CN107450324A - Consider the hypersonic aircraft adaptive fusion method of angle of attack constraint - Google Patents

Consider the hypersonic aircraft adaptive fusion method of angle of attack constraint Download PDF

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CN107450324A
CN107450324A CN201710789277.0A CN201710789277A CN107450324A CN 107450324 A CN107450324 A CN 107450324A CN 201710789277 A CN201710789277 A CN 201710789277A CN 107450324 A CN107450324 A CN 107450324A
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mrow
mover
mtd
mfrac
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CN107450324B (en
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许斌
郭雨岩
程怡新
张睿
史忠科
凡永华
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Northwestern Polytechnical University
Shenzhen Institute of Northwestern Polytechnical University
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Shenzhen Institute of Northwestern Polytechnical University
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    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
    • G05B13/02—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric
    • G05B13/04—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators
    • G05B13/042—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators in which a parameter or coefficient is automatically adjusted to optimise the performance

Abstract

The invention discloses a kind of hypersonic aircraft adaptive fusion method for considering angle of attack constraint, for solving the technical problem of existing hypersonic aircraft control method poor practicability.Technical scheme is that Aircraft Angle of Attack is limited in given range, ensures the normal work of scramjet engine；For actuator failures situation, robust adaptive adjustment control strategy is given, the influence brought using the effective compensation failure of Redundant Control mechanism is to ensure the security of system.For model uncertainty.The present invention combines amplitude limit design and provides controller with Barrier type liapunov functions, it can be ensured that the angle of attack can be constrained in given range, ensure scramjet engine normal work.Model uncertainty is handled by neural network learning to handle instead of linear parameterization, is simplified model analysis, is easy to practical application.It is good for actuator failures situation, the influence brought using the effective adaptive equalization failure of Redundant Control mechanism, practicality.

Description

Consider the hypersonic aircraft adaptive fusion method of angle of attack constraint
Technical field
The present invention relates to a kind of hypersonic aircraft control method, more particularly to a kind of high ultrasound for considering angle of attack constraint Fast aircraft adaptive fusion method.
Background technology
Hypersonic aircraft refers to the aircraft to be flown in endoatmosphere with more than the five times velocities of sound, due to its protrusion Flight performance make it that the whole world is hit in real time, therefore by extensive concern both domestic and external.Air suction type hypersonic flight Device is more using scramjet engine as power resources, because this kind of engine eliminates the compressor of conventional jet formula engine Component, its intake efficiency is extremely sensitive to Aircraft Angle of Attack, only when Aircraft Angle of Attack is limited in certain limit, super burn Punching engine just can normal work.The current research for hypersonic aircraft considers less, shortage for angle of attack limitation The correlative study of the control law constrained the angle of attack.In addition, hypersonic aircraft is due to flight environment of vehicle harshness, flight course X factor is more, and its actuator is likely to occur the failure such as stuck and further results in flight unstability.
《Fault-tolerant control using command filtered adaptive back-stepping technique:application to hypersonic longitudinal flight dynamics》(Bin Xu, Yuyan Guo, Yuan Yuan, Yonghua Fan, Danwei Wang,《International Journal of Adaptive Control and Signal Processing》,2016,30(4):553-577) text flies for hypersonic Row device vertical passage devises adaptive fusion rule, while is linear parameterization form design adaptive law by model conversation It is estimated, but linear parameterization form is difficult to obtain in practice, and do not consider to attack in the controller design of the paper Angle restricted problem, causes this method to be difficult to engineer applied.
The content of the invention
In order to overcome the shortcomings of existing hypersonic aircraft control method poor practicability, the present invention provides a kind of consideration and attacked The hypersonic aircraft adaptive fusion method of angle constraint.Aircraft Angle of Attack is limited in given range by this method, Ensure the normal work of scramjet engine；For actuator failures situation, robust adaptive adjustment control strategy is given, The influence brought using the failure of Redundant Control mechanism effective compensation is to ensure the security of system.For model uncertainty.This Invention combine amplitude limit design with Barrier type liapunov functions provide controller, it can be ensured that the angle of attack can be constrained on to Determine in scope, ensure scramjet engine normal work.Model uncertainty is handled by neural network learning to replace linearly Parameterized treatment, model analysis is simplified, be easy to practical application.For actuator failures situation, using Redundant Control, mechanism has The influence that brings of effect adaptive equalization failure, ensures the security of system, and practicality is good.
The technical solution adopted for the present invention to solve the technical problems：A kind of hypersonic aircraft for considering angle of attack constraint Adaptive fusion method, it is characterized in comprising the following steps：
Step 1: establish hypersonic aircraft vertical passage kinetic model：
Wherein, Represent Dynamic pressure, ρ represent atmospheric density,It is aerodynamic parameter,Represent mean aerodynamic chord, S Represent pneumatic area of reference；V represents speed, and γ represents flight path angle, and h represents height, and α represents the angle of attack, and q represents angle of pitch speed Degree；Wherein u=[u1,u2,…,un]TFor n control surface deflection angle to be designed,For unknown failure parameter, δ=diag { δ1,δ2,…,δn, take δ when i-th of actuator breaks downi =1, otherwise take δi=0, λ=[λ1,λ2,…,λn]TFor unknown parameter；β is throttle valve opening；T, D, L and MyyRepresent and push away respectively Power, resistance, lift and pitch rotation torque；m、Iyy, μ and r representation qualities, the rotary inertia of pitch axis, gravitational coefficients and away from The distance in the earth's core.
Step 2: define height tracing error eh=h-hd, design flight-path angle instruction γd：
In formula, hdHighly to instruct,For the first differential highly instructed, kh>0, ki>0.Consider that cruise section flight-path angle becomes Change small, the first differential of flight-path angle instructionIt is taken as zero.
Take x1=γ, x2=α, x3=q；Formula (3)-(5) can be written as Strict-feedback form：
Wherein, fi,gi, i=1,2,3 is the unknown nonlinear function obtained according to hypersonic vehicle.g1= ωg1θg1, g2=1, g3=ωg3θg3, whereinFor known terms,For not Know aerodynamic parameter item.
Step 3: define flight path angle tracking error：
e1=x1-γd (8)
Design angle of attack virtual controlling amount：
In formula, k1>0。For the f obtained by RBF neural1Estimate, whereinFor the optimal power of neutral net The estimate of weight vector, θ1For RBF functional vectors.WhereinFor θg1Estimate.
Define modeling error：
WhereinObtained by following formula：
Wherein η1>0 is provided by designer.DesignAdaptive law is as follows：
Wherein γ1>0、γz1>0、δ1>0.DesignAdaptive law is as follows：
Wherein
In order that the angle of attack meets given constraints, x is made2cX is obtained by following saturation element2cl：
Wherein, x2cmFor x2cThe upper bound.
It is as follows to design firstorder filter：
X in formula2dFor x2clThe signal obtained afterwards by wave filter (15), α2>0。
Define angle of attack tracking error：
e2=x2-x2d (16)
Construct Barrier liapunov functionsWherein kbFor error e2The upper bound.Design the angle of pitch Speed virtual controlling amount：
In formula, k2>0,For the f obtained by RBF neural2Estimate, whereinFor the optimal power of neutral net The estimate of weight vector, θ2For RBF functional vectors.
Define modeling error：
WhereinObtained by following formula：
Wherein η2>0.DesignAdaptive law is as follows：
Wherein γ2>0、γz2>0、δ2>0。
It is as follows to design firstorder filter：
X in formula3dFor x3cThe signal obtained afterwards by wave filter (21), α3>0。
Define pitch rate tracking error：
e3=x3-x3d (22)
Design assistant signal u*It is as follows：
In formula, k3>0。For the f obtained by RBF neural3Estimate, whereinFor the optimal power of neutral net The estimate of weight vector, θ3For RBF functional vectors.WhereinFor θg3Estimate.
It is as follows to design each control surface deflection：
WhereinAdaptive law is as follows：
Wherein Γ1i>0 and Γ2i>0, sgn (g3) it is g3Sign function, g herein3Known to symbol.
Define modeling error：
WhereinObtained by following formula：
Wherein η3>0.DesignAdaptive law is as follows：
Wherein γ3>0、γz3>0、δ3>0.DesignAdaptive law is as follows：
Wherein
Step 4: define speed tracing error：
In formula, VdFor speed command.It is as follows to design throttle valve opening：
In formula, kpV>0、kiV>0、kdV>0。
Step 5: according to obtained each angle of rudder reflection uiWith throttle valve opening β, the dynamics of hypersonic aircraft is returned to Model (1)-(5), control is tracked to height and speed.
The beneficial effects of the invention are as follows：Aircraft Angle of Attack is limited in given range by this method, ensures ultra-combustion ramjet hair The normal work of motivation；For actuator failures situation, robust adaptive adjustment control strategy is given, utilizes Redundant Control machine The influence that brings of failure of structure effective compensation is to ensure the security of system.For model uncertainty.The present invention is set with reference to amplitude limit Meter provides controller with Barrier type liapunov functions, it can be ensured that the angle of attack can be constrained in given range, ensured super Burning ramjet normal work.Model uncertainty is handled by neural network learning to handle instead of linear parameterization, is simplified Model analysis, is easy to practical application.For actuator failures situation, the effective adaptive equalization failure of Redundant Control mechanism is utilized The influence brought, ensures the security of system, and practicality is good.
The present invention is elaborated with reference to the accompanying drawings and detailed description.
Brief description of the drawings
Fig. 1 is the flow chart for the hypersonic aircraft adaptive fusion method that the present invention considers angle of attack constraint.
Embodiment
Reference picture 1.The present invention considers the hypersonic aircraft adaptive fusion method specific steps of angle of attack constraint It is as follows：
Step 1: establish hypersonic aircraft vertical passage kinetic model：
Wherein, V represents speed, and γ represents flight path angle, and h represents height, and α represents the angle of attack, and q represents rate of pitch,Wherein u=[u1 u2]TFor each angle of rudder reflection,For unknown failure parameter, δ= diag{δ1 δ2, take δ when i-th of actuator breaks downi=1, otherwise take δi=0, λ=[λ1 λ2]T=[0.8 0.8]T。β For throttle valve opening；T, D, L and MyyThrust, resistance, lift and pitch rotation torque are represented respectively；m、Iyy, μ and r represent matter Amount, the rotary inertia of pitch axis, gravitational coefficients and the distance away from the earth's core.Related torque and parameter definition is as follows：
WhereinDynamic pressure is represented, ρ represents atmospheric density,Mean aerodynamic chord is represented, S represents pneumatic ginseng Examine area.
Step 2: define height tracing error eh=h-hd, design flight-path angle instruction γd：
In formula, hdHighly to instruct, provided by designer,For the first differential highly instructed, kh=0.5, ki= 0.05.Consider that the change of cruise section flight-path angle is small, the first differential of flight-path angle instructionIt is taken as zero.
Take x1=γ, x2=α, x3=q；Formula (3)-(5) can be written as Strict-feedback form：
Wherein, fi,gi, i=1,2,3 is the nonlinear function obtained according to hypersonic vehicle.g1=ωg1 θg1, g2=1, g3=ωg3θg3, whereinFor known terms,To be unknown Aerodynamic parameter item.
Step 3: define flight path angle tracking error：
e1=x1-γd (8)
Design angle of attack virtual controlling amount：
In formula, k1=1.WhereinFor θg1Estimate.Obtained by RBF neural f1Estimate, whereinFor the estimate of neutral net optimal weights vector, θ1For RBF functional vectors.
Define modeling error：
WhereinObtained by following formula：
Wherein η1=2.DesignAdaptive law is as follows：
Wherein γ1=2, γz1=1, δ1=0.1.DesignAdaptive law is as follows：
Wherein
In order that the angle of attack meets given constraints, x is made2cPass through following saturation element：
Wherein, x2cm=0.1.
Make x2clX is obtained by following firstorder filter2d：
α in formula2=0.05.
Define angle of attack tracking error：
e2=x2-x2d (16)
Construct Barrier liapunov functionsWherein kb=0.022.It is empty to design pitch rate Intend controlled quentity controlled variable：
K in formula2=1.For the f obtained by RBF neural2Estimate, whereinFor the optimal power of neutral net The estimate of weight vector, θ2For RBF functional vectors.
Define modeling error：
WhereinObtained by following formula：
Wherein η2=2.DesignAdaptive law is as follows：
Wherein γ2=0.2, γz2=0.5, δ2=0.01.
Make x3cX is obtained by following firstorder filter3d：
α in formula3=0.05.
Define pitch rate tracking error：
e3=x3-x3d (22)
Design assistant signal u*It is as follows：
K in formula3=5.For the f obtained by RBF neural3Estimate, whereinFor the optimal power of neutral net The estimate of weight vector, θ3For RBF functional vectors.
For double actuator situations, design self-adjusted block rule is as follows：
In formula, adaptive law is as follows：
Wherein Γ1i=3, Γ2i=0.7, i=1,2.
Define modeling error：
WhereinObtained by following formula：
Wherein η3=2.DesignAdaptive law is as follows：
Wherein γ3=0.1, γz3=0.05, δ3=0.01.DesignAdaptive law is as follows：
Wherein
Step 4: given speed instructs Vd, define speed tracing error：
It is as follows to design throttle valve opening：
In formula, kpV=0.5, kiV=0.001, kdV=0.01.
Step 5: according to obtained angle of rudder reflection u1、u2With throttle valve opening β, the dynamics of hypersonic aircraft is returned to Model, control is tracked to height and speed.Designed controller can ensure that the angle of attack is limited in ± 0.122rad in this example In the range of (± 7 °).
Unspecified part of the present invention belongs to art personnel's common knowledge.

Claims (1)

  1. A kind of 1. hypersonic aircraft adaptive fusion method for considering angle of attack constraint, it is characterised in that including following step Suddenly：
    Step 1: establish hypersonic aircraft vertical passage kinetic model：
    <mrow> <mover> <mi>V</mi> <mo>&amp;CenterDot;</mo> </mover> <mo>=</mo> <mfrac> <mrow> <mi>T</mi> <mi> </mi> <mi>c</mi> <mi>o</mi> <mi>s</mi> <mi>&amp;alpha;</mi> <mo>-</mo> <mi>D</mi> </mrow> <mi>m</mi> </mfrac> <mo>-</mo> <mfrac> <mrow> <mi>&amp;mu;</mi> <mi>s</mi> <mi>i</mi> <mi>n</mi> <mi>&amp;gamma;</mi> </mrow> <msup> <mi>r</mi> <mn>2</mn> </msup> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow>
    <mrow> <mover> <mi>h</mi> <mo>&amp;CenterDot;</mo> </mover> <mo>=</mo> <mi>V</mi> <mi> </mi> <mi>s</mi> <mi>i</mi> <mi>n</mi> <mi>&amp;gamma;</mi> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>2</mn> <mo>)</mo> </mrow> </mrow>
    <mrow> <mover> <mi>&amp;gamma;</mi> <mo>&amp;CenterDot;</mo> </mover> <mo>=</mo> <mfrac> <mrow> <mi>L</mi> <mo>+</mo> <mi>T</mi> <mi> </mi> <mi>s</mi> <mi>i</mi> <mi>n</mi> <mi>&amp;alpha;</mi> </mrow> <mrow> <mi>m</mi> <mi>V</mi> </mrow> </mfrac> <mo>-</mo> <mfrac> <mrow> <mi>&amp;mu;</mi> <mo>-</mo> <msup> <mi>V</mi> <mn>2</mn> </msup> <mi>r</mi> <mi>c</mi> <mi>o</mi> <mi>s</mi> <mi>&amp;gamma;</mi> </mrow> <mrow> <msup> <mi>Vr</mi> <mn>2</mn> </msup> </mrow> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>3</mn> <mo>)</mo> </mrow> </mrow>
    <mrow> <mover> <mi>&amp;alpha;</mi> <mo>&amp;CenterDot;</mo> </mover> <mo>=</mo> <mi>q</mi> <mo>-</mo> <mover> <mi>&amp;gamma;</mi> <mo>&amp;CenterDot;</mo> </mover> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>4</mn> <mo>)</mo> </mrow> </mrow>
    <mrow> <mover> <mi>q</mi> <mo>&amp;CenterDot;</mo> </mover> <mo>=</mo> <mfrac> <msub> <mi>M</mi> <mrow> <mi>y</mi> <mi>y</mi> </mrow> </msub> <msub> <mi>I</mi> <mrow> <mi>y</mi> <mi>y</mi> </mrow> </msub> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>5</mn> <mo>)</mo> </mrow> </mrow>
    Wherein, Table Showing dynamic pressure, ρ represents atmospheric density,It is aerodynamic parameter,Represent Average aerodynamic string Long, S represents pneumatic area of reference；V represents speed, and γ represents flight path angle, and h represents height, and α represents the angle of attack, and q represents the angle of pitch Speed；Wherein u=[u1,u2,…,un]TFor n control surface deflection angle to be designed,For unknown failure parameter, δ=diag { δ1,δ2,…,δn, take δ when i-th of actuator breaks downi =1, otherwise take δi=0, λ=[λ1,λ2,…,λn]TFor unknown parameter；β is throttle valve opening；T, D, L and MyyRepresent and push away respectively Power, resistance, lift and pitch rotation torque；m、Iyy, μ and r representation qualities, the rotary inertia of pitch axis, gravitational coefficients and away from The distance in the earth's core；
    Step 2: define height tracing error eh=h-hd, design flight-path angle instruction γd：
    <mrow> <msub> <mi>&amp;gamma;</mi> <mi>d</mi> </msub> <mo>=</mo> <mi>arcsin</mi> <mrow> <mo>(</mo> <mfrac> <mrow> <mo>-</mo> <msub> <mi>k</mi> <mi>h</mi> </msub> <msub> <mi>e</mi> <mi>h</mi> </msub> <mo>-</mo> <msub> <mi>k</mi> <mi>i</mi> </msub> <mo>&amp;Integral;</mo> <msub> <mi>e</mi> <mi>h</mi> </msub> <mi>d</mi> <mi>t</mi> <mo>+</mo> <msub> <mover> <mi>h</mi> <mo>&amp;CenterDot;</mo> </mover> <mi>d</mi> </msub> </mrow> <mi>V</mi> </mfrac> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>6</mn> <mo>)</mo> </mrow> </mrow>
    In formula, hdHighly to instruct,For the first differential highly instructed, kh>0, ki>0；Consider that the change of cruise section flight-path angle is small, The first differential of flight-path angle instructionIt is taken as zero；
    Take x1=γ, x2=α, x3=q；Formula (3)-(5) can be written as Strict-feedback form：
    <mrow> <mtable> <mtr> <mtd> <mrow> <msub> <mover> <mi>x</mi> <mo>&amp;CenterDot;</mo> </mover> <mn>1</mn> </msub> <mo>=</mo> <msub> <mi>f</mi> <mn>1</mn> </msub> <mo>+</mo> <msub> <mi>g</mi> <mn>1</mn> </msub> <msub> <mi>x</mi> <mn>2</mn> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mover> <mi>x</mi> <mo>&amp;CenterDot;</mo> </mover> <mn>2</mn> </msub> <mo>=</mo> <msub> <mi>f</mi> <mn>2</mn> </msub> <mo>+</mo> <msub> <mi>g</mi> <mn>2</mn> </msub> <msub> <mi>x</mi> <mn>3</mn> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mover> <mi>x</mi> <mo>&amp;CenterDot;</mo> </mover> <mn>3</mn> </msub> <mo>=</mo> <msub> <mi>f</mi> <mn>3</mn> </msub> <mo>+</mo> <msub> <mi>g</mi> <mn>3</mn> </msub> <msub> <mi>&amp;delta;</mi> <mi>e</mi> </msub> </mrow> </mtd> </mtr> </mtable> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>7</mn> <mo>)</mo> </mrow> </mrow>
    Wherein, fi,gi, i=1,2,3 is the unknown nonlinear function obtained according to hypersonic vehicle；g1=ωg1θg1, g2=1, g3=ωg3θg3, whereinFor known terms,To be unknown pneumatic Parameter item；
    Step 3: define flight path angle tracking error：
    e1=x1-γd (8)
    Design angle of attack virtual controlling amount：
    <mrow> <msub> <mi>x</mi> <mrow> <mn>2</mn> <mi>c</mi> </mrow> </msub> <mo>=</mo> <mfrac> <mn>1</mn> <msub> <mover> <mi>g</mi> <mo>^</mo> </mover> <mn>1</mn> </msub> </mfrac> <mrow> <mo>(</mo> <mo>-</mo> <msub> <mover> <mi>f</mi> <mo>^</mo> </mover> <mn>1</mn> </msub> <mo>-</mo> <msub> <mi>k</mi> <mn>1</mn> </msub> <msub> <mi>e</mi> <mn>1</mn> </msub> <mo>+</mo> <msub> <mover> <mi>&amp;gamma;</mi> <mo>&amp;CenterDot;</mo> </mover> <mi>d</mi> </msub> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>9</mn> <mo>)</mo> </mrow> </mrow>
    In formula, k1>0；For the f obtained by RBF neural1Estimate, whereinFor neutral net optimal weights to The estimate of amount, θ1For RBF functional vectors；WhereinFor θg1Estimate；
    Define modeling error：
    <mrow> <msub> <mover> <mi>x</mi> <mo>~</mo> </mover> <mn>1</mn> </msub> <mo>=</mo> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>-</mo> <msub> <mover> <mi>x</mi> <mo>^</mo> </mover> <mn>1</mn> </msub> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>10</mn> <mo>)</mo> </mrow> </mrow>
    WhereinObtained by following formula：
    <mrow> <msub> <mover> <mover> <mi>x</mi> <mo>^</mo> </mover> <mo>&amp;CenterDot;</mo> </mover> <mn>1</mn> </msub> <mo>=</mo> <msub> <mover> <mi>f</mi> <mo>^</mo> </mover> <mn>1</mn> </msub> <mo>+</mo> <msub> <mover> <mi>g</mi> <mo>^</mo> </mover> <mn>1</mn> </msub> <msub> <mi>x</mi> <mn>2</mn> </msub> <mo>+</mo> <msub> <mi>&amp;eta;</mi> <mn>1</mn> </msub> <msub> <mover> <mi>x</mi> <mo>~</mo> </mover> <mn>1</mn> </msub> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>11</mn> <mo>)</mo> </mrow> </mrow>
    Wherein η1>0 is provided by designer；DesignAdaptive law is as follows：
    <mrow> <msub> <mover> <mover> <mi>&amp;omega;</mi> <mo>^</mo> </mover> <mo>&amp;CenterDot;</mo> </mover> <mn>1</mn> </msub> <mo>=</mo> <msub> <mi>&amp;gamma;</mi> <mn>1</mn> </msub> <mo>&amp;lsqb;</mo> <mrow> <mo>(</mo> <msub> <mi>e</mi> <mn>1</mn> </msub> <mo>+</mo> <msub> <mi>&amp;gamma;</mi> <mrow> <mi>z</mi> <mn>1</mn> </mrow> </msub> <msub> <mover> <mi>x</mi> <mo>~</mo> </mover> <mn>1</mn> </msub> <mo>)</mo> </mrow> <msub> <mi>&amp;theta;</mi> <mn>1</mn> </msub> <mo>-</mo> <msub> <mi>&amp;delta;</mi> <mn>1</mn> </msub> <msub> <mover> <mi>&amp;omega;</mi> <mo>^</mo> </mover> <mn>1</mn> </msub> <mo>&amp;rsqb;</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>12</mn> <mo>)</mo> </mrow> </mrow>
    Wherein γ1>0、γz1>0、δ1>0；DesignAdaptive law is as follows：
    Wherein
    In order that the angle of attack meets given constraints, x is made2cX is obtained by following saturation element2cl：
    <mrow> <msub> <mi>x</mi> <mrow> <mn>2</mn> <mi>c</mi> <mi>l</mi> </mrow> </msub> <mo>=</mo> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <msub> <mi>x</mi> <mrow> <mn>2</mn> <mi>c</mi> <mi>m</mi> </mrow> </msub> </mtd> <mtd> <mrow> <mi>i</mi> <mi>f</mi> </mrow> </mtd> <mtd> <mrow> <msub> <mi>x</mi> <mrow> <mn>2</mn> <mi>c</mi> </mrow> </msub> <mo>&gt;</mo> <msub> <mi>x</mi> <mrow> <mn>2</mn> <mi>c</mi> <mi>m</mi> </mrow> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <msub> <mi>x</mi> <mrow> <mn>2</mn> <mi>c</mi> </mrow> </msub> </mtd> <mtd> <mrow> <mi>i</mi> <mi>f</mi> </mrow> </mtd> <mtd> <mrow> <mo>-</mo> <msub> <mi>x</mi> <mrow> <mn>2</mn> <mi>c</mi> <mi>m</mi> </mrow> </msub> <mo>&lt;</mo> <msub> <mi>x</mi> <mrow> <mn>2</mn> <mi>c</mi> </mrow> </msub> <mo>&lt;</mo> <msub> <mi>x</mi> <mrow> <mn>2</mn> <mi>c</mi> <mi>m</mi> </mrow> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>-</mo> <msub> <mi>x</mi> <mrow> <mn>2</mn> <mi>c</mi> <mi>m</mi> </mrow> </msub> </mrow> </mtd> <mtd> <mrow> <mi>i</mi> <mi>f</mi> </mrow> </mtd> <mtd> <mrow> <msub> <mi>x</mi> <mrow> <mn>2</mn> <mi>c</mi> </mrow> </msub> <mo>&lt;</mo> <mo>-</mo> <msub> <mi>x</mi> <mrow> <mn>2</mn> <mi>c</mi> <mi>m</mi> </mrow> </msub> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>14</mn> <mo>)</mo> </mrow> </mrow>
    Wherein, x2cmFor x2cThe upper bound；
    It is as follows to design firstorder filter：
    <mrow> <msub> <mi>&amp;alpha;</mi> <mn>2</mn> </msub> <msub> <mover> <mi>x</mi> <mo>&amp;CenterDot;</mo> </mover> <mrow> <mn>2</mn> <mi>d</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>x</mi> <mrow> <mn>2</mn> <mi>d</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>x</mi> <mrow> <mn>2</mn> <mi>c</mi> <mi>l</mi> </mrow> </msub> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>15</mn> <mo>)</mo> </mrow> </mrow>
    X in formula2dFor x2clThe signal obtained afterwards by wave filter (15), α2>0；
    Define angle of attack tracking error：
    e2=x2-x2d (16)
    Construct Barrier liapunov functionsWherein kbFor error e2The upper bound；Design pitch rate Virtual controlling amount：
    <mrow> <msub> <mi>x</mi> <mrow> <mn>3</mn> <mi>c</mi> </mrow> </msub> <mo>=</mo> <mfrac> <mn>1</mn> <msub> <mi>g</mi> <mn>2</mn> </msub> </mfrac> <mo>&amp;lsqb;</mo> <mo>-</mo> <msub> <mover> <mi>f</mi> <mo>^</mo> </mover> <mn>2</mn> </msub> <mo>-</mo> <msub> <mi>k</mi> <mn>2</mn> </msub> <msub> <mi>e</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <msubsup> <mi>k</mi> <mi>b</mi> <mn>2</mn> </msubsup> <mo>-</mo> <msubsup> <mi>e</mi> <mn>2</mn> <mn>2</mn> </msubsup> <mo>)</mo> </mrow> <mo>-</mo> <msub> <mover> <mi>g</mi> <mo>^</mo> </mover> <mn>1</mn> </msub> <msub> <mi>e</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <msubsup> <mi>k</mi> <mi>b</mi> <mn>2</mn> </msubsup> <mo>-</mo> <msubsup> <mi>e</mi> <mn>2</mn> <mn>2</mn> </msubsup> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mover> <mi>x</mi> <mo>&amp;CenterDot;</mo> </mover> <mrow> <mn>2</mn> <mi>d</mi> </mrow> </msub> <mo>&amp;rsqb;</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>17</mn> <mo>)</mo> </mrow> </mrow>
    In formula, k2>0,For the f obtained by RBF neural2Estimate, whereinFor neutral net optimal weights to The estimate of amount, θ2For RBF functional vectors；
    Define modeling error：
    <mrow> <msub> <mover> <mi>x</mi> <mo>~</mo> </mover> <mn>2</mn> </msub> <mo>=</mo> <msub> <mi>x</mi> <mn>2</mn> </msub> <mo>-</mo> <msub> <mover> <mi>x</mi> <mo>^</mo> </mover> <mn>2</mn> </msub> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>18</mn> <mo>)</mo> </mrow> </mrow> 2
    WhereinObtained by following formula：
    <mrow> <msub> <mover> <mover> <mi>x</mi> <mo>^</mo> </mover> <mo>&amp;CenterDot;</mo> </mover> <mn>2</mn> </msub> <mo>=</mo> <msub> <mover> <mi>f</mi> <mo>^</mo> </mover> <mn>2</mn> </msub> <mo>+</mo> <msub> <mi>g</mi> <mn>2</mn> </msub> <msub> <mi>x</mi> <mn>3</mn> </msub> <mo>+</mo> <msub> <mi>&amp;eta;</mi> <mn>2</mn> </msub> <msub> <mover> <mi>x</mi> <mo>~</mo> </mover> <mn>2</mn> </msub> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>19</mn> <mo>)</mo> </mrow> </mrow>
    Wherein η2>0；DesignAdaptive law is as follows：
    <mrow> <mover> <mover> <mi>&amp;omega;</mi> <mo>^</mo> </mover> <mo>&amp;CenterDot;</mo> </mover> <mo>=</mo> <msub> <mi>&amp;gamma;</mi> <mn>2</mn> </msub> <mo>&amp;lsqb;</mo> <mrow> <mo>(</mo> <mfrac> <msub> <mi>e</mi> <mn>2</mn> </msub> <mrow> <msubsup> <mi>k</mi> <mi>b</mi> <mn>2</mn> </msubsup> <mo>-</mo> <msubsup> <mi>e</mi> <mn>2</mn> <mn>2</mn> </msubsup> </mrow> </mfrac> <mo>+</mo> <msub> <mi>&amp;gamma;</mi> <mrow> <mi>z</mi> <mn>2</mn> </mrow> </msub> <msub> <mover> <mi>x</mi> <mo>~</mo> </mover> <mn>2</mn> </msub> <mo>)</mo> </mrow> <msub> <mi>&amp;theta;</mi> <mn>2</mn> </msub> <mo>-</mo> <msub> <mi>&amp;delta;</mi> <mn>2</mn> </msub> <msub> <mover> <mi>&amp;omega;</mi> <mo>^</mo> </mover> <mn>2</mn> </msub> <mo>&amp;rsqb;</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>20</mn> <mo>)</mo> </mrow> </mrow>
    Wherein γ2>0、γz2>0、δ2>0；
    It is as follows to design firstorder filter：
    <mrow> <msub> <mi>&amp;alpha;</mi> <mn>3</mn> </msub> <msub> <mover> <mi>x</mi> <mo>&amp;CenterDot;</mo> </mover> <mrow> <mn>3</mn> <mi>d</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>x</mi> <mrow> <mn>3</mn> <mi>d</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>x</mi> <mrow> <mn>3</mn> <mi>c</mi> </mrow> </msub> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>21</mn> <mo>)</mo> </mrow> </mrow>
    X in formula3dFor x3cThe signal obtained afterwards by wave filter (21), α3>0；
    Define pitch rate tracking error：
    e3=x3-x3d (22)
    Design assistant signal u*It is as follows：
    <mrow> <msup> <mi>u</mi> <mo>*</mo> </msup> <mo>=</mo> <mfrac> <mn>1</mn> <msub> <mover> <mi>g</mi> <mo>^</mo> </mover> <mn>3</mn> </msub> </mfrac> <mo>&amp;lsqb;</mo> <mo>-</mo> <msub> <mover> <mi>f</mi> <mo>^</mo> </mover> <mn>3</mn> </msub> <mo>-</mo> <msub> <mi>k</mi> <mn>3</mn> </msub> <msub> <mi>e</mi> <mn>3</mn> </msub> <mo>-</mo> <mfrac> <mrow> <msub> <mi>g</mi> <mn>2</mn> </msub> <msub> <mi>e</mi> <mn>2</mn> </msub> </mrow> <mrow> <mo>(</mo> <msubsup> <mi>k</mi> <mi>b</mi> <mn>2</mn> </msubsup> <mo>-</mo> <msubsup> <mi>e</mi> <mn>2</mn> <mn>2</mn> </msubsup> <mo>)</mo> </mrow> </mfrac> <mo>+</mo> <msub> <mover> <mi>x</mi> <mo>&amp;CenterDot;</mo> </mover> <mrow> <mn>3</mn> <mi>d</mi> </mrow> </msub> <mo>&amp;rsqb;</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>23</mn> <mo>)</mo> </mrow> </mrow>
    In formula, k3>0；For the f obtained by RBF neural3Estimate, whereinFor neutral net optimal weights to The estimate of amount, θ3For RBF functional vectors；WhereinFor θg3Estimate；
    It is as follows to design each control surface deflection：
    <mrow> <msub> <mi>u</mi> <mi>i</mi> </msub> <mo>=</mo> <msub> <mover> <mi>k</mi> <mo>^</mo> </mover> <mrow> <mn>1</mn> <mi>i</mi> </mrow> </msub> <msup> <mi>u</mi> <mo>*</mo> </msup> <mo>+</mo> <msub> <mover> <mi>k</mi> <mo>^</mo> </mover> <mrow> <mn>2</mn> <mi>i</mi> </mrow> </msub> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>24</mn> <mo>)</mo> </mrow> </mrow>
    WhereinAdaptive law is as follows：
    <mrow> <mtable> <mtr> <mtd> <mrow> <msub> <mover> <mover> <mi>k</mi> <mo>^</mo> </mover> <mo>&amp;CenterDot;</mo> </mover> <mrow> <mn>1</mn> <mi>i</mi> </mrow> </msub> <mo>=</mo> <mo>-</mo> <mi>sgn</mi> <mrow> <mo>(</mo> <msub> <mi>g</mi> <mn>3</mn> </msub> <mo>)</mo> </mrow> <msub> <mi>&amp;Gamma;</mi> <mrow> <mn>1</mn> <mi>i</mi> </mrow> </msub> <msub> <mi>e</mi> <mn>3</mn> </msub> <msup> <mi>u</mi> <mo>*</mo> </msup> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mover> <mover> <mi>k</mi> <mo>^</mo> </mover> <mo>&amp;CenterDot;</mo> </mover> <mrow> <mn>2</mn> <mi>i</mi> </mrow> </msub> <mo>=</mo> <mo>-</mo> <mi>sgn</mi> <mrow> <mo>(</mo> <msub> <mi>g</mi> <mn>3</mn> </msub> <mo>)</mo> </mrow> <msub> <mi>&amp;Gamma;</mi> <mrow> <mn>2</mn> <mi>i</mi> </mrow> </msub> <msub> <mi>e</mi> <mn>3</mn> </msub> </mrow> </mtd> </mtr> </mtable> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>25</mn> <mo>)</mo> </mrow> </mrow>
    Wherein Γ1i>0 and Γ2i>0, sgn (g3) it is g3Sign function, g herein3Known to symbol；
    Define modeling error：
    <mrow> <msub> <mover> <mi>x</mi> <mo>~</mo> </mover> <mn>3</mn> </msub> <mo>=</mo> <msub> <mi>x</mi> <mn>3</mn> </msub> <mo>-</mo> <msub> <mover> <mi>x</mi> <mo>^</mo> </mover> <mn>3</mn> </msub> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>26</mn> <mo>)</mo> </mrow> </mrow>
    WhereinObtained by following formula：
    <mrow> <msub> <mover> <mover> <mi>x</mi> <mo>^</mo> </mover> <mo>&amp;CenterDot;</mo> </mover> <mn>3</mn> </msub> <mo>=</mo> <msub> <mover> <mi>f</mi> <mo>^</mo> </mover> <mn>3</mn> </msub> <mo>+</mo> <msub> <mover> <mi>g</mi> <mo>^</mo> </mover> <mn>3</mn> </msub> <msub> <mi>&amp;delta;</mi> <mi>e</mi> </msub> <mo>+</mo> <msub> <mi>&amp;eta;</mi> <mn>3</mn> </msub> <msub> <mover> <mi>x</mi> <mo>~</mo> </mover> <mn>3</mn> </msub> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>27</mn> <mo>)</mo> </mrow> </mrow>
    Wherein η3>0；DesignAdaptive law is as follows：
    <mrow> <msub> <mover> <mover> <mi>&amp;omega;</mi> <mo>^</mo> </mover> <mo>&amp;CenterDot;</mo> </mover> <mn>3</mn> </msub> <mo>=</mo> <msub> <mi>&amp;gamma;</mi> <mn>3</mn> </msub> <mo>&amp;lsqb;</mo> <mrow> <mo>(</mo> <msub> <mi>e</mi> <mn>3</mn> </msub> <mo>+</mo> <msub> <mi>&amp;gamma;</mi> <mrow> <mi>z</mi> <mn>3</mn> </mrow> </msub> <msub> <mover> <mi>x</mi> <mo>~</mo> </mover> <mn>3</mn> </msub> <mo>)</mo> </mrow> <msub> <mi>&amp;theta;</mi> <mn>3</mn> </msub> <mo>-</mo> <msub> <mi>&amp;delta;</mi> <mn>3</mn> </msub> <msub> <mover> <mi>&amp;omega;</mi> <mo>^</mo> </mover> <mn>3</mn> </msub> <mo>&amp;rsqb;</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>28</mn> <mo>)</mo> </mrow> </mrow>
    Wherein γ3>0、γz3>0、δ3>0；DesignAdaptive law is as follows：
    Wherein
    Step 4: define speed tracing error：
    <mrow> <mover> <mi>V</mi> <mo>~</mo> </mover> <mo>=</mo> <msub> <mi>V</mi> <mi>d</mi> </msub> <mo>-</mo> <mi>V</mi> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>30</mn> <mo>)</mo> </mrow> </mrow>
    In formula, VdFor speed command；It is as follows to design throttle valve opening：
    <mrow> <mi>&amp;beta;</mi> <mo>=</mo> <msub> <mi>k</mi> <mrow> <mi>p</mi> <mi>V</mi> </mrow> </msub> <mover> <mi>V</mi> <mo>~</mo> </mover> <mo>+</mo> <msub> <mi>k</mi> <mrow> <mi>i</mi> <mi>V</mi> </mrow> </msub> <mo>&amp;Integral;</mo> <mover> <mi>V</mi> <mo>~</mo> </mover> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mi>d</mi> <mi>t</mi> <mo>+</mo> <msub> <mi>k</mi> <mrow> <mi>d</mi> <mi>V</mi> </mrow> </msub> <mfrac> <mrow> <mi>d</mi> <mover> <mi>V</mi> <mo>~</mo> </mover> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow> <mrow> <mi>d</mi> <mi>t</mi> </mrow> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>31</mn> <mo>)</mo> </mrow> </mrow>
    In formula, kpV>0、kiV>0、kdV>0；
    Step 5: according to obtained each angle of rudder reflection uiWith throttle valve opening β, the kinetic model of hypersonic aircraft is returned to (1)-(5), control is tracked to height and speed.
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