CN106406095A - Trajectory tracking control method for input-output asymmetrically limited full-drive surface ship - Google Patents

Abstract

The invention relates to a trajectory tracking control method for an input-output asymmetrically limited full-drive surface ship. The trajectory tracking control method comprises the steps of: conducting error calculation according to a given trajectory expected tracking value; then conducting trajectory kinematic control calculation according to a trajectory kinematical equation, so as to obtain a virtual control law; approximating an uncertain item in a surface ship model by utilizing a neural network, designing an auxiliary control system to solve the saturation problem of actuating mechanisms, and then acquiring a control quantity based on a surface ship kinematical equation; and finally applying the control quantity to the surface ship model. In practical application, state quantities such as trajectory and speed of the surface ship are measured by sensors, and the control quantity obtained through calculation by adopting the trajectory tracking control method is transmitted to the actuating mechanisms such as a steering engine and a propeller, thus a trajectory tracking control function of the surface ship resisting the uncertain item, resisting disturbance and resisting asymmetric saturation problem of the actuating mechanisms can be realized.

Description

The asymmetric limited full driving surface vessel Trajectory Tracking Control method of input and output

Technical field

The present invention provides a kind of asymmetric limited full driving surface vessel Trajectory Tracking Control method of input and output, and it is Input and output are subject to the full driving unmanned water surface naval vessel of asymmetric restriction, provide a kind of tracking expectation rail of suppression external disturbance impact The new control method of mark, belongs to automatic control technology field.

Background technology

In recent years, the motor control research for unmanned water surface naval vessel is more and more.Wherein, Trajectory Tracking Control is as one Individual typical motor control, the work for aspects such as navigation, intelligence exploration and intelligence investigations is all of great importance.So we Need the controller with high performance tracking trajectory capacity a kind of for unmanned water surface ship design, thus realizing surface vessel Accurate reference track or virtual objects.But it may appear that inputting the problem of saturation, thus leading to performance in real application systems Degeneration, lead-lag, generation undersuing or even system are unstable.Simultaneously as the propeller of surface vessel can only export Positive power, or when executor's effectiveness partial loss, asymmetric input saturated conditions all can occur.Additionally, working as water surface warship When a narrow river is advanced, the flight path of ship is strictly limited it is therefore desirable to consider limited by output ship by the two sides in river course Problem.When flight path be not river course middle when, system output restriction be also asymmetrical.

Therefore invention " a kind of input and output asymmetric limited full driving surface vessel Trajectory Tracking Control method " is handle Problem above is as point of penetration, and proposes targetedly, to solve the surface vessel that input and output are subject to asymmetric restricted problem Trajectory Tracking Control is theoretical.Introduce bounded liapunov function, hyperbolic tangent function and Nussbaum function solution time-varying non- The problem that symmetry inputs and outputs limit；Estimate indeterminate and the external disturbance of bounded using adaptive algorithm；Meanwhile, utilize Instruction wave filter avoids the derivative operation of complexity.This method solve the asymmetric limited problem of input and output it is ensured that system Asymptotic Stability, can achieve reliable track following, be that surface vessel Trajectory Tracking Control engineering provides one kind and efficiently may be used The design meanses of row.

Content of the invention

(1) purpose：It is an object of the invention to provide a kind of asymmetric limited full driving surface vessel rail of input and output Mark tracking and controlling method, controls engineer can to realize surface vessel in the method and resist not while with reference to actual parameter Determine item, disturbance rejection, anti-input and output be subject to asymmetric restriction Trajectory Tracking Control.

(2) technical scheme：The present invention " the asymmetric limited full driving surface vessel Trajectory Tracking Control side of input and output Method ", its main contents and step are：First Error Calculation is carried out by given track expectation pursuit gain；Then moved according to track Equation carries out track kinesiology control and is calculated virtual controlling rule；Approached in surface vessel model not using neutral net Determine item, Design assistant control system solves the problems, such as damp constraint, be subsequently based on surface vessel kinetics equation and controlled Amount processed；This controlled quentity controlled variable is used for surface vessel model the most at last.In the middle of practical application, the state such as the track of surface vessel, speed Amount is obtained by sensor measurement, and will be transmitted to the actuators such as steering wheel and propeller by the calculated controlled quentity controlled variable of the method, Can achieve the anti-indeterminate of surface vessel, disturbance rejection, the Trajectory Tracking Control function of the asymmetric saturation problem of anti-actuator.

The present invention " the asymmetric limited full driving surface vessel Trajectory Tracking Control method of input and output ", its concrete steps As follows：

Step one gives expectation pursuit path：Given desired plane position (x_d,y_d)；Given expectation yaw angle ψ_d；Expect with Track track is expressed as η_d=[x_d,y_d,ψ_d]^T.

Step 2 track following Error Calculation：Calculate error z between actual path and desired trajectory₁=η-η_d.

Step 3 is processed to input saturation part：Introduce smooth piecewise functionApproximate description executor's model.

Step 4 virtual controlling amount α₁₀Calculate：Calculate virtual needed for the error eliminating between desired trajectory and actual path Controlled quentity controlled variable α₁₀.

Step 5 virtual controlling amount α₂₀Calculate：Calculate virtual needed for the error eliminating between desired speed and actual speed Controlled quentity controlled variable α₂₀.

Step 6 system design of control law：Calculate needed for the error eliminating between executor's desired output and reality output Controlled quentity controlled variable φ.

Wherein, the given expectation pursuit path described in step one includes：Expect that pursuit path is η_d=[x_d,y_d,ψ_d ]^T, three representation in components implications are：(x_d,y_d) represent desired plane position, ψ_dRepresent expectation yaw angle.

Wherein, the computational methods of the track following error described in step 2 are as follows：

z₁=η-η_d

η is actual path under inertial coodinate system for the surface vessel, η=[x, y, ψ]^T, wherein, (x, y) represents water surface warship The position of ship, ψ represents yaw angle.

Wherein, input saturation part is processed described in step 3, its computational methods is as follows：

With reference to the accompanying drawings 1, initially set up the inertial coodinate system shown in figure and body coordinate system.Thus can get surface vessel Three Degree Of Freedom Nonlinear Equations of Motion：

Wherein, η=[x, y, ψ]^TIt is the actual path on naval vessel under inertial coodinate system, (x, y) represents the position of surface vessel Put, ψ represents yaw angle.υ=[u, v, r]^TFor velocity under body coordinate system for the naval vessel, u, v, r are respectively velocity edge The decomposition amount of hull coordinate system, represents pace, lateral velocity and yaw rate respectively.R (ψ) is spin matrix, meets R^-1(ψ)=R^T(ψ)：

M is nonsingular, symmetrical positive definite inertial matrix.C (υ) is centripetal matrix, and D (υ) is damping matrix.Three's table respectively Show as follows：

B (t)=[b₁(t) b₂(t) b₃(t)]^TFor indeterminate, including not modeling indeterminate and unknown time-varying Interference volume.Output for saturation executor and the input of system.Executor's input is defeated The relation going out may be expressed as：

Wherein,It is the controlled quentity controlled variable not considered under executor's saturation, the input of saturation executor can be regarded as.WithIt is τ respectively_iBound.But now input and the relation curve of output are rough it is impossible to be entered using Backstepping Row design.Therefore define a smooth piecewise functionCarry out approximate representation executor input Output relation.

Then the equation of motion of surface vessel is rewritable is

Wherein, It is the functional vector of a bounded,C ＞ 0, φ are for it Need the control law designing afterwards.

Wherein, calculating virtual controlling amount α described in step 4₁₀, its computational methods is as follows：

1) calculate the error of actual path and given desired trajectory：z₁=η-η_d.

2) give asymmetric export-restriction：k_cT () is system bottoming, k_dT () exports the upper limit for system, then in output Lower limit and the difference of given desired trajectory

k_αi=η_di-k_ci, k_bi=k_di-η_di, (i=1,2,3).

3) calculate z₁Derivative：

4) design virtual controlling amount α₁₀：

Wherein k₁=diag (k₁₁,k₁₂,k₁₃) for positive definite symmetrical matrix；k_α1＞ 0, p >=0 is positive integer,

Q=diag (Q₁,Q₂,Q₃), and

e₁For the state of aid system, it is expressed as

Wherein,For the constant of a very little, k_e1＞ 1, γ₁＞ 0,

Δα₁=α₁-α₁₀.By differential tracking filter as shown in Figure 2, can be by α_i0(i=1,2) obtain α_iAnd Its derivative value

Thus the derivative operation of complexity can be avoided.

Wherein, calculating virtual controlling amount α described in step 5₂₀, its computational methods is as follows：

1) calculate the error of actual speed and desired speed：z₂=v- α₁.

2) calculate z₂Derivative：

3) design virtual controlling amount α₂₀：

Wherein, k_α2＞ 0,e₂With e₁Similar, it is a state variable of aid system, be expressed as

Wherein,For the constant of a very little, k_e2＞ 1, γ₂＞ 0,

Δα₂=α₂-α₂₀.

4) adaptive law design：Design adaptive lawBy the indeterminate in model with And external disturbance passes through adaptive algorithm approximate evaluation,

Wherein γ_f,γ_σ＞ 0, ρ ∈ R⁺.

Wherein, the system design of control law described in step 6, its method for designing is as follows：

1) reality output of executor and the error of desired output are calculated：

2) calculate z₃Derivative：Wherein Θ=diag (θ₁,θ₂,θ₃),By Extreme difficulties can be brought to design and analysis in the Θ of time-varying, introduce Nussbaum function battle array N=diag (N₁(χ₁),N₂(χ₂),N₃ (χ₃)),

3) design controlled quentity controlled variable φ：

Wherein k₃=diag (k₃₁,k₃₂,k₃₃), it is the symmetrical matrix of positive definite.

(3) advantage and effect：

The present invention " the surface vessel Trajectory Tracking Control method of the asymmetric saturation of executor ", compared with the prior art, it is excellent Putting is：

1) this method avoids model linearization, may be directly applied to nonlinear model, and step is succinctly efficient, and can guarantee that and be Gradually the stability of system；

2) this method can effectively solve the problem that the asymmetric saturation problem of executor, significantly improves non-due to actuator The adverse effect that symmetrical saturation problem causes for system stability and various aspects of performance；

3) this method, by carrying out asymmetric restriction to output, can make surface vessel when narrow river is advanced, can The track reference flight path leaning on；

4) using adaptive algorithm good inhibit the model uncertainty and external disturbance interference effect to system；

5) this method algorithm structure is simple, and fast response time is it is easy to Project Realization.

In application process, control engineer can according to actual requirement give surface vessel any desired track with corresponding Input and output limit, and actuator will be directly transferred to by the calculated controlled quentity controlled variable of the method and realize Trajectory Tracking Control Function.

Brief description

Fig. 1 is surface vessel illustraton of model of the present invention.

Fig. 2 is the composition frame chart of median filter of the present invention.

Symbol description is as follows：

η_dη_d=[x_d,y_d,ψ_d]^TFor expecting surface vessel travel track, wherein (x_d,y_d) represent desired plane position, ψ_d Represent yaw angle.

η η=[x, y, ψ]^TActual path for surface vessel；

υ υ=[u, v, r]^TFor the velocity of surface vessel, u, v, r be respectively velocity along hull coordinate system point Xie Liang；

α₁₀α₁₀For designed virtual controlling amount；

α₂₀α₂₀For designed virtual controlling amount；

α₁α₁For the desired speed of surface vessel, can be by α₁₀Obtained by wave filter；

α₂α₂For the desired output of executor, can be by α₂₀Obtained by wave filter；

z₁z₁For the error between desired trajectory and actual path；

z₂z₂For the error between desired speed and actual speed；

z₃z₃For the error between desired speed and actual speed；

B b (t)=[b₁(t)b₂(t)b₃(t)]^TFor indeterminate, including the interference not modeling power and unknown time-varying Amount；

For not considering the system input quantity under executor's saturation；

Output for saturation executor and system input；

For a smooth piecewise function, for approximate representation executor's saturation Model；

For a bounded function；

B B be model indeterminate b withSum；

k_c(t) k_cT () is the minimum export-restriction of system；

k_d(t) k_dT () is that the maximum output of system limits；

φ φ is system control amount；

The minima being limited by system input quantity；

The maximum being limited by system input quantity；

e₁,e₂e₁,e₂The state variable of aid system；

Estimated value for indeterminate；

Specific embodiment

Below in conjunction with the accompanying drawings, technical scheme is described further.

The present invention " the asymmetric limited full driving surface vessel Trajectory Tracking Control method of input and output ", its concrete steps As follows：Step one：Given expectation pursuit gain

1) as shown in figure 1, with a fixing point as initial point, x-axis points to the north, y-axis points to east, sets up inertial coordinate System；With the construction geometry center in surface vessel model as initial point, x-axis points to the head on naval vessel, and y-axis, perpendicular to x-axis, sets up body Coordinate system.

2) desired trajectory giving is η_d=[x_d,y_d,ψ_d]^T, three representation in components implications are：(x_d,y_d) represent that expectation is flat Face position, ψ_dRepresent yaw angle.

Step 2：Calculate track following error z₁

z₁=η-η_d

Step 3：Input saturation part is processed

With reference to the accompanying drawings 1, initially set up the inertial coodinate system shown in figure and body coordinate system.Thus can get surface vessel Three Degree Of Freedom Nonlinear Equations of Motion：

Wherein, η=[x, y, ψ]^TIt is the actual path on naval vessel under inertial coodinate system, (x, y) represents the position of surface vessel Put, ψ represents yaw angle.υ=[u, v, r]^TFor velocity under body coordinate system for the naval vessel, u, v, r are respectively velocity edge The decomposition amount of hull coordinate system, represents pace, lateral velocity and yaw rate respectively.R (ψ) is spin matrix, meets R^-1(ψ)=R^T(ψ)：

M is nonsingular, symmetrical positive definite inertial matrix.C (υ) is centripetal matrix, and D (υ) is damping matrix.Three's table respectively Show as follows：

B (t)=[b₁(t)b₂(t)b₃(t)]^TFor indeterminate, including not modeling the dry of indeterminate and unknown time-varying The amount of disturbing.Output for saturation executor and the input of system.Executor's input and output Relation may be expressed as：

Wherein,It is the controlled quentity controlled variable not considered under executor's saturation, the input of saturation executor can be regarded as.WithPoint

It is not τ_iBound.But now input and the relation curve of output are rough it is impossible to use Backstepping It is designed.Therefore fixed

An adopted smooth piecewise functionCarry out approximate representation executor's input and output to close System.

Then the equation of motion of surface vessel is rewritable is

Wherein, It is the functional vector of a bounded,C ＞ 0, φ are for it Need the control law designing afterwards.

Step 4：Calculate virtual controlling amount α₁₀

1) calculate the error of actual path and given desired trajectory：z₁=η-η_d.

2) give asymmetric export-restriction：k_cT () is system bottoming, k_dT () exports the upper limit for system, then in output Lower limit and the difference of given desired trajectory

k_αi=η_di-k_ci, k_bi=k_di-η_di, (i=1,2,3).

3) calculate z₁Derivative：

4) design virtual controlling amount α₁₀：

Wherein k₁=diag (k₁₁,k₁₂,k₁₃) for positive definite symmetrical matrix；k_α1＞ 0, p >=0 is positive integer,

Q=diag (Q₁,Q₂,Q₃), and

e₁For the state of aid system, it is expressed as

Wherein,For the constant of a very little, k_e1＞ 1, γ₁＞ 0,

Δα₁=α₁-α₁₀.By differential tracking filter as shown in Figure 2, can be by α_i0(i=1,2) obtain α_iAnd Its derivative value

Thus the derivative operation of complexity can be avoided.

Step 5：Calculate virtual controlling amount α₂₀

1) calculate the error of actual speed and desired speed：z₂=v- α₁.

2) calculate z₂Derivative：

3) design virtual controlling amount α₂₀：

Wherein, k_α2＞ 0,e₂With e₁Similar, it is a state variable of aid system, be expressed as

Wherein,For the constant of a very little, k_e2＞ 1, γ₂＞ 0,

Δα₂=α₂-α₂₀.

4) adaptive law design：Design adaptive lawBy the indeterminate in model with And external disturbance passes through adaptive algorithm approximate evaluation,

Wherein γ_f,γ_σ＞ 0, ρ ∈ R⁺.

Step 6：Design system control law

1) reality output of executor and the error of desired output are calculated：

2) calculate z₃Derivative：Wherein Θ=diag (θ₁,θ₂,θ₃),By Extreme difficulties can be brought to design and analysis in the Θ of time-varying, introduce Nussbaum function battle array N=diag (N₁(χ₁),N₂(χ₂),N₃ (χ₃)),

3) design controlled quentity controlled variable φ：

Wherein k₃=diag (k₃₁,k₃₂,k₃₃), it is the symmetrical matrix of positive definite.

Claims (6)

1. a kind of asymmetric limited full driving surface vessel Trajectory Tracking Control method of input and output it is characterised in that：Specifically Step is as follows：

Step one gives expectation pursuit path：Given desired plane position (x_d,y_d)；Given expectation yaw angle ψ_d；Expect to follow the tracks of rail Trace description is η_d=[x_d,y_d,ψ_d]^T；

Step 2 track following Error Calculation：Calculate error z between actual path and desired trajectory₁=η-η_d；

Step 3 is processed to input saturation part：Introduce smooth piecewise functionApproximate description executor's model；

Step 4 virtual controlling amount α₁₀Calculate：Calculate the virtual controlling needed for error eliminating between desired trajectory and actual path Amount α₁₀；

Step 5 virtual controlling amount α₂₀Calculate：Calculate the virtual controlling needed for error eliminating between desired speed and actual speed Amount α₂₀；

Step 6 system design of control law：Calculate the control needed for error eliminating between executor's desired output and reality output Amount φ.

2. the asymmetric limited full driving surface vessel Trajectory Tracking Control method of input and output according to claim 1, It is characterized in that：The computational methods of the track following error described in step 2 are as follows：

z₁=η-η_d

η is actual path under inertial coodinate system for the surface vessel, η=[x, y, ψ]^T, wherein, (x, y) represents the position of surface vessel Put, ψ represents yaw angle.

3. the asymmetric limited full driving surface vessel Trajectory Tracking Control method of input and output according to claim 1, It is characterized in that：Input saturation part is processed described in step 3, its computational methods is as follows：

Initially set up inertial coodinate system and body coordinate system；Thus can get the Three Degree Of Freedom Nonlinear Equations of Motion of surface vessel：

Wherein, η=[x, y, ψ]^TIt is the actual path on naval vessel under inertial coodinate system, (x, y) represents the position of surface vessel, ψ table Show yaw angle；υ=[u, v, r]^TFor velocity under body coordinate system for the naval vessel, u, v, r are respectively velocity and sit along hull The decomposition amount of mark system, represents pace, lateral velocity and yaw rate respectively；R (ψ) is spin matrix, meets R^-1(ψ)= R^T(ψ)：

$R\left(\mathrm{\ψ}\right)=\left[\begin{array}{ccc}cos\mathrm{\ψ}& -\sin \mathrm{\ψ}& 0\\ \sin \mathrm{\ψ}& \cos \mathrm{\ψ}& 0\\ 0& 0& 1\end{array}\right]$

M is nonsingular, symmetrical positive definite inertial matrix；C (υ) is centripetal matrix, and D (υ) is damping matrix；Three represents such as respectively Under：

$M=\left[\begin{array}{ccc}{m}_{11}& 0& 0\\ 0& m_{22}& m_{23}\\ 0& m_{32}& m_{33}\end{array}\right],D\left(\mathrm{\υ}\right)=\left[\begin{array}{ccc}{d}_{11}\left(u\right)& 0& 0\\ 0& d_{22}(v,r)& d_{23}(v,r)\\ 0& d_{32}(v,r)& d_{33}(v,r)\end{array}\right],$

$C\left(\mathrm{\υ}\right)=\left[\begin{array}{ccc}0& 0& -m_{22}v-m_{23}r\\ 0& 0& m_{11}u\\ m_{22}v+m_{23}r& -m_{11}u& 0\end{array}\right]$

B (t)=[b₁(t) b₂(t) b₃(t)]^TFor indeterminate, including the interference not modeling indeterminate and unknown time-varying Amount；Output for saturation executor and the input of system；Executor inputs The relation of output may be expressed as：

Wherein,It is the controlled quentity controlled variable not considered under executor's saturation, the input of saturation executor can be regarded as；WithIt is τ respectively_iBound；But now input and the relation curve of output are rough it is impossible to be carried out using Backstepping Design；Therefore define a smooth piecewise functionCarry out approximate representation executor input defeated Go out relation；

Then the equation of motion of surface vessel is rewritable is

Wherein, It is the functional vector of a bounded,C ＞ 0, φ are to need afterwards Control law to be designed.

4. the asymmetric limited full driving surface vessel Trajectory Tracking Control method of input and output according to claim 1, It is characterized in that：Calculating virtual controlling amount α described in step 4₁₀, its computational methods is as follows：

1) calculate the error of actual path and given desired trajectory：z₁=η-η_d；

2) give asymmetric export-restriction：k_cT () is system bottoming, k_dT () exports the upper limit for system, then export bound Difference with given desired trajectory

k_αi=η_di-k_ci, k_bi=k_di-η_di, (i=1,2,3)；

3) calculate z₁Derivative：

${\stackrel{\·}{z}}_1=\stackrel{\·}{\mathrm{\η}}-{\stackrel{\·}{\mathrm{\η}}}_d=R\left(\mathrm{\ψ}\right)z_2+R\left(\mathrm{\ψ}\right){\mathrm{\α}}_{10}+R\left(\mathrm{\ψ}\right){\mathrm{\Δ\α}}_1-{\stackrel{\·}{\mathrm{\η}}}_d$

4) design virtual controlling amount α₁₀：

${\mathrm{\α}}_{10}=R^{-1}\left(\mathrm{\ψ}\right)\left(\right(-k_1+\stackrel{\‾}{\mathrm{\ι}}\left(t\right))z_1+k_{\mathrm{\α}1}{e}_1+{\stackrel{\·}{\mathrm{\η}}}_d-\frac{k_{\mathrm{\α}1}^2}{2}{Q}^T{z}_1^{2p-1}),$

Wherein k₁=diag (k₁₁,k₁₂,k₁₃) for positive definite symmetrical matrix；k_α1＞ 0, p >=0 is positive integer,

${\mathrm{\ι}}_i=\sqrt{{\left(\frac{{\stackrel{\·}{k}}_{ai}}{k_{ai}}\right)}^2+{\left(\frac{{\stackrel{\·}{k}}_{bi}}{k_{bi}}\right)}^2+{\mathrm{\β}}_i},i=1,2,3({\mathrm{\β}}_i>0);$

Q=diag (Q₁,Q₂,Q₃), and

$Q_i=\frac{q_i}{k_{bi}^{2p}-z_{1i}^{2p}}+\frac{1-q_i}{k_{ai}^{2p}-z_{1i}^{2p}},(i=1,2,3,q_i=\left\{\begin{array}{c}1,z_{1i}>0\\ 0,z_{1i}\≤0\end{array}\right.);$

e₁For the state of aid system, it is expressed as

${\stackrel{\·}{e}}_1=\left(\begin{array}{ccc}-k_{e1}{e}_1-f_1{e}_1+{\mathrm{\γ}}_1{\mathrm{\Δ\α}}_1,& if& \left|\right|e_1\left|\right|>{\stackrel{\‾}{e}}_1\\ 0,& if& \left|\right|e_1\left|\right|\≤{\stackrel{\‾}{e}}_1\end{array}\right.,$

Wherein,For the constant of a very little, k_e1＞ 1, γ₁＞ 0,Δ α₁=α₁-α₁₀；By differential tracking filter, can be by α_i0(i=1,2) obtain α_iAnd its derivative value

5. the asymmetric limited full driving surface vessel Trajectory Tracking Control method of input and output according to claim 1, It is characterized in that：Calculating virtual controlling amount α described in step 5₂₀, its computational methods is as follows：

1) calculate the error of actual speed and desired speed：z₂=v- α₁；

2) calculate z₂Derivative：

$M{\stackrel{\·}{z}}_2=M\stackrel{\·}{\mathrm{\υ}}-M{\stackrel{\·}{\mathrm{\α}}}_1=-C\left(\mathrm{\υ}\right)\mathrm{\υ}-D\left(\mathrm{\υ}\right)\mathrm{\υ}+z_3+{\mathrm{\α}}_{20}+{\mathrm{\Δ\α}}_2+B-M{\stackrel{\·}{\mathrm{\α}}}_1$

3) design virtual controlling amount α₂₀：

${\mathrm{\α}}_{20}=-k_2{z}_2-R^T\left(\mathrm{\ψ}\right)Q^T{z}_1^{2p-1}+C\left(\mathrm{\υ}\right)\mathrm{\υ}+D\left(\mathrm{\υ}\right)\mathrm{\υ}+M{\stackrel{\·}{\mathrm{\α}}}_1-Tanh\left(\frac{z_2}{\mathrm{\ρ}}\right)\widehat{\mathrm{\σ}}+k_{\mathrm{\α}2}{e}_2,$

Wherein, k_α2＞ 0,e₂With e₁Similar, it is a state variable of aid system, be expressed as

${\stackrel{\·}{e}}_2=\left(\begin{array}{ccc}-k_{e2}{e}_2-f_2{e}_2+{\mathrm{\γ}}_2{\mathrm{\Δ\α}}_2,& if& \left|\right|e_2\left|\right|>{\stackrel{\‾}{e}}_2\\ 0,& if& \left|\right|e_2\left|\right|\≤{\stackrel{\‾}{e}}_2\end{array}\right.,$

Wherein,For the constant of a very little, k_e2＞ 1, γ₂＞ 0, Δα₂=α₂-α₂₀；

4) adaptive law design：Design adaptive lawBy the indeterminate in model and outward Adaptive algorithm approximate evaluation is passed through in portion's disturbance,

Wherein γ_f,γ_σ＞ 0, ρ ∈ R⁺.

6. the asymmetric limited full driving surface vessel Trajectory Tracking Control method of input and output according to claim 1, It is characterized in that：System design of control law described in step 6, its method for designing is as follows：

1) reality output of executor and the error of desired output are calculated：

2) calculate z₃Derivative：Wherein Θ=diag (θ₁,θ₂,θ₃),Due to when The Θ becoming can bring extreme difficulties to design and analysis, introduces Nussbaum function battle array N=diag (N₁(χ₁),N₂(χ₂),N₃ (χ₃)),

3) design controlled quentity controlled variable φ：

Wherein k₃=diag (k₃₁,k₃₂,k₃₃), it is the symmetrical matrix of positive definite.