CN114706298B - USV robust model-free track tracking controller design method based on preset performance - Google Patents

Abstract

The invention discloses a design method of a USV robust model-free track tracking controller based on preset performance, and belongs to the field of automatic control of intelligent bodies. The method comprises the following steps: step one, establishing a kinematic and dynamic model of the unmanned surface vehicle; step two, defining kinematic and dynamic errors according to the kinematic and dynamic models of the unmanned surface vehicle and forming a tracking error dynamic model; step three, designing a conversion function; step four, selecting an error conversion formula; step five, based on the design of the step three and the step four, establishing an error matrix definition and an unconstrained dynamics system; and step six, designing a model-free controller. The invention can avoid the reduction of the required calculation load caused by the self-adaptive law calculation process in the existing research, ensures the transient and steady state behaviors of ideal tracking errors by adjusting the parameters of the preset performance matrix, and finally realizes the design of the USV track tracking controller.

Description

USV robust model-free track tracking controller design method based on preset performance

Technical Field

The invention relates to a design method of a USV robust model-free track tracking controller based on preset performance, and belongs to the field of automatic control of intelligent bodies.

Background

Over the past few decades, unmanned Surface Vessels (USV) have been attracting academic research interest due to their wide marine application prospects, such as inspection, surveillance, and marine research. For these application scenarios described above, although the mission scenario is set to a severe marine environment, it is generally desirable for the USV to perform satisfactory trajectory tracking control. Therefore, the problem of anti-interference track tracking control naturally becomes a research hot spot. To solve this problem, related researchers have used several advanced control design tools including Sliding Model Control (SMC), back-step control (BP) and model predictive control. Notably, model-dependent techniques account for a significant portion of the effort, and the requirements of accurate model parameters and complex control systems limit the practical application of these approaches.

To eliminate the dependency of the model parameters, approximator-based methods such as Neural Networks (NNs) and fuzzy control strategies are employed on the one hand. In particular, the combination of neural networks and fuzzy systems can improve the approximation accuracy of the system nonlinearity. With Minimum Learning Parameters (MLP), the computational burden of huge neural network weights can be reduced. Another similar control algorithm based on MLP neural networks has also been proposed to solve the problem of co-formation control. On the other hand, data-driven control schemes have also been a control method that affects profound. It is worth noting that continuous PID based controllers were successfully used for fully driven and underactuated marine unmanned aerial vehicles, respectively.

In addition to system uncertainty and ocean disturbances, preset control performance has recently attracted considerable research attention from the control community. While ensuring transient and steady state performance of the system output response is critical to safely completing offshore tasks. However, due to its engineering characteristics, it is difficult to theoretically build a formula for transient performance (i.e., convergence speed and overshoot) during the design of the relevant controller. In view of this challenge, bechlioulis and rovihake creatively visualize prescribed performance as tracking error constraints through prescribed performance functions, and then convert "constrained" systems to equivalent "unconstrained" systems through error conversion methods. Later, such control frames were widely used in various fields, such as spacecraft, drones and drones. A specified performance fault-tolerant control scheme is designed through a backstepping technology and an adaptive law of an area tracking task. Considering that input saturation may lead to serious degradation in control performance, researchers have introduced auxiliary dynamic systems into the study to address the impact of input amplitude and rate constraints. The stability of the member variables of the above scheme is theoretically guaranteed by applying infinite time. This means that the constraint state asymptotically converges to its equilibrium in an infinite time. With high real-time tasks, such convergence speeds may not be suitable. Therefore, a non-singular terminal sliding mode technique is employed to achieve limited time convergence with faster convergence speed. While the methods in the prior art all succeed in ensuring that a particular system signal evolves within a time-varying preselected region, prior confirmation of model parameters is required for deployment of these control schemes.

Based on the above discussion, a model-free parameter control algorithm meeting specified performance indicators is proposed to achieve the trajectory tracking task of the MSV.

Disclosure of Invention

The invention aims to provide a design method of a USV robust model-free track tracking controller based on preset performance, which can avoid the reduction of required calculation load caused by the self-adaptive law calculation process in the existing research, ensure the transient and steady state behaviors of ideal tracking errors by adjusting the parameters of a preset performance matrix, finally realize the design of the USV track tracking controller and solve the problem that external interference and parameter disturbance cannot be accurately modeled in the USV control theory research.

The design method of the USV robust model-free track tracking controller based on the preset performance comprises the following steps of:

step one, establishing a kinematic and dynamic model of the unmanned surface vehicle;

step two, defining kinematic and dynamic errors according to the kinematic and dynamic models of the unmanned surface vehicle and forming a tracking error dynamic model;

step three, designing a conversion function;

step four, selecting an error conversion formula;

step five, based on the design of the step three and the step four, establishing an error matrix definition and an unconstrained dynamics system;

and step six, designing a model-free controller.

Further, in the first step, specifically, a kinematic and dynamic model of the unmanned surface vessel is established, as follows:

wherein ,τ＝τ_v Is the actual control vector;is an unknown nonlinear function consisting of hydrodynamic, model parameter perturbation, and the proposed control algorithm is completely model parameter independent, so the term M given in equation (2) will not be considered as a controller parameter, generating the desired trajectory as follows:

wherein ,η_d ＝[x _d ,y _d ,ψ _d ] ^T and υ_d ＝[u _d ,v _d ,r _d ] ^T Is a desired kinematic and kinetic signal; f (f) _d (t)＝[f _d,1 (t),f _d,2 (t),f _d,3 (t)] ^T Providing the required kinetic vector.

Further, in the second step, specifically,

kinematic errors are defined and expressed as:

η _e ＝η-η _d (4)

the kinetic error is expressed as:

υ _e ＝J(ψ)υ-J(ψ _d )υ _d (5)

thus, the tracking error dynamics model is derived as:

wherein j=j (ψ), J _d ＝J(ψ _d )，S＝S(r)，S _d ＝S(r _d ) The method is a simple writing method; λ=jsj ^T F= (λj) _d -J _d S _d )υ _d -J _d f _d All are known nonlinear functions, and related variables are obtained from the on-board sensor; d=jm ^-1 f (t, v) is an unknown function representing the lumped uncertainty.

Further, in step three, specifically,

to give error eta _e Conversion error μ= [ μ ] with a priori guaranteed evolution region ₁ ,μ ₂ ,μ ₃ ] ^T Is designed as follows:

μ＝diag ^-1 (ρ)η _e (7)

wherein ρ= [ ρ ] ₁ ,ρ ₂ ,ρ ₃ ] ^T Representing a preset performance function vector, and expressing elements in the vector as rho _i ＝(ρ _0,i -ρ _∞,i )exp(-κ _i t)+ρ _∞,i I=1, 2,3, where ρ ₀ Is the initial value of ρ (t); ρ _∞ The maximum allowable value of the tracking error is selected according to task requirements; kappa is the convergence rate of the preset performance function for a vector x= [ x ] ₁ ,x ₂ ,x ₃ ] ^T In terms of this, the symbol diag (x) is defined as diag { x } ₁ ,x ₂ ,x ₃ }，

By selecting appropriate design parameters ρ _0,i ,ρ _∞,i and κ_i To characterize the tracking error eta of demand _e In both transient and steady state conditions.

Further, in step four, specifically,

the following error conversion formula is designed to convert the constrained error into an equivalent unconstrained error:

wherein ,expressed as a compact vector of transformation functions, and more particularly,is composed of->Given.

Further, in step five, specifically,

based on the designs of step three and step four, an error matrix is defined as follows:

where k=diag { K ₁ ,K ₂ ,K ₃ Is a matrix of design parameters in which the elements satisfy K _i Differentiating the above expression and substituting the expression into the expression (8) to obtain a dynamic expression of the unconstrained error system, wherein the dynamic expression is larger than 0:

wherein, in the last step of the above formula, for convenience, the following symbols are defined: and λ _ij ,F _i ,D _i ,(JM ^-1 ) _ij τ _υ,i Are elements of the ith row and the jth column of a given corresponding matrix,

the equivalent overwrite of formula (10) is as follows:

wherein ,

as long as eta _e,i I=1, 2,3 is strictly in the region- ρ _i (t)＜η _e,i ＜ρ _i (t) inner evolution, thenEnd-to-end remains bounded and, furthermore, once ω _i (t) at |eta _e,i (0)|＜ρ _0,i Is bounded on the premise that a conclusion is obtained:is composed of->Defined by the properties of (a) and, in addition, review ω _i The limit of (t) is a direct result of the limit of s (t), and thus the control objective is expressed as a problem of stabilizing the error dynamic system formula (10).

Further, in step six, specifically,

in order to guarantee the stability of s (t), the following model-free controller is proposed:

where β is the strictly positive control gain; Θ=diag { θ ₁ ,θ ₂ ,θ ₃ Is a user-defined matrix and has θ _i ＞0,i＝1,2,3，

By adjusting beta, K to adjust the control performance within a predetermined range,

the design parameters theta are selected to ensure that s (0) theta s (0) < 1 is true, is a sufficient condition for the stability of the resulting closed-loop control system,

thus, the architecture of the model-free trajectory tracking controller as shown in equation (12) is compact and is easy to implement because there are no model parameters, where the terms (1-s ^T Θs) ^-1 And Θs are used to ensure that the novel error system as shown in equation (11) is eventually consistent asymptotically stable in the presence of external disturbances,

itemsIs embedded in the formula (9), tracking error eta _e,i The steering is predetermined to be ρ _∞,i Is near zero and has a predetermined minimum convergence rate exp (- κ) _i t) exhibits a maximum preset overshoot ρ _0,i 。

The invention has the following beneficial effects:

1) By means of sliding mode technology, a robust non-parameter model control scheme is proposed. Since the calculation process of the adaptive law is not needed, compared with an algorithm based on online estimation, the control scheme provided by the invention has less calculation burden.

2) In other model-free control methods of USV, it is difficult to ensure that the transient and steady state behavior of the tracking error is ideal. In contrast, the control scheme proposed by the present invention is developed with a preset performance matrix, so that the desired transient and steady state performance can be obtained by adjusting the parameters.

3) The control scheme proposed by the present invention is very user/designer friendly due to its simple architecture and few parameters.

Drawings

Fig. 1 is a time response of a closed loop system signal at different K values, where β=400;

FIG. 2 is a time response of a closed loop system signal at different beta values, where K=diag ([ 1;1 ]);

FIG. 3 is a graph of USV track tracking position under different conditions;

FIG. 4 is a graph of USV longitudinal speed versus time for different conditions;

FIG. 5 is a graph of USV lateral velocity time response for different conditions;

FIG. 6 is a graph of USV yaw rate versus time for different conditions;

FIG. 7 is a graph of USV longitudinal position error time response for different conditions;

FIG. 8 is a graph of USV lateral position error time response for different conditions;

FIG. 9 is a graph of USV heading angle position error time response under different conditions;

FIG. 10 is a graph of USV longitudinal control signal time response for different conditions;

FIG. 11 is a graph showing the time response of the USV lateral control signal under different conditions;

FIG. 12 is a graph showing the time response of the USV yaw control signal under different conditions;

fig. 13 is a flowchart of a design method of a USV robust model-free trajectory tracking controller based on preset performance.

Detailed Description

The following description of the embodiments of the present invention will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.

The invention aims to solve the problem that external interference and parameter disturbance cannot be accurately modeled in USV control theory research, provides a USV track tracking controller design method based on a preset performance control technology and a robust non-parameter model technology, can avoid the reduction of required calculation load caused by a self-adaptive law calculation process in the existing research, can ensure ideal transient and steady state behaviors of tracking errors by adjusting parameters of a preset performance matrix, and can finally realize the design of a USV track tracking controller.

Referring to fig. 13, the object of the present invention is achieved by:

the first step, a kinematic and dynamic model of the unmanned surface vessel is established, as follows:

wherein ,τ＝τ_v Is the actual control vector;is an unknown nonlinear function and consists of fluid dynamics, model parameter perturbation and the like. Notably, the proposed control algorithm is entirely model parameter independent, and therefore the term M given in (2) will not be considered as a controller parameter, generating the required trajectory as follows:

wherein ,η_d ＝[x _d ,y _d ,ψ _d ] ^T and υ_d ＝[u _d ,v _d ,r _d ] ^T Is a desired kinematic and kinetic signal; f (f) _d (t)＝[f _d,1 (t),f _d,2 (t),f _d,3 (t)] ^T Providing the required kinetic vector.

A second step of defining kinematics, dynamics errors and forming a tracking error dynamics model,

kinematic errors are defined and expressed as:

η _e ＝η-η _d (4)

the kinetic error is expressed as:

υ _e ＝J(ψ)υ-J(ψ _d )υ _d (5)

thus, the tracking error dynamics model is derived as:

wherein j=j (ψ), J _d ＝J(ψ _d )，S＝S(r)，S _d ＝S(r _d ) The method is a simple writing method; λ=jsj ^T F= (λj) _d -J _d S _d )υ _d -J _d f _d All are known nonlinear functions, and related variables can be obtained from the on-board sensor; d=jm ^-1 f (t, v) is an unknown function representing the lumped uncertainty.

Third step, design of conversion function

To give error eta _e Conversion error μ= [ μ ] with a priori guaranteed evolution region ₁ ,μ ₂ ,μ ₃ ] ^T Is designed as follows:

μ＝diag ^-1 (ρ)η _e (7)

wherein ρ= [ ρ ] ₁ ,ρ ₂ ,ρ ₃ ] ^T Representing a preset performance function vector, and expressing elements in the vector as rho _i ＝(ρ _0,i -ρ _∞,i )exp(-κ _i t)+ρ _∞,i I=1, 2,3, where ρ ₀ Is the initial value of ρ (t); ρ _∞ For the maximum allowable value of the tracking error, the selection of the value is dependent on task requirements; kappa is the convergence rate of the preset performance function. For a vector x= [ x ] ₁ ,x ₂ ,x ₃ ] ^T In terms of this, the symbol diag (x) is defined as diag { x } ₁ ,x ₂ ,x ₃ }。

The design of the conversion error (7) is such that we can choose the appropriate design parameter ρ _0,i ,ρ _∞,i and κ_i To characterize the tracking error eta of demand _e In both transient and steady state conditions.

Fourth, the error conversion formula is selected

For the design of the third step, mu is present for any t > 0 _i Should be constrained to intervalsThe design of the transfer function therefore increases the difficulty of the controller design to some extent. The following error conversion formula is designed to convert the constrained error into an equivalent unconstrained error:

wherein ,expressed as a compact vector of transformation functions, and more particularly,is composed of->Given.

Fifth step, error matrix definition and unconstrained dynamic system establishment

Based on the designs of step three and step four, an error matrix is defined as follows:

where k=diag { K ₁ ,K ₂ ,K ₃ Is a matrix of design parameters in which the elements satisfy K _i Differentiating the above expression and substituting the expression into the expression (8) to obtain a dynamic expression of the unconstrained error system, wherein the dynamic expression is larger than 0:

wherein, in the last step of the above formula, for convenience, the following symbols are defined: and λ _ij ,F _i ,D _i ,(JM ^-1 ) _ij τ _υ,i Are elements of the ith row and the jth column of a given corresponding matrix,

to facilitate the subsequent design of model-free controllers and the analysis of the stability of the resulting closed-loop system, (10) can be equivalently rewritten in a compact form as follows:

wherein ,

notably, as long as η _e,i I=1, 2,3 is strictly in the region- ρ _i (t)＜η _e,i ＜ρ _i (t) inner evolution, thenShould remain bounded all the time. Furthermore, once ω _i (t) at |eta _e,i (0)|＜ρ _0,i On the premise of being bounded, we can conclude that: />Is composed of->Defined by the properties of (a). And have a review of omega _i The limit of (t) is a direct result of the limit of s (t), and thus, the control objective can be expressed as a problem of stabilizing the error dynamics system (10).

Sixth step, model-free controller design

In order to guarantee the stability of s (t), the present chapter proposes a model-free controller as follows:

where β is the strictly positive control gain; Θ=diag { θ ₁ ,θ ₂ ,θ ₃ Is a user-defined matrix and has θ _i ＞0,i＝1,2,3。

It is noted that the control performance can be adjusted within a predetermined range by adjusting β, K as shown in fig. 1 and fig. 2.

The specific analysis is as follows: a larger K will result in a larger control input signal, a slower convergence speed and a higher control accuracy, while a larger β will result in a better performance of the closed loop control system, but at the same time a larger demand for control input. The design parameters Θ are chosen to ensure that s (0) Θs (0) < 1 holds, which is a sufficient condition for the stability of the resulting closed loop control system.

Based on the above description and analysis, it can be appreciated that the architecture of the model-free trajectory tracking controller as shown in equation (12) is compact and easy to implement because there are no model parameters. Wherein items (1-s ^T Θs) ^-1 And Θs are used to ensure that the new error system as shown in equation (11) is eventually consistent asymptotically stable in the presence of external disturbances.

In order for the proposed control scheme to have preset performance, the termIs embedded in equation (9), thus, tracking error η _e,i The steering is predetermined to be ρ _∞,i Is near zero and has a predetermined minimum convergence rate exp (- κ) _i t) exhibits a maximum preset overshoot ρ _0,i 。

The invention is described in further detail below with reference to the drawings and the detailed description.

The first step, a kinematic and dynamic model of the unmanned surface vessel is established, as follows:

wherein ,τ＝τ_v Is the actual control vector;is an unknown nonlinear function and consists of fluid dynamics, model parameter perturbation and the like. It is worth noting that the proposed control algorithm is completely model parameter independent, and therefore the term M given in (2) will not be considered as a controller parameter. It is worth noting that the dynamic parameter settings of the USV are not available for the proposed control scheme of the present invention, since the proposed control scheme introduces a model-free parameter design approach.

The required trajectory is generated as follows:

wherein ,η_d ＝[0,0,0] ^T and υ_d ＝[1,0,0] ^T The kinetic vector is expressed as follows:

second, defining kinematics and dynamics error and forming tracking error dynamics model

Kinematic errors are defined and expressed as:

η _e ＝η-η _d (5)

the kinetic error is expressed as:

υ _e ＝J(ψ)υ-J(ψ _d )υ _d (6)

thus, the tracking error dynamics model is derived as:

wherein j=j (ψ), J _d ＝J(ψ _d )，S＝S(r)，S _d ＝S(r _d ) The method is a simple writing method; λ=jsj ^T F= (λj) _d -J _d S _d )υ _d -J _d f _d All are known nonlinear functions, and related variables can be obtained from the on-board sensor; d=jm ^-1 f (t, v) is an unknown function representing the lumped uncertainty.

Third step, design of conversion function

To give error eta _e Conversion error μ= [ μ ] with a priori guaranteed evolution region ₁ ,μ ₂ ,μ ₃ ] ^T Is designed as follows:

μ＝diag ^-1 (ρ)η _e (8)

wherein ρ= [ ρ ] ₁ ,ρ ₂ ,ρ ₃ ] ^T Representing a preset performance function vector, and expressing elements in the vector as rho ₁ (t)＝ρ ₂ (t)＝0.9exp(-0.15t)+0.1，ρ ₃ (t)＝0.26exp(-0.15t)+0.09。

The design of the conversion error (8) is such that we can choose the appropriate design parameter ρ _0,i ,ρ _∞,i and κ_i To characterize the tracking error eta of demand _e In both transient and steady state conditions.

Fourth, the error conversion formula is selected

For the design of the third step, mu is present for any t > 0 _i Should be constrained to intervalsThe design of the transfer function therefore increases the difficulty of the controller design to some extent. The following error conversion formula is designed to convert the constrained error into an equivalent unconstrained error:

wherein ,expressed as a compact vector of transformation functions, and more particularly,is composed of->Given.

Fifth step, error matrix definition and unconstrained dynamic system establishment

Based on the design of the third and fourth steps, an error matrix is defined as follows:

wherein K=diag {1.05,1.05,0.65} is a design parameter matrix, and the elements therein satisfy K _i > 0. Differentiating the above formula and substituting the formula (9) to obtain a dynamic expression of the unconstrained error system:

wherein, in the last step of the above formula, for convenience, the following symbols are defined: and λ _ij ,F _i ,D _i ,(JM ^-1 ) _ij τ _υ,i Are elements of the j-th column (i-th row) of the given corresponding matrix.

To facilitate the subsequent design of model-free controllers and the analysis of the stability of the resulting closed-loop system, (10) can be equivalently rewritten in a compact form as follows:

wherein ,

notably, as long as η _e,i I=1, 2,3 is strictly in the region- ρ _i (t)＜η _e,i ＜ρ _i (t) inner evolution, thenShould remain bounded all the time. Furthermore, once ω _i (t) at |eta _e,i (0)|＜ρ _0,i On the premise of being bounded, we can conclude that: />Is composed of->Defined by the properties of (a). And have a review of omega _i The limit of (t) is a direct result of the limit of s (t), and thus, the control objective can be expressed as a problem of stabilizing the error dynamics system (10).

Sixth step, model-free controller design

In order to guarantee the stability of s (t), the present chapter proposes a model-free controller as follows:

where β=400 is a strictly positive control gain; Θ = diag {0.9,0.9,0.9}.

The initial conditions of USV were chosen to be η= [ -0.4, -0.5, pi/18] ^T And v= [0.8, -0.1,0.05 ]] ^T . Setting different external interference conditionsIn the case of a comparative test, two working conditions (Scenario I and Scenario II) are considered to prove the robustness of the controller proposed in this chapter to the model disturbance and external disturbance.

Scenario I (condition 1): model perturbation g and external disturbance are obtained by referring to the relevant literatureThe method comprises the following steps:

scenario II (condition 2): the perturbation of the model is the same as in Scenario I. To more actually simulate external disturbances, a second order Gaussian-Markov process is deployed as follows:

wherein A=diag {3, 3}, B=diag {1, 1} and C=diag {100,100,100} are positive definite matrices,is zero-mean gaussian white noise.

As can be seen from fig. 3 to 6, the controller designed by the present invention can successfully track the required track in terms of kinematics and dynamics, and has ideal control tracking performance.

Fig. 7 to 9 depict the position error and the corresponding performance envelope. Obviously, the proposed controller can guarantee the desired performance index and is further satisfactorily robust against disturbances and uncertainties.

Fig. 10 to 12 show the time response of the control input signal. As we see, the proposed control scheme generates different driving forces (torques) in response to different external disturbances.

Analysis in connection with fig. 3 to 12 makes it possible to conclude that the interference has less influence on the closed-loop system of the proposed controller of the base Yu Benzhang, which means that the interference cancellation effect of the proposed controller is satisfactory.

The above embodiments are only for aiding in understanding the method of the present invention and its core idea, and those skilled in the art can make several improvements and modifications in the specific embodiments and application scope according to the idea of the present invention, and these improvements and modifications should also be considered as the protection scope of the present invention.

Claims (3)

1. The USV robust model-free track tracking controller design method based on the preset performance is characterized by comprising the following steps of:

step one, establishing a kinematic and dynamic model of the unmanned surface vehicle;

step two, defining kinematic and dynamic errors according to the kinematic and dynamic models of the unmanned surface vehicle and forming a tracking error dynamic model;

step three, designing a conversion function;

step four, selecting an error conversion formula;

step five, based on the design of the step three and the step four, establishing an error matrix definition and an unconstrained dynamics system;

step six, designing a model-free controller,

in the third step, the first step, in particular,

to give error eta _e Conversion error μ= [ μ ] with a priori guaranteed evolution region ₁ ,μ ₂ ,μ ₃ ] ^T Is designed as follows:

μ＝diag ^-1 (ρ)η _e (7)

wherein ρ= [ ρ ] ₁ ,ρ ₂ ,ρ ₃ ] ^T Representing a preset performance function vector, and expressing elements in the vector as rho _i ＝(ρ _0,i -ρ _∞,i )exp(-κ _i t)+ρ _∞,i I=1, 2,3, where ρ ₀ Is the initial value of ρ (t); ρ _∞ The maximum allowable value of the tracking error is selected according to task requirements; kappa is the convergence rate of the preset performance function for a vector x= [ x ] ₁ ,x ₂ ,x ₃ ] ^T In terms of this, the symbol diag (x) is defined as diag { x } ₁ ,x ₂ ,x ₃ }，

By selecting appropriate design parameters ρ _0,i ,ρ _∞,i and κ_i To characterize the tracking error eta of demand _e In transient and steady state conditions;

in step four, the process is performed, in particular,

the following error conversion formula is designed to convert the constrained error into an equivalent unconstrained error:

wherein ,expressed as a compact vector of transformation functions, and more particularly,is composed of->Is given;

in the fifth step, the first step, in particular,

based on the designs of step three and step four, an error matrix is defined as follows:

where k=diag { K ₁ ,K ₂ ,K ₃ Is a matrix of design parameters in which the elements satisfy K _i Differentiating the above expression and substituting the expression into the expression (8) to obtain a dynamic expression of the unconstrained error system, wherein the dynamic expression is larger than 0:

wherein, in the last step of the above formula, for convenience, the following symbols are defined: and λ _ij ,F _i ,D _i ,(JM ^-1 ) _ij τ _υ,i Are elements of the ith row and the jth column of a given corresponding matrix,

the equivalent overwrite of formula (10) is as follows:

wherein ,

as long as eta _e,i I=1, 2,3 is strictly in the region- ρ _i (t)＜η _e,i ＜ρ _i (t) inner evolution, thenEnd-to-end remains bounded and, furthermore, once ω _i (t) at |eta _e,i (0)|＜ρ _0,i Is bounded on the premise that a conclusion is obtained:is composed of->Defined by the properties of (a) and, in addition, review ω _i The limit of (t) is a direct result of the limit of s (t), and thus the control objective is expressed as a problem of stabilizing the error dynamic system formula (10);

in step six, the process is performed, in particular,

in order to guarantee the stability of s (t), the following model-free controller is proposed:

where β is the strictly positive control gain; Θ=diag { θ ₁ ,θ ₂ ,θ ₃ Is a user-defined matrix and has θ _i ＞0,i＝1,2,3，

By adjusting beta, K to adjust the control performance within a predetermined range,

the design parameters theta are selected to ensure that s (0) theta s (0) < 1 is true, is a sufficient condition for the stability of the resulting closed-loop control system,

thus, the architecture of the model-free trajectory tracking controller as shown in equation (12) is compact and is easy to implement because there are no model parameters, where the terms (1-s ^T Θs) ^-1 And Θs are used to ensure that the novel error system as shown in equation (11) is eventually consistent asymptotically stable in the presence of external disturbances,

itemsIs embedded in the formula (9), tracking error eta _e,i The steering is predetermined to be ρ _∞,i Is near zero and has a predetermined minimum convergence rate exp (- κ) _i t) exhibits a maximum preset overshoot ρ _0,i 。

2. The method for designing the USV robust model-free trajectory tracking controller based on the preset performance according to claim 1, wherein in the first step, specifically, a kinematic and dynamic model of the unmanned surface vessel is built as follows:

wherein ,τ＝τ_v Is the actual control vector;is an unknown nonlinear function consisting of hydrodynamic, model parameter perturbation, and the proposed control algorithm is completely model parameter independent, so the term M given in equation (2) will not be considered as a controller parameter, generating the desired trajectory as follows:

wherein ,η_d ＝[x _d ,y _d ,ψ _d ] ^T and υ_d ＝[u _d ,v _d ,r _d ] ^T Is a desired kinematic and kinetic signal; f (f) _d (t)＝[f _d,1 (t),f _d,2 (t),f _d,3 (t)] ^T Providing the required kinetic vector.

3. The method for designing a USV robust model-free trajectory tracking controller based on preset performance according to claim 2, wherein, in the second step, specifically,

kinematic errors are defined and expressed as:

η _e ＝η-η _d (4)

the kinetic error is expressed as:

υ _e ＝J(ψ)υ-J(ψ _d )υ _d (5)

thus, the tracking error dynamics model is derived as:

wherein j=j (ψ), J _d ＝J(ψ _d )，S＝S(r)，S _d ＝S(r _d ) The method is a simple writing method; λ=jsj ^T F= (λj) _d -J _d S _d )υ _d -J _d f _d All are known nonlinear functions, and related variables are obtained from the on-board sensor; d=jm ^-1 f (t, v) is an unknown function representing the lumped uncertainty.