Unmanned ship parallel path tracking control method based on deep neural network predictor

Abstract

The invention provides an unmanned ship parallel path tracking controller based on a deep neural network predictor, and the controller comprises a calculation experiment module and a parallel system module, and the parallel system module and the calculation experiment module carry out the data transmission. The calculation experiment module comprises a data stack module, an inner ring slow feature learning device and an outer ring fast learning device; the parallel system module comprises a virtual unmanned ship system, a parallel path tracking controller, an actual unmanned ship system and an actual controller. The invention provides a parallel path tracking control law, a path tracking problem is expanded from a real space to a virtual space, and interaction between the virtual space and the real space is realized.

Description

Technical Field

[0001] The present invention relates to the technical field of unmanned ship control, and in particular, to an unmanned ship parallel path tracking controller based on a deep neural network predictor. Background Art

[0002] An unmanned ship is a ship that can operate independently on water, with autonomy and intelligence capabilities, and is crucial for water transportation. In the past few decades, the path tracking technology of unmanned ships has received extensive attention, and its advantage lies in being able to handle spatial and temporal constraints separately to achieve smooth transient behavior.

[0003] Existing unmanned ship path tracking control methods include traditional control methods, PID control methods, optimal control methods, sliding mode control methods, fuzzy control methods, line-of-sight guidance methods, model predictive control methods, feedback linearization methods, adaptive control methods, etc.

[0004] Among existing unmanned ship path tracking control methods, there are still some problems that need to be solved urgently: In existing unmanned ship parallel control technologies, when dealing with complex systems, the path tracking problem has not been extended from the real world to the virtual domain, nor has effective interaction between the virtual space and the real space been achieved. In existing unmanned ship deep neural network predictors, in terms of handling regression problems, optimization of the training data set has not been achieved through inner-loop and outer-loop fast learners, and the reliability and generalization ability in practical applications are poor. Existing unmanned ship path tracking control technologies have not achieved virtual interaction and parallel interaction, nor have they paid attention to the fast learning ability for unknown dynamics, resulting in the inability to achieve real-time synchronization between the artificial system and the actual system. Summary of the Invention

[0005] In view of this, the purpose of the present invention is to propose an unmanned ship parallel path tracking controller based on a deep neural network predictor to solve the technical problem that existing unmanned ship path tracking control methods have not extended the path tracking problem from the real world to the virtual domain.

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

[0007] An unmanned ship parallel path tracking controller based on a deep neural network predictor, including a computational experiment module and a parallel system module, and data transmission is carried out between the parallel system module and the computational experiment module;

[0008] The computational experiment module includes a data stack module, an inner-loop slow feature learner, and an outer-loop fast learner;

[0009] The parallel system module includes a virtual unmanned ship system, a parallel path tracking controller, an actual unmanned ship system, and an actual controller.

[0010] Further, the data stack module receives the estimated value information of the surge speed, sway speed, and yaw angular velocity of the unmanned ship from the virtual unmanned ship system, the estimated value information of the unmanned ship position parameters, and the estimated value information of the heading angle parameters of the unmanned ship; the data stack module receives the estimated unknown dynamics from the outer loop fast learning module;

[0011] The data stack module sends the information of the surge speed, sway speed, and yaw angular velocity of the unmanned ship, the unmanned ship position parameter information, and the unmanned ship heading angle parameter information to the inner loop slow feature learning module;

[0012] The inner loop slow feature learning module receives the information of the surge speed, sway speed, and yaw angular velocity of the unmanned ship, the unmanned ship position parameter information, and the unmanned ship heading angle parameter information from the data stack module; the inner loop slow feature learning module sends the learned basis function vector to the outer loop fast learning module;

[0013] The outer loop fast learning module receives the basis function vector and sends the estimated unknown dynamics to the virtual unmanned ship system and the data stack module;

[0014] The virtual unmanned ship system receives the control input information of the unmanned ship from the parallel path tracking controller and the estimated unknown dynamics from the outer loop fast learning module; the virtual unmanned ship system sends the estimated value information of the surge speed, sway speed, and yaw angular velocity of the unmanned ship, the estimated value information of the unmanned ship position parameters, and the estimated value parameter information of the unmanned ship heading angle to the data stack module;

[0015] The parallel path tracking controller receives the unmanned ship position parameter information and the unmanned ship heading angle parameter information sent by the actual unmanned ship system; the parallel path tracking controller sends the control input information of the unmanned ship to the virtual unmanned ship system;

[0016] The actual unmanned ship system receives the control input information of the unmanned ship from the actual controller and the wind condition information from the outer loop fast learning module; the actual unmanned ship system sends the information of the surge speed, sway speed, and yaw angular velocity of the unmanned ship, the unmanned ship position parameter information, and the unmanned ship heading angle parameter information to the data stack module;

[0017] The actual controller receives the unmanned ship position parameter information and the unmanned ship heading angle parameter information sent by the actual unmanned ship system; the parallel path tracking controller sends the control input information of the unmanned ship to the actual unmanned ship system.

[0018] Further, the dynamic models of the virtual unmanned ship model and the actual unmanned ship model are as follows:

[0019]

[0020]

[0021] wherein, and represent the position parameters of the unmanned ship, and θ∈(-π,π] represents the course angle of the unmanned ship; represents the vector of the surge velocity, sway velocity and yaw angular velocity of the unmanned ship in the unmanned ship; represents the inertia matrix, F(ν) = [F1(ν), F2(ν), F3(ν)] T is a non-linear function simulating hydrodynamic damping and centrifugal / Coriolis forces; represents the control input vector; represents the unknown ocean disturbance vector, covering factors such as wind, waves and currents;

[0022] is the rotation matrix, and the specific form is as follows:

[0023]

[0024] The parameterized path of the unmanned ship is:

[0025] η b (ξ) = [x b (ξ), y b (ξ), ψ b (ξ)] T

[0026] wherein, x b (ξ) and y b (ξ) respectively represent the X coordinate and Y coordinate of the reference path in the fixed ground coordinate system, and ψ b (ξ) represents the tangent angle of the path, and ψ b (ξ) = atan2(x b ′, y b ′) is used to define the path variable respectively. Define the path variable.

[0027] Furthermore, the formula of the data stack module is as follows:

[0028]

[0029] In the formula, Si is the stack, is the element to be pushed.

[0030] Furthermore, the formula of the inner loop slow feature learner is as follows:

[0031]

[0032] In the formula, Meet the conditions and represent the ideal weights, and E1(ν,d), E2(ν,d), E3(ν,d) represent the learned basis vectors;

[0033] E υ (ν,d) = e υ,m (α υ,m-1 , e υ,m-1 (α υ,m-2 , e υ,m-2 (…)))

[0034] In the formula, α represents an inner-loop weight, m represents the number of hidden layers of the deep network, and υ is 1, 2, 3; is the vector of the approximation error of the deep neural network;

[0035]

[0036] In the formula, M is the size of the sample training set; i = 1, 2,..., N, representing the marked pairs of input values and target values drawn from the data buffer B according to the same joint distribution; represents the l2 norm loss function;

[0037] The update rule of the inner-layer weights is as follows:

[0038]

[0039] In the formula, μ is the learning rate and k is the number of iterations of the deep neural network;

[0040] The design of the selection conditions for recording data is as follows:

[0041]

[0042] In the formula, p = 1, 2,..., p max is the index of the data point in the buffer B, is a constant.

[0043] Furthermore, the formula of the outer-loop fast learner is as follows:

[0044]

[0045] In the formula, represents the predicted return, Proj represents the projection operator; E1(ν,d), E2(ν,d), E3(ν,d) represent the learned basis vectors; represents the predicted value of the ideal weight.

[0046] Furthermore, the formula of the virtual unmanned ship system is as follows:

[0047]

[0048] In the formula, and respectively represent the estimated values of η and ν; D η = diag{d η1 , d η2 , d η3}, D ν = diag{d ν1 , d ν2 , d ν3} is the control gain matrix, and d η1 , d η2 , d η3 , d ν1 , d ν2 , d ν3 is a positive constant; represents 's estimated value.

[0049] Furthermore, the formula of the parallel path tracking controller is as follows:

[0050]

[0051] In the formula, x1 is the position and heading tracking error vector, and x2 is the motion speed tracking error vector; the time derivative of x1 along the kinematic direction is:

[0052]

[0053] In the formula, and represent the path update speed, and the update law of ξ s is:

[0054]

[0055] In the formula, and represent positive constants.

[0056] Furthermore, in the actual unmanned ship system:

[0057] The dynamic model of the unmanned ship is expressed as:

[0058]

[0059] In the formula, d = [V w , ρ w T represents the wind condition,​ Represents the uncertainty inside the model and external disturbances;

[0060]

[0061]

[0062] In the formula, Represents the air density; Represents the relative wind speed; κ w Represents the relative wind direction; Is the wind coefficient; Represents the total length of the unmanned ship; Refer to the lateral and frontal projected wind areas respectively.

[0063] Furthermore, the formula of the actual controller is as follows:

[0064]

[0065] In the formula, Is a constant to be designed, Is the design value;

[0066]

[0067]

[0068] In the formula, A c = diag{a c1 , a c2 , a c3}, Is a constant to be designed; Is the design value.

[0069] Compared with the prior art, the present invention has the following advantages:

[0070] Compared with the existing unmanned ship path tracking control methods, the present invention proposes a parallel path tracking control law, which extends the path tracking problem from the real space to the virtual space and realizes the interaction between the virtual space and the real space.

[0071] Compared with the existing unmanned ship deep neural network estimator design methods, the present invention proposes an online learning virtual unmanned ship system, which trains data through the inner loop and the outer loop fast learners, improving the reliability and generalization ability of practical applications to adapt to different marine environments.

[0072] Compared with the existing path tracking control methods for unmanned ships, the present invention proposes a control method that combines the weights of the last layer of the outer loop learner with the features obtained from the inner loop learner in deep learning, focusing on rapid learning of unknown dynamics and enabling real-time synchronization between the artificial system and the actual system. BRIEF DESCRIPTION OF THE DRAWINGS

[0073] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for use in the description of the embodiments or the prior art. Obviously, the drawings in the following description are some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can be obtained based on these drawings.

[0074] Figure 1 It is the logic diagram of the controller of the present invention.

[0075] Figure 2 It is the schematic diagram of the path tracking performance of the present invention.

[0076] Figure 3 It is the schematic diagram of the position tracking performance of the present invention.

[0077] Figure 4 It is the schematic diagram of the speed tracking performance of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0078] In order to enable those skilled in the art to better understand the solution of the present invention, the following will clearly and completely describe the technical solutions in the embodiments of the present invention with reference to the drawings in the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, rather than all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

[0079] It should be noted that the terms "first", "second", etc. in the specification and claims of the present invention and the above drawings are used to distinguish similar objects, and do not necessarily need to describe a specific order or sequence. It should be understood that such used data can be interchanged under appropriate circumstances so that the embodiments of the present invention described here can be implemented in an order other than those illustrated or described here. In addition, the terms "comprising" and "having" and any variations thereof are intended to cover non-exclusive inclusion. For example, a process, method, system, product or device that includes a series of steps or units does not necessarily have to be limited to those steps or units clearly listed, but may include other steps or units not clearly listed or inherent to these processes, methods, products or devices.

[0080] Such as Figure 1As shown in the figure, the present invention provides an unmanned ship parallel path tracking controller based on a deep neural network estimator, which includes a computational experiment module and a parallel system module, and the parallel system module and the computational experiment module transmit data to each other;

[0081] The computational experiment module includes a data stack module, an inner loop slow feature learner, and an outer loop fast learner;

[0082] The parallel system module includes a virtual unmanned ship system, a parallel path tracking controller, an actual unmanned ship system, and an actual controller.

[0083] The data stack module receives the estimated value information of the surge speed, sway speed, and yaw angular velocity of the unmanned ship, the estimated value information of the unmanned ship position parameters, and the estimated value information of the unmanned ship heading angle parameters from the virtual unmanned ship system; the data stack module receives the predicted unknown dynamics from the outer loop fast learning module; the data stack module sends the information of the surge speed, sway speed, and yaw angular velocity of the unmanned ship, the unmanned ship position parameter information, and the unmanned ship heading angle parameter information to the inner loop slow feature learning module; the inner loop slow feature learning module receives the information of the surge speed, sway speed, and yaw angular velocity of the unmanned ship, the unmanned ship position parameter information, and the unmanned ship heading angle parameter information from the data stack module; the inner loop slow feature learning module sends the learned basis function vector to the outer loop fast learning module; the outer loop fast learning module sends the predicted unknown dynamics to the virtual unmanned ship system and the data stack module; the computational experiment module sends the predicted unknown dynamics of the outer loop fast learning module to the virtual unmanned ship system;

[0084] The virtual unmanned ship system receives the control input information of the unmanned ship from the parallel path tracking controller and the predicted unknown dynamics from the outer loop fast learning module; the virtual unmanned ship system sends the estimated value information of the surge speed, sway speed, and yaw angular velocity of the unmanned ship, the estimated value information of the unmanned ship position parameters, and the estimated value parameter information of the unmanned ship heading angle to the data stack module;

[0085] The parallel path tracking controller receives the unmanned ship position parameter information and the unmanned ship heading angle parameter information sent by the actual unmanned ship system; the parallel path tracking controller sends the control input information of the unmanned ship to the virtual unmanned ship system;

[0086] The actual unmanned ship system receives the control input information of the unmanned ship from the actual controller and the wind condition information from the outer loop fast learning module; the actual unmanned ship system sends the information of the surge speed, sway speed, and yaw angular velocity of the unmanned ship, the unmanned ship position parameter information, and the unmanned ship heading angle parameter information to the data stack module;

[0087] The actual controller receives the unmanned ship position parameter information and the course angle parameter information sent by the actual unmanned ship system; the parallel path tracking controller sends the control input information of the unmanned ship to the actual unmanned ship system.

[0088] When describing the dynamic model of a three-degree-of-freedom unmanned ship, it can be expressed as:

[0089]

[0090]

[0091] In this formula, and represent the unmanned ship position parameters, and θ ∈ (-π, π] refers to the course angle of the unmanned ship; represents the vector of the surge speed, sway speed, and yaw angular velocity of the unmanned ship in the unmanned ship; is the inertia matrix, F(ν) = [F1(ν), F2(ν), F3(ν)] T is a nonlinear function that simulates hydrodynamic damping and centrifugal / Coriolis forces; represents the control input vector; then represents the unknown ocean disturbance vector, covering factors such as wind, waves, and currents. is the rotation matrix, and its specific form is as follows:

[0092]

[0093] The parameterized path of the unmanned ship is:

[0094]

[0095] In the formula, x b (ξ) and y b (ξ) represent the X coordinate and Y coordinate of the reference path in the fixed ground coordinate system respectively, ψ b (ξ) represents the tangent angle of the path, and ψ b (ξ) = atan2(x b ′, y b ′) respectively define the path variables using to define the path variables.

[0096] Data stack:

[0097]

[0098] In the formula, Si is the stack, is the element to be pushed.

[0099] Inner loop slow feature learner:

[0100]

[0101] In the formula, satisfies the condition and represent the ideal weights. E1(ν,d), E2(ν,d), E3(ν,d) represent the learned basis vectors.

[0102] E υ (ν,d) = e υ,m (α υ,m-1 , e υ,m-1 (α υ,m-2 , e υ,m-2 (…))) (7)

[0103] In the formula, α represents an inner-loop weight, m represents the number of hidden layers of the deep network, and υ is 1, 2, 3. is the vector of the approximation error of the deep neural network.

[0104]

[0105] In the formula, M is the size of the sample training set; i = 1, 2,..., N, represents the labeled pairs of input values and target values drawn from the data buffer B according to the same joint distribution; represents the l2-norm loss function.

[0106] The update rule of the inner-layer weights is as follows:

[0107]

[0108] In the formula, μ is the learning rate, and k is the number of iterations of the deep neural network. The selection condition for recording data is designed as follows:

[0109]

[0110] In the formula, p = 1, 2,..., p max is the index of the data point in the buffer B, is a small constant.

[0111] Outer-loop fast learner:

[0112]

[0113] In the formula, represents the predicted return, and "Proj" refers to the projection operator. E1(ν,d), E2(ν,d), E3(ν,d) represent the learned basis vectors. represents the predicted value of the ideal weight.

[0114] Virtual unmanned ship system:

[0115]

[0116]

[0117] Wherein, and respectively represent the estimated values of η and ν; D η = diag{d η1 , d η2 , d η3}, D ν = diag{d ν1 , d ν2 , d ν3} is the control gain matrix, where d η1 , d η2 , d η3 , d ν1 , d ν2 , d ν3 is a positive constant; represents 's estimated value.

[0118] Parallel path tracking controller:

[0119]

[0120]

[0121] Wherein, x1 is the position and heading tracking error vector, and x2 is the motion speed tracking error vector. The time derivative of x1 along the kinematic direction is:

[0122]

[0123] Wherein, and represent the path update speed, and the update law of ξ s is designed as

[0124]

[0125] Wherein, and represent positive constants.

[0126] Actual unmanned ship system:

[0127] The unmanned ship model is considered to represent a large seagoing ship with a length of 76.2 meters. The parameters of the unmanned ship in the cyber-physical system are:

[0128]

[0129] The dynamic model (2) of the unmanned ship can be expressed as:

[0130]

[0131] where d = [V w , ρ w T represents the wind condition, represents the uncertainties inside the model and external disturbances.

[0132]

[0133] where represents the air density; represents the relative wind speed; κ w refers to the relative wind direction; is the wind coefficient; represents the total length of the unmanned ship; refer to the lateral and frontal projected wind areas respectively.

[0134] Actual controller:

[0135]

[0136] where is a constant to be designed, is the design value.

[0137]

[0138]

[0139] where A c = diag{a c1 , a c2 , a c3}, are constants to be designed; is the design value.

[0140] Example

[0141] The external disturbance parameters are selected as follows: The initial wind speed V w and the initial wind direction κ w follow the uniform distributions V w ~ U(0, 1) m / s and κ w ~ U(-180, 180)°, and the per-second change rates of the wind speed conditions satisfy ΔV w ~ U(-0.1, 0.1) m / s, Δκ w ​~U(-0.1, 0.1)°. The initial state of the unmanned ship is set as η0 = [-100, 150, -1] T , ν0 = [1, 0, 0] T . The internal neural network of the deep neural network predictor contains two hidden layers, including 300 and 200 neurons respectively, and a tangent sigmoid transfer function. The learning rate μ is selected as 0.1. The buffer size p max is predefined as 1000, while the mini-batch size N is predefined as 100. Assume that the parameterized reference path is represented by x d (ξ) = 15ξ + 1, y d (ξ) = 500cos(0.02ξ), θ d = atan2(15, 10cos(0.02ξ)) of the sine signal, and the simulation results are respectively recorded in Figures 2 - 4 . Figure 2 shows the path tracking performance using the proposed parallel control method. Figure 3 respectively depicts the desired position η d of the unmanned ship, the real position η and the virtual position From which it can be seen that the virtual position signal can accurately track the reference path and the real position signal. Figure 4 respectively shows the command paths after the guidance signal ν c , the actual speed signal ν and the virtual speed signal ν. It can be seen that the virtual speed signal accurately tracks the guidance signal and the actual speed signal.

[0142] This paper studies the parallel path tracking control problem of an unmanned ship in a cyber-physical system based on the deep neural network predictor algorithm. This method uses the proposed deep neural network predictor algorithm to perform real-time modeling on the unmanned ship in the cyber-physical system. By applying the deep neural network predictor algorithm, the constructed artificial unmanned ship system can adapt to the changing marine environment. In the computational experiment stage, based on the state information of the artificial system, a parallel path tracking control strategy is designed. Through repeated computational experiments and parallel execution, the constructed artificial system and the actual system achieve temporal synchronization. The simulation results prove the effectiveness and reliability of the proposed parallel path tracking control method. Nevertheless, the currently proposed parallel path tracking control method is only applicable to fully actuated ships.

[0143] 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 foregoing embodiments, those of ordinary skill in the art should understand that: they can still modify the technical solutions recorded in the foregoing embodiments, or perform equivalent replacements on some or all of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. An unmanned ship parallel path tracking controller based on a deep neural network estimator, characterized in that, It includes a computational experiment module and a parallel system module, and data transmission is carried out between the parallel system module and the computational experiment module; The computational experiment module includes a data stack module, an inner-loop slow feature learner, and an outer-loop fast learner; The parallel system module includes a virtual unmanned ship system, a parallel path tracking controller, an actual unmanned ship system, and an actual controller.

2. The unmanned ship parallel path tracking control method based on a deep neural network estimator according to claim 1, characterized in that: The data stack module receives the estimated value information of the surge velocity, sway velocity, and yaw angular velocity of the unmanned ship, the estimated value information of the unmanned ship position parameters, and the estimated value information of the heading angle parameters of the unmanned ship from the virtual unmanned ship system; the data stack module receives the predicted unknown dynamics from the outer-loop fast learning module; The data stack module sends the information of the surge velocity, sway velocity, and yaw angular velocity of the unmanned ship, the unmanned ship position parameter information, and the unmanned ship heading angle parameter information to the inner-loop slow feature learning module; The inner-loop slow feature learning module receives the information of the surge velocity, sway velocity, and yaw angular velocity of the unmanned ship, the unmanned ship position parameter information, and the unmanned ship heading angle parameter information from the data stack module; the inner-loop slow feature learning module sends the learned basis function vector to the outer-loop fast learning module; The outer-loop fast learning module receives the basis function vector and sends the predicted unknown dynamics to the virtual unmanned ship system and the data stack module; The virtual unmanned ship system receives the control input information of the unmanned ship from the parallel path tracking controller and the predicted unknown dynamics from the outer-loop fast learning module; the virtual unmanned ship system sends the estimated value information of the surge velocity, sway velocity, and yaw angular velocity of the unmanned ship, the estimated value information of the unmanned ship position parameters, and the estimated value parameter information of the unmanned ship heading angle to the data stack module; The parallel path tracking controller receives the unmanned ship position parameter information and the unmanned ship heading angle parameter information sent by the actual unmanned ship system; the parallel path tracking controller sends the control input information of the unmanned ship to the virtual unmanned ship system; The actual unmanned ship system receives the control input information of the unmanned ship from the actual controller and the wind condition information from the outer-loop fast learning module; the actual unmanned ship system sends the information of the surge velocity, sway velocity, and yaw angular velocity of the unmanned ship, the unmanned ship position parameter information, and the unmanned ship heading angle parameter information to the data stack module; The actual controller receives the unmanned ship position parameter information and the unmanned ship heading angle parameter information sent by the actual unmanned ship system; the parallel path tracking controller sends the control input information of the unmanned ship to the actual unmanned ship system.

3. The method for controlling the parallel path tracking of an unmanned ship based on a deep neural network estimator according to claim 1, wherein The dynamic models of the virtual unmanned ship model and the actual unmanned ship model are as follows: Among them, and represent the position parameters of the unmanned ship, and θ ∈ (-π, π] represents the heading angle of the unmanned ship; represents the vector of the surge velocity, sway velocity and yaw angular velocity of the unmanned ship in the unmanned ship; represents the inertia matrix, F(ν) = [F1(ν), F2(ν), F3(ν)] T is a non - linear function simulating hydrodynamic damping and centrifugal / Coriolis forces; represents the control input vector; represents the unknown ocean disturbance vector, covering factors such as wind, wave and current; is a rotation matrix, and its specific form is as follows: The parameterized path of the unmanned ship is: η b (ξ) = [x b (ξ), y b (ξ), ψ b (ξ)] T where x b (ξ) and y b (ξ) represent the X and Y coordinates of the reference path in the fixed ground coordinate system respectively, and ψ b (ξ) represents the tangent angle of the path. ψ b (ξ) = atan2(x b ′, y b ′) respectively define the path variables using the path variables.

4. The unmanned ship parallel path tracking control method based on a deep neural network estimator according to claim 1, wherein The formula of the data stack module is as follows: where Si is the stack, is the element to be pushed.

5. The unmanned ship parallel path tracking control method based on a deep neural network estimator according to claim 1, wherein The formula of the inner-loop slow feature learner is as follows: wherein, satisfies the condition and represent the ideal weights, and E1(ν,d), E2(ν,d), E3(ν,d) represent the learned basis vectors; E υ (ν, d) = e υ,m (α υ,m-1 , e υ,m-1 (α υ,m-2 , e υ,m-2 (…))) Where α represents an inner loop weight, m represents the number of hidden layers of the deep network, and υ is 1, 2, 3; is the vector of the approximation error of the deep neural network; where M is the size of the sample training set; denotes a pair of tags of an input value and a target value drawn from the data buffer B according to the same joint distribution; denotes the l2 norm loss function; The inner-layer weight update rule is as follows: Where μ is the learning rate and k is the iteration number of the deep neural network; The selection condition for recording data is designed as follows: where p = 1, 2, ..., p max is the index of the data point in buffer B is a constant 6. The method for controlling the parallel path tracking of an unmanned ship based on a deep neural network estimator according to claim 1, wherein The formula of the outer-loop fast learner is as follows: In the formula, represents the predicted return, Proj represents the projection operator; E1(ν,d), E2(ν,d), E3(ν,d) represent the learned basis vectors; represents the predicted value of the ideal weight.

7. The unmanned ship parallel path tracking control method based on a deep neural network estimator according to claim 1, wherein The formula of the virtual unmanned ship system is as follows: In the formula, and represent the estimated values of η and ν respectively; D η = diag{d η1 , d η2 , d η3}, D ν = diag{d ν1 , d ν2 , d ν3} are control gain matrices, and d η1 , d η2 , d η3 , d ν1 , d ν2 , d ν3 is a positive constant; denotes 's estimated value.

8. The method for controlling the parallel path tracking of an unmanned ship based on a deep neural network estimator according to claim 1, characterized in that The formula of the parallel path tracking controller is as follows: Wherein, x1 is the position and heading tracking error vector, and x2 is the motion speed tracking error vector; the time derivative along the kinematic direction x1 is: In the formula, and represent the path update speed, and the update rule of ξ s is as follows: In the formula, and represent positive constants.

9. The unmanned ship parallel path tracking control method based on a deep neural network estimator according to claim 1, wherein In the actual unmanned ship system: The dynamic model of the unmanned ship is expressed as: where d = [V w , ρ w T represents the wind conditions, indicating the uncertainties inside the model and external disturbances;​ In the formula, represents the air density; represents the relative wind speed; κ w represents the relative wind direction; is the wind coefficient; represents the total length of the unmanned ship; respectively refer to the lateral and frontal projected wind areas.

10. The unmanned ship parallel path tracking control method based on a deep neural network estimator according to claim 1, wherein The formula of the actual controller is as follows: In the formula, is a constant to be designed, is the design value; where A c = diag{a c1 , a c2 , a c3}, are constants to be designed; is the design value.

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