) make the derivative of V with respect to time satisfy

[0304]

[0305] To make the above formula negative definite, select the following parameter values to be designed: p 1 = 9, q 2 = 3 and q 3 = 1. Therefore, the above formula can be written as

[0306]

[0307] Furthermore, it satisfies the negative definite condition of the overall Lyapunov function of the system; thus far, by using the improved adaptive backstepping control strategy, the design of the adaptive controllers (135) and (140) for the hypersonic vehicle system with non-linear parameterization (32)-(37) and the design process of the parameter update laws (116), (121), (126), (131), (136) and (141) are completed; the conclusions of the system stability analysis and parameter convergence performance analysis are:

[0308] For the hypersonic vehicle systems (1)-(8) that satisfy the assumptions, the designed adaptive controllers (135) and (140) and the parameter update laws (116), (121), (126), (131), (136) and (141) ensure the global boundedness of all closed-loop signals and achieve the global adaptive regulation of the non-zero equilibrium point.

[0309] Specifically, in step 4, during the adaptive control design process, the design parameters are selected as p 1 = 9, q 2 = 3 and q 3 = 1.

[0310] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0311] 1. According to the flight data of the hypersonic vehicle provided by NASA, the present invention uses the data fitting method to fit the aerodynamic coefficient and moment coefficient of the vehicle, and fits the discrete aerodynamic data into a continuous aerodynamic expression, so as to establish a non-linear parametric longitudinal dynamics model of the hypersonic vehicle; the discrete flight data is fitted into an aerodynamic model in the form of a trigonometric function, which verifies that the trigonometric fitting function has better effect and higher reliability than the polynomial fitting function, and then establishes a non-linear parametric longitudinal model of the vehicle.

[0312] 2. Aiming at the established non-linear parametric longitudinal dynamics model of the hypersonic vehicle, according to the time-scale separation principle, the longitudinal dynamic model of the vehicle is transformed into a velocity subsystem and a flight path angle subsystem with state coupling. While effectively dealing with non-linear parameterization dynamics by using the function bounding technique and online estimating the unknown parameters of the system by using the adaptive technique, an adaptive control strategy integrating non-linear parameterization adaptive technique and parameter separation technique is proposed to achieve the global adaptive regulation of the non-linear parametric vehicle control system.

[0313] 3. The present invention proposes a parameter separation strategy for the non-linear parametric hypersonic vehicle system. This strategy forms re-parametrized dynamic characteristics, which characterize the main non-linear characteristics of the system and help to handle the uncertainties in the control design process, and proposes a non-linear transformation technique applicable to non-linear parametric systems.

[0314] 4. For the adaptive control problem of a non - linear parameterized hypersonic vehicle model, a new function - inclusion technique, a new adaptive parameter - estimation algorithm, and an improved adaptive back - stepping control strategy are used. Without any constraints on system parameters and state variables, the function - inclusion technique gives an upper - bound function of the dynamics of the non - linear parameterized system, and this upper - bound function has a linearly parameterized form. When designing the adaptive control for each subsystem, the Young's inequality is used to scale the interconnected system states, and appropriate parameters are designed for error compensation. The improved adaptive back - stepping control strategy greatly improves the applicability and robustness of the control algorithm, thus ensuring the global stability of the closed - loop system. Description of the Drawings

[0315] Figure 1 It is a flowchart of the method according to an embodiment of the present invention.

[0316] Figure 2 It is the curve - fitting step according to an embodiment of the present invention.

[0317] Figure 3a - - 3c are respectively the trigonometric - function fitting curves of the aerodynamic coefficients C D (α), C L (α), C M (α) of the present invention in an embodiment.

[0318] Figure 4a - - 4c are respectively the polynomial - function fitting curves of the aerodynamic coefficients C D (α), C L (α), C M (α) of the present invention in an embodiment.

[0319] Figure 5a - - 5c are respectively the two fitting - function curves of the aerodynamic coefficients C D (α), C L (α), C M (α) of the present invention in an embodiment.

[0320] Figure 6 It is the state - error response of the hypersonic vehicle system according to an embodiment of the present invention.

[0321] Figure 7 It is the parameter - estimation response of the hypersonic vehicle system according to an embodiment of the present invention.

[0322] Figure 8 It is the elevator - deflection control - input response according to an embodiment of the present invention.

[0323] Figure 9 It is the throttle - control - input response according to an embodiment of the present invention.

[0324] Figure 10 It is a schematic diagram for comparing the state error response curves under two control methods. Among them, the solid line is obtained by a control method proposed by the present invention, and the dashed line is obtained by a control method based on Jacobian linearization. Specific implementation manners

[0325] An adaptive regulation control method for a non-linear parametric hypersonic vehicle of the present invention is applicable to solving the problem that when uncertainties such as actuator failures, structural damages, and sensor failures occur in a hypersonic vehicle, the uncertainty of the system dynamic function becomes more significant, thereby leading to the uncertainty of the system structure. The present invention uses a data fitting method to fit the aerodynamic data of the non-linear parametric hypersonic vehicle, fits the discrete aerodynamic data into expressions of aerodynamic force and aerodynamic moment with a trigonometric function form, and gives a fitting curve graph; by comparing with the existing aerodynamic model with a polynomial structure, it shows from two aspects of fitting index and graphical analysis that the established aerodynamic model with a trigonometric function structure has higher accuracy, thereby establishing a longitudinal dynamics model of the non-linear parametric hypersonic vehicle; through coordinate transformation, the non-zero equilibrium point of the hypersonic vehicle is transferred to the origin, and after designing virtual control signals and actual control signals, the design of the nominal controller is completed, and a Lyapunov function is selected to perform stability analysis on the non-linear parametric hypersonic vehicle model system with engine dynamics; for a more accurate non-linear parametric hypersonic vehicle model, first, by analyzing the action magnitudes of the two control inputs of the vehicle on the vehicle system, the longitudinal model of the vehicle is transformed into a flight path angle subsystem and a speed subsystem with interconnected state variables; secondly, according to different control tasks and different operating environments, a new non-linear control strategy is proposed to achieve the desired control objectives, that is, using techniques such as function inclusion technology, parameter separation technology, inequality technology, backstepping control method, computer simulation technology, and semi-physical simulation technology, etc., to design a continuous adaptive controller to overcome the problems brought by non-linear parametric dynamics, system parameter uncertainties, and interconnected state variables in the two subsystems, thereby ensuring the global stability of the closed-loop signal and the adaptive regulation of the non-zero equilibrium point. For other flight stages of the hypersonic vehicle, the method designed above in the present invention is still effective. Therefore, a non-linear parametric hypersonic vehicle system with disturbances is given, and combined with disturbance rejection and noise cancellation methods, an adaptive control strategy is adopted to solve the sensing device noise and external disturbances in the non-linear parametric hypersonic vehicle system, thereby improving the robust performance of the adaptive controller under the condition of disturbances. Finally, the proposed non-linear control strategy is simulated to verify the effectiveness of the control algorithm, providing a control theory basis and design reference for the safe flight of the vehicle.

[0326] The present invention will be further described in detail below with reference to the accompanying drawings.

[0327] A method for adaptive regulation control of a non - linear parameterized hypersonic vehicle of the present invention includes the following steps:

[0328] Step 1: Use the data fitting method for comparative analysis. Perform polynomial function curve fitting and trigonometric function curve fitting on the existing publicly available processed flight data respectively to obtain the expressions of the aerodynamic force and aerodynamic moment coefficients of the longitudinal model of the hypersonic vehicle, and give the fitting curve diagrams.

[0329] Furthermore, the specific process of Step 1 is as follows:

[0330] Step 1 - 1: The longitudinal model (1)-(4) and the aerodynamic coefficients (9)-(14) of the hypersonic vehicle have a linear parameterized form. However, the actual longitudinal model of the hypersonic vehicle has a complex structure and generally does not have a linear parameterized form. Therefore, it is necessary to study a series of non - linear parameterized aerodynamic models of hypersonic vehicles. Establish a non - linear parameterized aerodynamic model of the hypersonic vehicle based on the known flight data, and it will be shown that the non - linear parameterized aerodynamic model in expressions (5)-(8) will have higher accuracy than the linear parameterized aerodynamic models in the existing literature.

[0331] The longitudinal dynamics model of the hypersonic vehicle is given as

[0332]

[0333]

[0334]

[0335]

[0336] where the engine thrust T, drag D, lift L, and pitching moment M yy are

[0337]

[0338]

[0339]

[0340]

[0341] The aerodynamic coefficients and moment coefficients in the above formula are as follows:

[0342]

[0343]

[0344]

[0345]

[0346]

[0347]

[0348] And the engine throttle dynamics model is represented by the following second-order system:

[0349]

[0350] where the aircraft state includes velocity V, flight path angle γ, angle of attack α, pitch rate q, engine throttle setting Φ, and engine throttle derivative The aircraft control inputs include elevator deflection δ and engine throttle control command Φ c , and the physical constants include gravitational acceleration g, aircraft mass m, moment of inertia I yy , air density ρ, wing reference area S, mean aerodynamic chord Natural frequency ω n and damping ratio ∈.

[0351] A hypersonic vehicle with engine dynamics has two basic control actions, namely, increasing and decreasing the flight path angle and increasing and decreasing the speed during horizontal flight. Among them, the flight path angle is determined by the elevator deflection δ in (8), and the speed during horizontal flight is mainly determined by the engine throttle control command Φ in (15) c . Specifically, the six state variables of a hypersonic vehicle with engine dynamics and the two control inputs [δ, Φ c T affect the dynamic changes in equations (1)-(4) through thrust T, drag D, lift L, and pitching moment M yy . Due to changes in the vehicle payload or component aging, the and in the aerodynamic models (9)-(14) are system parameters that are unknown quantities, and all states of the hypersonic vehicle are measurable.

[0352] ​Step 1-2: Perform data fitting. The core idea of the data fitting method is to find a suitable non-linear continuous function to approximate discrete data points. Therefore, by applying this method, the discrete data points obtained from experiments and mechanism analysis can be integrated into a continuous analytical form for model analysis and controller design. This method is divided into three steps: The first step is to obtain discrete data, which is the data source for the fitting work. Different forms of discrete data need to be processed into a standard form. The second step is to determine the fitting function. In this step, the basic function form needs to be set according to the specific influence relationship of the data and the mechanism model of the research object, and then an optimization algorithm is used to solve the specific parameters in the function. After this step, a continuous form of the fitting function model can be obtained. The third step is to calculate the fitting index to test the fitting effect. The specific steps are as Figure 2 shown.

[0353] In the process of fitting the longitudinal dynamic aerodynamic coefficient of the non-linear hypersonic vehicle in the present invention, since NASA has made the flight data public, the discrete data can be directly obtained without obtaining it again through experiments and mechanism analysis. In the process of the second step, since the non-linear parametric modeling of the longitudinal dynamic aerodynamic coefficient of the hypersonic vehicle can better reflect the high precision of the model, the fitting function form is set as the trigonometric function form. In the third step, the superiority of the trigonometric function fitting is verified by comparing the fitting indexes (sum of squared errors SSE and correlation coefficient CD) and intuitive diagrams.

[0354] Step 1-3: Before performing non-linear parametric modeling, introduce two important fitting indexes in the data fitting method: sum of squared errors SSE and correlation coefficient CD. These two indexes are used to evaluate the fitting effect and accuracy.

[0355] A data set has n values, labeled as y 1 , …, y n , and these values are associated with the fitting values f 1 , …, f n . Define an error e i = y i - f i , i = 1, …, n, representing the difference between the actual data and the fitting value. The sum of squared errors SSE is defined as

[0356]

[0357] The correlation coefficient CD is defined as

[0358]

[0359] Among them, is the mean of a set of discrete data

[0360] If the sum of squared errors SSE is closer to 0, it indicates that the model selection is better and the result of data prediction will be more accurate. If the square of the correlation coefficient CD is closer to 1, it indicates that the model fitting effect is better and the coefficient will be more persuasive.

[0361] Step 1-4, fitting of longitudinal dynamics model data: In addition to the dynamic equation, the hypersonic vehicle model also includes expressions of aerodynamic coefficients, aerodynamic moment coefficients, and thrust coefficients. Therefore, the accuracy of the hypersonic vehicle model is mainly reflected in the accurate aerodynamic model. Based on the existing data, re-fit the drag coefficient C D (α), lift coefficient C L (α), and moment coefficient C M (α) in equations (12)-(14), and plot the discrete aerodynamic data points as a fitting curve graph according to different angles of attack α.

[0362] Step 1-4-1, trigonometric function fitting

[0363] Since the existing literature provides aerodynamic data, in terms of obtaining data, using the original data already meets the needs of data analysis work. Therefore, there is no need to obtain the aerodynamic data of the hypersonic vehicle through other experimental derivations. Analyzing the variation law of the aerodynamic data, it is not difficult to find that the expression obtained by trigonometric function fitting is more accurate than the expression obtained by polynomial fitting. Then, use the new expression to re-establish the dynamic equations of the drag coefficient C D (α), lift coefficient C L (α), and moment coefficient C M (α) as

[0364] C D (α) = 1.631 - 0.8702cos(0.04987α) + 0.1957sin(0.04987α) (18)

[0365] C L (α) = 0.08289sin(0.03914α - 0.02531) (19)

[0366] C M (α) = -0.1461 + 0.1645cos(0.05314α) - 0.08719sin(0.05314α) (20)

[0367] Their corresponding sums of squared errors SSE are 1.99×10 -4 , 2.26×10 -5 and 4.16×10 -7, and the corresponding correlation coefficients CD are 0.9999, 0.9960, and 0.9990 respectively. According to the determined trigonometric function form, the drag coefficient C D (α), lift coefficient C L (α), and moment coefficient C M (α) are plotted against the angle of attack α, as shown in Figures 3a - 3c . The '×' represents discrete aerodynamic data, and the curve is the fitted trigonometric function curve.

[0368] Step 1-4-2, Polynomial function fitting

[0369] For hypersonic vehicles, polynomial function fitting is performed using the same data, and the obtained dynamic equations for the drag coefficient C D (α), lift coefficient C L (α), and moment coefficient C M (α) are as follows

[0370] C D (α) = 3.493×10 -4 α 2 + 0.02216α + 0.7421 (21)

[0371] C L (α) = 1.653×10 -3 α + 0.01206 (22)

[0372] C M (α) = -4.871×10 -6 α 2 - 0.008197α + 0.02365 (23)

[0373] Their corresponding sum of squared errors SSE are 4.01×10 -3 , 8.74×10 -4 and 2.71×10 -3 , and the corresponding correlation coefficients CD are 0.9970, 0.8454, and 0.9962 respectively. As shown in Figures 4a - 4c . The '×' represents discrete aerodynamic data, and the curve is the fitted polynomial function curve.

[0374] Step 2: By comparing the fitting metrics and fitting curves of the two different function curve fitting methods of polynomial functions and trigonometric functions, it is further explained that the trigonometric function curve fitting method is more accurate.

[0375] Furthermore, the specific process of Step 2 is as follows:

[0376] Step 2-1. Comparison between polynomial function fitting and trigonometric function fitting. According to the definition of the fitting index, the sum of squared errors obtained by trigonometric function fitting is closer to 0, and the correlation coefficient obtained is closer to 1. Therefore, according to the data fitting process of the longitudinal dynamics model, it can be known that the aerodynamic coefficients obtained by trigonometric function fitting are more accurate than those obtained by polynomial function fitting.

[0377] In addition, the polynomial function fitting curve and the trigonometric function fitting curve are plotted simultaneously into Figures 5a - 5c . The × represents discrete data points, the solid line represents the trigonometric function fitting curve, and the dashed line represents the polynomial fitting function curve. It can be intuitively seen that the trigonometric function fitting method can better match the actual discrete data compared with the polynomial function fitting method.

[0378] Step 2-2. Explanation of non-linear parameterized aerodynamic coefficients. Through the trigonometric function fitting method, a hypersonic vehicle aerodynamic model with aerodynamic force coefficients and moment coefficients in trigonometric function form can be obtained. The following are two explanations for this model.

[0379] a. Considering the uncertainty of the aerodynamic coefficients and further ensuring the accuracy of curve fitting, the aerodynamic coefficient expressions in the dynamic equations of the drag coefficient, lift coefficient, and moment coefficient in the gliding state are characterized as aerodynamic coefficient functions with unknown parameters:

[0380]

[0381]

[0382]

[0383] For C L (α), C D (α) and C M (α) in equations (24)-(26), the unknown aerodynamic coefficients themselves contain significant uncertainties in aerodynamic coefficients, such as structural uncertainties and parameter uncertainties. Note that these specific non-linear parameterized functions are only some representative examples, and more general or different non-linear parameterized fitting functions can also be considered within the framework of the proposed adaptive control scheme.

[0384] b. According to the idea of dominant control input, the speed state is mainly affected by the engine throttle opening Φ, and the engine throttle opening control command Φ cThe engine throttle opening Φ is controlled by the engine second-order dynamic equation (15); the flight attitude is controlled by the elevator deflection angle δ. Therefore, the longitudinal dynamics model of a hypersonic vehicle with engine dynamics can be divided into two interrelated subsystems: the speed subsystem and the flight path angle subsystem. Establishing models for the two interrelated subsystems respectively becomes an important task in the design work.

[0385] So far, a complete longitudinal dynamics model of a non-linear parametric hypersonic vehicle with engine dynamics has been established.

[0386]

[0387]

[0388]

[0389]

[0390] Among them, the engine thrust T, drag D, lift L and pitching moment M yy are

[0391]

[0392]

[0393]

[0394]

[0395] The aerodynamic coefficients and moment coefficients in the above formula are as follows:

[0396]

[0397]

[0398]

[0399]

[0400]

[0401]

[0402] And the engine throttle opening dynamics model is expressed as:

[0403]

[0404] It can be seen from the longitudinal dynamics model of the hypersonic vehicle that:

[0405] a. The speed V of a hypersonic vehicle is related to the thrust T, drag D, gravitational coefficient g, angle of attack α, and flight path angle γ of the vehicle.

[0406] b. The flight path angle γ of a hypersonic vehicle is related to the thrust T, lift L, gravitational coefficient g, angle of attack α, and speed V of the vehicle.

[0407] c. The angle of attack α of a hypersonic vehicle is related to the thrust T, lift L, gravitational coefficient g, angle of attack α, speed V, and pitch angular velocity q of the vehicle.

[0408] d. The pitch angular velocity q of a hypersonic vehicle is related to the pitch moment M yy and the moment of inertia I of the vehicle itself yy itself.

[0409] e. The throttle opening Φ of the engine is related to the damping coefficient ∈ and natural frequency ρ of the engine itself.

[0410] Therefore, the established longitudinal dynamic model of the high-precision hypersonic vehicle belongs to a class of nonlinear parametric multivariable uncertain nonlinear cascade systems.

[0411] Step 3: Transfer the non-zero equilibrium point of the hypersonic vehicle to the origin through coordinate transformation. After designing the virtual control signal and actual control signal, the design of the nominal controller is completed, and the Lyapunov function is selected to analyze the stability of the nonlinear parametric hypersonic vehicle model system with engine dynamics.

[0412] Furthermore, the specific process of Step 3 is as follows:

[0413] Step 3-1: In the cruise stage of the hypersonic vehicle, the non-zero equilibrium point of the hypersonic vehicle dynamics model (1)-(12), (15), and (27)-(28) with engine throttle dynamics is expressed as

[0414]

[0415] The non-zero equilibrium point is transformed into the coordinate origin by defining the following coordinate transformation:

[0416] x 1 = γ, x 2 = α - α * , x 3 = q (30)

[0417]

[0418] Based on this, the dynamic model of the improved hypersonic vehicle (1)-(4) and engine throttle opening (15) can be expressed as

[0419]

[0420]

[0421]

[0422]

[0423]

[0424]

[0425] wherein, u 1 = δ - δ * , δ * and respectively represent their ideal values under cruise conditions. The functions g 1 (z 1 ), g 3 (z 1 ), k 1 (z 1 , x 2 ) and k 3 are

[0426]

[0427]

[0428]

[0429]

[0430] wherein, the uncertain nonlinear functions f i and h i , i = 1, 2, 3, j = 1, 3 are expressed as

[0431]

[0432]

[0433]

[0434]

[0435]

[0436] Since f i and h j are both continuous functions and fi h(0) = 0 j f(0) = 0, obtaining the non - linear function f i and h j function upper bound of

[0437]

[0438]

[0439]

[0440]

[0441]

[0442] where γ 1 (z 1 ) ≥ 1, γ 2 (z 1 ) ≥ 1, γ 3 (x 2 , x 3 , z 1 ) ≥ 1 and λ 1 (z 1 , x 2 ) ≥ 1 are all known functions, and are all unknown parameters, and their specific expressions are as follows:

[0443]

[0444]

[0445]

[0446]

[0447]

[0448]

[0449]

[0450]

[0451]

[0452]

[0453] Step 3-2: To clarify the basic idea of the improved inversion control strategy, nominal control design is carried out for the transformed aircraft dynamics model control system (32)-(37) without unknown parameters.

[0454] To achieve the desired control objective, the following coordinate transformation is introduced:

[0455] ξ 1 = x 1 - α 0 α 0 = 0 (61)

[0456]

[0457]

[0458] η 1 = z 1 - β 0 β 0 = 0 (64)

[0459]

[0460]

[0461] where α i , β i are virtual control signals, ξ j , η j are the errors between the state variables of the aircraft dynamics model control system and the virtual control signals, is a positive function to be determined.

[0462] Step 3-3: Process of nominal system control design. For the transformed aircraft dynamics model control system (32)-(37) with a relative degree of {3, 3}, the improved inversion control process includes:

[0463] Step 3-3-1: a) Design the nominal virtual signal α 1 , and for the flight path angle subsystem (32)-(34), select the first positive definite function

[0464]

[0465] Positive definite function The time derivative of is

[0466]

[0467] where is the combined value of the flight path angle subsystem constant and the flight path angle subsystem parameters, defined as

[0468]

[0469] Select the virtual control signal α 1

[0470]

[0471] where p 1 is a constant to be determined, so as to obtain

[0472]

[0473] b) Design the nominal virtual control signal β 1 , for the velocity subsystem (35)-(37), select the first positive definite function

[0474]

[0475] The positive definite function The time derivative of is

[0476]

[0477] where is the combined value of the velocity subsystem constant and the velocity subsystem parameters, defined as

[0478]

[0479] Select the virtual control signal β 1

[0480]

[0481] where q 1 is a constant to be determined, so as to obtain

[0482]

[0483] Step 3-3-2, a) Design the nominal virtual control signal α 2 , for the course angle subsystem (32)-(34), select the second positive definite function

[0484]

[0485] The positive definite function The time derivative of is

[0486]

[0487] where

[0488] and is a combined value of the track angle subsystem constant and the track angle subsystem parameter, defined as

[0489]

[0490] Select the virtual control signal α 2

[0491]

[0492] where p 2 is a constant to be determined, thus obtaining

[0493]

[0494] b) Design the nominal virtual control signal β 2 , and select the second positive definite function for the velocity subsystem (35)-(37)

[0495]

[0496] The positive definite function The time derivative of is

[0497]

[0498] where

[0499] and is a combined value of the velocity subsystem constant and the velocity subsystem parameter, defined as

[0500]

[0501] Select the virtual control signal β 2

[0502]

[0503] where q 2 is a constant to be determined, thus obtaining

[0504]

[0505] Step 3-3-3, a) Design the nominal actual control μ 1 , and select the third positive definite function for the track angle subsystem (32)-(34)

[0506]

[0507] Positive definite function The time derivative of

[0508]

[0509] wherein,

[0510]

[0511] and is a combined value of the track angle subsystem constant and the track angle subsystem parameter, defined as

[0512]

[0513] Select the actual control signal μ 1

[0514]

[0515] wherein, p 3 is a constant to be determined, so as to obtain

[0516]

[0517] b) Design the nominal actual control signal μ 2 , select the third positive definite function for the speed subsystem (35)-(37)

[0518]

[0519] Positive definite function The time derivative of

[0520]

[0521] wherein, and is a combined value of the speed subsystem constant and the speed subsystem parameter, defined as

[0522]

[0523] Select the actual control signal μ 2

[0524]

[0525] wherein, q 3 is a constant to be determined,[[]] so as to obtain

[0526]

[0527] Step 3-4, Stability analysis: For the converted nonlinear parametric hypersonic vehicle dynamics model control system (32)-(37), select the Lyapunov function

[0528]

[0529] From the above nominal control design process, the designed nominal control signals μ 1 (90) and μ 2 (95) make the derivative of the Lyapunov function be

[0530]

[0531] By selecting p 1 = 9, p 2 = 11 / 2, p 3 = 3 / 2, q 1 = 13 / 2, q 2 = 3 and q 3 = 1, the derivative

[0532]

[0533] Next, adopt the above nominal controller design to conduct stability analysis on the nonlinear parametric hypersonic vehicle model system with engine dynamics, and thus obtain the following conclusions.

[0534] For the nonlinear parametric longitudinal model (1)-(4) of the vehicle and the engine throttle opening dynamics (15) that satisfy the assumption conditions, the designed nominal control signals (90) and (95) ensure the stability of the closed-loop system and achieve the global exponential convergence of the vehicle state.

[0535] Proof: Define the state variable of the closed-loop system γ(t) = [ξ(t), η(t)] T , where ξ(t) = [ξ 1 (t), ξ 2 (t), ξ 3 (t)] T , η(t) = [η 1 (t), η 2 (t), η 3 (t)] T . From (99), we can get So is a monotonically non-increasing function. Therefore, for any initial state ξ(t 0 ), η(t 0), it can be obtained that Therefore, the nominal control signals (90) and (95) ensure that the closed-loop signals are globally bounded.

[0536] Define According to the definition of the Lyapunov function, it is obtained that

[0537]

[0538] Inequalities (98) and (99) show that satisfies the differential inequality

[0539]

[0540] Therefore, according to inequality (101), it can be obtained that

[0541]

[0542] According to (100) and (102), it is further obtained that

[0543]

[0544] Therefore, for any Υ(t 0 ) ∈ R 6 , the origin is globally exponentially stable. According to (61)-(66), x i and z i globally exponentially converge to the origin. Further, according to (30) and (31), the state variables of the hypersonic vehicle dynamics model control system globally exponentially converge to the non-zero equilibrium point in (29)

[0545] It is found from the above control design and proof process that for a class of multivariable nonlinear systems without unknown parameters, by using the improved backstepping method and constructing a nonlinear state feedback controller, the designed controller can ensure that the closed-loop system state is exponentially convergent, and the exponential convergence rate depends on the control parameters g 11 , g 31 , k 2 . At the same time, by designing the control for the nominal system with known system parameters, the nonlinear state feedback controller not only ensures the matching condition in the adaptive control process, but also ensures the stabilizability of the adaptive control strategy for system parameter uncertainties.

[0546] Step 4. For a more accurate non - linear parameterized hypersonic vehicle model, first, by analyzing the influence of the two control inputs of the vehicle on the vehicle system, the longitudinal model of the non - linear parameterized hypersonic vehicle with engine dynamics is decomposed into two interconnected non - linear parameterized subsystems: the velocity subsystem and the flight path angle subsystem. For these two subsystems, the backstepping method is used to design an adaptive controller to ensure that all signals of the closed - loop system are globally bounded and the state variables of the system are globally asymptotically regulated to non - zero equilibrium points.

[0547] Furthermore, the specific process of Step 4 is as follows:

[0548] Step 4 - 1. Since the controllers designed for non - linear systems are generally in the form of non - linear functions, the adaptive control signals in the non - linear systems (32) - (37) can be expressed as

[0549]

[0550]

[0551]

[0552] where \(x = [x 1 ,x 2 ,x 3 T ,z = [z 1 ,z 2 ,z 3 T , and is the estimated value of the nominal parameter :

[0553]

[0554]

[0555]

[0556]

[0557]

[0558]

[0559] It should be noted that when the parameter in the above formula ​​When it is known, the nominal control signal is designed in step 3 of the present invention. Now, for the system (32)-(37) with unknown parameters, based on the improved backstepping control strategy and adaptive control method, an adaptive control signal is designed to ensure the global stability of all system states.

[0560] Coordinate transformation. For the flight path angle subsystem (32)-(34) representing the aircraft attitude and the velocity subsystem (35)-(37) representing the aircraft velocity, the following state errors and virtual control signals are defined:

[0561] ξ 1 =x 1 -α 0 α 0 =0 (107)

[0562]

[0563]

[0564] η 1 =z 1 -β 0 β 0 =0 (110)

[0565]

[0566]

[0567] where α i and β i , i = 0, 1, 2 are the virtual control signals to be designed below, a 10 , a 20 , b 10 and b 20 are all positive definite functions.

[0568] Step 4-2. Adaptive design under unknown parameters. The adaptive control design process for the flight path angle subsystem (32)-(34) and the velocity subsystem (35)-(37) will be given step by step below.

[0569] Step 4-2-1. a) Design the virtual control signal α 1 and the parameter update law For the flight path angle subsystem (32)-(34), select the following positive definite function

[0570]

[0571] where, is the parameter estimation error. Combining equations (32), (38), (47), (69), (107), (108) and the Young inequality, the derivative of the function V 1 is as follows:

[0572]

[0573] Select the virtual control signal α in the following form 1 and the parameter update law as

[0574]

[0575]

[0576] where and p 1 is the parameter to be designed, and thus

[0577]

[0578] b) Design the virtual control signal β 1 and the parameter update law For the velocity subsystem (35)-(37), select the following positive definite function

[0579]

[0580] where is the parameter estimation error. Combining equations (35), (40), (50), (74), (110), (111) and the Young inequality, the derivative of the function W 1 is as follows:

[0581]

[0582] Select the virtual control signal β in the following form 1 and the parameter update law as

[0583]

[0584]

[0585] where and b 11 = q 1 . q 1 is the parameter to be designed, and thus

[0586]

[0587] Step 4-2-2, a) Design the virtual control signal α 2 and the parameter update law For the track angle subsystem (32)-(34), select the following positive definite function

[0588]

[0589] where is the parameter estimation error. Combining equations (33), (108), (109), (117) and the Young's inequality, the derivative of the function V 2 is as follows:

[0590]

[0591] Select the virtual control signal v in the following form 2 and the parameter update law is

[0592]

[0593]

[0594] where a 22 = π 11 +

[0595] π 12 + π 13 , and

[0596] p 2 is the parameter to be designed. Then, we can obtain

[0597]

[0598] b) Design the virtual control signal β 2 and the parameter update law For the velocity subsystem (35)-(37), select the following positive definite function:

[0599]

[0600] where is the parameter estimation error. Combining equations (111) and (112), the derivative of the function W 2 is as follows:

[0601]

[0602] Select the virtual control signal β in the following form 2 and the parameter update law as

[0603]

[0604]

[0605] where

[0606] and

[0607] q 2 is the parameter to be designed. Then, we can obtain

[0608]

[0609] Step 4-2-3, a) Design the actual control μ 1 and the parameter update law For the track angle subsystem (32)-(34), select the following positive definite function:

[0610]

[0611] where is the parameter estimation error. Combining Eqs. (107)-(109), the derivative of the function V 3 is as follows:

[0612]

[0613] Select the actual control signal μ in the following form 1 and the parameter update law as

[0614]

[0615]

[0616] where and

[0617]

[0618] p 3 is the parameter to be designed. Then, we can obtain

[0619]

[0620] b) Design the virtual control signal μ 2 and the parameter update law For the velocity subsystem (35)-(37), select the following positive definite function:

[0621]

[0622] where is the parameter estimation error. Combining equations (110)-(112), the derivative of W 3 is

[0623]

[0624] Select the actual control signal μ with the following form 2 and the parameter update law as

[0625]

[0626]

[0627] where b 31 = q 3 + 1,

[0628] and

[0629]

[0630]

[0631] q 3 is the parameter to be designed, and then we can obtain

[0632]

[0633] Step 4-3. Stability analysis: Based on the above design steps, for the non-linear parameterized system (32)-(37) after coordinate transformation, define the following Lyapunov function:

[0634]

[0635]

[0636] It is easy to obtain that the Lyapunov function defined in (143) is positive definite and radially unbounded.

[0637] The control signals (135) and (140) and the parameter update laws (116), (121), (126), (131), (136), and (141) of the above design make the derivative of V with respect to time satisfy

[0638]

[0639] To make the above formula negative definite, select the following parameter values to be designed: p 1 = 9, q 2 = 3 and q 3 = 1, so the above formula can be written as

[0640]

[0641] Furthermore, the negative definite condition of the overall Lyapunov function of the system is satisfied. Thus, by using the improved adaptive backstepping control strategy, the design of the adaptive controllers (135) and (140) for the hypersonic vehicle system with nonlinear parameterizations (32)-(37), as well as the design process of the parameter update laws (116), (121), (126), (131), (136), and (141), are completed. The following presents the stability analysis of the system and the convergence performance analysis of the parameters. The main conclusions are as follows:

[0642] For the hypersonic vehicle system (1)-(8) that satisfies the assumptions, the designed adaptive controllers (135) and (140) and the parameter update laws (116), (121), (126), (131), (136), and (141) guarantee the global boundedness of all closed-loop signals and achieve the global adaptive regulation of the non-zero equilibrium point.

[0643] Proof: Define the state variables of the closed-loop system as where, ξ(t) = [ξ 1 (t), ξ 2 (t), ξ 3 (t)] T , η(t) = [η 1 (t), η 2 (t), η 3 (t)] T , Since the Lyapunov function is a continuous positive definite function, there exist K ∞ functions ν 1 and ν 2 that satisfy

[0644] v 1 (||Ψ||) ≤ V(Ψ) ≤ v 2 (||Ψ||) (146)

[0645] Since Therefore, for any initial value Ψ(0), there exists a positive constant ε such that v 2 (ε) ≥ V(Ψ(0)). According to the equation a positive constant κ = κ(ε) can be found such that v 2 (ε) ≤ v 1 (κ). The non-negativity in expression (145) indicates that

[0646] V(Ψ(t)) ≤ V(Ψ(0)) < ∞, t > 0 (147)

[0647] Combined with equation (146), for any initial state Ψ(0), there is

[0648] v 1 (||Ψ||) ≤ V(Ψ) ≤ V(Ψ(0)) ≤ v 2 (ε) ≤ v 1 (κ) (148)

[0649] This indicates that ||Ψ|| < κ < ∞. Combining it can be obtained that

[0650]

[0651] Combined with equations (107)-(112), the state errors ξ i and η i the definitions of and the smoothness of the virtual control signals α i and η i guarantee that the aircraft state variables x i and z i , i = 1, 2, 3, j = 1, …, 6 are all bounded. According to equations (107)-(112), it can be known that and are also both bounded. Based on equations (164) and (166), it can be obtained that

[0652]

[0653] Combined with Barbalat's lemma, it is obtained that Similarly, it can be obtained that According to equations (107)-(112), it can be obtained that and Combined with the coordinate transformations (30) and (31), the state variables of the hypersonic vehicle system asymptotically tend to the non-zero equilibrium point defined by equation (29).

[0654] In the above adaptive control design process, the design parameter is selected as p​1 = 9, q 2 = 3 and q 3 = 1. Since the design parameters of the controller affect not only the convergence speed of the controller but also the amplitude of the controller. Specifically, increasing the design parameters p i and q i , can improve the control convergence speed and reduce the convergence time, but will lead to an increase in the control amplitude and increase the burden on the controller. Therefore, appropriate selection of the design parameters is made according to the actual control requirements.

[0655] Step 5. For other flight phases of the hypersonic vehicle, the above-designed method is still effective. Therefore, a hypersonic vehicle system with perturbed nonlinear parameterization will be given, and the robust performance of the proposed adaptive controller under wind perturbation will be studied.

[0656] Furthermore, the specific process of Step 5 is as follows:

[0657] Step 5-1. Discussion on the control design for other flight phases of the hypersonic vehicle. For other phases of the hypersonic vehicle, such as the reentry phase and the climb phase, the longitudinal model of the vehicle also has the basic structure in Equations (1)-(4). The main difference from the longitudinal model in the cruise phase is the aerodynamic and moment coefficients in Equations (9)-(12), (27), and (28), that is, the aerodynamic coefficients in different phases are all different. For example, in the reentry phase and the maneuver phase of the hypersonic vehicle, the longitudinal model of the vehicle is mainly approximated by the dynamic equations of unpowered gliding. Among them, "T cosα" in the velocity subsystem (1) and "T sinα" in the flight path angle subsystem (2) no longer exist. Similarly, and also no longer exist. Since the basic structure of the entire longitudinal model of the vehicle has not changed, and there are still parameter uncertainties in the system model in the form of nonlinear parameterization during other flight phases, the proposed control strategy for the cruise phase is still effective in other flight phases.

[0658] Step 5-2. System model with perturbation. In practical engineering applications, control systems often have noise and perturbation, which affect the stability of the system. Therefore, it is very meaningful to study the noise and perturbation existing in the hypersonic vehicle system. Currently, there are often some technical problems in such research, such as the identification of perturbation and noise uncertainties, and the description of the dynamic correlation among the system input, perturbation, and noise. A type of hypersonic vehicle system model with noise and perturbation is

[0659]

[0660]

[0661]

[0662]

[0663] where d(t)=[d 1 (t), d 2 (t), d 3 (t), d 4 (t)] T ∈R 4 is an unknown disturbance vector, such as the turbulent disturbance existing in the atmospheric space. When measuring the state variables of the system, noise may be generated in the aircraft sensor devices, interfering with the measurement of the state variables of the aircraft. The noise in the sensing device can be expressed as

[0664] V s =V + w 1 (t), γ s =γ + w 2 (t) (155)

[0665] α s =α + w 3 (t), q s =q + w 4 (t) (156)

[0666] where ω i (t), i = 1, …, 4 is the sensor noise. It is necessary to combine disturbance suppression and noise cancellation methods and adopt an adaptive control strategy to solve the sensing device noise and external disturbances in the hypersonic aircraft system with nonlinear parameterization, thereby enhancing the robustness of the controller.

[0667] The following conducts simulation verification on an embodiment method of the present invention:

[0668] Step F1. The parameters of the hypersonic aircraft system model are as follows: m = 9375 slug, S = 17 ft 2 , ρ = 6.7429×10 -5 slug / ft 3 , I yy = 7×10 6 slug·ft 2 , and g = 32 ft / s 2 , the engine dynamic parameter is ∈ = 0.7, ω n = 20. The following gives the aerodynamic coefficients of the hypersonic aircraft system C Mδ = -1.2897, ω 1 = 4.987×10 -2 , ω 2 = 5.314×10 -2 。Except for some fixed physical quantities, these conditions apply to all flight situations. The airspeed at the equilibrium state is selected as V * = 15060 ft / s. According to the improved hypersonic vehicle and the dynamic model of the engine throttle opening, the equilibrium point of the vehicle is α * = 0.1551 rad, V * = 15060 ft / s, γ * = 0 rad, Φ * = 2.4498, q * = 0 rad / s, δ * = 0.0137 rad,

[0669] Step F2: For the flight path angle subsystem and the speed subsystem, control signals u 1 and u 2 , as well as the parameter update law The initial conditions of the flight path angle subsystem and the speed subsystem are selected as [x 1 (0), x 2 (0), x 3 (0), y 1 (0), y 2 (0), y 3 (0),] T = [0.6, 0.1, 1.2, 100, 0.2, 0.1] T , and the initial conditions of the parameter estimation The state error response curve of the longitudinal system of the hypersonic vehicle with engine dynamics is as shown in Figure 6 , and the parameter estimation response curve is as shown in Figure 7 . It can be seen from the response curves that both the state error and the parameter estimation are bounded signals, and the state variables of the vehicle are asymptotically adjusted to non-zero equilibrium points. In addition, the two control inputs of the system are the elevator deflection angle δ and the throttle control Φ c , and their dynamic responses are shown in Figure 8 and Figure 9 , respectively, thus indicating that the control inputs are continuous and bounded signals.

[0670] Step F3: Comparative simulation with the Jacobi linearization method. At the equilibrium point x eand the control input δ * , the linearized system under

[0671]

[0672] where the matrices A and B are

[0673]

[0674]

[0675] According to the rank criterion rank[B, AB, A 2 B, …, A 5 B] = 6, the linearized system is completely controllable.

[0676] Due to the parameter uncertainties of the hypersonic vehicle, the true Jacobian matrix should include perturbation uncertainties, i.e., ΔA = λA and ΔB = λB, where λ is a suitable constant. The state Jacobian matrix and the input Jacobian matrix of the hypersonic vehicle model with perturbation uncertainties can be written as A λ = A + λA and B λ = B + λB. Substituting them into the linearized system, the linear system with uncertain perturbations can be obtained:

[0677]

[0678] For the uncertain linear system, 1% of the nominal values of the matrices A and B (λ = 0.01) is selected as the small perturbation uncertainty coefficient, and the state error response of the hypersonic vehicle system is simulated. The same initial condition x(0) = [0.6, 0.1, 1.2, 100, 0.2, 0.1] is chosen T , and the simulation results are as Figure 10 shown.

[0679] Step F4. The dynamic response of the system state error variable shows that under the same system parameters, equilibrium points, and initial conditions, the method proposed in the present invention is superior to the linearization-based control method.

Claims

1. An adaptive regulation control method for a non - linear parameterized hypersonic vehicle, characterized in that, it includes the following steps: Step 1: Use the data fitting method for comparative analysis. Respectively perform polynomial function curve fitting and trigonometric function curve fitting on the existing publicly available processed flight data to obtain the expressions of the aerodynamic force and aerodynamic moment coefficients of the longitudinal model of the hypersonic vehicle, and give the fitting curve graphs; Step 2: By comparing the fitting indexes and fitting curve graphs under the two different function curve fitting methods of polynomial function and trigonometric function, it shows that the trigonometric function curve fitting method is more accurate; Step 3: Transfer the non - zero equilibrium point of the hypersonic vehicle to the origin through coordinate transformation. After designing the virtual control signal and the actual control signal, complete the design of the nominal controller, and select the Lyapunov function to conduct stability analysis on the non - linear parameterized hypersonic vehicle model system with engine dynamics; Step 4: For the more accurate non - linear parameterized hypersonic vehicle model, by analyzing the action magnitudes of the two control inputs of the vehicle on the vehicle system, decompose the longitudinal model of the non - linear parameterized hypersonic vehicle with engine dynamics into two interconnected non - linear parameterized subsystems: the speed subsystem and the flight path angle subsystem; for the speed subsystem and the flight path angle subsystem, use the backstepping method to design the adaptive controller to ensure that all signals of the closed - loop system are globally bounded, and globally asymptotically regulate the state variables of the system to the non - zero equilibrium point; Step 5: For other flight phases of the hypersonic vehicle, according to the above - mentioned design method, give the non - linear parameterized hypersonic vehicle system with disturbances, and study the robust performance of the proposed adaptive controller under wind disturbance conditions.

2. The adaptive regulation control method for a non - linear parameterized hypersonic vehicle according to claim 1, characterized in that, the process of step 1 includes: Step 1 - 1: Establish a non - linear parameterized aerodynamic model of the hypersonic vehicle based on the known flight data, indicating that the non - linear parameterized aerodynamic model in expressions (5) - (8) has higher accuracy than the existing linear parameterized aerodynamic model: The longitudinal dynamics model of the hypersonic vehicle is Among them, the engine thrust T, drag D, lift L, and pitching moment M yy are The aerodynamic force coefficient and moment coefficient in the above formula are as follows: And the engine throttle dynamics model is represented by the following second - order system: Among them, the aircraft state includes speed V, flight path angle γ, angle of attack α, pitch rate q, engine throttle opening Φ, and engine throttle opening derivative The aircraft control input includes elevator deflection angle δ and engine throttle opening control command Φ c , and the physical constants include gravitational acceleration g, aircraft mass m, moment of inertia I yy , air density ρ, wing reference area s, mean aerodynamic chord Natural frequency ω n and damping ratio ∈; A hypersonic vehicle with engine dynamics has two basic control actions, namely, the increase and decrease of the flight path angle and the increase and decrease of the speed during horizontal flight. Among them, the flight path angle is determined by the elevator deflection angle δ in (8), and the speed during horizontal flight is mainly controlled by the engine throttle opening command Φ in (15). c Determined; specifically, the six state variables of a hypersonic vehicle with engine dynamics And two control inputs [δ, Φ c T Affect the dynamic changes in equations (1)-(4); due to changes in the vehicle payload or component aging, the yy In the aerodynamic models (9)-(14) and And Are all system parameters with unknown values, and all states of the hypersonic vehicle are measurable;​ Step 1 - 2: Perform data fitting, that is: find a suitable non - linear continuous function to approximate the discrete data points, including: obtain discrete data, fit the existing data and process different forms of discrete data into standard forms; determine the fitting function, set the basic function form according to the specific influence relationship of the data and the mechanism model of the research object, and then use the optimization algorithm to solve the specific parameters in the function to obtain the continuous - form fitting function model; calculate the fitting index to test the fitting effect; Step 1 - 3: Use the sum of squared errors SSE and the correlation coefficient CD to judge the fitting effect and accuracy; A data set has n values, labeled y 1 , …, y n , and these values are associated with the fitted values f 1 , …, f n ; define an error e i = y i - f i , i = 1, …, n, representing the difference between the actual data and the fitted value; the sum of squared errors SSE is defined as The correlation coefficient CD is defined as wherein, is the mean value of discrete data The closer the sum of squared errors SSE is to 0, the better the model selection, and the more accurate the data prediction result will be; if the square of the correlation coefficient CD is closer to 1, it indicates a better model fitting effect and the coefficient will be more persuasive; Steps 1-4, longitudinal dynamics model data fitting: Based on the existing data, re-fit the drag coefficient C D (α), lift coefficient C L (α) and moment coefficient C M (α), and plot the discrete aerodynamic data points as a fitting curve graph according to different angles of attack α; Step 1-4-1, Trigonometric function fitting: Based on the aerodynamic data in existing literature, analyze the variation law of the aerodynamic data. It can be found that the expression obtained by trigonometric function fitting is more accurate than the expression obtained by polynomial fitting. Then, use the new expression to re-establish the drag coefficient C D (α), lift coefficient C L (α) and moment coefficient C M (α) of the dynamic equation is C D (α) = 1.631 - 0.8702cos(0.04987α) + 0.1957sin(0.04987α) (18) C L (α) = 0.08289 sin(0.03914a - 0.02531) (19) C M (α) = -0.1461 + 0.1645cos(0.05314a) - 0.08719sin(0.05314a) (20) Their corresponding sum of squared errors SSEs are 1.99×10 -4 , 2.26×10 -5 and 4.16×10 -7 , and the corresponding correlation coefficients CD are 0.9999, 0.9960 and 0.9990 respectively; Plot the curves of the drag coefficient C D (α), lift coefficient C L (α) and moment coefficient C M (α) against the angle of attack α; Step 1-4-2, Polynomial Function Fitting: The hypersonic vehicle performs polynomial function fitting using the same data to obtain the drag coefficient C D (α), lift coefficient C L (α), and the dynamic equations of the moment coefficient C M (α) are as follows C D (α) = 3.493×10 -4 α 2 + 0.02216a + 0.7421 (21) C L (α)＝1.653×10 -3 α+0.01206 (22) C M (α)＝-4.871×10 -6 α 2 -0.008197α+0.02365 (23) Their corresponding sum of squared errors SSEs are 4.01×10 -3 , 8.74×10 -4 and 2.71×10 -3 , and the corresponding correlation coefficients CD are 0.9970, 0.8454 and 0.9962 respectively.

3. An adaptive regulation control method for a non - linear parametric hypersonic vehicle according to claim 1, characterized in that, the process of step 2 includes: Step 2 - 1, Comparison between polynomial function fitting and trigonometric function fitting: According to the definition of the fitting index, the sum of squared errors obtained by trigonometric function fitting is closer to 0, and the obtained correlation coefficient is closer to 1. Therefore, according to the data fitting process of the longitudinal dynamics model, it can be known that the aerodynamic coefficients obtained by trigonometric function fitting are more accurate than those obtained by polynomial function fitting; Step 2 - 2, Explanation of non - linear parametric aerodynamic coefficients: Through the trigonometric function fitting method, an aerodynamic model of a hypersonic vehicle with aerodynamic force coefficients and moment coefficients in trigonometric function form can be obtained. The characteristics of this model are: Step 2 - 2 - 1, Considering the uncertainty of the aerodynamic coefficients and ensuring the accuracy of curve fitting, the aerodynamic coefficient expressions of the dynamic equations of the drag coefficient, lift coefficient, and moment coefficient in the gliding state are characterized as aerodynamic coefficient functions with unknown parameters: For C in equations (24)-(26) L (α), C D (α) and C M (α), the unknown aerodynamic coefficients themselves contain significant uncertainties of the aerodynamic coefficients, including structural uncertainties and parametric uncertainties. These specific non-linear parametric functions are only some representative examples, and more general or different non-linear parametric fitting functions can also be considered within the framework of the proposed adaptive control scheme; Step 2-2-2: According to the dominant control input idea, the speed state is mainly affected by the engine throttle opening Φ, and the engine throttle opening control command Φ c controls the engine throttle opening Φ through the engine second-order dynamic equation (15); the flight attitude is controlled by the elevator deflection angle δ; therefore, the longitudinal dynamics model of the hypersonic vehicle with engine dynamics is divided into two interrelated subsystems: the speed subsystem and the flight path angle subsystem, and models are established for these two interrelated subsystems respectively; So far, a complete longitudinal dynamics model of a non - linear parametric hypersonic vehicle with engine dynamics has been established Among them, the engine thrust T, the drag D, the lift L, and the pitching moment M yy are The aerodynamic force coefficients and moment coefficients in the above formula are as follows: And the engine throttle opening dynamics model is expressed as:

4. An adaptive regulation control method for a non - linear parametric hypersonic vehicle according to claim 1, characterized in that, the process of step 3 includes: Step 3 - 1, In the cruise stage of the hypersonic vehicle, the non - zero equilibrium points of the hypersonic vehicle dynamics models (1)-(12), (15) and (27)-(28) with engine throttle dynamics are expressed as The non - zero equilibrium points are transformed into the coordinate origin by defining the following coordinate transformation: x 1 = γx 2 = α - α * x 3 = q(30) Based on this, the dynamics models of the improved hypersonic vehicle (1)-(4) and engine throttle opening (15) can be expressed as where, u 1 = δ - δ * , δ * and respectively represent their ideal values under cruise conditions, the functions g 1 (z 1 ), g 3 (z 1 ), k 1 (z 1 , x 2 ) and k 3 are Among them, the uncertain nonlinear functions f i and h i , where i = 1, 2, 3 and j = 1, 3 are expressed as Since f i and h j are both continuous functions and f i (0) = 0, h j (0) = 0, the upper bounds of the non - linear functions f i and h j are obtained where γ 1 (z 1 ) ≥ 1, γ 2 (z 1 ) ≥ 1, γ 3 (x 2 , x 3 , z 1 ) ≥ 1 and λ 1 (z 1 , x 2 ) ≥ 1 are all known functions, and are all unknown parameters, and their specific expressions are as follows: Step 3 - 2, For the transformed vehicle dynamics model control system (32)-(37) without unknown parameters, a nominal control design is carried out; the following coordinate transformation is introduced: ξ 1 = x 1 - α 0 α 0 = 0 (61) η 1 = z 1 - β 0 β 0 = 0 (64) where α i , β i are virtual control signals, ξ j , η j are the errors between the state variables of the aircraft dynamics model control system and the virtual control signals, is a positive function to be determined; Step 3 - 3, Nominal system control design: For the transformed vehicle dynamics model control system (32)-(37), its relative order is {3,3}, and the improved backstepping control process includes: Step 3-3-1, a) Design a nominal virtual signal α 1 ; for the track angle subsystems (32)-(34), select the first positive definite function Positive definite function The time derivative of wherein, is a combined value of the track angle subsystem constant and the track angle subsystem parameter, and is defined as Select the virtual control signal α 1 where p 1 is a constant to be determined, so as to obtain b) Design nominal virtual control signal β 1 ; for the speed subsystem (35)-(37), select the first positive definite function Positive definite function The time derivative of Among them, is the combined value of the speed subsystem constant and the speed subsystem parameter, defined as Select the virtual control signal β 1 where q 1 is a constant to be determined, thus obtaining Step 3-3-2, a) Design a nominal virtual control signal α 2 ; for the track angle subsystem (32)-(34), select the second positive definite function Positive definite function The time derivative of Among them, and is a combined value of the track angle subsystem constants and the track angle subsystem parameters, defined as Select the virtual control signal α 2 where p 2 is a constant to be determined, so as to obtain b) Design the nominal virtual control signal β 2 ; Select the second positive definite function for the speed subsystem (35)-(37) Positive definite function The time derivative of Among them, and is a combined value of the speed subsystem constants and speed subsystem parameters, defined as Select the virtual control signal β 2 where q 2 is a constant to be determined, so as to obtain Step 3-3-3, a) Design the nominal actual control μ 1 ; Select the third positive definite function for the track angle subsystems (32)-(34) Positive definite function whose time derivative is Among them, and is a combined value of the track angle subsystem constant and the track angle subsystem parameter, defined as Select the actual control signal μ 1 where p 3 is a constant to be determined, thus obtaining b) Design the nominal actual control signal μ 2 ; Select the third positive definite function for the speed subsystem (35)-(37) Positive definite function The time derivative of Among them, and is a combined value of the speed subsystem constant and the speed subsystem parameter, defined as Select the actual control signal μ 2 where q 3 is a constant to be determined, so as to obtain Step 3 - 4, Stability analysis: For the transformed non - linear parametric hypersonic vehicle dynamics model control system (32)-(37), select the Lyapunov function From the above nominal control design process, the designed nominal control signals μ 1 (90) and μ 2 (95) make the derivative of the Lyapunov function be By choosing p 1 = 9, p 2 = 11 / 2, p 3 = 3 / 2, q 1 = 13 / 2, q 2 = 3 and q 3 = 1, the derivative Therefore, using the above nominal controller design, the stability analysis of the non - linear parametric hypersonic vehicle model system with engine dynamics is carried out, and the conclusion is: For the longitudinal model (1)-(4) of a non-linear parametric aircraft and the engine throttle opening dynamics (15) that satisfy the assumed conditions, the designed nominal control signals (90) and (95) ensure the stability of the closed-loop system and achieve the global exponential convergence of the aircraft states; Proof: Define the state variables of the closed-loop system as γ(t) = [ξ(t), η(t)], T where ξ(t) = [ξ 1 (t), ξ 2 (t), ξ 3 (t)] T , and η(t) = [η 1 (t), η 2 (t), η 3 (t)] T ; It can be obtained from (99) that Therefore is a monotonically non-increasing function; For any initial states ξ(t 0 ), η(t 0 ), it can be obtained that Therefore, the nominal control signals (90) and (95) ensure that the closed-loop signals are globally bounded; Definition According to the definition of the Lyapunov function, we obtain Inequalities (98) and (99) show that satisfy the differential inequality According to inequality (101), it can be obtained that According to (100) and (102), it can be further obtained that Therefore, for any γ(t 0 ) ∈ R 6 , the origin is globally exponentially stable; according to (61)-(66), x i and z i globally exponentially converge to the origin; according to (30) and (31), the state variables of the hypersonic vehicle system globally exponentially converge to the non-zero equilibrium point in (29) 5. An adaptive regulation control method for a non-linear parametric hypersonic aircraft according to claim 1, characterized in that the process of step 4 includes: Step 4-1: The adaptive control signal in the non-linear system (32)-(37) can be expressed as where x = [x 1 , x 2 , x 3 T , z = [z 1 , z 2 , z 3 T , and is the estimated value of the nominal parameter :​​ For the aircraft dynamics model control system (32)-(37) with unknown parameters, based on the improved backstepping control strategy and adaptive control method, an adaptive control signal is designed to ensure the global stability of all system states; Coordinate transformation: For the flight path angle subsystem (32)-(34) representing the aircraft attitude and the speed subsystem (35)-(37) representing the aircraft speed, the following state errors and virtual control signals are defined: ξ 1 = x 1 - α 0 α 0 = 0 (107) η 1 = z 1 - β 0 β 0 = 0 (110) where α i and β i , i = 0, 1, 2 are virtual control signals to be designed in the following, a 10 , a 20 , b 10 , b 20 are all positive definite functions; Step 4-2: Adaptive design under the condition of unknown parameters, including the adaptive control design of the flight path angle subsystem (32)-(34) and the speed subsystem (35)-(37): Step 4-2-1, a) Design the virtual control signal α 1 and the parameter update law For the trajectory angle subsystems (32)-(34), select the following positive definite function wherein, is the parameter estimation error; combining equations (32), (38), (47), (69), (107), (108) and Young's inequality, the derivative of the function V 1 is as follows: Select a virtual control signal α in the following form 1 and a parameter update law as Among them, and p 1 is the parameter to be designed, so as to obtain b) Design the virtual control signal β 1 and the parameter update law For the velocity subsystem (35)-(37), select the following positive definite function wherein, is the parameter estimation error; combining equations (35), (40), (50), (74), (110), (111) and Young's inequality, the derivative of the function W 1 is as follows: Select a virtual control signal β in the following form 1 and a parameter update law as Among them, and b 11 = q 1 ; q 1 is a parameter to be designed, thus obtaining Step 4-2-2, a) Design the virtual control signal α 2 and the parameter update law For the track angle subsystem (32)-(34), select the following positive definite function wherein, is the parameter estimation error; combining Equation (33), (108), (109), (117) and Young's inequality, the derivative of the function V 2 is as follows: Select a virtual control signal α in the following form 2 and a parameter update law as Among them, a 22 = π 11 + π 12 + π 13 , and p 2 is a parameter to be designed. Furthermore, it can be obtained that b) Design the virtual control signal β 2 and the parameter update law For the velocity subsystem (35)-(37), select the following positive definite function wherein, is the parameter estimation error; Combining equations (111) and (112), the derivative of the function W 2 is as follows: Select a virtual control signal β in the following form 2 and a parameter update law as Among them, and q 2 is a parameter to be designed, and then we can obtain Step 4-2-3, a) Design the actual control μ 1 and the parameter update law For the track angle subsystem (32)-(34), select the following positive definite function where, is the parameter estimation error; combining equations (107)-(109), the derivative of the function V 3 is as follows: Select the actual control signal μ having the following form 1 and the parameter update law as Among them, and p 3 is the parameter to be designed, and then b) Design the virtual control signal μ 2 and the parameter update law For the velocity subsystem (35)-(37), select the following positive definite function Among them, is the parameter estimation error; combining equations (110)-(112), the 3 derivative of W is Select the actual control signal μ in the following form 2 and the parameter update law as wherein, b 31 = q 3 + 1, and q 3 is a parameter to be designed, and then Step 4-3: Stability analysis: Based on the above design steps, for the non-linear parametric system (32)-(37) after coordinate transformation, the following Lyapunov function is defined: It is easy to obtain that the Lyapunov function defined in (143) is positive definite and radially unbounded; The designed control signals (135) and (140) and the parameter update laws (116), (121), (126), (131), (136) and (141) make the derivative of V with respect to time satisfy To make the above expression negative definite, select the following parameter values to be designed: p 1 = 9, q 2 = 3 and q 3 = 1, so the above expression can be written as Furthermore, it satisfies the negative definite condition of the overall Lyapunov function of the system; thus far, by using the improved adaptive backstepping control strategy, the design of the adaptive controllers (135) and (140) for the hypersonic aircraft system with non-linear parameterization (32)-(37) and the design process of the parameter update laws (116), (121), (126), (131), (136) and (141) are completed; the conclusions of the system stability analysis and the parameter convergence performance analysis are: For the hypersonic aircraft system (1)-(8) that satisfies the assumptions, the designed adaptive controllers (135) and (140) and the parameter update laws (116), (121), (126), (131), (136) and (141) ensure the global boundedness of all closed-loop signals and achieve the global adaptive regulation of non-zero equilibrium points.

6. An adaptive regulation control method for a non-linear parametric hypersonic aircraft according to claim 5, characterized in that In step 4, during the adaptive control design process, the design parameters are selected as p 1 = 9, q 2 = 3 and q 3 = 1.

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