CN114265308A - Anti-saturation model-free preset performance track tracking control method for autonomous water surface vehicle - Google Patents

Anti-saturation model-free preset performance track tracking control method for autonomous water surface vehicle Download PDF

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CN114265308A
CN114265308A CN202111050133.6A CN202111050133A CN114265308A CN 114265308 A CN114265308 A CN 114265308A CN 202111050133 A CN202111050133 A CN 202111050133A CN 114265308 A CN114265308 A CN 114265308A
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CN114265308B (en
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黄兵
张恩华
张磊
毛磊
张传林
陈健桦
罗靖
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Harbin Engineering University
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Abstract

The invention discloses an anti-saturation model-free preset performance track tracking control method for an autonomous water surface vehicle, and belongs to the technical field of unmanned ship anti-interference control. The anti-saturation model-free preset performance track tracking control method of the autonomous water surface vehicle comprises the following steps: step one, establishing an unmanned ship dynamic model considering external interference; step two, establishing a saturation function model; designing an anti-saturation controller independent of model information; and step four, verifying the stability and robustness of the unmanned ship control system. The invention can realize saturation tracking control only by adjusting the preset performance parameters by designing the error conversion equation and the saturation function model, has simple structure and few design parameters, and has good applicability in the aspect of engineering.

Description

Anti-saturation model-free preset performance track tracking control method for autonomous water surface vehicle
Technical Field
The invention relates to an anti-saturation model-free preset performance track tracking control method for an autonomous water surface vehicle, and belongs to the technical field of unmanned ship anti-interference control.
Background
In recent decades, with the scarcity of land resources, marine resources have received attention from more and more scholars. In marine exploration, an unmanned ship can arrive and keep on a desired track within a specified time, a specified engineering task is completed, and the unmanned ship has excellent performance in tasks such as oil production, pipe laying and supply and the like by virtue of low cost and high efficiency, so that the tracking control problem of the unmanned ship is undoubtedly of high practical significance.
However, with the ever-increasing sophistication of work environments, the design of unmanned boat tracking control is becoming a challenge. Since drone tracking performance depends largely on control system interference rejection and stability, the design of high performance drone controllers still faces many challenges. On one hand, due to the complex operation environment and the high coupling and nonlinearity of the unmanned ship, an accurate model is difficult to obtain, and accurate tracking cannot be achieved. On the other hand, since a large control deviation and an estimated tracking error are often encountered during the task execution, it is difficult to effectively implement tracking control by the conventional adaptive control method and the like.
Disclosure of Invention
The invention aims to provide an anti-saturation model-free preset performance track tracking control method of an autonomous surface vehicle, which designs an unmanned ship anti-saturation tracking control method completely independent of model information by selecting a proper preset performance function under the condition of not needing on-line estimation of external interference so as to realize track tracking of the unmanned ship and solve the problems in the prior art.
An anti-saturation model-free preset performance track tracking control method of an autonomous water surface vehicle is characterized by comprising the following steps of:
step one, establishing an unmanned ship dynamic model considering external interference;
step two, establishing a saturation function model;
designing an anti-saturation controller independent of model information;
and step four, verifying the stability and robustness of the unmanned ship control system.
Further, in the step one, specifically:
the unmanned ship dynamics model established in the first step is as follows:
Figure BDA0003252433850000021
Figure BDA0003252433850000022
wherein eta is [ x, y, psi ═ x, y, psi]TRepresenting the position and the yaw angle of the unmanned ship under the geocentric coordinate system;
Figure BDA0003252433850000023
representing linear and angular velocities in a body coordinate system
Figure BDA0003252433850000024
Is the inertial matrix of the system;
Figure BDA0003252433850000025
is an unknown nonlinear function including hydrodynamic and model parameter perturbations;
Figure BDA0003252433850000026
representing the actual control force;
Figure BDA0003252433850000027
indicating a desired control input; r (ψ) is a coordinate transformation matrix defined as follows:
Figure BDA0003252433850000028
further, in the second step, specifically:
the following matrices and lemmas are defined:
R＝R(ψ),Rd＝R(ψd),
Figure BDA0003252433850000029
theorem 1 is introduced as follows:
for non-linear systems
Figure BDA00032524338500000210
Wherein
Figure BDA00032524338500000211
Figure BDA00032524338500000212
For a non-empty set, if f (t, x (t)) satisfies RippSitz continuity, it is found that there is a maximum solution for x (t) as follows:
Figure BDA00032524338500000213
theorem 2 is introduced as follows:
for continuous positive definite function V (x) if k is satisfied1||x||≤V(x)≤k2L x l, and
Figure BDA00032524338500000214
wherein
Figure BDA0003252433850000031
α, β are both positive numbers, then x (t) satisfies a semi-global uniform final bounding,
aiming at the singularity problem brought by a hard equation adopted by the traditional saturation control, the saturation control is realized by designing a smooth saturation function, and the definition is as follows:
Figure BDA0003252433850000032
Figure BDA0003252433850000033
in the formula of alphai＞0，β＞0，
Figure BDA0003252433850000034
In a limited interval approaching
Figure BDA0003252433850000035
And is positive,/i(beta), i is 1,2,3, the density function satisfies li(β)≥0，
By defining the controller
Figure BDA0003252433850000036
To obtain the following formula:
Figure BDA0003252433850000037
substituting the designed smooth saturation function to obtain:
Figure BDA0003252433850000038
by definition
Figure BDA0003252433850000039
The following conclusions were made:
Figure BDA00032524338500000310
namely, for the condition that the upper bound of the control input signal is known, the saturation control is realized by reasonably adjusting the parameters so as to avoid the occurrence of the singular condition.
Further, in step three, specifically:
establishing an unconstrained tracking error control function comprising:
the target tracking trajectory is defined as follows:
Figure BDA00032524338500000311
Figure BDA00032524338500000312
wherein etad＝[xd,yd,ψd]TIn order to be the target track,
Figure BDA00032524338500000313
in order to be able to set the desired motion parameters,
the tracking error is further defined as:
Figure BDA0003252433850000041
Figure BDA0003252433850000042
wherein
Figure BDA0003252433850000043
By definition E ═ RWRT，
Figure BDA0003252433850000044
The above formula is simplified as follows:
Figure BDA0003252433850000045
Figure BDA0003252433850000046
wherein E ═ RWRT，
Figure BDA0003252433850000047
As a known non-linearity parameter of the system,
Figure BDA0003252433850000048
representing an unknown disturbance outside, and being bounded,
designing an unconstrained error conversion equation as follows:
Figure BDA0003252433850000049
wherein mui＝ηe,i/ρi,i＝1,2,3，ηe＝[ηe,1,ηe,2,ηe,3]TIndicating tracking error, rho (t) ═ rho1(t),ρ2(t),ρ3(t)]TThe performance function representing the preset is defined as follows:
ρi(t)＝(ρ0,i-ρ∞,i)exp(-κit)+ρ∞,i,i＝1,2,3
in the formula, a preset parameter rho0,i＞|ηe,i(0)|，ρ∞,iIs a preset maximum value of the tracking error, κiThe convergence speed of the tracking error can be adjusted, the set parameters are positive numbers,
thus, an unconstrained error transfer function is derived
Figure BDA00032524338500000410
Is smooth and strictly increasing, and satisfies
Figure BDA00032524338500000411
And
Figure BDA00032524338500000412
further obtaining an inverse function of the error transformation function to obtain etaeAnd ω (μ) as follows:
Figure BDA0003252433850000051
wherein ω is-1(μi) Also satisfies the requirements of smoothness and strict increment and satisfies
Figure BDA00032524338500000510
And-1 < omega-1(μi)＜1，
Therefore, ω is predefined-1(μi) And obtaining that the tracking error meets the following properties:
Figure BDA0003252433850000052
the tracking error problem studied translates into ω (μ)i) Stability problem, design unconstrained error control equation as follows:
Figure BDA0003252433850000053
wherein K is diag { K ═ K1,K2,K3}，KiIf the tracking error is more than 0, the following equation is obtained by derivation:
Figure BDA0003252433850000054
Figure BDA0003252433850000055
by definition
Figure BDA0003252433850000056
And
Figure BDA0003252433850000057
the simplification is as follows:
Figure BDA0003252433850000058
wherein
Figure BDA0003252433850000059
And the controller is designed as follows:
Figure BDA0003252433850000061
where k is the strict positive control gain, Θ ═ diag { θ }1,θ2,θ3Is a matrix that can be designed by the user, and satisfies θi> 0, i-1, 2, 3.
Further, in step four, specifically:
to verify the stability and robustness of the unmanned boat control system, μ is definediThe time derivative of (a) is as follows:
Figure BDA0003252433850000062
Figure BDA0003252433850000063
satisfies the continuous and local integrability of Liphoz, and omega (mu)i) I is 1,2,3 is predetermined and is limited to Γiμ by introducing theorem 1 (═ 1,1)i(t) in the interval ΓiWithin a maximum value, i.e.
Figure BDA0003252433850000064
The Lyapunov function was chosen as follows:
Figure BDA0003252433850000065
the derivation can be:
Figure BDA0003252433850000066
due to ηd，
Figure BDA00032524338500000611
All satisfy [0, tmax) Bounded within the interval, thus giving
Figure BDA00032524338500000612
M-1And E is also bounded by the sum of,
by defining the following parameters:
Figure BDA0003252433850000067
Figure BDA0003252433850000068
Figure BDA0003252433850000069
Figure BDA00032524338500000610
wherein a isi,biI ═ 1,2,3 and qiWhere i is 1 and 2 are both positive numbers, substituting the derivative of the function of Helapunov, by defining sT(0) Thetas (0) < 1, eventually proving that the tracking error will converge to within the specified range.
The invention has the following beneficial effects: the invention can realize saturation tracking control only by adjusting the preset performance parameters by designing an error conversion equation and a saturation function model, has simple structure and few design parameters, and has good applicability in the aspect of engineering.
Drawings
FIG. 1 is a flow chart of an anti-saturation model-free default performance trajectory tracking control method of an autonomous surface vehicle of the present invention;
FIG. 2 is a saturated input model;
FIG. 3(a) is a two-dimensional plane tracking diagram, and FIGS. 3(b), 3(c) and 3(d) are forward, yaw and yaw velocity diagrams, respectively;
fig. 4(a), fig. 4(b) and fig. 4(c) are tracking errors of x, y and heading, and fig. 4(d), fig. 4(e) and fig. 4(f) are control moment diagrams of three directions of forward movement, rolling and heading respectively.
Detailed Description
The technical solutions in the embodiments of the present invention will be described clearly and completely with reference to the accompanying drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The invention is described in further detail below with reference to the accompanying drawings and the detailed description.
As shown in fig. 1, the limited time tracking control method for the under-actuated unmanned ship comprises the following steps:
firstly, establishing an unmanned ship dynamics model as follows:
Figure BDA0003252433850000081
Figure BDA0003252433850000082
where eta is [ x, y, psi [ ]]TRepresenting the position and the yaw angle of the unmanned ship under the geocentric coordinate system;
Figure BDA00032524338500000813
representing linear and angular velocities in a body coordinate system
Figure BDA0003252433850000083
Is the inertial matrix of the system;
Figure BDA0003252433850000084
is an unknown nonlinear function including hydrodynamic and model parameter perturbations;
Figure BDA00032524338500000814
representing the actual control force;
Figure BDA00032524338500000815
indicating a desired control input; r (ψ) is a coordinate transformation matrix defined as follows:
Figure BDA0003252433850000085
secondly, defining a saturation function:
for the convenience of subsequent derivation, we define the following matrices and lemmas:
R＝R(ψ),Rd＝R(ψd),
Figure RE-GDA0003514145640000082
theorem 1 is introduced as follows:
for non-linear systems
Figure RE-GDA0003514145640000083
x(0)∈ΩxWherein f (t, x (t)):
Figure RE-GDA0003514145640000084
for a non-empty set, if f (t, x (t)) satisfies RippSitz continuity, it can be concluded that there is a maximum solution for x (t) as follows:
Figure BDA00032524338500000810
theorem 2 is introduced as follows:
for continuous positive definite function V (x) if k is satisfied1||x||≤V(x)≤k2L x l, and
Figure RE-GDA0003514145640000086
wherein k is1,k2:
Figure RE-GDA0003514145640000087
And alpha and beta are positive numbers, x (t) satisfies the semi-global consistent final bounded.
Aiming at the singularity problem caused by a hard equation adopted by the traditional saturation control, the invention realizes the saturation control by designing a smooth saturation function, and the definition is as follows:
Figure BDA00032524338500000816
Figure BDA0003252433850000091
in the formula of alphai＞0，β＞0，
Figure BDA0003252433850000092
In a limited interval approaching
Figure BDA00032524338500000912
And is positive,/i(beta), i is 1,2,3, the density function satisfies li(β)≥0。
By defining the controller
Figure BDA00032524338500000913
The following formula can be obtained:
Figure BDA0003252433850000093
substituting the designed smooth saturation function can obtain:
Figure BDA0003252433850000094
by definition
Figure BDA0003252433850000095
The following conclusions can be drawn:
Figure BDA0003252433850000096
that is, for the case that the upper bound of the control input signal is known, the singular case can be avoided by reasonably adjusting the parameters to realize saturation control.
Thirdly, establishing an unconstrained tracking error control function, which comprises the following steps:
the target tracking trajectory is defined as follows:
Figure BDA0003252433850000097
Figure BDA0003252433850000098
wherein etad＝[xd,yd,ψd]TIn order to be the target track,
Figure BDA00032524338500000914
is the desired motion parameter.
The tracking error is further defined as:
Figure BDA0003252433850000099
Figure BDA00032524338500000910
wherein
Figure BDA00032524338500000911
By definition E ═ RWRT，
Figure BDA0003252433850000101
The above formula is simplified as follows:
Figure BDA0003252433850000102
Figure BDA0003252433850000103
wherein E ═ RWRT，
Figure BDA0003252433850000104
As a known non-linearity parameter of the system,
Figure BDA0003252433850000105
represents an unknown disturbance of the outside world and is bounded.
Establishing an unconstrained tracking error control function comprising:
designing an unconstrained error conversion equation as follows:
Figure BDA0003252433850000106
wherein mui＝ηe,i/ρi,i＝1,2,3，ηe＝[ηe,1,ηe,2,ηe,3]TIndicating tracking error, rho (t) ═ rho1(t),ρ2(t),ρ3(t)]TThe performance function representing the preset is defined as follows:
ρi(t)＝(ρ0,i-ρ∞,i)exp(-κit)+ρ∞,i,i＝1,2,3
in the formula, a preset parameter rho0,i＞|ηe,i(0)|，ρ∞,iIs a preset maximum value of the tracking error, κiThe convergence speed of the tracking error can be adjusted, and the set parameters are positive numbers.
Therefore we can derive an unconstrained error transfer function
Figure BDA0003252433850000108
Is smooth and strictly increasing, and meets
Figure BDA0003252433850000109
And
Figure BDA00032524338500001010
further obtaining an inverse function of the error transformation function to obtain etaeAnd ω (μ) are as follows:
Figure BDA0003252433850000107
wherein ω is-1(μi) Also satisfies the requirements of smoothness and strict increment and satisfies
Figure BDA00032524338500001011
And-1 < omega-1(μi)＜1。
Therefore, only ω is predefined-1(μi) We can conclude that the tracking error satisfies the following property:
Figure BDA0003252433850000111
the tracking error problem studied thus translates into ω (μ)i) Stability issues, and therefore design an unconstrained error control equation, as follows:
Figure BDA0003252433850000112
wherein K is diag { K ═ K1,K2,K3}，KiIf the tracking error is more than 0, the following equation is obtained by derivation:
Figure BDA0003252433850000113
Figure BDA0003252433850000114
by definition
Figure BDA0003252433850000115
And
Figure BDA0003252433850000116
the simplification is as follows:
Figure BDA0003252433850000117
wherein
Figure BDA0003252433850000118
And the controller is designed as follows:
Figure BDA0003252433850000119
where k is the strict positive control gain, Θ ═ diag { θ }1,θ2,θ3Is a matrix that can be designed by the user, and satisfies θi＞0,i＝1,2,3。
Fourthly, defining mu in order to verify the stability and robustness of the unmanned boat control systemiThe time derivative of (a) is as follows:
Figure BDA0003252433850000121
it can be known that
Figure BDA0003252433850000129
Satisfies the continuous and local integrability of Liphoz, and omega (mu)i) I is 1,2,3 is predetermined and is limited to ΓiBy lemma 1, we derive μi(t) in the interval ΓiWithin a maximum value, i.e.
Figure BDA00032524338500001210
The Lyapunov function was chosen as follows:
Figure BDA0003252433850000122
the derivation can be:
Figure BDA0003252433850000123
due to ηd，
Figure BDA0003252433850000124
All satisfy [0, tmax) Bounded within the interval, and thus can be derived
Figure BDA00032524338500001211
M-1And E is also bounded.
By defining the following parameters:
Figure BDA0003252433850000125
Figure BDA0003252433850000126
Figure BDA0003252433850000127
Figure BDA0003252433850000128
wherein a isi,biI ═ 1,2,3 and qiWhere i is 1 and 2 are both positive numbers, substituting the derivative of the function of Helapunov, by defining sT(0) Thetas (0) < 1, eventually proving that the tracking error will converge to within the specified range.
The performance of the above controller is then demonstrated and verified by a simulation example.
The control parameters and constraint boundaries are shown in table 1:
Figure BDA0003252433850000131
TABLE 1
The desired trajectory is defined as follows:
fd,1(t)＝0.01cos(0.015πt)
fd,2(t)＝-0.05sin(0.1πt)
fd,3(t)＝0.01cos(0.02πt)
wherein eta isd＝[0,0,0]T，
Figure BDA0003252433850000132
The initial state vector is defined as:
η(0)＝[-0.4,0.5,π/18]T，
Figure BDA0003252433850000133
by defining model perturbations and external perturbations as follows:
Figure 1
Figure BDA0003252433850000135
to model a more realistic external perturbation, a second order Gaussian-Markov process is designed as follows:
Figure BDA0003252433850000136
Figure BDA0003252433850000137
τd＝z1
wherein
Figure BDA0003252433850000138
And Ω, diag {100,100,100} are positive definite matrices.
The detailed simulation results are shown in fig. 2-4. These results demonstrate that the proposed controller is able to guarantee the desired performance index and has good disturbance resistance and robustness.
The above embodiments are only for assisting understanding of the method of the present invention and the core idea thereof, and a person skilled in the art may make several modifications and decorations on the specific embodiments and application scope according to the idea of the present invention, and these modifications and decorations should also be regarded as the protection scope of the present invention.

Claims (5)

1. An anti-saturation model-free preset performance track tracking control method of an autonomous water surface vehicle is characterized by comprising the following steps of:
step one, establishing an unmanned ship dynamic model considering external interference;
step two, establishing a saturation function model;
designing an anti-saturation controller independent of model information;
and step four, verifying the stability and robustness of the unmanned ship control system.
2. The anti-saturation model-free preset performance trajectory tracking control method for the autonomous surface vehicle according to claim 1, characterized in that in step one, specifically:
the model of the unmanned ship dynamics established in step one is as follows:
Figure FDA0003252433840000011
Figure FDA0003252433840000012
wherein eta is [ x, y, psi ═ x, y, psi]TRepresenting the position and the yaw angle of the unmanned ship under the geocentric coordinate system; theta ═ u, v, r]TRepresenting linear and angular velocities in a body coordinate system
Figure FDA0003252433840000013
Is the inertial matrix of the system;
Figure FDA0003252433840000014
is an unknown nonlinear function including hydrodynamic and model parameter perturbations; t (tau)θ)＝[T(τθ,1),T(τθ,1),T(τθ,1)]TRepresenting the actual control force; tau isθIndicating a desired control input; r (ψ) is a coordinate transformation matrix defined as follows:
Figure FDA0003252433840000015
3. the anti-saturation model-free preset performance trajectory tracking control method of the autonomous surface vehicle according to claim 1, characterized in that in step two, specifically:
the following matrices and lemmas are defined:
Figure FDA0003252433840000016
theorem 1 is introduced as follows:
for non-linear systems
Figure FDA0003252433840000021
Wherein
Figure FDA00032524338400000213
For a non-empty set, if f (t, x (t)) satisfies RipHitz continuity, it is found that there is a maximum solution for x (t) as follows:
Figure FDA0003252433840000024
theorem 2 is introduced as follows:
for continuous positive definite function V (x) if k is satisfied1||x||≤V(x)≤k2L x l, and
Figure FDA0003252433840000025
wherein
Figure FDA0003252433840000026
α, β are both positive numbers, then x (t) satisfies a semi-global uniform final bounding,
aiming at the singularity problem brought by a hard equation adopted by the traditional saturation control, the saturation control is realized by designing a smooth saturation function, and the definition is as follows:
T(τθ,i)＝ciτθ,i-di,i＝1,2,3
Figure FDA0003252433840000027
in the formula of alphai＞0，β＞0，
Figure FDA0003252433840000028
Approaches to tau in a finite intervalθ,maxiI is 1,2,3 and is positive, li(beta), i is 1,2,3, the density function satisfies li(β)≥0，
By defining the controller z (τ)θ,i,β)＝max(τθ,i-β,min(0,τθ,i+ β)) gives the formula:
Figure FDA0003252433840000029
substituting the designed smooth saturation function to obtain:
Figure FDA00032524338400000210
by definition
Figure FDA00032524338400000211
The following conclusions were made:
Figure FDA00032524338400000212
namely, for the condition that the upper bound of the control input signal is known, the saturation control is realized by reasonably adjusting the parameters so as to avoid the occurrence of the singular condition.
4. The anti-saturation model-free preset performance trajectory tracking control method of the autonomous surface vehicle according to claim 1, characterized in that in step three, specifically:
establishing an unconstrained tracking error control function comprising:
the target tracking trajectory is defined as follows:
Figure FDA0003252433840000031
Figure FDA0003252433840000032
wherein etad＝[xd,yd,ψd]TIs a target track, θd＝[ud,vd,rd]TIn order to be able to set the desired motion parameters,
the tracking error is further defined as:
Figure FDA0003252433840000033
Figure FDA0003252433840000034
wherein theta ise＝R(ψ)θ-R(ψd)θd，
Figure FDA0003252433840000035
By definition E ═ RWRT，
Figure FDA0003252433840000036
The above formula is simplified as follows:
Figure FDA0003252433840000037
Figure FDA0003252433840000038
wherein E ═ RWRT，
Figure FDA0003252433840000039
As a known non-linearity parameter of the system,
Figure FDA00032524338400000310
representing an unknown disturbance outside, and being bounded,
designing an unconstrained error conversion equation as follows:
Figure FDA00032524338400000311
wherein mui＝ηe,i/ρi,i＝1,2,3，ηe＝[ηe,1,ηe,2,ηe,3]TIndicating tracking error, rho (t) ═ rho1(t),ρ2(t),ρ3(t)]TThe representative preset performance function is defined as follows:
ρi(t)＝(ρ0,i-ρ∞,i)exp(-κit)+ρ∞,i,i＝1,2,3
in the formula, a preset parameter rho0,i＞|ηe,i(0)|，ρ∞,iIs a preset maximum value of the tracking error, κiThe convergence rate of the tracking error can be adjusted, the set parameters are positive numbers,
thus, an unconstrained error transfer function is derived
Figure FDA0003252433840000041
Is smooth and strictly increasing, and satisfies
Figure FDA0003252433840000042
And
Figure FDA0003252433840000043
further obtaining an inverse function of the error transformation function to obtain etaeAnd ω (μ) as follows:
Figure FDA0003252433840000044
wherein ω is-1(μi) Also satisfies the requirements of smoothness and strict increment and satisfies
Figure FDA0003252433840000045
And-1 < omega-1(μi)＜1，
Therefore, ω is predefined-1(μi) And obtaining that the tracking error meets the following properties:
Figure FDA0003252433840000046
the tracking error problem studied translates into ω (μ)i) Stability problem, design unconstrained error control equation as follows:
Figure FDA0003252433840000047
wherein K is diag { K ═ K1,K2,K3}，KiIf the tracking error is more than 0, the following equation is obtained by derivation:
Figure FDA0003252433840000048
Figure FDA00032524338400000411
by definition
Figure FDA0003252433840000049
And
Figure FDA00032524338400000410
the simplification is as follows:
Figure FDA0003252433840000051
wherein
Figure FDA0003252433840000052
And the controller is designed as follows:
Figure FDA0003252433840000053
where k is the strict positive control gain, Θ ═ diag { θ }1,θ2,θ3Is a matrix that can be designed by the user, and satisfies θi> 0, i-1, 2, 3.
5. The anti-saturation model-free preset performance trajectory tracking control method of the autonomous surface vehicle according to claim 1, characterized in that in step four, specifically:
to verify the stability and robustness of the unmanned boat control system, μ is definediThe time derivative of (a) is as follows:
Figure FDA0003252433840000054
Figure FDA0003252433840000055
satisfies the continuous and local integrability of Liphoz, and omega (mu)i) I is 1,2,3 is predetermined and is limited to Γiμ by introducing theorem 1 (═ 1,1)i(t) in the interval ΓiWithin a maximum value, i.e.
Figure FDA0003252433840000056
The Lyapunov function was chosen as follows:
Figure FDA0003252433840000057
the derivation can be:
Figure FDA0003252433840000058
due to ηd，θdAll satisfy [0, tmax) Bounded within the interval, thus giving
Figure FDA0003252433840000059
M-1And E is also bounded by the sum of,
by defining the following parameters:
Figure FDA0003252433840000061
Figure FDA0003252433840000062
Figure FDA0003252433840000063
Figure FDA0003252433840000064
wherein a isi,biI ═ 1,2,3 and qiWhere i is 1 and 2 are both positive numbers, substituting the derivative of the function of Helapunov, by defining sT(0) Thetas (0) < 1, eventually proving that the tracking error will converge to within the specified range.
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