An underactuated ship event-triggered finite-time tracking control method

Abstract

The present application belongs to the technical field of automatic control of ships, and particularly relates to an event-triggered finite-time tracking control method for an underactuated ship, which comprises the following steps: establishing a mathematical model of the underactuated ship; and designing control instructions for a longitudinal control law and a steering control law. In the present application, the nonlinear dynamic uncertain terms in the longitudinal and steering of the mathematical model of the underactuated ship are reconstructed by using a neural network approximation technique, a finite-time disturbance estimator is established, and the overall uncertainty including unknown external disturbances and inaccessible parts in the longitudinal and steering is reconstructed online, so that fast and accurate online reconstruction of complex uncertainty can be realized, the accuracy requirement of the online disturbance estimation technique on the ship motion model is released, the application range of the online disturbance estimation technique is expanded, and an event-triggered control method is introduced to inhibit unnecessary wear of the driver.

Description

Technical Field

[0001] This invention belongs to the field of ship automatic control technology, specifically relating to a finite-time tracking control method for underactuated ship events. Background Technology

[0002] During navigation, ships face complex and ever-changing environments, frequently encountering the influence of wind, waves, and currents. Simultaneously, ships themselves exhibit numerous uncertainties, such as uncertainties in ship parameters, measurement uncertainties in sensing equipment, and sudden failures in the propulsion system. These factors pose significant challenges to the safe navigation of intelligent ships. Furthermore, ships are limited in maneuverability and the physical constraints of their propulsion systems. In addition to these inherent limitations, they also face constraints imposed by the navigation environment. Therefore, ship trajectory tracking control is a classic nonlinear control system, characterized by nonlinearity, incompleteness, constraints, uncertainties in the ship model, and external environmental disturbances. It is easily affected by changes in model parameters and external disturbances such as wind, waves, and currents, and also exhibits large time delays and underactuated characteristics. To address these issues, the following existing technologies have been disclosed: The paper "Trajectory tracking sliding mode control of underactuated AUVs" utilizes lateral errors to construct an integral sliding mode surface to solve the linear trajectory tracking problem. The paper "Nonlinear sliding modeformation control for underactuated surface vessels" introduces bow angle errors to design first- and second-order sliding mode surfaces, proposing an underactuated ship trajectory tracking control method. It should be noted that the aforementioned studies on ship trajectory tracking all assume that the ship model is known. However, most ships navigating at sea typically experience model uncertainties and are affected by unknown external disturbances such as wind, waves, and currents. To address this issue, the paper "Adaptive output-feedback control with prescribed performance for trajectory tracking of underactuated surface vessels" employs a parameter compression algorithm to handle persistent disturbances and model uncertainties, and designs a ship trajectory tracking controller based on given performance. The paper "Robust adaptive tracking control of an underactuated ship with guaranteed transient performance" designs an adaptive state feedback controller and a parameter estimator to estimate external disturbances and unknown system parameters, ultimately proposing a robust adaptive control method for underactuated ships. It should be noted that the dynamic parameters in the above techniques need to satisfy parameterization decomposition conditions.To address this condition, the papers "Robust adaptive neural networks control for dynamic positioning of ships with unknown saturation and time-delay" and "Adaptive Neural Output Feedback Control for MSVs With Predefined Performance" utilize neural networks to reconstruct the unknown dynamics of ships and design an adaptive law to estimate the bounds of complex disturbances, including unknown external disturbances, and the estimation error of the neural network. Clearly, this approach is conservative.

[0003] Furthermore, in terms of tracking control performance and control design, low conservatism and broad model requirements align with practical engineering needs. Neural network-based approximators and disturbance observers possess unique advantages in reconstructing dynamic uncertainties and external disturbances. However, in control design principles, neural network-based approximators, due to their inherent characteristics, cannot accurately reconstruct external disturbances. An irreconcilable contradiction exists between neural network-based approximators and disturbance observers in control design.

[0004] Therefore, there is an urgent need to develop a new finite-time tracking control method for underactuated ships to solve the above problems. Summary of the Invention

[0005] The purpose of this invention is to provide a finite-time tracking control method for underactuated ship events.

[0006] To address the aforementioned technical problems, this invention provides a finite-time tracking control method for underactuated ships triggered by events, comprising: establishing a mathematical model of the underactuated ship; estimating and compensating for longitudinal composite uncertainty using longitudinal neural network approximation technology and longitudinal disturbance estimation technology, and introducing control instructions for longitudinal event-triggered control calculation to design a longitudinal control law; or estimating and compensating for steering composite uncertainty using steering neural network approximation technology and steering disturbance estimation technology, and introducing control instructions for steering event-triggered control calculation to design a longitudinal control law.

[0007] In one embodiment, the method for establishing a mathematical model of an underactuated ship includes:

[0008] Underactuated ship kinematic equations:

[0009] Underactuated ship dynamics equations:

[0010] in,

[0011] Where x, y, and ψ represent the ship's forward displacement, lateral drift displacement, and heading angle in the inertial coordinate system, respectively;

[0012] υ=[uvr] T Let u, v, and r be the velocity vector of the ship in the attached coordinate system, where u, v, and r represent the forward velocity, lateral drift velocity, and bow roll angular velocity of the ship in the hull coordinate system, respectively.

[0013] f = [f u f v f r ] T Represents the nonlinear dynamic terms of the ship model;

[0014] τ=[τ u 0τ r ] T For the control force and torque of underactuated ships, τ u τ r These represent the longitudinal propulsion force and steering moment of the ship, respectively. Since underactuated ships do not have a drive mechanism on their lateral sides, τ v =0;

[0015] τ w =[τ wu τ wv τ wr ] T This indicates time-varying interference caused by the external environment;

[0016] m 11 m 22 m 33 The inertial parameter m represents the inertial parameter including the added mass.

[0017] d 11 d 22 d 33 d 32 d 23 This represents the hydrodynamic damping coefficient of the ship system.

[0018] In one embodiment, the method for designing control commands for longitudinal control laws based on a longitudinal neural network approximation technique and a longitudinal disturbance estimation technique using a longitudinal event triggering protocol, according to an underactuated ship mathematical model, includes:

[0019] The longitudinal nonlinear dynamic uncertainty is approximated online in real time using a neural network, and the longitudinal composite disturbance is calculated using a longitudinal disturbance observer to account for the neural network approximation error and the time-varying disturbances of the external environment in the longitudinal direction.

[0020] By estimating and compensating for longitudinal composite uncertainty through longitudinal nonlinear dynamic uncertainty, longitudinal composite disturbance neural network approximation technology, and disturbance estimation technology, the control command of the longitudinal control law is designed by introducing longitudinal event-triggered control calculation.

[0021] In one embodiment, the method for designing control commands for steering control laws based on a mathematical model of an underactuated ship, employing steering neural network approximation technology and steering disturbance estimation technology, and introducing a steering event triggering protocol includes:

[0022] The nonlinear dynamic uncertainty of the steering is approximated online in real time using a neural network. A steering disturbance observer is designed to calculate the composite steering disturbance based on the neural network approximation error and time-varying disturbances from the external environment during steering. Furthermore, a steering event-triggered control method is introduced to design the steering control law and calculate the steering control command.

[0023] The composite disturbance uncertainty is estimated and compensated by using nonlinear dynamic uncertainty terms, steering neural network technology, and disturbance estimation technology. The steering event triggering control method is introduced to calculate the control command for the designed steering control law.

[0024] In one embodiment, the longitudinal nonlinear dynamic uncertainty term f u (υ)=W u *T s(υ)+ε1; where, υ=[uv r] T Let s(υ) = [h1(υ), ..., h1(υ)] be the input vector of the neural network. n (υ)] T W represents the radial basis function vector of the neural network. u * =[w u,1 * w u,2 * …w u,n * ] T ∈R n×1 ε1 represents the weight vector from the hidden layer to the output layer, and ε1 is the neural network approximation error.

[0025] In one embodiment, the longitudinal perturbation observer:

[0026] Longitudinal composite disturbance: Where β, β1, β2 ∈ R 3 ×3 Let be the positive definite diagonal matrix to be designed, and δ be the constant to be designed, and δ satisfies 0.5≤δ<1.

[0027] In one embodiment, the longitudinal control law τ u control commands

[0028]

[0029] The event triggering protocol is as follows:

[0030]

[0031] Among them, γ1>0, γ2>0, Ξ, τ uo , τ u1 p z Design constant;

[0032] This represents measurement error.

[0033] In one embodiment, the shift is to the nonlinear dynamic uncertainty term f r (υ)=W r *T s(υ)+ε2;

[0034] Where, υ=[uvr] T Let s(υ) = [h1(υ), ..., h1(υ)] be the input vector of the neural network. n (υ)] T W represents the radial basis function vector of the neural network. r * =[w r,1 * w r,2 * …w r,n * ] T ∈R n×1 ε represents the weight vector from the hidden layer to the output layer, and ε2 is the neural network approximation error.

[0035] In one embodiment, the perturbation observer is turned:

[0036] Steering compound disturbance: Where β, β3, β4 ∈ R 3 ×3 Let be the positive definite diagonal matrix to be designed, and δ be the constant to be designed, and δ satisfies 0.5≤δ<1.

[0037] In one embodiment, the steering control law τ r control commands

[0038]

[0039] The event triggering protocol is as follows:

[0040]

[0041] Among them, γ3>0, γ4>0, Π, τ ro , τ r1 p ψ Design constant;

[0042] This represents measurement error.

[0043] The beneficial effects of this invention are that it reconstructs the nonlinear dynamic uncertainties in the longitudinal and steering aspects of the mathematical model of an underactuated ship by using neural network approximation technology, establishes a finite-time disturbance estimator, and reconstructs the overall uncertainty in the longitudinal and steering aspects, including unknown external disturbances and inaccessible parts, online. This enables rapid and accurate online reconstruction of complex uncertainties, reduces the precision requirements of online disturbance estimation technology on the ship motion model, expands the application scope of online disturbance estimation technology, and introduces an event-triggered control method to suppress unnecessary wear of the drive.

[0044] Other features and advantages of the invention will be set forth in the description which follows, and will be apparent in part from the description, or may be learned by practicing the invention.

[0045] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, preferred embodiments are described below in detail with reference to the accompanying drawings. Attached Figure Description

[0046] To more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the specific embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0047] Figure 1 This is a flowchart of the finite-time tracking control method for triggering ship events according to the present invention;

[0048] Figure 2 A schematic diagram illustrating the basic principle of underactuated ship trajectory tracking in this invention.

[0049] Figure 3 Tracking performance curves in the xy plane of this invention;

[0050] Figure 4 The reference position and actual position response curves provided by this invention;

[0051] Figure 5 The tracking error variation curve of the present invention;

[0052] Figure 6 The control input τ of the present invention u τ r Line graph;

[0053] Figure 7 The norm of the weight vector estimate of this invention The curve of change;

[0054] Figure 8 The composite uncertainty F of the present invention u F r The curve of change;

[0055] Figure 9 The trigger time and response diagram at the moment of triggering in this invention. Detailed Implementation

[0056] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0057] Example 1

[0058] In this embodiment, as Figures 1 to 9 This embodiment provides a finite-time tracking control method for underactuated ships triggered by events, which includes: establishing a mathematical model of the underactuated ship; estimating and compensating for longitudinal composite uncertainty through longitudinal neural network approximation technology and longitudinal disturbance estimation technology, and introducing control instructions for longitudinal event-triggered control calculation to design the longitudinal control law; or estimating and compensating for steering composite uncertainty through steering neural network approximation technology and steering disturbance estimation technology, and introducing control instructions for steering event-triggered control calculation to design the longitudinal control law.

[0059] In this embodiment, the present invention reconstructs the nonlinear dynamic uncertainties in the longitudinal and steering directions of the underactuated ship mathematical model by employing neural network approximation technology, establishes a finite-time disturbance estimator, and performs online reconstruction of the overall uncertainty in the longitudinal and steering directions, including unknown external disturbances and inaccessible parts. This enables rapid and accurate online reconstruction of complex uncertainties, reduces the precision requirements of online disturbance estimation technology on the ship motion model, expands the application scope of online disturbance estimation technology, and introduces an event-triggered control method to suppress unnecessary wear of the drive.

[0060] In this embodiment, the method for establishing a mathematical model of an underactuated ship includes:

[0061] Underactuated ship kinematic equations:

[0062] Underactuated ship dynamics equations:

[0063] in, Where x, y, and ψ represent the ship's forward displacement, lateral drift displacement, and heading angle in the inertial coordinate system, respectively;

[0064] υ=[uvr] T Let u, v, and r be the velocity vector of the ship in the attached coordinate system, where u, v, and r represent the forward velocity, lateral drift velocity, and bow roll angular velocity of the ship in the hull coordinate system, respectively.

[0065] f = [f u f v f r ] T Represents the nonlinear dynamic terms of the ship model;

[0066] τ=[τ u 0τ r ] T For the control force and torque of underactuated ships, τ u τ r These represent the longitudinal propulsion force and steering moment of the ship, respectively. Since underactuated ships do not have a drive mechanism on their lateral sides, τ v =0;

[0067] τ w =[τ wu τ wv τ wr ] T This indicates time-varying interference caused by the external environment;

[0068] m 11 m 22 m 33 The inertial parameter m represents the inertial parameter including the added mass.

[0069] d 11 d 22 d 33 d 32 d 23 This represents the hydrodynamic damping coefficient of the ship system.

[0070] Assumption 1: External disturbance τ acting on an underactuated vessel wu τ wv τ wr For time-varying disturbances and with bounded first derivatives, satisfying

[0071]

[0072] Among them, represents the upper bound of the external environmental interference and the boundary value is unknown, d wu > 0, d wv > 0, d wr > 0 represents the upper bound of the first derivative of the external environmental interference and the boundary value is unknown.

[0073] Assume that the desired trajectory η of the ship d = [x d , y d , ψ d T and its first derivative second derivative are all bounded.

[0074] Assume 3 The nonlinear dynamics f ι (υ)(ι = u, v, r) are unknown.

[0075] Assume 4 The cross drift velocity v of the ship is passive bounded, that is, there exists an unknown constant satisfying

[0076] For the design and analysis of ship tracking control, the following definitions and theorems are given:

[0077] Definition 1 Consider the nonlinear system:

[0078]

[0079] Among them, x ∈ R n is the state variable of the system, Ω0 is a spherical domain containing the origin, and f(x) is a continuous function. For any initial condition x0, if there exists a constant σ > 0 and an adjustment time function 0 < T(x0) < ∞ such that ||x(t)|| ≤ σ, t ≥ T(x0), then (6) can be said to be semi-globally practically finite-time stable.

[0080] Definition 2 For If the adjustment time function T(x0) is uniformly bounded, that is such that T(x0) ≤ T m , then (6) can be said to be semi-globally practically fixed-time stable.

[0081] Lemma 1 For the nonlinear system (6), assume that there exists a Lyapunov function V(x): Ω0 → R and any scalars a > 0, b > 0 and (6) such that the inequality holds, then the system (6) is finite-time stable, and its adjustment time T satisfies

[0082] ​

[0083] Where V(x0) is the initial value of V(x).

[0084] Lemma 2 for the system Where d is an unknown bounded perturbation, and satisfies If parameters δ1, k1, k2, and k3 satisfy 0 < δ1 < 1, k i If the value is greater than 0 (i = 1, 2, 3), then the following perturbation observer converges in finite time.

[0085]

[0086] in, and Let be the estimated values ​​of d and χ, respectively, and

[0087] Lemma 3 For any constant a i For all elements in R, i = 1, ..., n, 0 < ι, 1 < 1, the following inequality holds.

[0088]

[0089] Lemma 4 For a given set defined on a compact set Any nonlinear function β(Z):R n →R, can be represented by the radial basis function vector of a neural network. Approximate, then

[0090]

[0091] Where ε is the approximation error, and satisfies It is a constant.

[0092] φ(Z)=[φ1(Z)…φ ι (Z)] T is the radial basis function vector. This represents the ideal weight vector. l>1 represents the number of nodes in the neural network, φ i Let (Z), i=1,…l be the radial basis functions of the neural network, then the expression for the basis functions is:

[0093]

[0094] Where, ω i μ is the width of the Gaussian function; i is the i-th node of the hidden layer of the neural network; μ i =[μ i,1 ,…,μ i,n ] T denoted as the center point vector value of the Gaussian function.

[0095] Lemma 5: Given any real variables M, N and positive constants a, b, c, the following inequalities hold.

[0096]

[0097] The longitudinal virtual control law and steering virtual control law are designed, and the tracking error variable is defined as follows.

[0098] Where, x e y e ψ e These are the longitudinal position error, lateral position error, and heading angle position error, denoted as... J(ψ) is the transformation matrix between the inertial coordinate system and the attached coordinate system, and satisfies J(ψ) -1 =J(ψ) T ;x d y d ψ d These represent the x and y coordinates of the reference trajectory and the heading angle, respectively, where the ship's desired heading is given by the following equation.

[0099]

[0100] To more accurately describe the position and speed of a ship during its motion, and to study its maneuverability and motion laws, a system is established... Figure 2 The geodetic coordinate system and the attached coordinate system shown are used to represent the ship's motion process.

[0101] Figure 2 In the diagram, OXY is an inertial coordinate system, O is the initial position, OX is due north, OY is due east, and o b The midpoint of the line connecting the bow and stern of the ship, o b x b Along the ship's centerline towards the bow, o b y b Along the port side of the ship, AB is the reference trajectory.

[0102] According to the above Figure 2 The relationship shown reveals the variable x e y e and z e The following relationship exists

[0103] x e =z e cosψ d y e =z e sinψ d (15)

[0104] For variable z e ψe Taking the derivative, we get

[0105]

[0106]

[0107] Vertical virtual control law

[0108]

[0109] Turn to virtual control law

[0110]

[0111] Where, k ze1 >0, k ze2 >0, k ψe1 >0, k ψe2 >0 represents the design parameter.

[0112] It should be noted that, for α u Undefined. Therefore, in practical engineering, the following conditions are first assumed. Established and utilized The transformation ensures the validity of the assumption.

[0113] In this embodiment, the method for designing control commands for longitudinal control laws based on longitudinal nonlinear dynamic uncertainties, longitudinal composite disturbances, and longitudinal neural network approximation and disturbance estimation techniques in the mathematical model of underactuated ships, and by introducing a longitudinal event-triggered protocol, includes: approximating the longitudinal nonlinear dynamic uncertainties online in real time using a neural network; and calculating the longitudinal composite disturbance using a longitudinal disturbance observer to account for the neural network approximation error and the time-varying disturbances of the external environment in the longitudinal direction. That is, estimating and compensating for the longitudinal composite uncertainty using the longitudinal nonlinear dynamic uncertainties, longitudinal composite disturbance neural network approximation techniques, and disturbance estimation techniques. Furthermore, the method introduces longitudinal event-triggered control to calculate and design control commands for longitudinal control laws.

[0114] In this embodiment, the method for designing control commands for a steering control law based on the steering nonlinear dynamic uncertainty term and steering complex disturbance in the mathematical model of an underactuated ship, employing steering neural network approximation technology and steering disturbance estimation technology, and introducing a steering event-triggered protocol includes: approximating the steering nonlinear dynamic uncertainty term online in real time using a neural network; calculating the steering complex disturbance by designing a steering disturbance observer to account for the neural network approximation error and the time-varying disturbance of the external environment during steering; and designing a steering control law using a steering event-triggered control method to calculate the steering complex disturbance. In other words, the method estimates and compensates for the uncertainty of the complex disturbance using the steering nonlinear dynamic uncertainty term, steering neural network technology, and disturbance estimation technology. Finally, it introduces a steering event-triggered control method to calculate and design the control commands for the steering control law.

[0115] In this embodiment, to avoid affecting α u By direct differentiation, the following filter is introduced.

[0116]

[0117] Where, γ u For a first-order filter, μ u Let e ​​be the time constant, and let e be the velocity error. u =γ u -α u and

[0118]

[0119] in, It is a continuous function with a maximum value M. u .

[0120] In this embodiment, according to the backstepping design procedure, the following lateral velocity error is defined:

[0121] u e =u-γ u ;(twenty three)

[0122] For u e =u-γ u Differentiate and Substituting, we can obtain

[0123]

[0124] Due to f u (υ) represents the nonlinear dynamic uncertainty component, which cannot be directly used for the design of the longitudinal control law. Therefore, a neural network with the ability to reconstruct unknown nonlinearities online will be introduced here to address f. u (υ) Perform online refactoring.

[0125] According to Lemma 4, the unknown term f u (υ) can be equivalently written as a longitudinal nonlinear dynamic uncertainty term.

[0126] f u (υ)=W u *T s(υ)+ε1;(25)

[0127] Where, υ=[uvr] T Let s(υ) = [h1(υ), ..., h1(υ)] be the input vector of the neural network. n (υ)] T W represents the radial basis function vector of the neural network. u * =[w u,1 * w u,2 * …w u,n * ] T ∈R n×1 ε1 represents the weight vector from the hidden layer to the output layer, and ε1 is the neural network approximation error.

[0128] In this embodiment, substituting (25) into (23) yields...

[0129]

[0130] Where, ω u =τ wu +ε1, here we call ω u This is a longitudinal composite disturbance term.

[0131] Furthermore, equation (26) can be written as

[0132]

[0133] in, For weight error, This represents the parameter estimation error.

[0134] Considering the neural network approximation error ε1 and the time-varying disturbance τ of the external environment in the longitudinal direction. wu A perturbation observer based on the finite-time principle was designed to observe longitudinal composite perturbations ω. u Make an estimate.

[0135] Based on (26), the following longitudinal predictor is designed.

[0136]

[0137] in, Acquired using the following longitudinal perturbation observer.

[0138] In this embodiment, the longitudinal perturbation observer is:

[0139] Longitudinal composite disturbance:

[0140]

[0141] Where β, β1, β2 ∈ R 3×3 Let be the positive definite diagonal matrix to be designed, and δ be the constant to be designed, and δ satisfies 0.5≤δ<1.

[0142] In this embodiment, the longitudinal control law τ u control commands

[0143]

[0144] Weight Adaptive Law

[0145] The event triggering protocol is as follows:

[0146]

[0147] Among them, γ1>0, γ2>0, Ξ, τ uo , τ u1 p z Design constant;

[0148] This represents measurement error.

[0149] Furthermore, according to equations (30)-(32), we have

[0150]

[0151] Substituting (30) into the equation, we get...

[0152]

[0153] To avoid α r By direct differentiation, the following filter is introduced.

[0154]

[0155] Where, γ r For a first-order filter, μ r Let e ​​be the time constant, and let e be the velocity error. r =γ r -α r and

[0156]

[0157] According to (19), we can obtain

[0158]

[0159] in, It is a continuous function with a maximum value M. r .

[0160] Define the torque error as r e =r-γ r (38)

[0161] Differentiating (38) and substituting (2) into the equation, we get...

[0162]

[0163] Due to f in (39) r (υ) represents the uncertain part of the model, and the longitudinal control law cannot be directly designed. Therefore, a neural network control algorithm is used to address the uncertainty of f. r (υ) Approximation is performed, and in control engineering, neural networks have strong self-learning capabilities. They can approximate arbitrary functions, avoiding complex mathematical analysis of unknown functions and providing an effective solution for nonlinear control problems.

[0164] In this embodiment, the nonlinear dynamic uncertainty term is shifted.

[0165] f r (υ)=W r *T s(υ)+ε2;(40)

[0166] Where, υ=[uvr] T Let s(υ) = [h1(υ), ..., h1(υ)] be the input vector of the neural network. n (υ)] T W represents the radial basis function vector of the neural network. r * =[w r,1 * w r,2 * …w r,n * ] T ∈R n×1 ε represents the weight vector from the hidden layer to the output layer, and ε2 is the neural network approximation error.

[0167] Substituting (40) into (39), we get

[0168]

[0169] Where, ω r =τwr +ε2,ω r This is a composite disturbance term for steering.

[0170]

[0171] in, For weight error, It is ω r The estimated value. This represents the parameter estimation error.

[0172] Considering the neural network approximation error ε2 and the time-varying disturbance τ of the external environment in the longitudinal direction. wr A perturbation observer based on the finite-time principle was designed to observe the steering composite perturbation ω. r Make an estimate.

[0173] Based on (42), the following predictor is designed.

[0174]

[0175] in, Obtained through the following steering disturbance estimator.

[0176] In this embodiment, the steering disturbance observer

[0177]

[0178] Steering compound disturbance

[0179]

[0180] Where β, β3, β4 ∈ R 3×3 Let be the positive definite diagonal matrix to be designed, and δ be the constant to be designed, and δ satisfies 0.5≤δ<1.

[0181] In this embodiment, the steering control law τ r control commands

[0182]

[0183] Weight Adaptive Law

[0184]

[0185] The event triggering protocol is as follows:

[0186]

[0187] Among them, γ3>0, γ4>0, Π, τ ro , τ r1 p ψDesign constant;

[0188] This represents measurement error.

[0189] According to (42)-(44) and (46)-(47), we can obtain

[0190]

[0191] Substituting (45) into (49) gives

[0192]

[0193] A simulation study was conducted to verify the effectiveness of an underactuated ship event-triggered finite-time tracking control method based on a neural network disturbance observer.

[0194] The model parameters used in the simulation experiment are as follows:

[0195] m 11 =200, m 22 =250,m 33 =80,d 11 =70,d 22 =100, d 23 =40,d 32 =40, d 33 =80.

[0196] Reference trajectory η d =[x d ,y d ] T Depend on The equation is generated.

[0197] External disturbance settings:

[0198] τ w =[20(sin0.4t+cos0.3t),2(sin0.1t+cos0.4t),5(sin0.3t+cos0.2t)] T .

[0199] The design parameter is selected as: k ze1 =1,k ze2 =150,k ψe1 =14,k ψe2 =180, β=5, β1=0.1, β2=β3=0.2, β4=0.05, δ=0.6, γ1=4, γ2=0.0005, γ3=8, γ4=0.00001. Initial conditions [x(0),y(0),ψ(0)] T =[10,105,0] T The rest are set to 0.

[0200] This embodiment utilizes software for computer simulation research, and the results are as follows: Figures 3 to 8 As shown. In addition, in order to demonstrate the superiority of the proposed control scheme in this work, simulations were compared with the event-free triggering protocol and adaptive neural network control scheme (hereinafter referred to as the scheme [1]) and continuous control scheme proposed in the literature "Tracking control of poddedpropulsion unmanned surface vehicle with unknown dynamics and disturbance under input saturation". Figure 3 This represents a graph showing the tracking performance curves in the xy plane provided by the control embodiments of the present invention. Figure 4 The reference position and actual position response curves provided for the control embodiments of the present invention; Figures 3 to 4 The performance of the tracking control scheme is shown, which means that all of these schemes can force the underactuated ship to follow the reference trajectory. In comparison, the continuous control scheme has the fastest response speed, and the slowest is scheme [1]. To some extent, this highlights the advantages of finite-time control. Figure 5 The tracking error variation curve provided for the control embodiment of the present invention; from Figure 5 As can be seen, the control precision of the event-triggered scheme provided by the present invention is better than that of the comparative scheme [1]. The control precision of the continuous control scheme and the event-triggered scheme provided by the present invention are almost the same, indicating that the event-triggered control scheme provided by the present invention has advantages. Figure 6 The control input τ provided for the control embodiments of the present invention u τ r Curve graph; from Figure 6 It can be seen that, compared with the continuous control scheme and [1] scheme, the actuator's response to control commands is greatly reduced. Simulation comparison results are as follows: Figures 3 to 6 As shown, this illustrates the advantages of our proposed event-triggered control scheme in terms of control performance and actuator protection. Figure 7 This indicates the norm of the weight vector estimate provided by the control embodiment of the present invention. It is bounded; Figure 8 This demonstrates that the event-triggered neural network finite-time perturbation observer proposed in this invention can handle composite uncertainties F u F r (F u =f u +τ wu ,F r =f r +τ wr ) to build; Figure 9The response diagrams for the trigger time and departure instant provided in the control embodiment of the present invention show the event trigger time and number of times. It can be found that the maximum trigger time under event trigger protocols (33) and (48) is approximately 4s and 1.5s, respectively. Statistically, the number of triggers under the event trigger protocols is 2078s and 2258s, respectively. These results show that all signals in the closed-loop trajectory tracking control system are bounded and zero behavior is overcome. This proves Theorem 1.

[0201] In summary, this invention reconstructs the nonlinear dynamic uncertainties in the longitudinal and steering aspects of the mathematical model of an underactuated ship by employing neural network approximation technology, establishes a finite-time disturbance estimator, and performs online reconstruction of the overall uncertainty in the longitudinal and steering aspects, including unknown external disturbances and inaccessible parts. This enables rapid and accurate online reconstruction of complex uncertainties, reduces the precision requirements of online disturbance estimation technology on the ship motion model, expands the application scope of online disturbance estimation technology, and introduces an event-triggered control method to suppress unnecessary wear of the drive.

[0202] All the devices (parts whose specific structures are not specified) selected in this application are general standard parts or parts known to those skilled in the art. Their structures and principles can be learned by those skilled in the art through technical manuals or conventional experimental methods.

[0203] In the description of the embodiments of the present invention, unless otherwise explicitly specified and limited, the terms "installation," "connection," and "linking" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal connection of two components. Those skilled in the art can understand the specific meaning of the above terms in the present invention based on the specific circumstances.

[0204] In the description of this invention, it should be noted that the terms "center," "upper," "lower," "left," "right," "vertical," "horizontal," "inner," and "outer," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are used only for the convenience of describing the invention and for simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on the invention. Furthermore, the terms "first," "second," and "third" are used for descriptive purposes only and should not be construed as indicating or implying relative importance.

[0205] Based on the above-described preferred embodiments of the present invention, and through the foregoing description, those skilled in the art can make various changes and modifications without departing from the inventive concept. The technical scope of this invention is not limited to the contents of the specification, but must be determined according to the scope of the claims.

Claims

1. An underactuated marine vessel event-triggered finite-time tracking control method, characterized in that, Comprise: establishing a mathematical model of underactuated ship; By longitudinal neural network approximation technique, longitudinal disturbance estimation technique to estimate and compensate the longitudinal composite uncertainty, introduce the longitudinal event triggered control calculation design longitudinal control law control instruction, or By steering neural network approximation technique, steering disturbance estimation technique to estimate and compensate the steering composite uncertainty, introduce the steering event triggered control calculation design longitudinal control law control instruction; The method for establishing a mathematical model of underactuated ship comprises: Underactuated ship kinematic equation: Underactuated ship dynamics equations: wherein Wherein, x, y, ψ respectively represent the forward displacement, lateral displacement and heading angle of the ship in the inertial coordinate system; υ = [u v r] T υ is the velocity vector of the ship in the body-fixed coordinate system, and u, v, r represent the forward speed, cross drift speed, and yaw angular velocity of the ship in the body-fixed coordinate system, respectively. f = [f u f v f r ] T represents a nonlinear dynamic term of the ship model; τ = [τ u 0 τ r ] T τ u , τ r are the longitudinal propulsion force and the steering torque of the ship, respectively, since the underactuated ship has no driving device on the lateral side, i.e. τ v = 0. τ w = [τ wu τ wv τ wr ] T denotes time-varying disturbances caused by the outside environment; m 11 , m 22 , m 33 denotes the inertial parameter m including the additional mass d 11 , d 22 , d 33 , d 32 , d 23 represents the hydrodynamic damping coefficient of the ship system; According to the underactuated ship mathematical model, the longitudinal neural network approximation technique and the longitudinal disturbance estimation technique are used to introduce the method for designing the control instruction of the longitudinal control law by the longitudinal event triggered protocol, which comprises: The longitudinal nonlinear dynamic uncertainty term is approximated by a neural network in real time, and a longitudinal disturbance observer is designed to calculate the longitudinal composite disturbance for the neural network approximation error and the time-varying disturbance of the external environment in the longitudinal direction, and the longitudinal event triggered control is introduced to design the longitudinal control law, that is By neural network approximation technique, disturbance estimation technique to estimate and compensate the longitudinal composite uncertainty, introduce the longitudinal event triggered control design longitudinal control law control instruction; According to the underactuated ship mathematical model, the steering neural network approximation technique and the steering disturbance estimation technique are used to introduce the method for designing the control instruction of the steering control law by the steering event triggered protocol, which comprises: The steering nonlinear dynamic uncertainty term is approximated by a neural network in real time, and a steering disturbance observer is designed to calculate the steering composite disturbance for the neural network approximation error and the time-varying disturbance of the external environment in the steering direction, and the steering event triggered control is introduced to design the steering control law, that is By neural network technique, disturbance estimation technique to estimate and compensate the composite uncertainty, and introduce the steering event triggered control method to design the control instruction of the steering control law; Longitudinal nonlinear dynamic uncertainty term f u (v) = W u *T s(v) + e1; where υ = [u v r] T is the input vector of the neural network, s(υ) = [h1(υ),...,h n (υ)] T is the radial basis function vector of the neural network, W u * = [w u,1 * w u,2 * ... w u,n * T ∈ R n×1 is the weight vector from the hidden layer to the output layer, and ε1is the approximation error of the neural network.​ Longitudinal disturbance observer: Longitudinal complex perturbation: where β, β1, β2 ∈ R 3×3 is a positive definite diagonal matrix to be designed, and δ is a constant to be designed, and δ satisfies 0.5≤δ<1.

2. The underactuated ship event triggered finite time tracking control method according to claim 1, wherein, Longitudinal control law τ u Control command Event-triggered protocol is: wherein γ1>0, γ2>0, τ uo , τ u1 , p z are design constants; To measure error.

3. The underactuated ship event triggered finite time tracking control method according to claim 1, wherein, Turning to the nonlinear dynamic uncertainty term f r (v) = W r *T s(v) + ε2; where υ = [u v r] T is the input vector of the neural network, s(υ) = [h1(υ),...,h n (υ)] T is the radial basis function vector of the neural network, W r * = [w r,1 * w r,2 * ... w r,n * ] T ∈ R n×1 is the weight vector from the hidden layer to the output layer, and ε2 is the approximation error of the neural network.

4. The underactuated ship event triggered finite time tracking control method according to claim 3, wherein, Steering disturbance observer: Turning to the composite perturbation: Wherein, β, β3, β4∈R 3×3 is a positive definite diagonal matrix to be designed, and δ is a constant to be designed, and δ satisfies 0.5≤δ<1.

5. The underactuated ship event triggered finite time tracking control method according to claim 4, wherein, Steering control law τ r Control command The event-triggered protocol is: wherein γ3> 0, γ4> 0, τ ro , τ r1 , p ψ are design constants; To measure error.

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