Memory-based event triggering specified time performance control method applied to under-actuated ASV

Abstract

The invention discloses a memory-based event triggering specified time performance control method applied to an under-actuated ASV, and the method comprises the steps: constructing a preset specified time performance function, obtaining a trajectory tracking constraint according to an initial condition, enabling the function to customize convergence time, and eliminating a constraint problem that an initial error must be within a performance boundary; based on a deep neural network DNN, according to an ASV kinetic model, an optimized ASV kinetic model containing DNN modeling errors is obtained, a modeling error approximation observer is constructed, the DNN modeling errors in the optimized ASV kinetic model are subjected to approximation processing so as to construct a deep learning controller, unknown dynamics of ASV is learned by designing the deep learning controller, and the ASV dynamic model is obtained. The learning accuracy is improved; the interpretability of the DNN is enhanced; based on the constructed memory event triggering mechanism, the method is used for optimizing communication resource utilization, dynamic adjustment can be carried out according to real-time data and historical data, when a control signal changes suddenly, the memory event triggering mechanism preferentially considers the historical data, and the problem that a traditional event triggering mechanism excessively depends on the real-time data is solved.

Description

Technical Field

[0001] The present invention relates to the field of marine engineering technology, and in particular to a memory-based event-triggered specified time performance control method for under-actuated ASVs. Background Art

[0002] Autonomous surface vehicles (ASVs) have been widely used in various maritime missions due to their advantages of small size, low cost and high autonomy due to the characteristics of fewer control inputs than degrees of freedom. In recent years, more and more research has focused on the motion control problem of non-fully driven ASVs, especially trajectory tracking control, which has high timeliness. In actual marine missions, ASVs face unknown, time-varying dynamics and are restricted by limited communication bandwidth. In this case, developing effective control strategies is crucial to achieving high-performance trajectory tracking. The current trajectory tracking control methods for autonomous surface vehicles include the following:

[0003] The control performance of ASVs is particularly critical in narrow and crowded waterways. Predicted performance control (PPC) improves performance by constraining the system state within predefined boundaries. Recently, PPC has been successfully applied to various ASV tasks, including formation control and trajectory tracking. However, in crowded waterways, traditional PPC may increase the risk of collision and reduce navigation accuracy. By improving the PPC function, collision avoidance and connectivity in the formation control of non-fully driven ASVs are achieved. In general, PPC faces challenges from practical problems, including uncertainty in convergence time and strict constraints on initial errors. In order 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 boundaries within a user-defined time. However, the strict initial error constraints imposed by PTPF are often difficult to meet in practical applications, and solving the impact of strict initial error constraints in PTPF has become an important research direction.

[0004] Accurately modeling the unknown time-varying dynamics of ASVs is essential for achieving high-performance trajectory tracking control. Deep neural networks (DNNs) have been considered an ideal tool for modeling complex systems due to their powerful nonlinear representation capabilities and feature memory. 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 not suitable for dynamic environments due to their high cost and limited scalability for model retraining.

[0005] Marine communications are limited by limited bandwidth, and traditional fixed-interval transmission mechanisms have difficulty overcoming this limitation. In contrast, event-triggered mechanisms (ETMs) have variable transmission intervals and transmit data only when necessary, thus avoiding unnecessary bandwidth waste. It should be noted that traditional ETMs mainly rely on the error between the current data and the previous trigger data to decide whether to transmit. This design makes ETM overly sensitive to instantaneous data fluctuations and ignores historical information, which may lead to poor adaptability in actual sea conditions. For example, in high-precision tracking tasks, fluctuations in control signals or system failures may cause the ETM trigger threshold to be determined by invalid signals, thereby wasting communication resources and reducing performance. To solve this problem, METM is proposed to optimize the use of communication resources and combine historical data. However, METM relies on long-term data, and when system failures or anomalies occur, the stored data inevitably deviates from normal values, resulting in performance degradation; therefore, designing effective detection rules to prevent such problems has become a key research focus. Summary of the invention

[0006] The present invention provides a memory-based event-triggered specified time performance control method applied to an under-driven ASV to overcome the above technical problems.

[0007] In order to achieve the above object, the technical solution of the present invention is:

[0008] A memory-based event-triggered time performance control method for underactuated ASV, comprising the following steps:

[0009] S1: Construct a mathematical model of underactuated ASV;

[0010] Obtaining the ASV dynamics model containing unknown dynamic terms based on the underactuated ASV mathematical model;

[0011] S2: Obtain tracking data volume according to the underactuated ASV mathematical model;

[0012] And the tracking data volume includes relative distance and relative azimuth angle;

[0013] The tracking position error is defined according to the amount of tracking data, and the initial condition of the tracking position error is obtained based on the constructed sigmoid function;

[0014] Constructing a preset prescribed time performance function to obtain trajectory tracking constraints based on initial conditions;

[0015] S3: constructing an error conversion function for limiting the tracking position error according to the trajectory tracking constraint;

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

[0017] S4: Based on the deep neural network DNN, the optimized ASV dynamics model including the DNN modeling error is obtained according to the ASV dynamics model;

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

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

[0020] A deep learning controller is constructed according to the tracking variable error combined with the ASV dynamics estimation model and the virtual control law. Based on the constructed memory event trigger mechanism, tracking control of the under-actuated ASV is achieved according to the deep learning controller.

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

[0022] S11: Construct the mathematical model of underactuated ASV, which is expressed as

[0023]

[0024] Where: 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 the forward speed, lateral speed and yaw angular velocity; q represents the control input and q = [q u ,0,q r ] T ;q u ,q r represents the control input provided by the thruster and rudder; M, C(ν), 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 transform the hull coordinate system into the inertial coordinate system; represents the first derivative of η; represents the first derivative of v.

[0025] S12: According to the underactuated ASV mathematical model, an ASV dynamics model with unknown dynamic terms is obtained, and the expression of the ASV dynamics model with 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 * represents the nominal mass of the non-diagonal inertia matrix; G(v,q,d) represents the unknown dynamic terms of the ASV dynamic model; M represents the non-diagonal inertia mass matrix.

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

[0030] S21: Obtain tracking data volume according to the underactuated ASV mathematical model;

[0031] And the tracking data volume includes relative distance and relative azimuth angle;

[0032] The expressions of the relative distance and relative azimuth angle are:

[0033]

[0034] θ=atan2(Δy,Δx)

[0035] Δx=x l -x,Δy=y l -y

[0036] φ=θ-ψ

[0037] Where: d represents the relative distance, φ represents the relative azimuth angle and d min <d<d max , d min ,d max Respectively represent the maximum and minimum values ​​of the relative distance; represents the upper limit of the relative azimuth angle; θ represents the desired heading angle; Δx, Δy represent the intermediate parameters; x l ,y l Indicates the horizontal and vertical coordinates of the desired trajectory position;

[0038] S22: Define the tracking position error based on the amount of tracking data, and its expression is:

[0039] e k =kk d ,k=d,φ

[0040] Where: e k represents the tracking position error; k represents the relative distance or relative azimuth angle; k d Indicates the expected relative distance or expected relative azimuth angle;

[0041] S23: Define the sigmoid function of the underactuated ASV system to convert the initial tracking position error e of the underactuated ASV system k (0), not necessarily constrained within a predefined area;

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

[0043]

[0044] Where: α and T q represents the design parameter; 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 of the tracking position error;

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

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

[0048]

[0049] S25: constructing a preset specified time performance function;

[0050] And the expression of the preset specified time performance function is

[0051]

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

[0053] Where: represents constant gain; T m Indicates transition time; T f Indicates the set time; represents an intermediate parameter piecewise function; represents the rate constant that controls time decay; t 0 Indicates the start time, i.e. the moment when the control process begins; Indicates that the system is guaranteed to be within the set time T fThe function of the target task completed within a certain period of time; represents the control gain; represents the gain matrix; express The steady-state value of and represents a positive design constant; represents the error convergence control variable; express The first derivative of for The abbreviated form of , k = d, φ;

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

[0055] And the expression of trajectory tracking constraint is

[0056]

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

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

[0059] S31: constructing an error conversion function for limiting the tracking position error according to the trajectory tracking constraint;

[0060] And the expression of the error transfer function is

[0061]

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

[0063]

[0064] Where: γ=[γ u ,γ v ,γ r ] T represents the virtual control law of forward speed, lateral speed and yaw angular velocity, ζ u ,ζ v ,ζ r represents 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 represents the design parameter, β u ,β v ,β v Represents auxiliary system variables; Σ d Indicates the intermediate parameter quantity; Indicates d d The first derivative of is represented as a design parameter and β u ,β v ,β r , represents the unknown parameters, and is determined by the forward pilot speed u l Estimated value of With lateral leading speed v l Estimated value of get; Indicates unknown parameters Estimate of π k , represents an intermediate variable; and k=d,φ;χ φ Represents the regulation function of the yaw angle.

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

[0066] S41: Based on the deep neural network DNN, an optimized ASV dynamics model including the DNN modeling error is obtained according to the ASV dynamics model;

[0067] The expression of the optimized ASV dynamics model including the DNN modeling error is

[0068]

[0069] Where: It means that the dynamic key data features of ASV are learned and captured in the unseen input domain based on the deep neural network DNN according to the preset historical tracking trajectory data, and the dynamic key data features are the velocity vector, control input and unknown disturbance; the loss function of the dynamic key data features of ASV learned and captured based on the deep neural network DNN is E b (L t );G 0 represents the DNN modeling error and G 0 =[Gu0 ,G v0 ,G r0 ], G u0 ,G v0 ,G r0 They represent the forward velocity error, lateral velocity error, and yaw angular velocity error modeled by DNN respectively; Represents the weight of the 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 at the tth iteration; represents the learning value used to quantify the dynamic key data of ASV at the tth iteration; b represents the true distribution; B represents the distribution of historical tracking trajectory data;

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

[0071] And the expression of the modeling error approximation observer is

[0072]

[0073] Where: represents the estimate of v; Represents G 0 The estimate and M 1 ,M 2 represents the observer parameter matrix and I represents the observer parameters; 3 represents the 3×3 identity matrix; express The first derivative of express The first derivative of express The simplified form of v = [u, v, r] T .

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

[0075] S51: Obtain the tracking variable error according to the ASV dynamics estimation model and the virtual control law, and the expression of the tracking variable error is:

[0076] z=v-γ-ζ

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

[0078] S52: A deep learning controller is constructed 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] Where: u1 ,η u1 ,ξ r1 ,η r1 Both represent auxiliary system variables used to adjust the dynamic response of the control input, that is, the gain coefficient or adjustment factor ε related to the controller adjustment u ,ε r represents the error term associated with the control signal; represents the external disturbance estimate or estimated control parameter obtained based on the modulus error approximation observer; μ u ,μ r represents the system tuning parameter used to control the dynamic response of the error, represents the reference quality associated with the control inputs u and r; represents the estimated parameter used to adjust the control input; ∈ c k represents the regulation constant used to limit the control input amplitude; u ,k v ,k r ,Γ p ,v p represents a positive design parameter; Represents χ p The estimated value of ω p With ω r represents the intermediate parameter 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 trigger mechanism, and based on the constructed memory event trigger mechanism, implement tracking control of the under-actuated ASV according to the deep learning controller;

[0082] The memory event triggering mechanism constructed is specifically

[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] Where: Indicates that at t j The control output of the deep learning controller at each moment; p (t) represents the trigger error of the memory event trigger mechanism and ξ p1 ,ξ p2 represents the preset threshold parameter; η p1 ,η p2 ,η p3 Indicates the intermediate parameter quantity; q p (t) represents the time interval [t j ,t j+1 ) within the actual control input; t j ,t j+1 represents the time parameter; q p (t-τ) represents the delayed control input at the time of delay τ; J p represents the design parameters;

[0089] And rewrite the memory event trigger mechanism as

[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] Where: α p1 ,α p2 Both represent intermediate parameter variables; α p represents the design parameters and αp∈[-1,1]; q p Indicates q p (t) is an abbreviation of

[0093] According to the trigger error of the memory event trigger mechanism and combined with the rewritten memory event trigger mechanism, the actual control input of the underdriven ASV is expressed as

[0094]

[0095] The beneficial effects of the present 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 system initial conditions or parameters, and removing the limitation of the existing PPC method that assumes that the initial error must be within the constraint boundary;

[0097] (2) The present invention is based on a deep neural network DNN, obtains an optimized ASV dynamics model including a DNN modeling error according to an ASV dynamics model, and optimizes the DNN modeling error in the ASV dynamics model through a constructed modeling error approximation observer. The present invention proposes a deep learning method based on DNN, realizes real-time online learning of ASV unknown dynamics. Compared with offline learning methods, this method eliminates the need for large-scale data storage, provides real-time estimation and compensation of DNN learning errors, and enhances interpretability.

[0098] (3) Based on the constructed memory event trigger mechanism METC, the tracking control of the under-driven ASV is realized according to the deep learning controller. The METC proposed in the present invention allows the trigger conditions to be adjusted according to historical data and real-time data. When the control signal changes suddenly, METC emphasizes historical data, which solves the problem of traditional ETM's over-reliance on real-time data. Under METC, data utilization is improved, and excessive redundancy of historical data is prevented. BRIEF DESCRIPTION OF THE DRAWINGS

[0099] 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 creative labor.

[0100] Figure 1 A flow chart of the present invention applied to the memory-based event-triggered specified time performance control method of under-actuated ASV;

[0101] Figure 2 A control architecture block diagram for the control design of the memory-based event-triggered online deep learning controller in this embodiment;

[0102] Figure 3 Schematic diagram of planetary trajectory simulation of the method in this embodiment;

[0103] Figure 4 Schematic diagram of position error comparison in this embodiment;

[0104] Figure 5 This is a schematic diagram of angle error comparison in this embodiment;

[0105] Figure 6 Schematic diagram of the simulation of the learning performance of the deep neural network DNN in this embodiment;

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

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

[0108] Fig. 9 is a schematic diagram of the time interval between events in this embodiment;

[0109] Fig.10 This is a schematic diagram of the comparison of initial points outside the constraint boundary in this embodiment;

[0110] Fig.11 Schematic diagram of the relative distance when the initial point is outside the constraint boundary in this embodiment. DETAILED DESCRIPTION

[0111] In order to make the purpose, technical solution and advantages of the embodiments of the present invention clearer, the technical solution 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 described embodiments are 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 creative work are within the scope of protection of the present invention.

[0112] This embodiment provides a memory-based event-triggered time performance control method for under-driven ASV, such as Figure 1 to Figure 2 As shown, the specific steps include:

[0113] S1: Construct a mathematical model of underactuated ASV;

[0114] Obtaining the ASV dynamics model containing unknown dynamic terms based on the underactuated ASV mathematical model;

[0115] The specific steps include:

[0116] S11: Construct the mathematical model of underactuated ASV, which is expressed as

[0117]

[0118] 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 speed, lateral speed and yaw angular velocity; q represents the control input and q = [q u ,0,q r ] T ;q u ,q r represents the control inputs provided by the thrusters and rudder; denote the mass matrix, the Coriolis matrix and the hydrodynamic damping matrix respectively; d denotes 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; Represents the rotation matrix used to transform the hull coordinate system into the inertial coordinate system; represents the first derivative of η; represents the first derivative of v.

[0119] S12: According to the underactuated ASV mathematical model, an ASV dynamics model with unknown dynamic terms is obtained, and the expression of the ASV dynamics model with 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 * represents the nominal mass of the non-diagonal inertia matrix; G(v,q,d) represents the unknown dynamic terms of the ASV dynamic model; M represents the non-diagonal inertia mass matrix.

[0123] S2: Obtain tracking data volume according to the underactuated ASV mathematical model;

[0124] The tracking data volume includes relative distance and relative azimuth angle; the tracking position error is defined according to the tracking data volume, and the initial condition of the tracking position error is obtained based on the constructed sigmoid function; a preset specified time performance function is constructed to obtain the trajectory tracking constraint according to the initial condition;

[0125] The specific steps include:

[0126] S21: Obtain tracking data volume according to the underactuated ASV mathematical model;

[0127] And the tracking data volume includes relative distance and relative azimuth angle;

[0128] The expressions of the relative distance and relative azimuth angle are:

[0129]

[0130] θ=atan2(Δy,Δx)

[0131] Δx=x l -x,Δy=y l -y

[0132] φ=θ-ψ

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

[0134] S22: Define the tracking position error based on the amount of tracking data, and its expression is:

[0135] e k =kk d ,k=d,φ

[0136] Where: e k represents the tracking position error; k represents the relative distance or relative azimuth angle; k d Indicates the expected relative distance or expected relative azimuth angle;

[0137] S23: To avoid the constraints of initial conditions, that is, the tracking error e k (0) must start within a predefined region, that is, define the sigmoid function of the underactuated ASV system to convert the initial tracking position error e of the underactuated ASV system k (0), not necessarily constrained within a predefined area;

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

[0139]

[0140] Where: α and T q represents the design parameter; 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 of the tracking position error;

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

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

[0144]

[0145] S25: constructing a preset specified time performance function;

[0146] And the expression of the preset specified time performance function is

[0147]

[0148]

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

[0150] Where: represents constant gain; T m Indicates transition time; T f Indicates the set time; represents an intermediate parameter piecewise function; represents the rate constant that controls time decay and affects The rate of change of 0 Indicates the start time, i.e. the moment when the control process begins; Indicates that the system is guaranteed to be within the set time T f The function of the target task completed within a certain period of time; The control gain is used to represent the control strategy or acceleration factor of the follower; It indicates that the gain matrix is ​​used to weight the error and can adjust the error correction amount according to the state of the system; express The steady-state value of and represents a positive design constant; represents the error convergence control variable; express The first-order derivative of for The abbreviated form of , k = d, φ;

[0151] This embodiment also includes Theorem 1: that is, considering the preset specified time performance function, the state Able to f Converges to For t∈[T f ,∞) always holds true;

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

[0153] Assumption 2: Modeling Error G 0 and its time derivative It is bounded;

[0154] S26: in order to ensure high performance control in the trajectory tracking task, based on a preset prescribed time performance function, the trajectory tracking constraint is obtained according to the initial conditions;

[0155] And the expression of trajectory tracking constraint is

[0156]

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

[0158] S3: constructing an error conversion function for limiting the tracking position error according to the trajectory tracking constraint;

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

[0160] The specific steps include:

[0161] S31: in order to ensure that the tracking position error can converge to within the limit of the trajectory tracking constraint, construct an error conversion function for limiting the tracking position error according to the trajectory tracking constraint;

[0162] And the expression of the error transfer function is

[0163]

[0164] According to the error conversion function, this embodiment can infer that when z k →±∞, which is equivalent to and And z k =0 at e k =0;

[0165] Differentiating the error transfer function yields:

[0166] Where: and

[0167]

[0168] ξ k represents an auxiliary function containing the error and control gain;

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

[0170]

[0171] According to Assumption 2, it can be assumed that airborne sensors cannot usually be used to directly measure the leader's speed information. Define In the formula Yes estimates;

[0172] Consider the following Lyanov function:

[0173]

[0174] In order to facilitate stability verification, the above process can be combined to convert the Lyanov function V 1 The derivative of is derived as:

[0175]

[0176] Where: Indicates the time rate of change of the speed dynamic variable; k ξ represents the control gain constant, which is used to adjust the response speed or strength of the controller;

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

[0178]

[0179] Where: γ=[γ u ,γ v ,γ r ] T represents the virtual control law of forward speed, lateral speed and yaw angular velocity, ζ u ,ζ v ,ζ r represents 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 represents the design parameter, β u ,β v ,β v Represents auxiliary system variables; Σ d Indicates the intermediate parameter quantity; Indicates d d The first derivative of is represented as a design parameter and β u ,β v ,β r , represents the unknown parameters, and is determined by the forward pilot speed u l Estimated value of With lateral leading speed v l Estimated value of get; Indicates unknown parameters Estimate of π k , represents an intermediate variable; and k=d,φ;χ φ represents the regulation function of the yaw angle;

[0180] S4: Based on the deep neural network DNN, the optimized ASV dynamics model including the DNN modeling error is obtained according to the ASV dynamics model;

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

[0182] The specific steps include:

[0183] S41: In order to deal with the problem that G(v,q,d) is not applicable, this embodiment uses a deep neural network DNN to learn the unknown ASV (autonomous underwater vehicle) dynamics online, and the learned dynamics are expressed as in represents the weight of DNN, is a parameter space, where deep learning is based on the process of using many neurons to create multiple hidden layers to approximate functions by extracting features from input data. Deep neural networks (DNNs) combine data features through composite functions to map input x to output G(x,α), which is expressed as:

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

[0185] Where: G(x,α) represents the output of the neural network; ψ k represents the feature extraction of the kth layer; α k-1 represents the weight of the k-1th layer; α j represents the weight of the jth layer; ψ j represents the feature vector of the jth layer and j = 1, 2, ..., k; the online learning in this embodiment is a branch of machine learning, focusing on making predictions or decisions by sequentially processing data samples. Its goal is to improve learning accuracy by using previous results and preset data. The online learning task is as follows: Assume that the processed data sequence is Where t represents the number of iterations, and the true value of each output is expressed as Indicates that in the tth iteration, the learner uses x t Prediction Output Then receive the true value G t So as to calculate the loss, By following (x t ,G t ) adjusts the parameters and updates the model from Unlike offline learning, online learning updates the model as each new data point arrives, making it more efficient and scalable in practical applications that require fast response and large-scale data processing;

[0186] Therefore, this embodiment is based on the deep neural network DNN, and obtains an optimized ASV dynamics model including the DNN modeling error according to the ASV dynamics model;

[0187] The expression of the optimized ASV dynamics model including the DNN modeling error is

[0188]

[0189] Where: It means that the dynamic key data features of ASV are learned and captured in the unseen input domain based on the deep neural network DNN according to the preset historical tracking trajectory data, and the dynamic key data features are the velocity vector, control input and unknown disturbance; the loss function of the dynamic key data features of ASV learned and captured based on the deep neural network DNN is E b (L t );G 0 represents the DNN modeling error and G 0 =[G u0 ,G v0 ,G r0 ], G u0 ,G v0 ,G r0They represent the forward velocity error, lateral velocity error, and yaw angular velocity error modeled by DNN respectively; Represents the weight of the 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 at the tth iteration; represents the learning value used to quantify the dynamic key data of ASV at the tth iteration; b represents the true distribution; B represents the distribution of historical tracking trajectory data;

[0190] The goal of the deep neural network DNN in this embodiment is to capture the key data features of the dynamics of the autonomous surface vessel (ASV) in an unseen input domain, and the Adam optimizer is used in this embodiment 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, has better convergence and stability, and ensures that the influence of each input on the DNN is equal through the zero-mean normalization method. The trained DNN shows a strong generalization ability and can perform trajectory tracking without losing 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 the deep neural network DNN, 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 of the modulus error approximation observer is

[0194]

[0195] Where: represents an estimate of ν; Represents G 0 The estimate and M 1 ,M 2 represents the observer parameter matrix and I represents the observer parameters; 3 represents the 3×3 identity matrix; express The first derivative of express The first derivative of express The simplified form of ν=[u,v,r] T ;

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

[0197] A deep learning controller is constructed based on the tracking variable error combined with the ASV dynamics estimation model and the virtual control law. Based on the constructed memory event trigger mechanism, the tracking control of the under-actuated ASV is realized according to the deep learning controller.

[0198] The specific steps include:

[0199] S51: Obtain the tracking variable error according to the ASV dynamics estimation model and the virtual control law, and the expression of the tracking variable error is:

[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 taking the derivative of the tracking variable error, it is possible to obtain:

[0203]

[0204] And consider the following adaptive law Substitute the virtual control law and the derived tracking variable error into the Lyanov function V 1 , can get

[0205]

[0206] Where: 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 It is expressed as:

[0207]

[0208] Where: represents the design parameters and

[0209] In order to reduce the execution frequency, this embodiment introduces a memory event trigger mechanism based on relative threshold. According to the tracking variable error, the ASV dynamic estimation model and the virtual control law are combined to construct a deep learning controller, and the expression of the deep learning controller is:

[0210]

[0211] Where: u1 ,η u1 ,ξ r1 ,η r1 Both represent auxiliary system variables used to adjust the dynamic response of the control input, that is, the gain coefficient or adjustment factor ε related to the controller adjustment u ,ε r represents the error term associated with the control signal; represents the external disturbance estimate or estimated control parameter obtained based on the modulus error approximation observer; μ u ,μ r represents the system tuning parameter used to control the dynamic response of the error, represents the reference quality associated with the control inputs u and r; represents the estimated parameter used to adjust the control input; ∈ c k represents the regulation constant used to limit the control input amplitude; u ,k v ,k r ,Γ p ,v p represents a positive design parameter; Represents χ p The estimated value of ω p With ω r represents the intermediate parameter 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 trigger mechanism, and based on the constructed memory event trigger mechanism, implement tracking control of the under-actuated ASV according to the deep learning controller;

[0213] The memory event triggering mechanism constructed is specifically

[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 (|η p1 q p (t)+η p2 q p (t-τ)|)-|e p (t)|

[0219] Where: Indicates that at t j The control output of the deep learning controller at each moment; p (t) represents the trigger error of the memory event trigger mechanism and ξ p1 ,ξ p2 represents the preset threshold parameter; η p1 ,η p2 ,η p3 Indicates the intermediate parameter quantity; q p (t) represents the time interval [t j ,t j+1 ) within the actual control input; t j ,t j+1 represents the time parameter; q p (t-τ) represents the delayed control input at the time of delay τ; J p represents the design parameters;

[0220] In order to facilitate the controller design, the memory event trigger mechanism is rewritten as

[0221] e p =α p1 (ξ p1 η p1 q p (t)+ξ p1 η p2 q p (t-τ))+α p2 ηp3

[0222]

[0223] Where: α p1 ,α p2 Both represent intermediate parameter variables; α p represents the design parameters and α p ∈[-1,1];q p Indicates q p (t) is an abbreviation of

[0224] According to the trigger error of the memory event trigger mechanism and combined with the rewritten memory event trigger mechanism, the actual control input of the underdriven ASV is expressed as

[0225]

[0226] In this embodiment, in high-precision tracking tasks, the control signal is prone to fluctuations due to the complex and time-varying ocean environment; under the traditional trigger mechanism, the trigger threshold may be determined by invalid signals, resulting in waste of communication resources and performance degradation. In order to save communication resources and ensure system performance, a memory-based event trigger mechanism (METM) is proposed, whose trigger conditions can be adjusted according to historical and real-time data. When the control signal changes suddenly, METM emphasizes historical data, overcoming the limitation of the traditional trigger mechanism that over-relies on real-time data, thereby improving data utilization.

[0227] The stability analysis of the method in this embodiment is as follows:

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

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

[0230]

[0231] Where: matrices A and B are:

[0232]

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

[0234] QA+A T Q+δI 6 =0,

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

[0236]

[0237] And derive it to get:

[0238]

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

[0240]

[0241] Now, through the By defining the term, we can get:

[0242]

[0243] in, Is with external input Related constants, if the external input is bounded, then ∈ is also a bounded constant; based on the standard results of Lyapunov function analysis, we can know that the system state W 1 It is SGUUB (Semi-Globally Uniformly Ultimately Bounded).

[0244] Theorem 3: Considering the underactuated ASV mathematical model, PTPF constraint (trajectory tracking constraint), 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=V 1 +V 3

[0247] in Its derivative can be expressed as:

[0248]

[0249] Will Substitution Can get:

[0250]

[0251] And based on the deep learning controller, it can be deduced:

[0252]

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

[0254]

[0255] Will

[0256] Substitution

[0257] Can get:

[0258]

[0259] And further we can get:

[0260]

[0261] In the formula, C 1 ,C 2 is a positive number that satisfies the following conditions

[0262]

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

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

[0265] In order to demonstrate the effectiveness of the proposed method, this embodiment conducts the following numerical simulation cases:

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

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

[0268] The initial speed of the ship leader is as follows: u l =3m / s,v l =0m / s, rotation rate r L Meet the following conditions

[0269]

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

[0271] The initial condition of the follower is defined as: η=[-14,-13,η / 6] T and ν=[0,0,0] T ;

[0272] The data of ASV is collected online and used to train the DNN in real time. The DNN is constructed by three fully connected layers. The input dimension of the DNN is set to 8 and the output dimension is 3. The learning rate applied is 0.0001, ReLU is selected as the activation function, and the regression layer uses the mean square error as the loss function.

[0273] In order to demonstrate the effectiveness of the proposed method, this embodiment conducts a comparative analysis with the existing preset performance control algorithm. Figure 3 A comparison was made in Figure 3 Demonstrated trajectory tracking control plane. Figure 4 and Figure 5 It shows that the proposed method is more stable than the existing preset performance control algorithm in terms of position and angle errors. Figure 6 The loss function of DNN is shown. Figure 7 The observation accuracy of the created observer is shown. Figure 8 shows the actual control input, Fig. 9 The event interval under METC is shown.

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

[0275] Table 1. Performance index results

[0276]

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

[0278] Table 2. Comparison table of this implementation method, static event trigger mechanism and dynamic event trigger mechanism

[0279]

[0280] In summary, the proposed METM triggering times are less than those of conventional event triggering mechanisms (static event triggering mechanism and dynamic event triggering mechanism), thereby further saving communication resources.

[0281] In order to verify whether the initial point constraint in the traditional PPC method in this embodiment is removed, a set of comparative cases is added. In these cases, the initial position of ASV is set to [-20,-20], which is a situation where traditional PPC cannot be applied. Fig.10 and Fig.11 The trajectory and relative position of the proposed algorithm are shown when the initial point is outside the constraint boundary. The results show the advantages of the proposed algorithm because it does not impose constraints on the initial position of the ASV, only requiring it to remain within the sensor detection range. This method is more in line with the actual 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, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned 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. A memory-based event-triggered time-limited performance control method for under-actuated ASV, characterized in that: The specific steps include: S1: Construct a mathematical model of underactuated ASV; Obtaining the ASV dynamics model containing unknown dynamic terms based on the underactuated ASV mathematical model; S2: Obtain tracking data volume according to the underactuated ASV mathematical model; And the tracking data volume includes relative distance and relative azimuth angle; The tracking position error is defined according to the amount of tracking data, and the initial condition of the tracking position error is obtained based on the constructed sigmoid function; Constructing a preset prescribed time performance function to obtain trajectory tracking constraints based on initial conditions; S3: constructing an error conversion function for limiting the tracking position error according to the trajectory tracking constraint; And construct a virtual control law based on the error conversion function; S4: Based on the deep neural network DNN, the optimized ASV dynamics model including the DNN modeling error is obtained according to the ASV dynamics model; Construct a modeling error approximation observer to approximate and optimize the DNN modeling error in the ASV dynamics model and obtain the ASV dynamics estimation model; S5: Obtain tracking variable error based on ASV dynamics estimation model and virtual control law; A deep learning controller is constructed according to the tracking variable error combined with the ASV dynamics estimation model and the virtual control law. Based on the constructed memory event trigger mechanism, tracking control of the under-actuated ASV is achieved according to the deep learning controller.

2. The memory-based event-triggered specified time performance control method for under-actuated ASV according to claim 1, characterized in that: The S1 specifically includes the following steps: S11: Construct the mathematical model of underactuated ASV, which is expressed as 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 speed, lateral speed and yaw angular velocity; q represents the control input and q = [q u ,0,q r ] T ;q u ,q r represents the control input provided by the thruster and rudder; M, C(v), D(ν) 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 transform the hull coordinate system into the inertial coordinate system; represents the first derivative of η; represents the first derivative of v; S12: According to the underactuated ASV mathematical model, an ASV dynamics model with unknown dynamic terms is obtained, and the expression of the ASV dynamics model with unknown dynamic terms is: G(v,q,d)=-(M * ) -1 q+M -1 (-C(v)v-D(v)v+d+q) Where: M * represents the nominal mass of the non-diagonal inertia matrix; G(ν,q,d) represents the unknown dynamic terms of the ASV dynamic model; M represents the non-diagonal inertia mass matrix.

3. The memory-based event-triggered specified time performance control method for under-actuated ASV according to claim 2, characterized in that: The S2 specifically includes the following steps: S21: Obtain tracking data volume according to the underactuated ASV mathematical model; And the tracking data volume includes relative distance and relative azimuth angle; The expressions of the relative distance and relative azimuth angle are: θ=atan2(Δy,Δx) Δx=x l -x,Δy=y l -y φ=θ-ψ Where: d represents the relative distance, φ represents the relative azimuth angle and d min <d<d max , d min ,d max Respectively represent the maximum and minimum values ​​of the relative distance; represents the upper limit of the relative azimuth angle; θ represents the desired heading angle; Δx, Δy represent intermediate parameters; x l ,y l Indicates the horizontal and vertical coordinates of the desired trajectory position; S22: Define the tracking position error based on the amount of tracking data, and its expression is e k =kk d ,k=d,φ Where: e k represents the tracking position error; k represents the relative distance or relative azimuth angle; k d Indicates the expected relative distance or expected relative azimuth angle; S23: Define the sigmoid function of the underactuated ASV system to convert the initial tracking position error e of the underactuated ASV system k (0), not necessarily constrained within a predefined area; And the expression of sigmoid function S(t) is Where: α and T q represents the design parameter; t represents the time parameter; 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 of the 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: constructing a preset specified time performance function; And the expression of the preset specified time performance function is T q =cos((π(t-T m ))(T f -T m ) -1 ) Where: represents constant gain; T m Indicates transition time; T f Indicates the set time; represents an intermediate parameter piecewise function; It represents the rate constant of control time decay; t0 represents the starting time, i.e. the moment when the control process begins; Indicates that the system is guaranteed to be within the set time T f The function of the target task completed within a certain period of time; represents the control gain; represents the gain matrix; express The steady-state value of and represents a positive design constant; represents the error convergence control variable; express The first-order derivative of for The abbreviated form of , k = d, φ; S26: Based on a preset prescribed time performance function, obtaining trajectory tracking constraints according to initial conditions; And the expression of trajectory tracking constraint is Where: 1d ,δ 2d ,δ 1φ ,δ 2φ Represents a positive proportional coefficient used to adjust the error convergence speed; Represents the control variable used to adjust the convergence of relative distance and relative azimuth angle errors.

4. The memory-based event-triggered specified time performance control method for under-actuated ASV according to claim 3, characterized in that: The S3 specifically includes the following steps: S31: constructing an error conversion function for limiting the tracking position error according to the trajectory tracking constraint; And the expression of the error transfer function is S32: Construct a virtual control law based on the error conversion function, and the expression of the virtual control law is Where: γ=[γ u ,γ v ,γ r ] T represents the virtual control law of forward speed, lateral speed and yaw angular velocity, ζ u ,ζ v ,ζ r represents 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 represents the design parameter, β u ,β v ,β v Represents auxiliary system variables; Σ d Indicates the intermediate parameter quantity; Indicates d d The first derivative of is represented as a design parameter and β u ,β v ,β r , represents the unknown parameters, and is determined by the forward pilot speed u l Estimated value of With lateral leading speed v l Estimated value of get; Indicates unknown parameters Estimate of π k , represents an intermediate variable; and χ φ Represents the regulation function of the yaw angle.

5. The memory-based event-triggered specified time performance control method for under-actuated ASV according to claim 4, characterized in that: The S4 specifically comprises the following steps: S41: Based on the deep neural network DNN, an optimized ASV dynamics model including the DNN modeling error is obtained according to the ASV dynamics model; The expression of the optimized ASV dynamics model including the DNN modeling error is Where: It means that the dynamic key data features of ASV are learned and captured in the unseen input domain based on the deep neural network DNN according to the preset historical tracking trajectory data, and the dynamic key data features are the velocity vector, control input and unknown disturbance; the loss function of the dynamic key data features of ASV learned and captured based on the deep neural network DNN is E b (L t ); G0 represents the DNN modeling error and G0 = [G u0 ,G v0 ,G r0 ], G u0 ,G v0 ,G r0 They represent the forward velocity error, lateral velocity error, and yaw angular velocity error modeled by DNN respectively; 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 used to quantify the dynamic key data of ASV at the tth iteration; represents the learning value used to quantify the dynamic key data of ASV at the tth iteration; b represents the true distribution; B represents the distribution of historical tracking trajectory data; S42: construct a modeling error approximation observer to approximate and optimize the DNN modeling error in the ASV dynamics model, thereby obtaining the ASV dynamics estimation model; And the expression of the modeling error approximation observer is Where: represents an estimate of ν; represents the estimate of G0 and M1,M2 represent the observer parameter matrix and represents the observer parameters; I3 represents the 3×3 identity matrix; express The first derivative of express The first derivative of express The simplified form of ν=[u,v,r] T .

6. The memory-based event-triggered specified time performance control method for under-actuated ASV according to claim 5, characterized in that: The S5 specifically includes the following steps: S51: Obtain the tracking variable error according to the ASV dynamics estimation model and the virtual control law, and the expression of the tracking variable error is: z=ν-γ-ζ from=[from u ,With v ,With r ] T ζ=[ζ u ,ζ v ,ζ r ] T S52: A deep learning controller is constructed 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: Where: u1 ,η u1 ,ξ r1 ,η r1 Both represent auxiliary system variables used to adjust the dynamic response of the control input, that is, the gain coefficient or adjustment factor ε related to the controller adjustment u ,ε r represents the error term associated with the control signal; represents the external disturbance estimate or estimated control parameter obtained based on the modulus error approximation observer; μ u ,μ r represents the system tuning parameter used to control the dynamic response of the error, represents the reference quality associated with the control inputs u and r; represents the estimated parameter used to adjust the control input; ∈ c k represents the regulation constant used to limit the control input amplitude; u ,k v ,k r ,Γ p ,ν p represents a positive design parameter; Represents χ p The estimated value of ω p With ω r represents the intermediate parameter and ω u =z d π d cosφ,ω v =-z d π d sinφ and ω r =z φ π φ ; S53: construct a memory event trigger mechanism, and based on the constructed memory event trigger mechanism, implement tracking control of the under-actuated ASV according to the deep learning controller; The memory event triggering mechanism constructed is specifically |e p (t)|≥ξ p1 (|h p1 q p (t)+η p2 q p (t-τ)|)+η p3 or p1 =1st p2 or p3 =-J p or p3 +ξ p1 (|h p1 q p (t)+η p2 q p (t-τ)|)-|e p (t)| Where: Indicates that at t j The control output of the deep learning controller at each moment; p (t) represents the trigger error of the memory event trigger mechanism and ξ p1 ,ξ p2 represents the preset threshold parameter; η p1 ,η p2 ,η p3 Indicates the intermediate parameter quantity; q p (t) represents the time interval [t j ,t j+1 ) within the actual control input; t j ,t j+1 Represents the time parameter; q p (t-τ) represents the delayed control input at the time of delay τ; J p represents the design parameters; And rewrite the memory event trigger mechanism as e p =a p1 (x) p1 or p1 q p (t)+ξ p1 or p2 q p (t-τ))+α p2 or p3 Where: α p1 ,α p2 Both represent intermediate parameter variables; α p represents the design parameters and α p ∈[-1,1];q p Indicates q p (t) is an abbreviation of According to the trigger error of the memory event trigger mechanism and combined with the rewritten memory event trigger mechanism, the actual control input of the underdriven ASV is expressed as

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