Under-actuated asv based on memory event-triggered time-regulated performance control method

Abstract

The application discloses a kind of event trigger regulation time performance control method based on memory applied to underactuated ASV, including constructing preset regulation time performance function, to obtain trajectory tracking constraint according to initial condition, the function allows to define convergence time, and eliminates the constraint problem that initial error must be within performance boundary;Based on deep neural network DNN, according to ASV dynamics model, obtain the optimization ASV dynamics model containing DNN modeling error, construct modeling error approximation observer, approximate the DNN modeling error in optimization ASV dynamics model, to construct deep learning controller, learn the unknown dynamics of ASV by designing deep learning controller, improve the accuracy of learning and enhance the interpretability of DNN;Based on the memory event trigger mechanism constructed, it is used for optimizing communication resource utilization, and can be dynamically adjusted according to real-time data and historical data, when control signal mutation occurs, memory event trigger mechanism gives priority to historical data, overcome the problem that traditional event trigger mechanism excessively relies on real-time data.

Description

Technical Field

[0001] This invention relates to the field of marine technology engineering technology, and in particular to a memory-based event-triggered time performance control method for underactuated ASVs. Background Technology

[0002] Autonomous surface vehicles (ASVs), due to their fewer control inputs than degrees of freedom, possess advantages such as small size, low cost, and high autonomy, and are therefore widely used in various maritime missions. In recent years, increasing research has focused on the motion control problem of non-fully driven ASVs, especially trajectory tracking control, which has high time-sensitivity requirements. In actual maritime missions, ASVs face unknown, time-varying dynamics and are limited by finite communication bandwidth. In this context, developing effective control strategies is crucial for achieving high-performance trajectory tracking. Current trajectory tracking control methods for autonomous surface vehicles include the following:

[0003] In narrow and congested waterways, the control performance of ASVs is particularly critical. Predetermined performance control (PPC) improves performance by confining the system state within predefined boundaries. Recently, PPC has been successfully applied to various ASV tasks, including formation control and trajectory tracking. However, in congested waterways, traditional PPC may increase collision risk and reduce navigation accuracy. By improving the PPC function, collision avoidance and connectivity in non-fully driven ASV formation control are achieved. Typically, PPC faces challenges from practical problems, including uncertain convergence time and strict constraints on initial errors. To address the limitations of traditional PPC methods in terms of uncertain convergence time, PTPF is introduced. PTPF ensures that the system error converges to the specified boundary within a user-defined time. However, the strict initial error constraint imposed by PTPF is often difficult to meet in practical applications, and addressing the impact of the strict initial error constraint in PTPF has become an important research direction.

[0004] Accurate modeling of the unknown time-varying dynamics of ASVs is crucial for achieving high-performance trajectory tracking control. Deep neural networks (DNNs), due to their powerful nonlinear representation capabilities and feature memory, have been considered ideal tools for modeling complex systems. However, applying DNNs to ASV motion control faces three major challenges: the need for large amounts of training data, poor adaptability to complex environments, and the complexity of stability analysis. Traditional offline training methods are unsuitable for dynamic environments due to their high cost and limited scalability for model retraining.

[0005] Maritime communication is constrained by limited bandwidth, a limitation that traditional fixed-interval transmission mechanisms struggle to overcome. In contrast, Event Triggered Mechanisms (ETMs) offer variable transmission intervals, transmitting data only when necessary, thus avoiding unnecessary bandwidth waste. It's important to note that traditional ETMs primarily rely on the error between current data and the previous trigger data to determine transmission. This design makes ETMs overly sensitive to instantaneous data fluctuations, ignoring historical information and potentially leading to poor adaptability in real-world sea conditions. For example, in high-precision tracking tasks, fluctuations in control signals or system failures can cause the ETM trigger threshold to be determined by invalid signals, wasting communication resources and degrading performance. To address this issue, Medium Magnetic Mechanisms (METMs) have been proposed, optimizing communication resource usage and incorporating historical data. However, METMs rely on long-term data; when system failures or anomalies occur, the stored data inevitably deviates from normal values, leading to performance degradation. Therefore, designing effective detection rules to prevent such problems has become a key research focus. Summary of the Invention

[0006] This invention provides a memory-based event triggering time performance control method for underdriven ASVs to overcome the above-mentioned technical problems.

[0007] To achieve the above objectives, the technical solution of the present invention is as follows:

[0008] A memory-based event-triggered time performance control method for underdriven ASVs specifically includes the following steps:

[0009] S1: Construct a mathematical model for an underdriven ASV;

[0010] Obtain the dynamic model of ASV containing unknown dynamic terms based on the mathematical model of underactuated ASV;

[0011] S2: Obtain the amount of tracking data based on the underactuated ASV mathematical model;

[0012] Furthermore, the amount of tracking data includes relative distance and relative azimuth angle;

[0013] The tracking position error is defined based on the amount of tracking data, and the initial conditions for the tracking position error are obtained based on the constructed sigmoid function.

[0014] Construct a predefined time performance function to obtain trajectory tracking constraints based on initial conditions;

[0015] S3: Construct an error transformation function to limit the tracking position error based on the trajectory tracking constraints;

[0016] And construct a virtual control law based on the error transformation function;

[0017] S4: Based on the deep neural network (DNN), obtain an optimized ASV dynamic model that includes the modeling error of the DNN according to the ASV dynamic model;

[0018] Construct a modeling error approximation observer to approximate and process the DNN modeling error in the optimized ASV dynamics model, and obtain the ASV dynamics estimation model;

[0019] S5: Obtain the tracking variable error based on the ASV dynamic estimation model and the virtual control law;

[0020] A deep learning controller is constructed based on the tracking variable error, combined with the ASV dynamic estimation model and the virtual control law. Based on the constructed memory event triggering mechanism, the deep learning controller realizes the tracking control of the underactuated ASV.

[0021] Furthermore, S1 specifically includes the following steps:

[0022] S11: Construct the mathematical model of the underactuated ASV, its expression is as follows:

[0023]

[0024] In the formula: η represents the position and heading angle of the ASV, and η = [x, y, ψ]. T ν represents the velocity vector and ν = [u, v, r] T u, v, r represent forward velocity, lateral velocity, and yaw rate, respectively; q represents the control input and q = [q u ,0,q r ] T ;q u ,q r The control inputs provided by the thrusters and rudder are represented; M, C(ν), and D(v) represent the mass matrix, Coriolis matrix, and hydrodynamic damping matrix, respectively; d represents the unknown disturbance and d = [d u ,d v ,d r ] T ;d u ,d v ,d r Represents the external unknown disturbance of the underactuated ASV; R(ψ) represents the rotation matrix used to convert the hull coordinate system to the inertial coordinate system; Denotes the first derivative of η; Let v denote the first derivative of v.

[0025] S12: Obtain the ASV dynamic model containing unknown dynamic terms from the underactuated ASV mathematical model, and the expression of the ASV dynamic model containing unknown dynamic terms is:

[0026]

[0027] G(v,q,d)=-(M * ) -1 q+M -1 (-C(ν)vD(ν)ν+d+q)

[0028] Where: M * G(v,q,d) represents the nominal mass of the off-diagonal inertia matrix; G(v,q,d) represents the unknown dynamic term of the ASV dynamics model; M represents the off-diagonal inertia mass matrix.

[0029] Furthermore, S2 specifically includes the following steps:

[0030] S21: Obtain the amount of tracking data based on the underactuated ASV mathematical model;

[0031] Furthermore, the amount of tracking data includes relative distance and relative azimuth angle;

[0032] The expressions for the relative distance and relative azimuth angle are as follows:

[0033]

[0034] θ = atan2(Δy, Δx)

[0035] Δx=x l -x,Δy=y l -y

[0036] φ=θ-ψ

[0037] In the formula: d represents the relative distance, φ represents the relative azimuth angle, and d min <d<d max , d min ,d max These represent the maximum and minimum values ​​of the relative distance, respectively. The upper bound of the relative azimuth angle is represented by θ; the desired heading angle is represented by θ; Δx and Δy represent intermediate parameters; x l ,y l Represents the x-coordinate and y-coordinate of the desired trajectory position;

[0038] S22: Define the tracking position error based on the amount of tracking data; its expression is as follows:

[0039] e k =kk d ,k=d,φ

[0040] In the formula: e k Indicates the tracking position error; k represents the relative distance or relative azimuth angle; k d Indicates the desired relative distance or desired relative azimuth angle;

[0041] S23: Define the sigmoid function for the underactuated ASV system to be used to reduce the initial tracking position error e of the underactuated ASV system. k (0) does not necessarily have to be constrained to a predefined region;

[0042] And the expression for the sigmoid function S(t) is:

[0043]

[0044] In the formula: α and T q Indicates the design parameters; t represents the time parameter;

[0045] S24: Based on the sigmoid function S(t), the time modulation error E is obtained according to the tracking position error. k And E k =S(t)e k To obtain the initial conditions for tracking position error;

[0046] And the expression for the initial condition of the tracking position error is:

[0047] d min -d d <E d <d max -d d

[0048]

[0049] S25: Construct a predefined time performance function;

[0050] And the expression for the preset time performance function is:

[0051]

[0052] T q =cos((π(tT) m ))(T f -T m ) -1 )

[0053] In the formula: T represents constant gain; m Indicates the transition time; T f Indicates the set time; This represents a piecewise function with intermediate parameters; t0 represents the rate constant of control time decay; t0 represents the start time, i.e., the moment when the control process begins. This indicates that the system will ensure that the system is within the set time T. fThe function that determines the completion of the target task over time; Indicates control gain; Represents the gain matrix; express The steady-state value; and Indicates a positive design constant; This represents the error convergence control variable; express first derivative and for The abbreviated form is k = d, φ;

[0054] S26: Based on a preset time performance function, obtain trajectory tracking constraints according to initial conditions;

[0055] And the expression for the trajectory tracking constraint is:

[0056]

[0057] Where: δ 1d ,δ 2d ,δ 1φ ,δ 2φ This represents a positive proportionality coefficient used to adjust the convergence speed of the error; This represents the control variable used to adjust the convergence of relative distance and relative azimuth angle errors.

[0058] Furthermore, S3 specifically includes the following steps:

[0059] S31: Construct an error transformation function to limit the tracking position error based on the trajectory tracking constraints;

[0060] And the expression for the error transformation function is:

[0061]

[0062] S32: Construct a virtual control law based on the error transformation function, and the expression of the virtual control law is as follows:

[0063]

[0064] In the formula: γ=[γ u ,γ v ,γ r ] T The virtual control law representing the forward velocity, lateral velocity, and yaw rate, ζ u ,ζ v ,ζ r Indicates the intermediate parameter quantity and ζ u =α u tanh(β u ),ζv =α v tanh(β v ),ζ r =α r tanh(β r );α u ,α v ,α r Indicates the design parameter, β u ,β v ,β v Represents auxiliary system variables; Σ d Indicates the amount of intermediate parameters; d d The first derivative; Represented as design parameters and β u ,β v ,β r , Represents an unknown parameter, and is derived from the ship's forward pilot velocity u. l The estimated value With lateral leader velocity v l The estimated value get; Representing unknown parameters The estimate of π; k , Indicates an intermediate variable; and k = d, φ; χ φ The function representing the adjustment of the yaw angle.

[0065] Furthermore, S4 specifically includes the following steps:

[0066] S41: Based on the deep neural network (DNN), obtain an optimized ASV dynamic model that includes the modeling error of the DNN according to the ASV dynamic model;

[0067] The expression for the optimized ASV dynamics model, which includes DNN modeling errors, is:

[0068]

[0069] In the formula: This indicates that, based on a deep neural network (DNN), dynamic key data features of an ASV (Automatic Tracking Vehicle) are learned and captured within an unseen input domain using pre-defined historical tracking trajectory data. These dynamic key data features include the velocity vector, control input, and unknown disturbances. The loss function for learning and capturing these dynamic key data features based on the DNN is EL. b (L t G0 represents the DNN modeling error and G0 = [G u0 G v0 Gr0 ], G u0 G v0 G r0 These represent the forward velocity error, lateral velocity error, and yaw rate error in DNN modeling, respectively. Represents the weights of a deep neural network (DNN); Represents the parameter space; G t (v t ,q t ,d t ) represents the actual value used to quantify the dynamic key data of ASV in the t-th iteration; represents the learning value used to quantize the dynamic key data of ASV at the t-th iteration; b represents the true distribution; B represents the distribution of the historical tracking trajectory data.

[0070] S42: Construct a modeling error approximation observer to approximate and process the DNN modeling error in the optimized ASV dynamics model, thereby obtaining the ASV dynamics estimation model;

[0071] And the expression for modeling error approximating the observer is:

[0072]

[0073] In the formula: This represents an estimate of v; Describes the estimate of G0 and M1 and M2 represent the observer parameter matrices and I3 represents the observer parameters; I3 represents the 3×3 identity matrix. express The first derivative; express The first derivative; express The simplified form is given by v = [u, v, r]. T .

[0074] Furthermore, S5 specifically includes the following steps:

[0075] S51: Obtain the tracking variable error based on the ASV dynamic estimation model and the virtual control law, and the expression for the tracking variable error is as follows:

[0076] z = v - γ - ζ

[0077] z = [z u ,z v ,z r ] T ζ=[ζ u ,ζ v ,ζr ] T

[0078] S52: Construct a deep learning controller based on the tracking variable error, combined with the ASV dynamic estimation model and the virtual control law, and the expression of the deep learning controller is:

[0079]

[0080] In the formula: ξ u1 ,η u1 ,ξ r1 ,η r1 Both represent auxiliary system variables used to adjust the dynamic response of the control input, i.e., gain coefficients or adjustment factors ε related to controller regulation. u ,ε r This represents the error term related to the control signal; μ represents the external disturbance estimate or estimated control parameter obtained based on the modulus error approximation observer; u ,μ r These represent the system adjustment parameters used to control the dynamic response of the error. This represents the reference mass associated with the control inputs u and r; Represents the estimated parameters used to adjust the control input; ∈ c k represents the adjustment constant used to limit the amplitude of the control input; u ,k v ,k r ,Γ p ,v p Indicates a positive design parameter; Represents χ p The estimated value of ω; p With ω r Indicates the intermediate parameter quantity and ω u =z d π d cosφ,ω v =-z d π d sinφ and ω r =z φ π φ ;

[0081] S53: Construct a memory event triggering mechanism, and based on the constructed memory event triggering mechanism, implement tracking control of the underactuated ASV according to the deep learning controller;

[0082] Furthermore, the constructed memory event triggering mechanism is specifically as follows:

[0083]

[0084] |e p(t)|≥ξ p1 (|η p1 q p (t)+η p2 q p (t-τ)|)+η p3

[0085] η p1 =1-η p2

[0086]

[0087] η p3 =-J p η p3 +ξ p1 (|η p1 q p (t)+η p2 q p (t-τ)|)-|e p (t)|

[0088] In the formula: Indicates at t j The control output of the time-of-flight deep learning controller; e p (t) represents the triggering error of the memory event triggering mechanism and ξ p1 ,ξ p2 Indicates the preset threshold parameter; η p1 ,η p2 ,η p3 Indicates the amount of intermediate parameters; q p (t) represents the time interval [t] j ,t j+1 The actual control input within ) ; t j ,t j+1 Indicates the time parameter; q p (t-τ) represents the delay control input at time τ; J p Indicate design parameters;

[0089] Furthermore, the memory event triggering mechanism is rewritten as follows:

[0090] e p =α p1 (ξ p1 η p1 q p (t)+ξ p1 η p2 q p (t-τ))+α p2 η p3

[0091]

[0092] In the formula: α p1 ,α p2 Both represent intermediate parameter variables; α p Denotes the design parameters and αp∈[-1,1]; q p q p (t) is a shorthand form;

[0093] Based on the triggering error of the memory event triggering mechanism, and combined with the rewritten memory event triggering mechanism, the actual control input of the underactuated ASV is expressed as follows:

[0094]

[0095] The beneficial effects of this invention are as follows:

[0096] (1) The present invention obtains trajectory tracking constraints by constructing a preset time performance function, allowing users to customize the convergence time without relying on the initial conditions or parameters of the system, and removing the limitation of the existing PPC method that assumes the initial error must be within the constraint boundary.

[0097] (2) Based on the deep neural network (DNN), this invention obtains an optimized ASV dynamic model containing DNN modeling errors according to the ASV dynamic model, and approximates and processes the DNN modeling errors in the optimized ASV dynamic model by constructing a modeling error approximation observer. This invention proposes a deep learning method based on DNN, which realizes real-time online learning of unknown ASV dynamics. Compared with offline learning methods, this method eliminates the need for large-scale data storage and provides real-time estimation and compensation of DNN learning errors, enhancing interpretability.

[0098] (3) Based on the constructed memory event triggering mechanism METC, the tracking control of the underactuated ASV is realized by the deep learning controller. The METC proposed in this invention allows the triggering conditions to be adjusted according to historical data and real-time data. When the control signal changes abruptly, METC emphasizes historical data, which solves the problem of traditional ETM relying too much on real-time data. Under METC, the data utilization rate is improved, and at the same time, the excessive redundancy of historical data is prevented. Attached Figure Description

[0099] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the 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.

[0100] Figure 1This is a flowchart of the memory-based event-triggered time performance control method for underdriven ASVs according to the present invention;

[0101] Figure 2 This is a block diagram of the control architecture for the memory-based event-triggered online deep learning controller in this embodiment.

[0102] Figure 3 This is a schematic diagram of planetary trajectory simulation using the method in this embodiment;

[0103] Figure 4 This is a schematic diagram comparing positional errors in this embodiment;

[0104] Figure 5 This is a schematic diagram comparing angle errors in this embodiment;

[0105] Figure 6 This is a simulation diagram of the learning performance of the deep neural network (DNN) in this embodiment;

[0106] Figure 7 This is a simulation diagram of the observation accuracy of the modeling error approximation observer in this embodiment;

[0107] Figure 8 This is a simulation diagram of the control input in this embodiment;

[0108] Figure 9 This is a schematic diagram illustrating the time intervals between events in this embodiment;

[0109] Figure 10 This is a comparative diagram of the initial points outside the constraint boundary in this embodiment;

[0110] Figure 11 This is a schematic diagram showing the relative distance between the initial point and the constraint boundary in this embodiment. Detailed Implementation

[0111] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments 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.

[0112] This embodiment provides a memory-based event-triggered time-defined performance control method for underactuated ASVs, such as... Figures 1 to 2 As shown, the specific steps include:

[0113] S1: Construct a mathematical model for an underdriven ASV;

[0114] Obtain the dynamic model of ASV containing unknown dynamic terms based on the mathematical model of underactuated ASV;

[0115] Specifically, the following steps are included:

[0116] S11: Construct the mathematical model of the underactuated ASV, its expression is as follows:

[0117]

[0118] In the formula: η represents the position and heading angle of the ASV, and η = [x, y, ψ]. T v represents the velocity vector and v = [u, v, r] T u, v, r represent forward velocity, lateral velocity, and yaw rate, respectively; q represents the control input and q = [q u ,0,q r ] T ;q u ,q r This indicates the control inputs provided by the thrusters and rudder; Let d represent the mass matrix, Coriolis matrix, and hydrodynamic damping matrix, respectively; d represents the unknown disturbance and d = [d u ,d v ,d r ] T ;d u ,d v ,d r This indicates an unknown external disturbance to the underactuated ASV; This represents the rotation matrix used to convert the ship's coordinate system to an inertial coordinate system; Denotes the first derivative of η; Let v denote the first derivative of v.

[0119] S12: Obtain the ASV dynamic model containing unknown dynamic terms from the underactuated ASV mathematical model, and the expression of the ASV dynamic model containing unknown dynamic terms is:

[0120]

[0121] G(v,q,d)=-(M * ) -1 q+M -1 (-C(ν)ν-D(ν)ν+d+q)

[0122] Where: M * G(v,q,d) represents the nominal mass of the off-diagonal inertia matrix; G(v,q,d) represents the unknown dynamic term of the ASV dynamics model; M represents the off-diagonal inertia mass matrix.

[0123] S2: Obtain the amount of tracking data based on the underactuated ASV mathematical model;

[0124] Furthermore, the tracking data includes relative distance and relative azimuth angle; the tracking position error is defined based on the tracking data, and the initial conditions for the tracking position error are obtained based on the constructed sigmoid function; a preset time performance function is constructed to obtain trajectory tracking constraints based on the initial conditions;

[0125] Specifically, the following steps are included:

[0126] S21: Obtain the amount of tracking data based on the underactuated ASV mathematical model;

[0127] Furthermore, the amount of tracking data includes relative distance and relative azimuth angle;

[0128] The expressions for the relative distance and relative azimuth angle are as follows:

[0129]

[0130] θ = atan2(Δy, Δx)

[0131] Δx=x l -x,Δy=y l -y

[0132] φ=θ-ψ

[0133] In the formula: d represents the relative distance, φ represents the relative azimuth angle. Considering the physical constraints of the sensor, as well as the requirements for collision avoidance and connectivity, the relative distance and angle should satisfy d. min <d<d max , That is, the follower can only detect the leader, ensure connectivity, and avoid collisions when the constraints are met; min ,d max These represent the maximum and minimum values ​​of the relative distance, respectively, and are positive constants. θ represents a positive constant representing the upper bound of the relative azimuth angle; θ represents the desired heading angle; Δx and Δy represent intermediate parameters; x l ,y l Represents the x-coordinate and y-coordinate of the desired trajectory position;

[0134] S22: Define the tracking position error based on the amount of tracking data; its expression is as follows:

[0135] e k =kk d ,k=d,φ

[0136] In the formula: e k Indicates the tracking position error; k represents the relative distance or relative azimuth angle; k dIndicates the desired relative distance or desired relative azimuth angle;

[0137] S23: To avoid the constraints of the initial conditions, i.e., the tracking error e k (0) It must begin within a predefined region, i.e., define the sigmoid function of the underactuated ASV system to use the initial tracking position error e of the underactuated ASV system. k (0) does not necessarily have to be constrained to a predefined region;

[0138] And the expression for the sigmoid function S(t) is:

[0139]

[0140] In the formula: α and T q Indicates the design parameters; t represents the time parameter;

[0141] S24: Based on the sigmoid function S(t), the time modulation error E is obtained according to the tracking position error. k And E k =S(t)e k To obtain the initial conditions for tracking position error;

[0142] And the expression for the initial condition of the tracking position error is:

[0143] d min -d d <E d <d max -d d

[0144]

[0145] S25: Construct a predefined time performance function;

[0146] And the expression for the preset time performance function is:

[0147]

[0148]

[0149] T q =cos((π(tT) m ))(T f -T m ) -1 )

[0150] In the formula: T represents constant gain; m Indicates the transition time; T f Indicates the set time; This represents a piecewise function with intermediate parameters; This represents the rate constant controlling time decay and its effect The rate of change; t0 represents the start time, i.e., the moment when the control process begins; This indicates that the system will ensure that the system is within the set time T. f The function that determines the completion of the target task over time; Control gain is used to represent the follower's control strategy or acceleration factor. The gain matrix is ​​used to weight the error, and can adjust the error correction amount according to the system state. express The steady-state value; and Indicates a positive design constant; This represents the error convergence control variable; express first derivative and for The abbreviated form is k = d, φ;

[0151] This embodiment also includes Theorem 1: namely, considering a preset time performance function, state Able to complete within the specified time T f Convergence to For t∈[T] f (,∞) always holds true;

[0152] Assumption 1: The desired trajectory can be represented as η l (t)=[x l (t),y l (t),ψ l [t] and assume the velocity of the desired trajectory is u l and v l It is bounded, that is: and In the formula and It is an unknown positive constant;

[0153] Assumption 2: Modeling error G0 and its time derivative It is bounded;

[0154] S26: In order to ensure high-performance control in trajectory tracking tasks, trajectory tracking constraints are obtained based on the initial conditions according to the preset time performance function.

[0155] And the expression for the trajectory tracking constraint is:

[0156]

[0157] Where: δ1d ,δ 2d ,δ 1φ ,δ 2φ This represents a positive proportionality coefficient used to adjust the convergence speed of the error; This represents the control variable used to adjust the convergence of relative distance and relative azimuth angle errors;

[0158] S3: Construct an error transformation function to limit the tracking position error based on the trajectory tracking constraints;

[0159] And construct a virtual control law based on the error transformation function;

[0160] Specifically, the following steps are included:

[0161] S31: In order to ensure that the tracking position error can converge to the limit of the trajectory tracking constraint, an error transformation function is constructed to limit the tracking position error based on the trajectory tracking constraint;

[0162] And the expression for the error transformation function is:

[0163]

[0164] This embodiment can infer, based on the error transformation function, that when z... k As we approach ±∞, this is equivalent to and And z k =0 price at e k =0;

[0165] Differentiating the error transformation function yields:

[0166] In the formula: and

[0167]

[0168] ξ k This represents an auxiliary function that includes error and control gain;

[0169] By differentiating the tracking position error, we obtain:

[0170]

[0171] Based on hypothesis 2, it can be assumed that airborne sensors cannot typically be directly used to measure the speed information of leaders. Therefore, the definition is... In the formula Yes The estimate;

[0172] Consider the following Lyanov function:

[0173]

[0174] To facilitate stability verification, the derivative of the Lyanov function V1 can be derived by combining the above process as follows:

[0175]

[0176] In the formula: k represents the rate of change of the dynamic variable velocity over time. ξ It represents the control gain constant, used to adjust the controller's response speed or intensity;

[0177] S32: Construct a virtual control law based on the error transformation function, and the expression of the virtual control law is as follows:

[0178]

[0179] In the formula: γ=[γ u ,γ v ,γ r ] T The virtual control law representing the forward velocity, lateral velocity, and yaw rate, ζ u ,ζ v ,ζ r Indicates the intermediate parameter quantity and ζ u =α u tanh(β u ),ζ v =α v tanh(β v ),ζ r =α r tanh(β r );α u ,α v ,α r Indicates the design parameter, β u ,β v ,β v Represents auxiliary system variables; Σ d Indicates the amount of intermediate parameters; d d The first derivative; Represented as design parameters and β u ,β v ,β r , Represents an unknown parameter, and is derived from the ship's forward pilot velocity u. l The estimated value With lateral leader velocity v l The estimated value get; Representing unknown parameters The estimate of π; k, Indicates an intermediate variable; and k = d, φ; χ φ The adjustment function representing the yaw angle;

[0180] S4: Based on the deep neural network (DNN), obtain an optimized ASV dynamic model that includes the modeling error of the DNN according to the ASV dynamic model;

[0181] Construct a modeling error approximation observer to approximate and process the DNN modeling error in the optimized ASV dynamics model, and obtain the ASV dynamics estimation model;

[0182] Specifically, the following steps are included:

[0183] S41: In order to address the problem that G(v,q,d) is not applicable, this embodiment uses a deep neural network (DNN) to learn the unknown dynamics of the ASV (Autonomous Underwater Vehicle) online, and represents the learned dynamics as... in Represents the weights of the DNN. This is the parameter space, where deep learning is based on the process of approximating a function by extracting features from the input data using many neurons to create multiple hidden layers. Deep neural networks (DNNs) combine data features through composite functions, thus mapping the input x to the output G(x,α), whose expression is:

[0184] G(x,α)=ψ k (α k-1 ,ψ k-1 (α k-2 ,ψ k-2 (...)))

[0185] In the formula: G(x,α) represents the output of the neural network; ψ k α represents the feature extraction at the k-th layer; k-1 α represents the weight of the (k-1)th layer; j ψ represents the weight of the j-th layer; j Let represent the feature vector of the j-th layer, where j = 1, 2, ..., k; In this embodiment, online learning, as a branch of machine learning, focuses on making predictions or decisions by sequentially processing data samples. Its goal is to improve learning accuracy by utilizing previous results and preset data. The online learning task is as follows: Let the processed data sequence be... Where t represents the number of iterations, and the true value of each output is represented by... This means that in the t-th iteration, the learner uses x t Predicted output Then receive the real value G. t Therefore, the loss is calculated, such as By according to (x)t G t Adjusting parameters to update the model from... Unlike offline learning, online learning updates the model as each new data point arrives, making it more efficient and scalable in real-world applications that require rapid response and processing of large-scale data.

[0186] Therefore, this embodiment is based on a deep neural network (DNN) and obtains an optimized ASV dynamics model that includes the modeling error of the DNN based on the ASV dynamics model;

[0187] The expression for the optimized ASV dynamics model, which includes DNN modeling errors, is:

[0188]

[0189] In the formula: This indicates that, based on a deep neural network (DNN), dynamic key data features of an ASV (Automatic Tracking Vehicle) are learned and captured within an unseen input domain using pre-defined historical tracking trajectory data. These dynamic key data features include the velocity vector, control input, and unknown disturbances. The loss function for learning and capturing these dynamic key data features based on the DNN is EL. b (L t G0 represents the DNN modeling error and G0 = [G u0 G v0 G r0 ], G u0 G v0 G r0 These represent the forward velocity error, lateral velocity error, and yaw rate error in DNN modeling, respectively. Represents the weights of a deep neural network (DNN); Represents the parameter space; G t (v t ,q t ,d t ) represents the actual value used to quantify the dynamic key data of ASV in the t-th iteration; represents the learning value used to quantize the dynamic key data of ASV at the t-th iteration; b represents the true distribution; B represents the distribution of the historical tracking trajectory data.

[0190] The goal of the deep neural network (DNN) in this embodiment is to capture key data features of autonomous surface vessels (ASVs) dynamics in an unseen input domain. This embodiment uses the Adam optimizer to accelerate the training of the DNN and improve the optimization effect. The Adam optimizer combines the advantages of the Momentum and RMS Prop optimizers, and has better convergence and stability. The zero-mean normalization method ensures that each input has an equal impact on the DNN. The trained DNN exhibits strong generalization ability and can perform trajectory tracking without sacrificing performance. The structure of the deep neural network (DNN) in this embodiment is given in Algorithm 1.

[0191]

[0192] S42: In order to enhance the interpretability of deep neural networks (DNNs), a modeling error approximation observer is constructed based on the optimized ASV dynamics model to approximate the DNN modeling error in the optimized ASV dynamics model and obtain the ASV dynamics estimation model.

[0193] And the expression for the modulus error approximation observer is:

[0194]

[0195] In the formula: This represents an estimate of ν; Describes the estimate of G0 and M1 and M2 represent the observer parameter matrices and I3 represents the observer parameters; I3 represents the 3×3 identity matrix. express The first derivative; express The first derivative; express The simplified form is given by ν = [u, v, r]. T ;

[0196] S5: Obtain the tracking variable error based on the ASV dynamic estimation model and the virtual control law;

[0197] A deep learning controller is constructed based on the tracking variable error, combined with the ASV dynamic estimation model and the virtual control law. Based on the constructed memory event triggering mechanism, the deep learning controller is used to achieve tracking control of the underactuated ASV.

[0198] Specifically, the following steps are included:

[0199] S51: Obtain the tracking variable error based on the ASV dynamic estimation model and the virtual control law, and the expression for the tracking variable error is as follows:

[0200] z=ν-γ-ζ

[0201] z = [z u ,z v ,z r ] T ζ=[ζ u ,ζ v ,ζ r ] T

[0202] S52: In this embodiment, by differentiating the tracking variable error, we can obtain:

[0203]

[0204] And consider the following adaptive laws Substituting the virtual control law and the differentiated tracking variable error into the Lyanov function V1, we can obtain...

[0205]

[0206] In the formula: ω u =z d π d cosφ,ω v =-z d π d sinφ and ω r =z φ π φ And j = u, v, r, according to Lemma 1 and Assumption 2, the derivative of the Lyanov function in step S52 is... Represented as:

[0207]

[0208] In the formula: Indicate design parameters and

[0209] To reduce execution frequency, this embodiment introduces a memory event triggering mechanism based on a relative threshold. A deep learning controller is constructed by combining the tracking variable error with the ASV dynamic estimation model and the virtual control law. The expression of the deep learning controller is as follows:

[0210]

[0211] In the formula: ξ u1 ,η u1 ,ξ r1 ,η r1 Both represent auxiliary system variables used to adjust the dynamic response of the control input, i.e., gain coefficients or adjustment factors ε related to controller regulation. u ,εr This represents the error term related to the control signal; μ represents the external disturbance estimate or estimated control parameter obtained based on the modulus error approximation observer; u ,μ r These represent the system adjustment parameters used to control the dynamic response of the error. This represents the reference mass associated with the control inputs u and r; Represents the estimated parameters used to adjust the control input; ∈ c k represents the adjustment constant used to limit the amplitude of the control input; u ,k v ,k r ,Γ p ,v p Indicates a positive design parameter; Represents χ p The estimated value of ω; p With ω r Indicates the intermediate parameter quantity and ω u =z d π d cosφ,ω v =-z d π d sinφ and ω r =z φ π φ ;

[0212] S53: Construct a memory event triggering mechanism, and based on the constructed memory event triggering mechanism, implement tracking control of the underactuated ASV according to the deep learning controller;

[0213] Furthermore, the constructed memory event triggering mechanism is specifically as follows:

[0214]

[0215] |e p (t)|≥ξ p1 (|η p1 q p (t)+η p2 q p (t-τ)|)+η p3

[0216] η p1 =1-η p2

[0217]

[0218] η p3 =-J p η p3 +ξ p1 (|ηp1 q p (t)+η p2 q p (t-τ)|)-|e p (t)|

[0219] In the formula: Indicates at t j The control output of the time-of-flight deep learning controller; e p (t) represents the triggering error of the memory event triggering mechanism and ξ p1 ,ξ p2 Indicates the preset threshold parameter; η p1 ,η p2 ,η p3 Indicates the amount of intermediate parameters; q p (t) represents the time interval [t] j ,t j+1 The actual control input within ) ; t j ,t j+1 Indicates the time parameter; q p (t-τ) represents the delay control input at time τ; J p Indicate design parameters;

[0220] Furthermore, in order to facilitate controller design, the memory event triggering mechanism in this embodiment is rewritten as follows:

[0221] e p =α p1 (ξ p1 η p1 q p (t)+ξ p1 η p2 q p (t-τ))+α p2 η p3

[0222]

[0223] In the formula: α p1 ,α p2 Both represent intermediate parameter variables; α p Indicates the design parameters and α p ∈[-1,1];q p q p (t) is a shorthand form;

[0224] Based on the triggering error of the memory event triggering mechanism, and combined with the rewritten memory event triggering mechanism, the actual control input of the underactuated ASV is expressed as follows:

[0225]

[0226] In this embodiment, due to the complex and time-varying marine environment, control signals are prone to fluctuations in high-precision tracking tasks. Under traditional triggering mechanisms, the trigger threshold may be determined by invalid signals, leading to wasted communication resources and performance degradation. To save communication resources and ensure system performance, a memory-based event triggering mechanism (METM) is proposed. Its triggering conditions can be adjusted based on historical and real-time data. When the control signal undergoes a sudden change, METM emphasizes historical data, overcoming the limitation of traditional triggering mechanisms that over-rely on real-time data, thereby improving data utilization.

[0227] Stability analysis was performed on the method of this embodiment:

[0228] Theorem 2: Under the assumption ν p When set to 1, the deep learning controller is semi-globally consistent eventually bounded (SGUUB).

[0229] Proof: Define the error variable as and but The dynamic equation is

[0230]

[0231] In the formula: matrices A and B are respectively:

[0232]

[0233] And there exists a matrix Q such that:

[0234] QA+A T Q+δI6=0,

[0235] in It is a positive constant; consider the following Lyapunov function:

[0236]

[0237] And by taking its derivative, we get:

[0238]

[0239] Considering the properties of matrix Q, this embodiment can obtain:

[0240]

[0241] Now, through the By defining the terms, we can obtain:

[0242]

[0243] in, It is related to external input Related constants, if external input If it is bounded, then ∈ is also a bounded constant; based on the standard results of Lyapunov function analysis, we can know that the system state W1 is SGUUB (semi-globally consistent eventually bounded).

[0244] Theorem 3: Consider the underactuated ASV mathematical model, PTPF constraints (trajectory tracking constraints), METM (memory event triggering mechanism in S53), and control law (deep learning controller). Under Assumptions 1 and 2, the error in the closed-loop system can be guaranteed to be SGUUB;

[0245] Proof: Consider the following Lyapunov function V:

[0246] V = V1 + V3

[0247] in Its derivative can be expressed as:

[0248]

[0249] Will Substitution What can be obtained:

[0250]

[0251] Based on the deep learning controller, it can be deduced that:

[0252]

[0253] According to Young's inequality, we can obtain:

[0254]

[0255] Will

[0256] Substitution

[0257] What can be obtained:

[0258]

[0259] Furthermore, we can obtain:

[0260]

[0261] In the formula, C1 and C2 are positive numbers that satisfy the following conditions.

[0262]

[0263] Therefore, all signals in the closed-loop system are SGUUB.

[0264] This embodiment can be obtained from It is deduced that q(p) is differentiable, and stability analysis shows that all signals are bounded; therefore, there exists a constant such that... Know And at time t k time e(t) k The fact that t = 0 is intuitive. Furthermore, t min Must meet A lower bound is provided for the sampling interval; therefore, Zeno behavior can be effectively avoided, thus proving that the method of this embodiment is stable.

[0265] To demonstrate the effectiveness of the proposed method, the following numerical simulation examples were performed in this embodiment:

[0266] The design parameters are as follows: d max =15,d min =5,d d =10, θ d =π / 3, M1 = [10, 20, 10] T M2 = [15, 21, 11] T ,α=1,T q =10,T m =30,T f =60,α u =30,α v =20, κ u =5,k v =3,k r =2 External disturbances can be expressed as:

[0267] w=[1+sin(0.01t),0.7+cos(0.6t),0.3+sin(1.1t)] T

[0268] The initial velocity of the ship leader is as follows: u l =3m / s,v l =0 m / s, rotational speed r L The following conditions must be met

[0269]

[0270] The initial condition for the leader is defined as η l (0) = [0,0,0] T ;

[0271] The initial conditions for followers are defined as: η = [-14, -13, η / 6] T With ν = [0,0,0] T ;

[0272] The data from ASV was collected online and used to train the DNN in real time. The DNN was constructed from three fully connected layers with an input dimension of 8 and an output dimension of 3. The learning rate was 0.0001, ReLU was chosen as the activation function, and mean squared error was used as the loss function for the regression layer.

[0273] To demonstrate the effectiveness of the proposed method, this embodiment includes a comparative analysis with existing preset performance control algorithms. The proposed method differs from existing preset performance control algorithms in several ways. Figure 3 A comparison was made in the middle. Figure 3 The trajectory tracking control plane is shown. Figure 4 and Figure 5 The results show that the proposed method is more stable than existing preset performance control algorithms in terms of position and angle errors. Figure 6 This demonstrates the loss function of a DNN. Figure 7 This demonstrates the observation accuracy of the created observer. Figure 8 The actual control input was demonstrated. Figure 9 This demonstrates the event intervals under METC.

[0274] To further verify the comparison results, this embodiment introduces commonly used performance indicators for quantitative analysis, including mean absolute error. With average absolute input control The stability performance of the control system is reflected by MAE, while MAI is used to evaluate energy consumption. The results of the performance indicators are shown in Table 1.

[0275] Table 1. Performance Index Results

[0276]

[0277] Table 2 shows a comparison of the proposed METM with two mechanisms in previous studies (static event triggering mechanism and dynamic event triggering mechanism) in terms of triggering frequency;

[0278] Table 2. Comparison of this implementation method with static and dynamic event triggering mechanisms.

[0279]

[0280] In summary, the proposed METM triggers fewer times than conventional event-triggered mechanisms (static and dynamic event-triggered mechanisms), thus further saving communication resources.

[0281] To verify whether the initial point constraint in the traditional PPC method in this embodiment has been removed, a set of comparative cases was added. In these cases, the initial position of the ASV is set to [-20, -20], which is a situation where traditional PPC cannot be applied. Figure 10 and Figure 11 The results demonstrate the trajectory and relative position of the proposed algorithm when the initial point is outside the constraint boundaries. The results showcase the advantages of the proposed algorithm, as it does not impose constraints on the initial position of the ASV, only requiring it to remain within the sensor's detection range. This approach better aligns with the practical needs of marine missions.

[0282] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the foregoing embodiments, or make equivalent substitutions for some or all of the technical features; and these modifications or substitutions 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. A memory-based event-triggered time-regulated performance control method applied to an underactuated ASV, characterized in that, Specifically comprising the following steps: S1: constructing an underactuated ASV mathematical model; According to the underactuated ASV mathematical model, an ASV dynamics model containing unknown dynamic terms is obtained; S2: obtaining tracking data from the underactuated ASV mathematical model; And the tracking data includes relative distance and relative azimuth angle; According to the tracking data, the tracking position error is defined, and the initial condition of the tracking position error is obtained based on the constructed sigmoid function; Construct a preset time performance function to obtain trajectory tracking constraints according to the initial condition; S3: According to the trajectory tracking constraint, an error conversion function for limiting the tracking position error is constructed; And according to the error conversion function, a virtual control law is constructed; S4: Based on the deep neural network DNN, an optimized ASV dynamics model containing DNN modeling error is obtained according to the ASV dynamics model; Construct a modeling error approximation observer to approximate and process the DNN modeling error in the optimized ASV dynamics model, and obtain an ASV dynamics estimation model; S5: According to the ASV dynamics estimation model and the virtual control law, the tracking variable error is obtained; According to the tracking variable error, the ASV dynamics estimation model and the virtual control law are combined to construct a deep learning controller, and based on the constructed memory event trigger mechanism, the tracking control of the underactuated ASV is realized according to the deep learning controller.

2. The method for memory-based event-triggered time-regulated performance control applied to underactuated ASV according to claim 1, wherein, The S1 specifically comprises the following steps: S11: constructing an underactuated ASV mathematical model, whose expression is where: η represents the position and heading angle of the ASV and η = [x, y, ψ] T ; v represents the velocity vector and v = [u, v, r] T ; u, v, r represent the forward velocity, lateral velocity, and yaw rate; q represents the control input and q = [q u , 0, q r ] T ; q u , q r represent the control input provided by the thrusters and rudder; M, C(v), D(v) represent the mass matrix, Coriolis matrix, and hydrodynamic damping matrix, respectively; d represents the unknown disturbance and d = [d u , d v , d r ] T ; d u , d v , d r represent the external unknown disturbance of the underactuated ASV; R(ψ) represents the rotation matrix for transforming the body frame to the inertial frame; represents the first derivative of η; represents the first derivative of v; S12: According to the underactuated ASV mathematical model, an ASV dynamics model containing unknown dynamic terms is obtained, and the expression of the ASV dynamics model containing unknown dynamic terms is G(v, q, d) = -(M * ) -1 q + M -1 (-C(v)v - D(v)v + d + q) where: M * denotes the non-diagonal inertia matrix of the nominal mass; G(v, q, d) denotes the unknown dynamic terms of the ASV dynamics model; M denotes the non-diagonal inertia mass matrix.

3. The method according to claim 2, applied to underactuated ASV memory-based event-triggered prescribed time performance control, characterized in that, The S2 specifically comprises the following steps: S21: obtaining tracking data from the underactuated ASV mathematical model; And the tracking data includes relative distance and relative azimuth angle; The expression of the relative distance and the relative azimuth angle is θ=atan2(Δy,Δx) Δx = x l - x, Δy = y l - y φ=θ-ψ wherein d represents a relative distance, φ represents a relative azimuth angle and d min d < d max , d min d max represent a maximum and a minimum of the relative distance, respectively; represents an upper bound of the relative azimuth angle; θ represents a desired heading angle; Δx, Δy represent intermediate parameter quantities; x l y l represent a desired trajectory position x- and y-coordinate, respectively. S22: Define the tracking position error e according to the tracking data amount, which is expressed as e = k - k k = k - k d ,k = d, f where: e k represents a tracking position error; k represents a relative distance or a relative azimuth angle; k d represents a desired relative distance or a desired relative azimuth angle; S23: defining a sigmoid function of the underactuated ASV system for use in calculating an initial tracking position error e of the underactuated ASV system k (0), not necessarily constrained within a predefined region; And the expression of the sigmoid function S(t) is where: a and T q denotes a design parameter; t denotes a time parameter; S24: obtaining time modulation error E based on sigmoid function S(t) according to tracking position error k , and E k =S(t)e k to obtain initial conditions of tracking position error; and the expression of the initial condition of the tracking position error is d min -d d <E d <d max -d d S25: Construct a preset time performance function; And the expression of the preset time performance function is T q = cos((π(t - T m ))(T f -T m ) -1 ) In the formula: T represents constant gain; m Indicates the transition time; T f Indicates the set time; This represents a piecewise function with intermediate parameters; t0 represents the rate constant of control time decay; t0 represents the start time, i.e., the moment when the control process begins. This indicates that the system will ensure that the system is within the set time T. f The function that determines the completion of the target task over time; Indicates control gain; Represents the gain matrix; express The steady-state value; and Indicates a positive design constant; This represents the error convergence control variable; express first derivative and for The abbreviated form is k = d, φ; S26: Based on the preset time performance function, the trajectory tracking constraints are obtained according to the initial condition; And the expression of the trajectory tracking constraint is wherein: δ 1d , δ 2d , δ 1φ , δ 2φ represents a positive proportional coefficient for adjusting the error convergence speed; represents a control variable for adjusting the relative distance and relative azimuth angle error convergence.

4. The method according to claim 3, applied to underactuated ASV memory-based event-triggered prescribed time performance control, characterized in that, The S3 specifically comprises the following steps: S31: According to the trajectory tracking constraint, an error conversion function for limiting the tracking position error is constructed; And the expression of the error conversion function is S32: According to the error conversion function, a virtual control law is constructed, and the expression of the virtual control law is In the formula: γ=[γ u ,γ v ,γ r ] T The virtual control law representing the forward velocity, lateral velocity, and yaw rate, ζ u ,ζ v ,ζ r Indicates the intermediate parameter quantity and ζ u =α u tanh(β u ),ζ v =α v tanh(β v ),ζ r =α r tanh(β r );α u ,α v ,α r Indicates the design parameter, β u ,β v ,β v Represents auxiliary system variables; Σ d Indicates the amount of intermediate parameters; d d The first derivative; Represented as design parameters and β u ,β v ,β r , Represents an unknown parameter, and is derived from the ship's forward pilot velocity u. l The estimated value With lateral leader velocity v l The estimated value get; Representing unknown parameters The estimate of π; k , Indicates an intermediate variable; and χ φ The function representing the adjustment of the yaw angle.

5. The method for memory-based event-triggered time-regulated performance control of underactuated ASV according to claim 4, wherein, The S4 specifically comprises the following steps: S41: Based on the deep neural network DNN, an optimized ASV dynamics model containing DNN modeling error is obtained according to the ASV dynamics model; And the expression of the optimized ASV dynamics model containing DNN modeling error is wherein: represents learning and capturing the dynamic key data features of the ASV based on the deep neural network DNN according to the preset historical tracking trajectory data in the unseen input domain, and the dynamic key data features are velocity vectors, control inputs and unknown disturbances; wherein the loss function of the dynamic key data features of the ASV learned and captured based on the deep neural network DNN is E b (L t ); G0represents the DNN modeling error and G0= [G u0 ,G v0 ,G r0 ], G u0 ,G v0 ,G r0 respectively represent the forward velocity error, the lateral velocity error and the yaw angular velocity error modeled by the DNN; represents the weight of the deep neural network DNN; represents the parameter space; G t (ν t ,q t ,d t ) represents the actual value for quantifying the dynamic key data of the ASV at the tthiteration; represents the learning value for quantifying the dynamic key data of the ASV at the tthiteration; b represents the real distribution; B represents the distribution of the historical tracking trajectory data. S42: Construct a modeling error approximation observer to approximate and process the DNN modeling error in the optimized ASV dynamics model, and obtain an ASV dynamics estimation model; And the expression of the modeling error approximation observer is wherein: represents an estimate of v; represents an estimate of G0and M1, M2 represent observer parameter matrices and represents an observer parameter; I3 represents a 3x3 identity matrix; represents a first derivative of represents a first derivative of represents a simplified form of and v = [u, v, r] T .

6. The method according to claim 5, applied to underactuated ASV memory-based event-triggered prescribed time performance control, characterized in that, The S5 specifically comprises the following steps: S51: obtaining a tracking variable error according to the ASV dynamics estimation model and the virtual control law, and an expression of the tracking variable error is z = v - y - z z = [z u ,z v ,z r ] T ζ = [ζ u ,ζ v ,ζ r ] T S52: constructing a deep learning controller according to the tracking variable error and the ASV dynamics estimation model and the virtual control law, and an expression of the deep learning controller is where: ξ u1 ,η u1 ,ξ r1 ,η r1 all represent auxiliary system variables for adjusting the dynamic response of the control input, i.e. gain coefficients or adjustment factors related to the controller regulation ε u ,ε r represent error terms related to the control signal; represents an external disturbance estimate or an estimated control parameter based on the model error approximation observer; μ u ,μ r represents a system adjustment parameter for the dynamic response of the control error, represents the reference quality related to the control input u and r; represents an estimated parameter for adjusting the control input; ∈ c represents an adjustment constant for limiting the amplitude of the control input; k u ,k v ,k r ,Γ p ,ν p represents a positive design parameter; represents an estimated value of χ p ; ω p and ω r represent intermediate parameter quantities and ω u = z d π d cosφ, ω v =-z d π d sinφ and ω r =z φ π φ ; S53: constructing a memory event trigger mechanism, and realizing tracking control of the underactuated ASV according to the deep learning controller based on the constructed memory event trigger mechanism; and the constructed memory event trigger mechanism is specifically |e p (t)|≥ξ p1 (|η p1 q p (t)+η p2 q p (t-τ)|)+η p3 η p1 = 1 - η p2 η p3 = -J p η p3 + ξ p1 (|η p1 q p (t) + η p2 q p (t - τ) |) - |e p (t) | In the formula: represents the control output of the deep learning controller at time t j ; e p (t) represents the triggering error of the memory event triggering mechanism and ξ p1 , ξ p2 represents a preset threshold parameter; η p1 , η p2 , η p3 represents an intermediate parameter quantity; q p (t) represents the actual control input in the time interval [t j , t j+1 ]; t j , t j+1 represents a time parameter; q p (t-τ) represents a delay control input at time τ; J p represents a design parameter; and the memory event trigger mechanism is rewritten as e p = a p1 (ξ p1 η p1 q p (t) + ξ p1 η p2 q p (t - τ) ) + a p2 η p3 where: a p1 , a p2 both represent intermediate parameter variables; a p represents a design parameter and a p ∈ [-1, 1]; q p represents q p (t) in short form; according to the trigger error of the memory event trigger mechanism, and combining the rewritten memory event trigger mechanism, the actual control input of the underactuated ASV is represented as

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