CN110362110A - Adaptive neural network unmanned aerial vehicle flight path angle control method when a kind of fixed - Google Patents

Adaptive neural network unmanned aerial vehicle flight path angle control method when a kind of fixed Download PDF

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CN110362110A
CN110362110A CN201910628565.7A CN201910628565A CN110362110A CN 110362110 A CN110362110 A CN 110362110A CN 201910628565 A CN201910628565 A CN 201910628565A CN 110362110 A CN110362110 A CN 110362110A
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倪骏康
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    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
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    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
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Abstract

The present invention relates to it is a kind of fixed when adaptive neural network unmanned aerial vehicle flight path angle control method, comprising: establish unmanned plane longitudinal system flight-path angle dynamic mathematical models, establish the actuator model for having unknown nonlinear dead-zone；Determine idea output and export-restriction；Differentiator when designing neural network control device when fixing, auto-adaptive parameter more new law and fixing, track system output can within the set time with reference to output trajectory, while guaranteeing all state variable boundeds；Stability analysis is carried out to control system, controller parameter is determined according to stability analysis result.Method proposed by the invention has fully considered the limiting factors such as dead zone present in real system, the uncertain, export-restriction of system, suitable for such a more common nonlinear system of non-critical feedback system, it can thus be preferably applied in real system, guarantee the unmanned aerial vehicle flight path angle tracking coideal track within the set time.

Description

Adaptive neural network unmanned aerial vehicle flight path angle control method when a kind of fixed
Technical field
The present invention relates to industrial control fields, in particular to adaptive neural network unmanned aerial vehicle flight path angle is controlled when a kind of fixed Method processed.
Background technique
Unmanned plane shows the advantage than conventional airplane in many aspects, has been used for executing many complex tasks.From Dynamic flight control system can guarantee unmanned plane performance when unmanned plane executes special duty.The complexity of unmanned plane execution task Very high requirement is proposed to unmanned aerial vehicle (UAV) control time, control precision and system transient modelling and steady-state performance with particularity.Due to Flight environment of vehicle it is complicated and changeable, UAV system is a uncertain nonlinear system, which ties with non-critical feedback Structure is influenced by input dead zone and export-restriction, this brings very big difficulty to design controller.
Due to neural network have good unknown nonlinear Function approximation capabilities, ANN Control be do not know it is non-thread A kind of property good control method of system.In recent years, achieving many research achievements in terms of ANN Control.However, These research achievements are only for the nonlinear system for having Strict-feedback form.Non-critical feedback system is a kind of more common System form, strict feedback systems are considered its special shape.Due to nonlinear function packet in non-critical feedback system Containing entire state variable, the existing nerve network controller for strict feedback systems design is used to control non-critical feedback System will appear algebraic loop problem.It is non-linear therefore, it is necessary to which existing neural network control method is expanded to non-critical feedback System.
Convergence rate is the important performance indicator of control system, and existing neural network control method is only able to achieve asymptotic steady Stablize when fixed or limited.Asymptotic Stability, which not can guarantee system and realize in finite time, to be stablized, and is not used to convergence time requirement Stringent application.Stable convergence time depends on system initial value when limited, however, for many real systems, at the beginning of Beginning state is difficult to obtain.In addition, the convergence time stable when limited unbounded growth with the growth of initial value, which has limited have Application of the stability contorting in the very big real system control of initial value in limited time.In order to overcome above-mentioned deficiency, researcher proposes solid Timing stability.Gu timing stability is characterized mainly in that stable time boundary is a constant unrelated with initial value, this has Help convergence time estimation and controller design to meet the requirement of convergence time.However, there is presently no document reports to fix When adaptive neural network control method.
For inputting dead zone, existing document takes neural network and fuzzy logic to estimate and compensate dead-time voltage.However, Due to the Non-smooth surface characteristic of Dead zone, need to approach dead zone using more nodes, frequency of training and fuzzy rule non-thread Property, which increase computation burdens.Adaptive dead zone inverse approach be used to solve dead-time problem.However, unknown deadzone parameter from It adapts to rule and inputs u comprising actuator, and actuator input u is only capable of to obtain after determining deadzone parameter to be estimated, this makes It obtains this method and is difficult to actual implementation.The method in another kind processing dead zone is that dead zone is modeled as to the combination shape of linear term and distracter Interference is estimated using adaptive approach or robust method and compensated to formula.For export-restriction, existing document takes convex optimization side Method, however this method relies on computationally intensive algorithm.System changeover method is proved to be able to avoid export-restriction well.Most Closely, the design method based on barrier liapunov function is used for the treatment of export-restriction problem.However, there is presently no documents Report consolidates timing controlled with the system of dead zone and export-restriction.
Summary of the invention
Technical problems to be solved
In order to avoid the shortcomings of the prior art, adaptive neural network unmanned plane navigates when the present invention proposes a kind of fixed Mark angle control method, to meet UAV system to tracking time, tracking accuracy and system transient modelling and steady track performance High request, and consider controlling dead error and export-restriction generally existing in real system, enable unmanned aerial vehicle flight path angle solid It fixes time interior tracking coideal track.
Technical solution
Adaptive neural network unmanned aerial vehicle flight path angle control method when a kind of fixed, it is characterised in that steps are as follows:
Step 1: establish unmanned plane longitudinal system flight-path angle dynamic mathematical models:
In formula, γ indicates flight-path angle, and α indicates the angle of attack, qBIndicate rate of pitch, VtIndicate air speed, FTIndicate that engine pushes away Power, δeIndicate lifting angle of rudder reflection, M and IyIndicate quality and inertia, L (α, qB) andIndicate aerodynamic lift and pitching Torque, and have following expression:
In formula, S is with reference to aerofoil, and ρ indicates atmospheric density,Indicate mean chord, CLAnd CmIndicate lift and pitching moment Coefficient can be written as:
Wherein,For the Aerodynamic Coefficient contributed by rate of pitch lift and pitching moment；For the Aerodynamic Coefficient contributed by the angle of attack lift and pitching moment；For by lifting angle of rudder reflection to pitching The Aerodynamic Coefficient of torque contribution；For the lift coefficient under zero-incidence and rate of pitch；
Angle of rudder reflection δ will be gone up and downe=u is exported as actuator, has following expression:
In formula, v indicates actuator input to be designed, mrAnd mlIndicate that dead zone inputs slope, brAnd blIndicate that the dead zone right side is disconnected Point and left breakpoint；It is assumed that there are normal numbersSo that
Enable x1=γ, x2=α, x3=qB, then system (1) can indicate are as follows:
Y is system output in formula,g1(x1)=1, Since there are uncertain parameter, f in real systemi(x) and It is unknown function, wherein i=1,2,3；It is assumed thatSymbol be known, ifSymbol be positive, can be with Find constantSo thatIfSymbol be negative, constant can be foundMake ?Assuming that nonlinear function fi(x) meet Lipschitz condition, that is, there is arbitrary real number X1,X2∈Rl So that | fi(X2)-fi(X1)|≤Li||X2-X1| | meet, wherein LiFor Lipschitz constant；
Step 2: determining idea output yd=(10+2sin (0.5 π t)) °, export-restriction be | y |≤kd, it is assumed that it is ideal defeated Y outdAnd its equal bounded of derivative, it can find normal number B0, B1So that | yd|≤B0,
Step 3: differentiator when designing neural network control device when fixing, auto-adaptive parameter more new law and fixing, It track system output can within the set time with reference to output trajectory, while guaranteeing all state variable boundeds, specifically such as Under:
The practical control input of design are as follows:
In formula
In formula, χ3It is normal number, auxiliary variableIs defined as:
λ in formula3, θ3It is normal number, r is hidden nodes, and m, n, p, q are to meet m>n, the positive odd number of p<q, E3Have Following form:
Auto-adaptive parameterDynamic are as follows:
Λ3For normal number, ζ22The state of differentiator when to fix as follows:
μ in formulai=i μ-(i-1), μ ∈ (1,1+ ι), ι are sufficiently small positive number, differentiator gain L, M > 0, k1, k2, σ1, σ2 It selects so that following matrixes are Hurwitz matrix:
Error e3=x3-α2, virtual controlling α2Expression formula are as follows:
In formula, χ2For normal number, auxiliary variableIs defined as:
In formula,kc=kd-B0, λ2,θ2For normal number, E2For normal number, meet:
In formula, ψ is positive number, auto-adaptive parameterDynamic are as follows:
In formula, Λ2For normal number, ζ21The state of differentiator when to fix as follows:
ζ11Differentiator when being fixed；
Error e2=x2-α1, virtual controlling α1It is defined as
In formula, auxiliary variableIs defined as:
λ1And θ1For normal number, B1And E1It is defined as
ψ is normal number in formula；
Auto-adaptive parameterDynamic are as follows:
In formula, Λ1For normal number；
Step 4: unmanned aerial vehicle being controlled using the control parameter that step 3 determines, enables flight-path angle in the set time Reference track angle in interior tracking.
Beneficial effect
Adaptive neural network unmanned aerial vehicle flight path angle control method when proposed by the present invention a kind of fixed, relative to existing skill Art, in terms of novelty of the invention is embodied in following four:
(a), solid timing controlled is expanded to non-critical Feedback Nonlinear by the present invention.As far as we know, do not have also at present The stable control method when fixation for thering is document report to be directed to non-critical Feedback Nonlinear.
(b), the invention proposes simple effective methods to overcome the problems, such as algebraic loop.
(c), the present invention pushes away design for counter, and ANN Control and solid timing controlled combine, and solves complexity explosion Problem reduces auto-adaptive parameter number, realizes tracking error and converges to origin small neighbourhood within the set time.
(d), dead zone and export-restriction are considered in control design case when fixed, so that designed control program is for reality Engineering system has more common applicability.
The present invention compared with the existing technology, has the advantages that
(a), adaptive neural network control method when fixation proposed by the invention, has fully considered in real system and has deposited The limiting factors such as dead zone, the uncertain, export-restriction of system, it is such a more common to be suitable for non-critical feedback system Nonlinear system, it is thus possible to be preferably applied in real system.
(b), the control program proposed reduces calculation amount, easy to implement.Virtual control is estimated using differentiator when fixing The derivative of system avoids and counter pushes away design " computational complexity explosion " problem；Compared with traditional neural network control method, proposed Method needs the auto-adaptive parameter quantity updated to be greatly lowered, and adaptive updates rule design is also more simple, these are all dropped The low calculation amount of control algolithm；In practical controller design, designer is not necessarily in control precision, computation burden and real-time Compromise can be gone up, the control program proposed reduces the requirement to processor calculated performance, therefore reduce implement complexity and Difficulty.
(c), the control program proposed can guarantee the unmanned aerial vehicle flight path angle tracking coideal track within the set time, fit For requiring convergence time stringent task occasion.
Detailed description of the invention
The control flow chart of adaptive neural network control method when Fig. 1 is provided by the invention a kind of fixed
Fig. 2 is the time response of flight-path angle and its reference locus figure in the embodiment of the present invention
Fig. 3 is the time response figure of the angle of attack in the embodiment of the present invention
Fig. 4 is the time response figure of rate of pitch in the embodiment of the present invention
Fig. 5 is dead zone function input time curve graph in the embodiment of the present invention
Specific embodiment
Now in conjunction with embodiment, attached drawing, the invention will be further described:
Unmanned plane shows the advantage than conventional airplane in many aspects, has been used for executing many complex tasks.From Dynamic flight control system can guarantee unmanned plane performance when unmanned plane executes special duty.The complexity of unmanned plane execution task Very high requirement is proposed to unmanned aerial vehicle (UAV) control time, control precision and system transient modelling and steady-state performance with particularity.Due to Flight environment of vehicle it is complicated and changeable, UAV system is a uncertain nonlinear system, which ties with non-critical feedback Structure is influenced by input dead zone and export-restriction, this brings very big difficulty to design controller.
It please refers to shown in Fig. 1 to Fig. 5, the adaptive neural network control method when present invention provides a kind of fixed, including with Lower step:
The dynamic mathematical model of unmanned plane longitudinal system flight-path angle in step (1) are as follows:
In formula, γ indicates flight-path angle, qBIndicate rate of pitch, VtIndicate air speed, FTIndicate motor power, δeIt indicates Go up and down angle of rudder reflection, M and IyIndicate quality and inertia, L (α, qB) andIt indicates aerodynamic lift and pitching moment, and has Following expression:
In formula, S is with reference to aerofoil, and ρ indicates atmospheric density,Indicate mean chord, CLAnd CmIndicate lift and pitching moment Coefficient can be written as:
Wherein,For the Aerodynamic Coefficient contributed by rate of pitch lift and pitching moment； For the Aerodynamic Coefficient contributed by the angle of attack lift and pitching moment；To be contributed by lifting angle of rudder reflection pitching moment Aerodynamic Coefficient；For the lift coefficient under zero-incidence and rate of pitch.
Go up and down angle of rudder reflection u=δeIt is often taken as actuator output, there is following expression:
In formula, v indicates actuator input to be designed, mrAnd mlIndicate that dead zone inputs slope, brAnd blIndicate that the dead zone right side is disconnected Point and left breakpoint.
Reference output is y in step (2)d=(10+2sin (0.5 π t)) °, export-restriction be | y |≤kd。
Neural network control is restrained when step (3) design is fixed, realizes control target.Firstly, system (1) is written as The canonical form of control system.Enable x1=γ, x2=α, x3=qB, then system (1) can indicate are as follows:
Y is system output in formula,g1(x1)=1, Since there are uncertain parameter, f in real systemi(x) and It (i=1,2,3) is unknown function.
Next, neural network control is restrained when fixed for control system (6) design.Before controller design, To control parameter, controls gain and does following hypothesis with reference to output signal:
Assuming that 1: the parameter in dead zone (5) is unknown, but its breakpoint bl, brWith slope mr, mlIt is bounded, that is, deposits In normal numberSo that
Assuming that 2:Symbol be known.IfSymbol be positive, constant can be foundMake ?IfSymbol be negative, constant can be foundSo that
Assuming that 3: with reference to output ydAnd its equal bounded of derivative, normal number B can be found0,B1So that | yd|≤B0,
Assuming that 4: nonlinear function fi(x) meet Lipschitz condition, that is, there is arbitrary real number X1,X2∈RlSo that | fi (X2)-fi(X1)|≤Li||X2-X1| | meet, wherein LiFor Lipschitz constant.
Step 1: defining tracking error is e1=x1-yd, time-derivative can indicate are as follows:
Radial basis function neural network is for approaching unknown nonlinear function:
f1(x)=W1 *TS1(x)+ε1 (8)
W in formula1 *,S1(x) and ε1It respectively indicates radial basis function neural network best initial weights, Gaussian bases and approaches mistake Difference.There are normal numbersSo that
Define auxiliary variable:
In formulaλ1And θ1For normal number, r is hidden nodes, and m, n, p, q are to meet m The odd number of>n, p<q, B1And E1Is defined as:
ψ is normal number in formula.
For auto-adaptive parameter, more new law are as follows:
Λ in formula1For positive number.
Virtual controlling rule can be designed as:
Exported due to system and be restricted with reference to output | y |≤kdWith | yd|≤B0, then have | e1|≤kc, k in formulac+B0 =kd。
Step 2: approaching unknown nonlinear function f using radial basis function neural network2(x),e2Time-derivative are as follows:
In formulaS2(x) and ε2It respectively indicates radial basis function neural network best initial weights, Gaussian bases and approaches mistake Difference, there are normal numbersSo that
Differentiator is for estimating virtual controlling α when fixed1Derivative:
ζ in formula11,ζ21Differentiator state variable when being fixed, L, M > 0 selects appropriate k1,k2,σ1,σ2So that (16) and (17) matrix defined is Hurwitz matrix, μi=i μ-(i-1) and have μ ∈ (1,1+ ι), ι is sufficiently small positive number, sig (·)α=| |αsign(·)。
Design assistant variable are as follows:
λ in formula2,θ2,χ2For normal number, E2With following form:
For auto-adaptive parameter, adaptive law are as follows:
Virtual controlling rule design are as follows:
Step 3: approaching unknown nonlinear function f using radial basis function neural network3(x), then e3About leading for time Number can indicate are as follows:
In formula, W3 *,S3(x) and ε3For radial base neural net best initial weights, Gaussian radial basis function and approximate error can To find normal numberSo that
Differentiator is for obtaining virtual controlling α when fixed2Time-derivative:
It is defined as follows auxiliary variable:
λ in formula3,θ3,χ3For normal number, E3With following expression formula:
For auto-adaptive parameter, more new law be can be described as:
Auxiliary control input can be designed as:
Actuator input are as follows:
Further, stability analysis is carried out to control system, it was demonstrated that the solid timing stability of control system.Firstly, drawing Enter following lemma:
Lemma 1: for following system:
α > 0 in formula, β > 0, m, n, p, q are to meet m > n, the normal number of q > p.System (29) will be having for the upper bound in following formula Interior arrival origin in limited time:
Lemma 2: for z1∈ R and χ1> 0, then have:
Lemma 3: for any c > 0, a >=0, b > 0 then has:
Lemma 4: then have for any c > 1, a >=0, b≤a:
(a-b)c≥bc-ac (33)
Lemma 5: for any 0 < c≤1 and xi>=0, then have:
Lemma 6: for any c > 1 and xi>=0, then have:
Lemma 7: for differentiator (15), virtual controlling α1Time-derivative can following formula be the upper bound finite time Interior acquisition:
In formulaSymmetric positive definite matrix P1And Q1Meet:
Matrix A1As shown in (16) formula.
Symmetric positive definite matrix P and Q meet:
PA+ATP=-Q (38)
Matrix A is as shown in (17) formula.
Next, considering following liapunov function in the first step:
In formula
V1Time-derivative are as follows:
E in formula2=x2-α1.It enablesThen have:
In formula
Using lemma 2, then have:
Then, (40) become:
It is available using lemma 3-4:
Similar, it can be deduced that:
It is available that (45) and (46) are substituted into (44):
In second step, following liapunov function is constructed:
In formula
Seek V2Derivative:
It enablesThen have:
In formula
Then had using lemma 2:
(50)-(52) substitution (49) is then had:
As t >=Td1, differentiator can provide the accurate estimation of virtual controlling derivative, that is,It is then available:
It is available using the similar method of the same first step:
It is available according to lemma 2:
(55)-(57) are substituted into (54), available:
Third step, control error originated from input can indicate are as follows:
WhenSince the symbol of u' is by e3It determines, works as e3>0, then there is u'<0, and work as e3<0, then there is u'>0. Therefore, Wo MenyouSimilarly, whenWe also have
Consider following liapunov function:
In formula
V3Time-derivative are as follows:
It enablesThen have:
In formula
Using lemma 2, then have:
(62)-(64) substitution (61) can be obtained:
Similar to the first step, Wo Menyou:
Use lemma 2, Wo Menyou:
As t >=Td(l-1)When, differentiator can estimate the derivative of virtual controlling, i.e.,(66)-(68) are substituted into (65), (65) become:
Using lemma 5-6, then have:
In formula
By (70), closed-loop system ultimate bound can be calculated in we:
Outside the boundaryHowever, it is difficult to provide the analytic solutions of equation (71).Closed-loop system ultimate bound can be estimated It is calculated as:
V3Boundedness mean eiWithBounded.Due to ΘiIt is a constant, Wo MenyouIt is bounded.Due to e1 And ydBounded, we have system output y be bounded.In view of e1,It is bounded,χ1,λ1,θ1, r is constant, I HaveAnd α1It is bounded.Due to e2And α1It is bounded, we have system mode x2It is bounded.Due toWithIt is that continuous function has bounded domain, Wo MenyouAnd ζ12It is bounded.The ζ known to (15)11It is bounded.By In ζ12,e1,e2,It is bounded, andχ2, λ2, θ2, r is constant, then hasAnd α2It is bounded.Due to e3And α2 It is bounded, then system mode x3It is bounded.Similar, it can prove xi,αi,ζ1i,ζ2iIt is bounded with v.Therefore, own Closed signal is bounded.
Assuming that system, which exports y, passes through export-restriction in moment t=T, we have liapunov function V3It will become infinite, This and liapunov function V3Bounded is runed counter to, and therefore, system output will not be over export-restriction | y |≤kd。
We can find a constantSo thatThen (70) become:
It enablesThen (73) become:
Using lemma 1, we have V3Will withFor having for the upper bound Region is converged in limited time
If V3Reach regionThen haveTherefore, Tracking error will withTo reach compact set in the finite time in the upper bound It closes
(4) unmanned aerial vehicle flight path angle dynamic implementation is controlled using the control law that step (3) determine, so that unmanned aerial vehicle flight path angle The motion profile of coideal can be tracked, and guarantees that system output does not violate limitation.
Embodiment: unmanned aerial vehicle flight path angular motion state
Adaptive neural network control method is realizing nobody when illustrating above-mentioned fixed by taking unmanned aerial vehicle flight path angular motion state as an example Validity in machine track angle tracking ideal trajectory.Unmanned aerial vehicle flight path angular motion state can indicate are as follows:
WhereinAnd have
System parameter is chosen for Vt=100m/s, FT=8000N, M=9295.44kg, S=27.87m2, Iy= 75673.6kg·m2,ρ=1.7g/L, Deadzone parameter is selected as mr=1, br=0.6 °, ml=1.05, bl=-0.8 °.
Adaptive neural network control method when a kind of unmanned aerial vehicle flight path angular motion state of the present embodiment is fixed, including following step It is rapid:
(1) it determines control target: being y with reference to output signal selectiond=(10+2sin (0.5 π t)) °, export-restriction be | y | ≤22°.Control target is determined as system output can track the reference output of system within the set time, while make system Output is no more than limitation.
(2) to realize control target, control input is designed are as follows:
U' has following expression form in formula:
In formulaWith following expression form:
(3) λ is selected as according to liapunov function stability analysis, controller and differentiator parameteri=θi=10, r=5, χi=0.1, p=5, q=9, m=9, n=5, ψ=0.05, Λi=5, k1=5, k2=10, σ1=5, σ2=10, L=10, μ1= 1.2, μ2=1.4,It can be proved that this group of control parameter meets Li Ya Pu Nuofu stability.
(4) unmanned aerial vehicle flight path angle dynamic implementation is controlled using the control parameter that step (3) determine, so that unmanned aerial vehicle flight path Angle can track the motion profile of coideal, while system output being made to meet export-restriction | y |≤22 °.
The process of adaptive neural network control method is illustrated in Fig. 1 when provided a kind of fixed.Flight-path angle and its ginseng The time response for examining track is shown in Fig. 2.The time response of the angle of attack is shown in Fig. 3.The time response of rate of pitch is shown in Fig. 4.Extremely Area's control input time curve is shown in Fig. 5.As can be seen from these figures, system output refers to rail within the set time in tracking Mark, system output are not above limitation, other state variables and dead zone function input bounded.

Claims (1)

1. adaptive neural network unmanned aerial vehicle flight path angle control method when a kind of fixed, it is characterised in that steps are as follows:
Step 1: establish unmanned plane longitudinal system flight-path angle dynamic mathematical models:
In formula, γ indicates flight-path angle, and α indicates the angle of attack, qBIndicate rate of pitch, VtIndicate air speed, FTIndicate motor power, δe Indicate lifting angle of rudder reflection, M and IyIndicate quality and inertia, L (α, qB) andIndicate aerodynamic lift and pitching moment, And there is following expression:
In formula, S is with reference to aerofoil, and ρ indicates atmospheric density,Indicate mean chord, CLAnd CmIndicate lift and pitching moment coefficient, It can be written as:
Wherein,For the Aerodynamic Coefficient contributed by rate of pitch lift and pitching moment；For The Aerodynamic Coefficient that lift and pitching moment are contributed by the angle of attack；For the pneumatic system contributed by lifting angle of rudder reflection pitching moment Number；For the lift coefficient under zero-incidence and rate of pitch；
Angle of rudder reflection δ will be gone up and downe=u is exported as actuator, has following expression:
In formula, v indicates actuator input to be designed, mrAnd mlIndicate that dead zone inputs slope, brAnd blIndicate the right breakpoint in dead zone and Left breakpoint；It is assumed that there are normal numbers So that
Enable x1=γ, x2=α, x3=qB, then system (1) can indicate are as follows:
Y is system output in formula,g1(x1)=1, Since there are uncertain parameter, f in real systemi(x) and It is unknown function, wherein i=1,2,3；It is assumed thatSymbol be known, ifSymbol be positive, can be with Find constant So thatIfSymbol be negative, constant can be foundMake ?Assuming that nonlinear function fi(x) meet Lipschitz condition, that is, there is arbitrary real number X1,X2∈Rl So that | fi(X2)-fi(X1)|≤Li||X2-X1| | meet, wherein LiFor Lipschitz constant；
Step 2: determining idea output yd=(10+2sin (0.5 π t)) °, export-restriction be | y |≤kd, it is assumed that ideal output yd And its equal bounded of derivative, it can find normal number B0, B1So that | yd|≤B0,
Step 3: neural network control device when design is fixed, auto-adaptive parameter more new law and it is fixed when differentiator, make be System output can be tracked within the set time with reference to output trajectory, while guaranteeing all state variable boundeds, specific as follows:
The practical control input of design are as follows:
In formula
In formula, χ3It is normal number, auxiliary variableIs defined as:
λ in formula3, θ3It is normal number, r is hidden nodes, and m, n, p, q are to meet m>n, the positive odd number of p<q, E3With as follows Form:
Auto-adaptive parameterDynamic are as follows:
Λ3For normal number, ζ22The state of differentiator when to fix as follows:
μ in formulai=i μ-(i-1), μ ∈ (1,1+ ι), ι are sufficiently small positive number, differentiator gain L, M > 0, k1, k2, σ1, σ2Selection So that following matrixes are Hurwitz matrix:
Error e3=x3-α2, virtual controlling α2Expression formula are as follows:
In formula, χ2For normal number, auxiliary variableIs defined as:
In formula,kc=kd-B0, λ2,θ2For normal number, E2For normal number, meet:
In formula, ψ is positive number, auto-adaptive parameterDynamic are as follows:
In formula, Λ2For normal number, ζ21The state of differentiator when to fix as follows:
ζ11Differentiator when being fixed；
Error e2=x2-α1, virtual controlling α1It is defined as
In formula, auxiliary variableIs defined as:
λ1And θ1For normal number, B1And E1It is defined as
ψ is normal number in formula；
Auto-adaptive parameterDynamic are as follows:
In formula, Λ1For normal number；
Step 4: using step 3 determine control parameter to unmanned aerial vehicle control, enable flight-path angle within the set time with Reference track angle on track.
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