An adaptive trajectory tracking control method for unmanned vessels with event-triggered mechanism and signal quantization

Abstract

The present invention provides an adaptive trajectory tracking control method for an unmanned vessel with an event-triggered mechanism and signal quantization. The method comprises: quantizing the control signal using a uniform quantizer and describing the input quantization process and external interference using a linear analytical model; estimating the quantized state feedback information, system uncertainty, and external interference using a neural network observer; designing a quantitative feedback controller using the observation results of the neural network observer in combination with backstepping, dynamic surface technology, and an event-triggered mechanism; and proving the observation error of the neural network observer and the stability of the designed adaptive trajectory tracking control system for unmanned vehicles with an event-triggered mechanism and signal quantization based on Lyapunov stability theory. The technical solution of the present invention addresses the trajectory tracking problem of unmanned vessels under limited maritime communication bandwidth by designing a quantitative feedback controller to solve the problem of adaptive trajectory tracking control for unmanned vessels with an event-triggered mechanism and signal quantization.

Description

Technical Field

[0001] The present invention relates to the field of artificial intelligence technology, and in particular to an unmanned ship adaptive trajectory tracking control method with an event triggering mechanism and signal quantization. Background Art

[0002] Unmanned surface vehicles (USVs) possess intelligence and autonomy, enabling them to perform tasks in complex sea conditions and are widely used in marine engineering. To ensure the stability and performance of USVs during missions, it is crucial to study trajectory tracking control strategies.

[0003] Most trajectory control methods are designed based on the assumption of continuous feedback information. However, these control methods may encounter challenges when communication bandwidth is limited at sea. Therefore, it is meaningful to consider quantization issues when studying trajectory tracking control strategies for USVs.

[0004] Most quantization-related control methods consider state quantization and input quantization separately. However, in maritime practice, due to limited network channel bandwidth, both state quantization and input quantization should be considered simultaneously. Furthermore, event-triggered mechanisms can further conserve communication bandwidth, making it feasible to consider both event-triggered mechanisms and quantization simultaneously when designing control systems. Summary of the Invention

[0005] According to the above-mentioned problem of limited communication bandwidth in navigation practice, the present invention provides an unmanned ship adaptive trajectory tracking control method with event triggering mechanism and signal quantization for the USV trajectory tracking control system with input quantization and state quantization, which is more in line with the control law of the actuator in navigation practice. The present invention introduces a linear analysis model to describe the input quantization process, and there is no need to consider the prior information of the quantization parameters when designing the control law; at the same time, a neural network observer is used to estimate the quantized state signal, and a quantitative feedback controller is designed using the observation results of the neural network observer in combination with the backstepping method, dynamic surface technology and event triggering mechanism. The observation error of the neural network observer and the stability of the designed control system are proved based on the Lyapunov stability theory. The technical solution of the present invention is aimed at the trajectory tracking problem of USV under the condition of limited communication bandwidth at sea. By designing a quantitative feedback controller, the problem of USV adaptive trajectory tracking control with event triggering mechanism and signal quantization is solved.

[0006] The technical means adopted in the present invention are as follows:

[0007] An adaptive trajectory tracking control method for an unmanned vessel with an event triggering mechanism and signal quantization includes:

[0008] S1. Use a uniform quantizer to quantize the control signal and use a linear analysis model to describe the input quantization process and external interference;

[0009] S2, using a neural network observer to estimate the quantized state feedback information, system uncertainty, and external interference;

[0010] S3. Combining backstepping, dynamic surface technology and event triggering mechanism, using neural network observer observation results, design a quantitative feedback controller;

[0011] S4. Based on Lyapunov stability theory, the observation error of the neural network observer and the stability of the designed USV adaptive trajectory tracking control system with event triggering mechanism and signal quantization are proved.

[0012] Furthermore, step S1 specifically includes:

[0013] S11. Under the environmental interference of wind, waves and currents, the kinematic and dynamic models of the USV are constructed as follows:

[0014]

[0015] Where, (x, y) and ψ are the position and bow angle of the UAV, respectively; u, v, r are the forward velocity, lateral velocity and yaw angular velocity respectively; Q(τ u ), Q(τ v ) and Q(τ r ) are the control input τ u , τ v and τ r The quantitative value of is the environmental disturbance related to wind, waves and currents; R(ψ), M, C(ν) and D(ν) represent the transformation matrix, inertia matrix, Coriolis and centripetal force matrix and damping matrix respectively. c1=m 22 v+m 23 r,c2=m 11 u,d 11 =X u +X u|u| |u|+X uuu u 2 , d 22 =Y v +Y v|v| |v|+Y v|r| |r|,d 23 =Y r +Y r|v| |v|+Y r|r||r|,d 32 =Z v +Y v|v| |v|+Y v|r| |r|,d 33 =Z r +Y r|v| |v|+Y r|r| |r|, where m is the mass of the USV, and is the additional mass, x g is the center of gravity of USV, I Z is the inertia matrix about the vertical axis, X u 、X u|u| 、X uuu 、Y v 、Y v|v| 、Y v|r| 、Y r|v| 、Y r 、Y r|r| , Z v , Z v|v| , Z v|r| , Z r , Z r|v| and Z r|r| is the fluid dynamics coefficient;

[0016] S12, all state variables x, y, ψ, u, v, r and control input τ u ,τ v ,τ r Both are quantized using a uniform quantizer:

[0017]

[0018] Where s = x, y, ψ, u, v, r, τ u ,τ v ,τ r , j∈Z + ; h>0 indicates quantization step size; H1=h, H j+1 =H j +h; there is a positive constant Make the quantization error sQ(s) satisfy

[0019] S13, assuming external interference τ ωu , τ ωv and τ ωr is bounded, assuming an ideal reference trajectory is continuously differentiable, and η d and its differential term They are all bounded;

[0020] S14. Let Q(τ) = q1τ + q2, and define:

[0021]

[0022] Where a>0, q1 is time-varying and unknown, Since the sign remains unchanged during the quantization process, we know that q1>0; because Then Q(τ u )-τ u 、Q(τ v )-τ v and Q(τ r )-τ r is bounded, which means |q 2u |、|q 2v |and|q 2r | is also bounded.

[0023] Furthermore, step S2 specifically includes:

[0024] S21. Define uncertainties Then the USV kinematic and dynamic models are:

[0025]

[0026] S22. Approximate the unknown continuous function F(v) using a radial basis function neural network, where:

[0027] F(v)=W T Π(v)+ε

[0028] Where, represents the ideal weight, is the Gaussian function, n is the number of hidden layer nodes, is the observation error; ideal weight and observation errors respectively satisfy ‖W‖≤W * and ‖ε‖≤ε * , W * and ε * is a positive constant; Gaussian function Satisfy ‖Π‖≤Π * , Π * is a positive constant;

[0029] S23. Design a neural network observer as follows:

[0030]

[0031] Where, l1>0, l2>0, and The quantized state variables are Q(η)=[Q(x),Q(y),Q(ψ)] Τ and Q(τ)=[Q(u),Q(v),Q(r)] Τ The estimated value of is the estimated value of W, the approximation error Rotation Matrix

[0032] Furthermore, step S3 specifically includes:

[0033] S31. Define the error surface as follows:

[0034]

[0035] Where, α1, α2 and α3 are intermediate signals and The filtered signal;

[0036] S32. Define a first-order low-pass filter as follows:

[0037]

[0038] Where i = 1, 2, 3, is the filter gain;

[0039] S33, error surface Taking the derivative, we get:

[0040]

[0041] Defining intermediate signals for Where, κ1>0;

[0042] S34, error surface Taking the derivative, we get:

[0043]

[0044]

[0045] Where, κ2>0,

[0046] S35, design the intermediate signal and adaptive law respectively:

[0047]

[0048] Where, β, δ,σ,ξ, is a positive constant, L1=[tanh(Γ11 ),tanh(Γ 12 ),tanh(Γ 13 )] T , Γ1=[Γ 11 ,Γ 12 ,Γ 13 ] T , L2=[tanh(Γ 21 ),tanh(Γ 22 ),tanh(Γ 23 )] T , Γ2=[Γ 21 ,Γ 22 ,Γ 23 ] T ,

[0049] S36. Based on the time-varying threshold, design an event-driven strategy as follows:

[0050]

[0051] t k+1 =inf{t∈R,‖e(t)‖≥β‖τ‖+g}

[0052] Where g>0, e(t)=ω(t)-τ(t), we can see that there exists a continuous time-varying coefficient λ2(t) that satisfies λ2(t k )=0,λ2(t k+1 )=±1, and |λ2(t)|≤1, so that:

[0053] ω=τ+λ2(β‖τ‖+g)

[0054] =(1+λ2βsign(τ))τ+λ2g

[0055] =(1+λ1β)τ+λ2g

[0056] In the formula, λ1=λ2sign(τ), |λ1|=|λ2sign(τ)|≤1.

[0057] Furthermore, step S4 specifically includes:

[0058] S41, for the neural network observer in step S2, the observation error for Taking the derivative of the observation error, we get:

[0059]

[0060] Where, There exists a positive constant R * satisfy

[0061] S42. Define the error state equation of the observer as:

[0062]

[0063] Where,

[0064] S43. Let E=Tθ, Taking the derivative we get:

[0065]

[0066] Where, Λ0=diag(Λ,03), because ‖Π‖≤Π * , ‖W‖≤W * and ‖ε‖≤ε * , then G0 is bounded;

[0067] S44. Define the Lyapunov function as follows:

[0068]

[0069] Where p is a positive definite matrix. To analyze the stability of V1, consider the following set of simultaneous Lyapunov inequalities:

[0070]

[0071] Where ζ>0, To satisfy The boundary of the yaw angular velocity r;

[0072] S45, take the derivative of V1 and get:

[0073]

[0074] Where, Therefore, the observation error of the neural network observer is eventually uniformly bounded;

[0075] S46. Define the Lyapunov function as follows:

[0076]

[0077] S47. Derivative the filtering error to obtain:

[0078]

[0079] There is an upper bound function Then we have:

[0080]

[0081] Among them, the maximum value of Γ3 is recorded as Ω γ ;

[0082] S48. Taking the derivative of V2, we get:

[0083]

[0084] S49, due to If is a positive constant, then Since |λ2g|≤g and 1-β≤|1+λ1β|, we can get Then we have:

[0085]

[0086] because but Therefore, we have:

[0087]

[0088] because and Therefore, we have:

[0089]

[0090] Where, Therefore the control system is stable and all control signals are uniformly ultimately bounded.

[0091] Compared with the prior art, the present invention has the following advantages:

[0092] 1. This invention provides an adaptive trajectory tracking control method for an unmanned vessel with an event-triggered mechanism and signal quantization. This method considers both input and state quantization, making it more consistent with actuator control principles in maritime practice. Furthermore, a neural network observer is used to estimate the quantized state signal.

[0093] 2. The present invention provides an adaptive trajectory tracking control method for an unmanned ship with an event triggering mechanism and signal quantization, and proposes a linear analysis model for describing the input quantization process. Therefore, when designing the system controller, there is no need to input prior information of the quantization parameters, thereby improving the adaptability and versatility of the control system and simplifying the design process of the control law.

[0094] 3. The present invention provides an unmanned ship adaptive trajectory tracking control method with an event trigger mechanism and signal quantization, which takes into account both the event trigger mechanism and input quantization, aiming to save maritime communication resources and better suiting navigation practices with limited communication bandwidth.

[0095] Based on the above reasons, the present invention can be widely promoted in fields such as artificial intelligence. BRIEF DESCRIPTION OF THE DRAWINGS

[0096] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative labor.

[0097] Figure 1 Flow chart of the method of the present invention.

[0098] Figure 2 This is a diagram of the ship trajectory tracking results provided by an embodiment of the present invention.

[0099] Figure 3 This is a ship trajectory tracking error diagram provided by an embodiment of the present invention.

[0100] Figure 4 A comparison diagram of control input before and after quantization provided by an embodiment of the present invention.

[0101] Figure 5 This is a diagram showing the time interval between two consecutive event-triggered samplings provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0102] In order to enable those skilled in the art to better understand the solutions of the present invention, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the embodiments described are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts should fall within the scope of protection of the present invention.

[0103] It should be noted that the terms "first", "second", etc. in the description and claims of the present invention and the above-mentioned drawings are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that the numbers used in this way can be interchanged where appropriate, so that the embodiments of the present invention described herein can be implemented in an order other than those illustrated or described herein. In addition, the terms "including" and "having" and any variations thereof are intended to cover non-exclusive inclusions. For example, a process, method, system, product or device that includes a series of steps or units is not necessarily limited to those steps or units clearly listed, but may include other steps or units that are not clearly listed or inherent to these processes, methods, products or devices.

[0104] like Figure 1 As shown, the present invention provides an unmanned vessel adaptive trajectory tracking control method with an event triggering mechanism and signal quantization, comprising:

[0105] S1. Use a uniform quantizer to quantize the control signal and use a linear analysis model to describe the input quantization process and external interference;

[0106] S2, using a neural network observer to estimate the quantized state feedback information, system uncertainty, and external interference;

[0107] S3. Combining backstepping, dynamic surface technology and event triggering mechanism, using neural network observer observation results, design a quantitative feedback controller;

[0108] S4. Based on Lyapunov stability theory, the observation error of the neural network observer and the stability of the designed USV adaptive trajectory tracking control system with event triggering mechanism and signal quantization are proved.

[0109] In specific implementation, as a preferred embodiment of the present invention, step S1 specifically includes:

[0110] S11. Under the environmental interference of wind, waves and currents, the kinematic and dynamic models of the USV are constructed as follows:

[0111]

[0112] Where, (x, y) and ψ are the position and bow angle of the UAV, respectively; u, v, r are the forward velocity, lateral velocity and yaw angular velocity respectively; Q(τ u ), Q(τ v ) and Q(τ r ) are the control input τ u , τv and τ r The quantitative value of is the environmental disturbance related to wind, waves and currents; R(ψ), M, C(ν) and D(ν) represent the transformation matrix, inertia matrix, Coriolis and centripetal force matrix and damping matrix respectively. c1=m 22 v+m 23 r,c2=m 11 u,d 11 =X u +X u|u| |u|+X uuu u 2 , d 22 =Y v +Y v|v| |v|+Y v|r| |r|,d 23 =Y r +Y r|v| |v|+Y r|r| |r|,d 32 =Z v +Y v|v| |v|+Y v|r| |r|,d 33 =Z r +Y r|v| |v|+Y r|r| |r|, where m is the mass of the USV, and is the additional mass, x g is the center of gravity of USV, I Z is the inertia matrix about the vertical axis, X u 、X u|u| 、X uuu 、Y v 、Y v|v| 、Y v|r| 、Y r|v| 、Y r 、Y r|r| , Z v , Z v|v| , Z v|r| , Z r , Z r|v| and Z r|r| is the fluid dynamics coefficient;

[0113] S12, all state variables x, y, ψ, u, v, r and control input τ u ,τ v ,τ r Both are quantized using a uniform quantizer:

[0114]

[0115] Where s = x, y, ψ, u, v, r, τ u ,τ v ,τ r , j∈Z + ; h>0 indicates quantization step size; H1=h, H j+1 =H j +h; there is a positive constant Make the quantization error sQ(s) satisfy

[0116] S13, assuming external interference τ ωu , τ ωv and τ ωr is bounded, assuming an ideal reference trajectory is continuously differentiable, and η d and its differential term They are all bounded;

[0117] S14. Let Q(τ) = q1τ + q2, and define:

[0118]

[0119] Where a>0, q1 is time-varying and unknown, Since the sign remains unchanged during the quantization process, we know that q1>0; because Then Q(τ u )-τ u 、Q(τ v )-τ v and Q(τ r )-τ r is bounded, which means |q 2u |、|q 2v |and|q 2r | is also bounded.

[0120] In specific implementation, as a preferred embodiment of the present invention, step S2 specifically includes:

[0121] S21. Define uncertainties Then the USV kinematic and dynamic models are:

[0122]

[0123] S22. Approximate the unknown continuous function F(ν) using a radial basis function neural network (RBFNN), where:

[0124] F(v)=W T Π(v)+

[0125] Where, represents the ideal weight, is the Gaussian function, n is the number of hidden layer nodes, is the observation error; ideal weight and observation errors respectively satisfy ‖W‖≤W * and ‖ε‖≤ε * , W * and ε * is a positive constant; Gaussian function Satisfy ‖Π‖≤Π * , Π * is a positive constant;

[0126] S23. Design a neural network observer as follows:

[0127]

[0128] Where, l1>0, l2>0, and The quantized state variables are Q(η)=[Q(x),Q(y),Q(ψ)] Τ and Q(τ)=[Q(u),Q(v),Q(r)] Τ The estimated value of is the estimated value of W, the approximation error Rotation Matrix

[0129] In specific implementation, as a preferred embodiment of the present invention, step S3 specifically includes:

[0130] S31. Define the error surface as follows:

[0131]

[0132] Where, α1, α2 and α3 are intermediate signals and The filtered signal;

[0133] S32. Define a first-order low-pass filter as follows:

[0134]

[0135] Where i = 1, 2, 3, is the filter gain;

[0136] S33, error surface Taking the derivative, we get:

[0137]

[0138] Defining intermediate signals for Where, κ1>0;

[0139] S34, error surface Taking the derivative, we get:

[0140]

[0141]

[0142] Where, κ2>0,

[0143] S35, design the intermediate signal and adaptive law respectively:

[0144]

[0145] Where, β, δ,σ,ξ, is a positive constant, L1=[tanh(Γ 11 ),tanh(Γ 12 ),tanh(Γ 13 )] T , Γ1=[Γ 11 ,Γ 12 ,Γ 13 ] T , L2=[tanh(Γ 21 ),tanh(Γ 22 ),tanh(Γ 23 )] T , Γ2=[Γ 21 ,Γ 22 ,Γ 23 ] T ,

[0146] S36. Based on the time-varying threshold, design an event-driven strategy as follows:

[0147]

[0148] t k+1 =inf{t∈R,‖e(t)‖≥β‖τ‖+g}

[0149] Where g>0, e(t)=ω(t)-τ(t), we can see that there exists a continuous time-varying coefficient λ2(t) that satisfies λ2(t k )=0,λ2(tk+1 )=±1, and |λ2(t)|≤1, so that:

[0150] ω=τ+λ2(β‖τ‖+g)

[0151] =(1+λ2βsign(τ))τ+λ2g

[0152] =(1+λ1β)τ+λ2g

[0153] In the formula, λ1=λ2sign(τ), |λ1|=|λ2sign(τ)|≤1.

[0154] In specific implementation, as a preferred embodiment of the present invention, step S4 specifically includes:

[0155] S41, for the neural network observer in step S2, the observation error for Taking the derivative of the observation error, we get:

[0156]

[0157] Where, There exists a positive constant R * satisfy

[0158] S42. Define the error state equation of the observer as:

[0159]

[0160] Where,

[0161] S43. Let E=Tθ, Taking the derivative we get:

[0162]

[0163] Where, Λ0=diag(Λ,03), because ‖Π‖≤Π * , ‖W‖≤W * and ‖ε‖≤ε * , then G0 is bounded;

[0164] S44. Define the Lyapunov function as follows:

[0165]

[0166] Where p is a positive definite matrix. To analyze the stability of V1, consider the following set of simultaneous Lyapunov inequalities:

[0167]

[0168] Where ζ>0, To satisfy The boundary of the yaw angular velocity r;

[0169] S45, take the derivative of V1 and get:

[0170]

[0171] Where, Therefore, the observation error of the neural network observer is eventually uniformly bounded;

[0172] S46. Define the Lyapunov function as follows:

[0173]

[0174] S47. Derivative the filtering error to obtain:

[0175]

[0176] There is an upper bound function Then we have:

[0177]

[0178] Among them, the maximum value of Γ3 is recorded as Ω γ ;

[0179] S48. Taking the derivative of V2, we get:

[0180]

[0181] S49, due to If is a positive constant, then Since |λ2g|≤g and 1-β≤|1+λ1β|, we can get Then we have:

[0182]

[0183] because but Therefore, we have:

[0184]

[0185] because and Therefore, we have:

[0186]

[0187] Where, Therefore the control system is stable and all control signals are uniformly ultimately bounded.

[0188] Example

[0189] In order to verify the effectiveness of the solution of the present invention, this embodiment uses MATLAB to perform trajectory tracking control simulation. Figure 2-5 The initial states of the controlled objects are shown as The expected trajectory is ψ d =2sin(0.01t) trajectory tracking results, ship position and heading angle tracking results, tracking error and control input before and after quantization and the time interval between two consecutive event trigger sampling.

[0190] Figure 2 The ship trajectory tracking results are given. Figure 3 The ship position tracking results and bow angle tracking results are given. According to the simulation results, the designed controller has a good control effect on the ship and can well realize ship trajectory tracking.

[0191] Figure 4 and Figure 5 The control inputs before and after quantization are given. According to the simulation results, the quantization process reduces the execution frequency of the controller and the control amplitude, which can effectively alleviate the signal transmission burden in the network communication platform and is more in line with marine engineering practice.

[0192] The simulation results confirm that by considering the input quantization and event triggering mechanism in the control system, the quality of tracking control is not significantly sacrificed while ensuring the stability of the control system.

[0193] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the above embodiments, or replace some or all of the technical features therein with equivalents. However, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. An adaptive trajectory tracking control method for an unmanned vessel with an event triggering mechanism and signal quantization, characterized in that: include: S1. Use a uniform quantizer to quantize the control signal and use a linear analysis model to describe the input quantization process and external interference, including: S11. Under the environmental interference of wind, waves and currents, the kinematic and dynamic models of the USV are constructed as follows: Where, (x, y) and ψ are the position and bow angle of the UAV, respectively; u, v, r are the forward velocity, lateral velocity and yaw angular velocity respectively; Q(τ u ), Q(τ v ) and Q(τ r ) are the control input τ u , τ v and τ r The quantitative value of is the environmental disturbance related to wind, waves and currents; R(ψ), M, C(ν) and D(ν) represent the transformation matrix, inertia matrix, Coriolis and centripetal force matrix and damping matrix respectively. c1=m 22 v+m 23 r,c2=m 11 u,d 11 =X u +X u|u| |u|+X uuu u 2 , d 22 =Y v +Y v|v| |v|+Y v|r| |r|,d 23 =Y r +Y r|v| |v|+Y r|r| |r|,d 32 =Z v +Y v|v| |v|+Y v|r| |r|,d 33 =Z r +Y r|v| |v|+Y r|r| |r|, where m is the mass of the USV, and is the additional mass, x g is the center of gravity of USV, I Z is the inertia matrix about the vertical axis, X u 、X u|u| 、X uuu 、Y v 、Y v|v| 、Y v|r| 、Y r|v| 、Y r 、Y r|r| , Z v , Z v|v| , Z v|r| , Z r , Z r|v| and Z r|r| is the fluid dynamics coefficient; S12, all state variables x, y, ψ, u, v, r and control input τ u ,τ v ,τ r Both are quantized using a uniform quantizer: Where s = x, y, ψ, u, v, r, τ u ,τ v ,τ r , j∈Z + ; h>0 indicates quantization step size; H1=h, H j+1 =H j +h; there is a positive constant Make the quantization error sQ(s) satisfy S13, assuming external interference τ ωu , τ ωv and τ ωr is bounded, assuming an ideal reference trajectory is continuously differentiable, and η d and its differential term They are all bounded; S14. Let Q(τ) = q1τ + q2, and define: Where a>0, q1 is time-varying and unknown, Since the sign remains unchanged during the quantization process, we know that q1>0; because Then Q(τ u )-τ u 、Q(τ v )-τ v and Q(τ r )-τ r is bounded, which means |q 2u |、|q 2v |and|q 2r | is also bounded; S2. Use the neural network observer to estimate the quantized state feedback information, system uncertainty, and external interference, specifically including: S21. Define uncertainties Then the USV kinematic and dynamic models are: S22. Approximate the unknown continuous function F(v) using a radial basis function neural network, where: F(v)=W T P(v)+e Where, represents the ideal weight, is the Gaussian function, n is the number of hidden layer nodes, is the observation error; ideal weight and observation errors respectively satisfy ‖W‖≤W * and ‖ε‖≤ε * , W * and ε * is a positive constant; Gaussian function Satisfy ‖Π‖≤Π * , Π * is a positive constant; S23. Design a neural network observer as follows: Where, l1>0, l2>0, and The quantized state variables are Q(η)=[Q(x),Q(y),Q(ψ)] Τ and Q(τ)=[Q(u),Q(v),Q(r)] Τ The estimated value of is the estimated value of W, the approximation error Rotation Matrix S3. Combining backstepping, dynamic surface technology, and event triggering mechanism, using the neural network observer to observe the results, design a quantitative feedback controller, including: S31. Define the error surface as follows: Where, α1, α2 and α3 are intermediate signals and The filtered signal; S32. Define a first-order low-pass filter as follows: Where i = 1, 2, 3, is the filter gain; S33, error surface Taking the derivative, we get: Defining intermediate signals for Where, κ1>0; S34, error surface Taking the derivative, we get: Where, κ2>0, S35, design the intermediate signal and adaptive law respectively: where β, δ, σ, ξ, are positive constants, L1 = [tanh(Γ 11 ), tanh(Γ 12 ), tanh(Γ 13 )] T , Γ1 = [Γ 11 , Γ 12 , Γ 13 T ,​ L2=[tanh(Γ 21 ),tanh(Γ 22 ),tanh(Γ 23 )] T ,Γ2=[Γ 21 ,Γ 22 ,Γ 23 ] T , S36. Based on the time-varying threshold, design an event-driven strategy as follows: t k+1 =inf{t∈R,‖e(t)‖≥β‖τ‖+g} Where g>0, e(t)=ω(t)-τ(t), we can see that there exists a continuous time-varying coefficient λ2(t) that satisfies λ2(t k )=0,λ2(t k+1 )=±1, and |λ2(t)|≤1, so that: ω=τ+λ2(β‖τ‖+g) =(1+λ2βsign(τ))τ+λ2g =(1+λ1β)τ+λ2g In the formula, λ1=λ2sign(τ), |λ1|=|λ2sign(τ)|≤1; S4. Based on Lyapunov stability theory, prove the observation error of the neural network observer and the stability of the designed USV adaptive trajectory tracking control system with event triggering mechanism and signal quantization. Specifically: S41, for the neural network observer in step S2, the observation error for Taking the derivative of the observation error, we get: Where, There exists a positive constant R * satisfy S42. Define the error state equation of the observer as: Where, S43. Let E=Tθ, Taking the derivative we get: Where, Λ0=diag(Λ,03), because ‖Π‖≤Π * , ‖W‖≤W * and ‖ε‖≤ε * , then G0 is bounded; S44. Define the Lyapunov function as follows: Where p is a positive definite matrix. To analyze the stability of V1, consider the following set of simultaneous Lyapunov inequalities: Where ζ>0, To satisfy The boundary of the yaw angular velocity r; S45, take the derivative of V1 and get: Where, Therefore, the observation error of the neural network observer is eventually uniformly bounded; S46. Define the Lyapunov function as follows: S47. Derivative the filtering error to obtain: There is an upper bound function Then we have: Among them, the maximum value of Γ3 is recorded as Ω γ ; S48. Taking the derivative of V2, we get: S49, due to is a positive constant, then Since |λ2g|≤g and 1-β≤|1+λ1β|, we can get Then we have: because but Therefore, we have: because and Therefore, we have: Where, Therefore the control system is stable and all control signals are uniformly ultimately bounded.

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