Unmanned Ship Tracking Control Method Based on Offline Iteration and Online Adjustment of Deep Network

Abstract

The present invention discloses an unmanned ship tracking control method based on offline iteration and online adjustment of a deep network. A first approximation of an unknown non-linear dynamics is obtained through a pre-trained deep neural network; the first approximation of the unknown non-linear dynamics is adjusted online to obtain an estimated value of a final approximation of the unknown non-linear dynamics; furthermore, an adaptive law for the controller and the output layer weights is obtained to ensure that the state vector of the heading angle of the unmanned ship can track a desired smooth time-varying trajectory; and the tracking control of the unmanned ship based on offline iteration and online adjustment of the deep network is realized. By combining the deep neural network, the present invention potentially improves the approximation performance of the function, thereby achieving a better approximation effect on the unknown dynamics of more complex features.

Description

Technical Field

[0001] The present invention relates to the technical field of artificial intelligence, and particularly relates to an unmanned ship tracking control method based on offline iteration and online adjustment of a deep network. Background Art

[0002] With the development of automation control technology in the field of ocean engineering, unmanned surface vehicles (USVs) and deep neural networks have undoubtedly become the focus of attention of many scholars. Unmanned ships can replace humans to perform some dangerous and boring special offshore operation tasks, and have extremely high research value in protecting the safety of human lives at sea. Currently, they have been widely used in fields such as resource exploration, coastal surveillance, and military patrol and reconnaissance. As a more complex neural network, the deep neural network has a superior approximation performance for unknown dynamics with more complex characteristics. It has a stronger approximation ability for the complex characteristic dynamics such as wind, waves, and currents when the unmanned ship is sailing.

[0003] Due to the influence of complex sea conditions such as wind, waves, and ocean currents, the course tracking control performance of unmanned ships has faced severe challenges. Therefore, in order to ensure the safety and efficiency of navigation, it is necessary to improve the course tracking control of unmanned ships. Compared with general situations, in severe sea conditions, the navigation dynamics of unmanned ships will have more complex characteristics, and the traditional course tracking control based on a single-hidden-layer artificial neural network has a poor approximation effect for dynamics with more complex characteristics. Summary of the Invention

[0004] The present invention discloses an unmanned ship tracking control method based on offline iteration and online adjustment of a deep network to overcome the above technical problems.

[0005] To achieve the above object, the technical solution of the present invention is as follows:

[0006] An unmanned ship tracking control method based on offline iteration and online adjustment of a deep network, characterized by comprising the following steps:

[0007] S1: Establish a mathematical model for the course tracking control of an unmanned ship considering the influence of wind, waves, and currents, including uncertain disturbance terms, and transform the mathematical model for the course tracking control of the unmanned ship into a second-order state space equation, so as to obtain the continuous-time nonlinear dynamic system of the unmanned ship;

[0008] S2: Based on the continuous-time nonlinear dynamic system of the unmanned ship and a pre-trained deep neural network, perform offline iteration on the unknown nonlinear dynamics in the nonlinear dynamic system to obtain a first approximation of the unknown nonlinear dynamics; perform online adjustment on the first approximation of the unknown nonlinear dynamics to obtain an estimated value of the final approximation of the unknown nonlinear dynamics, so as to obtain an estimated value of the final approximation of the unknown nonlinear dynamics.

[0009] S3: According to the continuous-time nonlinear dynamic system of the unmanned ship and the estimated value of the final approximation of the unknown nonlinear dynamics, obtain the controller and the output layer weight adaptation law to ensure that the state vector of the heading angle of the unmanned ship can track the desired smooth time-varying trajectory; realize the tracking control of the unmanned ship based on offline iteration and online adjustment of the deep network.

[0010] Beneficial effects: A tracking control method for an unmanned ship based on offline iteration and online adjustment of a deep network according to the present invention obtains a first approximation of the unknown nonlinear dynamics through a pre-trained deep neural network; performs online adjustment on the first approximation of the unknown nonlinear dynamics to obtain an estimated value of the final approximation of the unknown nonlinear dynamics; and further obtains the controller and the output layer weight adaptation law to ensure that the state vector of the heading angle of the unmanned ship can track the desired smooth time-varying trajectory; realizes the tracking control of the unmanned ship based on offline iteration and online adjustment of the deep network. By combining the deep neural network, the present invention potentially improves the approximation performance of the function, thereby achieving a better approximation effect on the unknown dynamics of more complex features. Description of the Drawings

[0011] 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 following drawings are some embodiments of the present invention. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.

[0012] Figure 1 It is a flowchart of the tracking control method for an unmanned ship based on offline iteration and online adjustment of a deep network according to the present invention;

[0013] Figure 2 It is a mean square error simulation diagram of offline training of the deep neural network provided in this embodiment;

[0014] Figure 3 It is a loss simulation diagram of offline training of the deep neural network provided in this embodiment;

[0015] Figure 4 It is a trajectory simulation diagram of the ship's heading and the reference heading provided in this embodiment;

[0016] Figure 5 This is the simulation diagram of the ship's heading tracking error result provided in this embodiment;

[0017] Figure 6 This is the simulation diagram of the output layer weight convergence result provided in this embodiment;

[0018] Figure 7 This is the control input simulation diagram provided in this embodiment. Specific implementation manners

[0019] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Apparently, the described embodiments are some, but not all, of the embodiments of the present invention. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0020] This embodiment introduces an unmanned ship tracking control method based on deep network offline iteration and online adjustment, as Figure 1 shown, including the following steps:

[0021] S1: Establish a mathematical model for the heading tracking control of an unmanned ship considering the influence of wind, waves, and currents, including uncertain disturbance terms, and transform the mathematical model for the heading tracking control of the unmanned ship into a second-order state space equation, so as to obtain the continuous-time nonlinear dynamic system of the unmanned ship;

[0022] Specifically, in this embodiment, first, a mathematical model for the heading tracking control of an unmanned ship affected by sea conditions such as wind, waves, and currents is obtained, and then the mathematical model for the heading tracking control of the unmanned ship is converted into a second-order state space equation as the continuous-time nonlinear dynamic system in this embodiment;

[0023] Specifically, the continuous-time nonlinear dynamic system of the unmanned ship in this embodiment is obtained as follows:

[0024] S11: Establish a mathematical model expression for the heading tracking control of an unmanned ship considering the influence of wind, waves, and currents, including uncertain disturbance terms, as follows:

[0025]

[0026] δ w =α r +β r

[0027] In the formula: φ represents the heading angle of the unmanned ship, that is, the output signal of the autopilot; represents the first derivative of φ; Denotes the second derivative of φ; Denotes the time constant of ship maneuverability; Denotes a non - linear function with respect to the yaw angular velocity of the ship; both α and β denote non - linear coefficients of the yaw angular velocity of the ship; Denotes the unmanned ship rudder gain maneuverability index; δ denotes the control input of the unmanned ship rudder angle and heading control system; δ w Denotes the equivalent rudder angle caused by uncertain environmental disturbances; α r Represents the wind - drift angle; β r Represents the current - drift angle.

[0028] S12: According to the unmanned ship heading tracking control mathematical model, obtain the expression of the continuous - time non - linear dynamic system of the unmanned ship as follows:

[0029]

[0030] Where,

[0031] x1(t) = φ

[0032]

[0033] In the formula: x1(t) represents the state vector of the heading angle φ of the unmanned ship; x2(t) represents the state vector of the heading angular velocity of the unmanned ship of, Ω represents a subset of and is a compact set, represents the set of all real numbers; f(x2(t)) represents a differentiable non - linear dynamic with respect to x2(t), that is, an unknown non - linear dynamic; g represents a positive constant regarding ship maneuverability; u(t) represents the control input vector; d(t) represents uncertain environmental disturbances, where, ‖d(t)‖ ≤ d * , d * represents the upper bound of the uncertain environmental disturbance d(t); t represents the time variable; ‖d(t)‖ represents the two - norm of d(t).

[0034] S2: According to the continuous - time non - linear dynamic system of the unmanned ship, based on the pre - trained deep neural network, perform offline iteration on the unknown non - linear dynamic to obtain the first - step approximation of the unknown non - linear dynamic; perform online adjustment on the first - step approximation of the unknown non - linear dynamic to obtain an estimated value of the final approximation of the unknown non - linear dynamic;

[0035] Preferably, the method for obtaining the estimated value of the final approximation of the unknown non - linear dynamic is as follows:

[0036] S21: Based on historical experimental and simulation data, in this embodiment, for the historical heading angular velocity and unknown nonlinear dynamics of the ship, a first-order approximation of the unknown nonlinear dynamics is obtained based on a pre-trained deep neural network;

[0037] Specifically, in this embodiment, offline iteration is first performed. The collected past experimental and simulation data is used for pre-training the deep neural network to perform a first-order approximation of the unknown nonlinear dynamics f(x2(t)). The pre-trained deep neural network Φ * (x2(t)) is expressed as

[0038] The formula for obtaining the first-order approximation of the unknown nonlinear dynamics is as follows:

[0039]

[0040] where, W k represents the weight of the k-th hidden layer of the deep neural network; represents the index number of the hidden layer of the deep neural network, represents the set of positive integers; φ k represents the activation function of the k-th hidden layer of the deep neural network; represents the composition operation of functions; represents the pre-trained deep neural network; represents the set of all real numbers; f1(2(t)) represents the first-order approximation of the unknown nonlinear dynamics; x2(t) represents the heading angular velocity of the unmanned ship's state vector;

[0041] S22: Based on the first-order approximation of the unknown nonlinear dynamics, an online adjustment is performed on the first-order approximation of the unknown nonlinear dynamics based on a single-layer neural network constructed by the ideal output layer weight and the ideal activation function to obtain the final approximation of the unknown nonlinear dynamics;

[0042] Next, online adjustment is performed. Specifically, through an ideal weight, an ideal activation function, and the first-order approximation f1(x2(t)) of the unknown nonlinear dynamics, a single-layer neural network is constructed to further approximate the unknown differentiable nonlinear dynamics f(x2(t)) with respect to x2(t), and an online adjustment is performed on it.

[0043] Preferably, the formula for performing the online adjustment on the first-order approximation of the unknown nonlinear dynamics is as follows: Then the final approximation f′(x2(t)) of the unknown nonlinear dynamics obtained after the online adjustment can be expressed as;

[0044] f′(x2(t)) = W *T σ* (f1(x2(t))) + ε(x2(t)) = W *T σ * (Φ * (x2(t))) + ε(x2(t))

[0045] In the formula, represents the unknown bounded output layer weight vector, that is, the ideal output layer weight; L represents the number of nodes in the hidden layer of the output layer neural network; represents an L-dimensional vector space; represents W * transpose; represents an unknown bounded ideal activation function vector; represents the pre-trained deep neural network, represents the bounded unknown function reconstruction error related to the ideal output layer weight, ideal activation function and pre-trained deep neural network; T represents transpose.

[0046] S23: According to the final approximation of the unknown nonlinear dynamics, obtain an estimated value of the final approximation of the unknown nonlinear dynamics. Specifically, the deep neural network is pre-trained by collecting data from past experiments and simulations. Ideally, a large number of data sets obtained by running the same dynamic system under the same environmental conditions can be used for training the deep neural network. And the online adjustment strategy of the output layer weights based on Lyapunov has significant flexibility in data training.

[0047] Preferably, the method for obtaining an estimated value of the final approximation of the unknown nonlinear dynamics is as follows:

[0048] Define

[0049]

[0050] In the formula, represents the unknown bounded output layer weight vector, that is, the ideal output layer weight; is the estimated value of the ideal output layer weight W * ; represents the estimation error of the ideal output layer weight;

[0051] Then, the formula for obtaining an estimated value of the final approximation of the unknown nonlinear dynamics is as follows:

[0052] Specifically, to obtain an estimate of the unknown nonlinear dynamics, the estimate of the unknown nonlinear dynamics is the estimated value of the unknown nonlinear dynamics f(x2(t)) represented by the ideal weight, ideal activation function and pre-trained deep neural network:

[0053]

[0054] where, ε d represents the estimation error of the deep neural network, represents the estimated value of the pre-trained deep neural network for the unknown non-linear dynamics f′(x2(t)) in the i-th iteration; i represents the index number of the iteration times; is the estimated value of the ideal output layer weight W * ; represents the i-th estimated value of σ * ; represents the i-th estimated value of Φ * (x2(t));

[0055] where,

[0056]

[0057] where, represents the estimated value of the weight of the k-th hidden layer of the deep neural network in the i-th iteration; represents the activation function of the k-th hidden layer of the deep neural network in the i-th iteration;

[0058] S3: According to the continuous-time non-linear dynamic system of the unmanned ship, the estimated value of the final approximation of the unknown non-linear dynamics, design is carried out using the backstepping method to obtain the controller and the output layer weight adaptation law to ensure that the system state x1(t) can track the desired smooth time-varying trajectory x 1d (t); realizing the tracking control of the unmanned ship based on the offline iteration and online adjustment of the deep network.

[0059] Preferably, the method for obtaining the controller and the output layer weight adaptation law is as follows:

[0060] S31: In order to quantify the control objective, define the tracking error, and obtain the first tracking error related to the heading angle of the unmanned ship and the second tracking error related to the heading angular velocity of the unmanned ship;

[0061] The first tracking error is the difference between the state vector of the heading angle of the unmanned ship and the desired smooth time-varying trajectory;

[0062] The second tracking error is the difference between the state vector of the heading angular velocity of the unmanned ship and the virtual controller;

[0063]

[0064] where, x 1d (t) is the desired smooth time-varying trajectory; x 2d (t) is the virtual controller; e1(t) represents the first tracking error, that is, x1(t) and x 1d(t); e2(t) represents the second tracking error, i.e., the difference between x2(t) and x 2d (t); represents equivalent to;

[0065] S32: Based on the first tracking error, use the backstepping method to establish a virtual controller:

[0066] The design of the virtual controller is established as follows:

[0067]

[0068] where c1 is a positive constant used for designing the virtual controller;

[0069] S33: According to the estimated value of the final approximation of the unknown nonlinear dynamics and the estimated value of the ideal output layer weight W * , obtain the controller as follows;

[0070]

[0071] where c2 is a positive constant used for designing the controller; c s is a positive constant used for designing the compensation term; sgn(·) represents the sign function; g represents a positive constant regarding the ship's maneuvering performance; e1(t) represents the first tracking error, i.e., the difference between x1(t) and x 1d (t); e2(t) represents the second tracking error, i.e., the difference between x2(t) and x 2d (t); x 2d (t) is the virtual controller; represents the estimated value of the final approximation of the unknown nonlinear dynamics by the pre-trained deep neural network in the i-th iteration; is the estimated value of the ideal output layer weight W * ; u(t) represents the control input vector; represents the i-th estimated value of Φ * (x2(t)); represents the i-th estimated value of σ * ;

[0072] The output layer weight adaptation law is obtained as follows:

[0073]

[0074] where Γ represents an adaptive positive definite matrix, and τ is a positive constant used to adjust the adaptation law.

[0075] Preferably, it further includes S4: According to the Lyapunov theory, it is proved that according to the control input vector u(t) and the output layer weight adaptation law, the semi-global asymptotic tracking of the trajectory tracking error can be ensured. The method is as follows:

[0076] Specifically, since the offline iterative update of the inner layer features of the deep neural network introduces discontinuities into the adaptive algorithm, which in turn causes these discontinuities to be transmitted to the closed-loop error system. The general smooth Lyapunov-based stability analysis cannot achieve the ideal proof effect. Therefore, in this embodiment, a more rigorous non-smooth Lyapunov analysis is adopted to fully consider the time-piecewise discontinuity in the dynamics, so as to achieve the purpose of semi-global asymptotic tracking proof and ensure that the designed heading tracking controller has good tracking performance. Therefore, as long as it is proved that the constructed non-smooth Lyapunov function is less than zero, it can be proved that under the condition of selecting appropriate parameters, the designed tracking controller u(t) and the adaptation law can ensure the semi-global asymptotic tracking of the trajectory tracking error.

[0077] S41: Define Construct a non-smooth Lyapunov function:

[0078]

[0079] where: vec(·) represents the vectorization operation; z(t) represents an augmented vector; denotes equivalent to; V L (z) represents the non-smooth Lyapunov function; tr(·) represents the trace of a matrix;

[0080] S42: According to the continuous-time nonlinear dynamic system of the unmanned ship and the first tracking error and the second tracking error, the dynamics of the first tracking error e1(t) are represented as follows, and then the dynamics of the first tracking error e1(t) and the dynamics of the second tracking error e2(t) are obtained;

[0081] Among them, the dynamics of the first tracking error e1(t) are represented as follows:

[0082]

[0083] where: is the first-order differential of e1(t), representing the dynamics of the first tracking error e1(t);

[0084] The dynamics of the second tracking error e2(t) are represented as follows:

[0085]

[0086] S43: According to the virtual controller x 2d (t), the dynamics of the first tracking error e1(t), the control input vector u(t), and the dynamics of the second tracking error e2(t) The derivative of the non-smooth Lyapunov function V L (z) is expressed as

[0087]

[0088] S42: Define z as containing the Filippov solution. Among them, define the non-smooth Lyapunov function V L (z) along the Filippov trajectory The generalized time derivative of is

[0089]

[0090] In the formula: z represents the Filippov solution; K[·] represents the algorithm for calculating the Filippov differential inclusion; represents the differential of z(t); represents the Clarke generalized gradient of V L (z). Since V L (z) is continuously differentiable with respect to z, so represents the gradient operation;

[0091] Therefore, according to the derivative of the non-smooth Lyapunov function V L (z) Get the non-smooth Lyapunov function V L (z) along the Filippov trajectory The generalized time derivative satisfies:

[0092]

[0093] According to the operation properties of the matrix trace, for the real column matrix The trace of the outer product is equal to the inner product, that is, tr(ba T ) = a T b; where represents the n-dimensional vector space;

[0094] Therefore, it can be obtained that

[0095]

[0096] Specifically, when utilizing the approximation property of the universal function in this embodiment, there are often some known constants that can ensure that certain variables under consideration are bounded above. In this embodiment, there exist positive constants and satisfying and

[0097] S43: Since there exist positive constants and satisfying and Therefore, according to Young's inequality, we obtain

[0098]

[0099] where sup represents the supremum; ‖·‖ represents the two-norm;

[0100] Therefore, it can be seen that along the Filippov trajectory almost everywhere (a.e.) there exists belonging to denoted as

[0101]

[0102] Therefore, combining the inequality relationship obtained in S43, there must exist

[0103]

[0104] Therefore, when c s , d * , τ, satisfying when

[0105]

[0106] Thus, it is proved that under the condition of selecting appropriate parameters, according to the control input vector u(t) and the output layer weight adaptation law can ensure the semi-global asymptotic tracking of the trajectory tracking error;

[0107] where c = [c1 c2], e = [e1(t) e2(t)] T , c represents the row vector composed of c1 and c2; e represents the column vector composed of e1(t) and e2(t);

[0108] Specifically, in this embodiment, compared with the single-hidden-layer neural network, the deeper neural network has a more complex structure that can potentially improve the function approximation performance, and updates the hidden-layer weights through the backpropagation algorithm, so that it has a better approximation effect on the unknown dynamics of more complex features. The adaptive law of the output-layer weights of the DNN model is developed in real time using the Lyapunov-based method, and the inner-layer weights of the DNN are updated using a data-driven supervised learning algorithm. The real-time controller and the adaptive law enable the system to track the desired time-varying trajectory while compensating for unknown uncertainties.

[0109] A specific embodiment of the present invention is as follows:

[0110] To verify the effectiveness of the unmanned ship tracking control method based on the offline iteration and online adjustment of the deep neural network in this embodiment, this embodiment relies on MATLAB for computer simulation research. The parameter settings are as follows:

[0111] The simulation object is selected as the "Yukun" ship of Dalian Maritime University. The parameters of the ship are: the length between perpendiculars is 105m, the ship width is 18m, the rudder area is 11.46m 2 , the full-load speed is 16.7kn, the full-load draft at the ship's midsection is 5.2m, the full-load displacement is 5735.5m 3 , and the block coefficient is 0.5595. The steering gain maneuverability index of the unmanned ship is taken The time constant of ship maneuverability The nonlinear coefficients of the ship's yaw angular velocity are α = 100 and β = 200. The marine environmental interference parameters are set as: the wind direction ψ wind = 30°, the wind force level S = 5, the flow direction ψ current = 30°, and the flow velocity v current = 5kn. The ideal course of the unmanned ship is set as Select the parameters c1 = 100, c2 = 100, Γ = 0.1, τ = 1.

[0112] In the simulation experiment, the pre-trained deep neural network consists of 6 layers, including an input layer, 4 hidden layers, and an output layer. The layers are fully connected. The 4 hidden layers have 10, 5, 8, and 1 neurons respectively. Each layer uses tanh, tanh, relu, and tanh as activation functions respectively. Adam (Adaptive Moment Estimation) is used as the optimization algorithm, and the learning rate is fixed at 0.1. The Levenberg-Marquardt algorithm is used to train the weights of the deep neural network. For each DNN training iteration, 70% of the data is used for training, 15% for validation, and 15% for testing.

[0113] The results of the simulation experiment are shown in the figure: Figure 2It is the mean square error simulation diagram for the offline training of the deep neural network. It can be seen that the mean square error finally converges to 0.08; Figure 3 It is the loss simulation diagram for the offline training of the deep neural network. The final loss converges to 3.3×10 -3 ; Figure 4 It is the trajectory simulation diagram of the ship's heading and the reference heading provided in this embodiment. It can be seen that the designed controller has a good control effect on the ship and can quickly achieve ship heading tracking; Figure 5 It is the simulation diagram of the ship's heading tracking error result provided in this embodiment. It can be seen that under the action of the designed controller, the tracking error is bounded and stable; Figure 6 It is the simulation diagram of the convergence result of the output layer weights provided in this embodiment. The output layer weights finally converge stably; Figure 7 It is the control input simulation diagram provided in this embodiment. It can be seen that the controller has a good control effect;

[0114] The simulation results show that the controller designed based on the unmanned ship tracking control method of offline iteration and online adjustment of the deep network in this embodiment can well achieve ship heading tracking, and the tracking error can quickly converge to a smaller residual set. The considered deep network offline iteration and online adjustment method can effectively approximate the unknown dynamics of more complex features, and the controller designed based on the Lyapunov method can ensure excellent tracking control performance. The system control input curve is more in line with navigation practice. It further verifies the effectiveness and rationality of the unmanned ship tracking control method based on offline iteration and online adjustment of the deep neural network proposed in this embodiment.

[0115] The embodiments of the present invention have the following beneficial effects:

[0116] 1. The unmanned ship tracking control method based on offline iteration and online adjustment of the deep network provided in this embodiment. Considering that in extremely harsh sea conditions, the navigation dynamics of the unmanned ship will have more complex features, the traditional heading tracking control based on a single-hidden-layer artificial neural network does not have a good effect on approximating the dynamics of more complex features. Compared with the single-hidden-layer neural network, the deep neural network has a more complex structure that can potentially improve the function approximation performance and update the hidden layer weights through the backpropagation algorithm, so that it has a better approximation effect on the unknown dynamics of more complex features. Therefore, using the superior approximation ability of the deep neural network to train based on past navigation data can predict the dynamic characteristics of the unmanned ship in complex sea conditions, and by adding an online adjustment strategy and designing the output layer weight adaptation law, the flexibility of data training is improved.

[0117] 2. In this embodiment, a non-smooth Lyapunov function is constructed to prove the semi-global asymptotic tracking of the tracking error. Since the offline iterative update of the inner layer features of the deep neural network introduces discontinuities into the adaptive algorithm, these discontinuities are then propagated into the closed-loop error system. The ideal proof effect cannot be achieved by the general smooth Lyapunov-based stability analysis. Therefore, a more rigorous non-smooth Lyapunov analysis is adopted to fully consider the time-piecewise discontinuities in the dynamics, so as to achieve the purpose of semi-global asymptotic tracking proof, and thus ensure that the designed heading tracking controller has good tracking performance.

[0118] 3. In this embodiment, simulation experiments are carried out based on the MATLAB platform. Considering the offline training strategy of the deep neural network, the past navigation data is used for training to predict the unknown dynamics with complex features. An online adjustment strategy is adopted to design the adaptive law of the output layer weights, which improves the flexibility of data training. Moreover, the heading tracking controller designed based on Lyapunov enables it to have excellent tracking performance, which is more in line with navigation practice, further verifying the effectiveness and rationality of the unmanned ship tracking control method based on offline iteration and online adjustment of the deep neural network provided in this embodiment.

[0119] 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 them; 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 described in the foregoing embodiments, or equivalently replace 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 tracking control method based on offline iteration and online adjustment of a deep network, characterized in that It includes the following steps: S1: Establish a mathematical model for the heading tracking control of an unmanned ship considering the influence of wind, waves, and currents, including uncertain disturbance terms, and transform the mathematical model of the heading tracking control of the unmanned ship into a second-order state space equation, so as to obtain the continuous-time nonlinear dynamic system of the unmanned ship; S2: According to the continuous-time nonlinear dynamic system of the unmanned ship, based on a pre-trained deep neural network, perform offline iteration on the unknown nonlinear dynamics in the nonlinear dynamic system to obtain the first approximation of the unknown nonlinear dynamics; Perform online adjustment on the first approximation of the unknown nonlinear dynamics to obtain the final approximation of the unknown nonlinear dynamics, so as to obtain an estimated value of the final approximation of the unknown nonlinear dynamics; S3: According to the continuous-time nonlinear dynamic system of the unmanned ship and the estimated value of the final approximation of the unknown nonlinear dynamics, obtain the controller and the output layer weight adaptation law to ensure that the state vector of the heading angle of the unmanned ship can track the desired smooth time-varying trajectory; realize the tracking control of the unmanned ship based on offline iteration and online adjustment of the deep network; In the above S3, the method for obtaining the controller and the output layer weight adaptation law is as follows: S31: Obtain the first tracking error related to the heading angle of the unmanned ship and the second tracking error related to the heading angular velocity of the unmanned ship; The first tracking error is the difference between the state vector of the heading angle of the unmanned ship and the desired smooth time-varying trajectory; The second tracking error is the difference between the state vector of the heading angular velocity of the unmanned ship and the virtual controller; where, x 1d (t) is the desired smooth time-varying trajectory; x 2d (t) is the virtual controller; e1(t) represents the first tracking error, i.e., the difference between x1(t) and x 1d (t); e2(t) represents the second tracking error, i.e., the difference between x2(t) and x 2d (t); denotes equivalent to; x1(t) represents the state vector of the heading angle φ of the unmanned ship; x2(t) represents the state vector of the heading angular velocity of the unmanned ship; S32: According to the first tracking error, establish a virtual controller using the backstepping method: The establishment of the virtual controller is as follows: where, c1 is a positive constant used to design the virtual controller; S33: According to the estimated value of the final approximation of the unknown nonlinear dynamics and the estimated value of the ideal output layer weight, obtain the controller as follows; Among them, c2 is a positive constant used to design the controller; c s is a positive constant used to design the compensation term; sgn(·) represents the sign function; g represents a positive constant regarding the ship's maneuvering performance; e1(t) represents the first tracking error, that is, the difference between x1(t) and x 1d (t); e2(t) represents the second tracking error, that is, the difference between x2(t) and x 2d (t); x 2d (t) is the virtual controller; represents the estimated value of the final approximation of the unknown nonlinear dynamics by the pre-trained deep neural network in the i-th iteration; is the estimated value of the ideal output layer weight W * ; u(t) represents the control input vector; represents the i-th estimated value of Φ * (x2(t)); represents the i-th estimated value of σ * ; u(t) represents the control input vector; The output layer weight adaptation law is obtained as follows: where, Γ represents an adaptive positive definite matrix, and τ is a positive constant used to adjust the adaptation law.

2. The unmanned ship tracking control method based on offline iteration and online adjustment of a deep network according to claim 1, characterized in that In the above S2, the method for obtaining the estimated value of the final approximation of the unknown nonlinear dynamics is as follows: S21: According to the historical heading angular velocity of the ship and the unknown nonlinear dynamics, based on a pre-trained deep neural network, obtain the first approximation of the unknown nonlinear dynamics; The formula used to obtain the first approximation of the unknown nonlinear dynamics is as follows: Among them, W k represents the weights of the k-th hidden layer of the deep neural network; represents the index number of the hidden layer of the deep neural network, represents the set of positive integers; φ k represents the activation function of the k-th hidden layer of the deep neural network; represents the composition operation of functions; represents the pre-trained deep neural network; represents the set of all real numbers; f1(x2(t)) represents the first-order approximation of the unknown non-linear dynamics; x2(t) represents the heading angular velocity of the unmanned ship of the state vector; S22: According to the first approximation of the unknown nonlinear dynamics, obtain the final approximation of the unknown nonlinear dynamics; The formula used is as follows: f′(x2(t)) = W *T σ * (f1(x2(t))) + ε(x2(t)) = W *T σ * (Φ * (x2(t))) + ε(x2(t)) where \(f'(x_2(t))\) represents the final approximation of the unknown non - linear dynamics, represents the unknown bounded output - layer weight vector, that is, the ideal output - layer weight; \(L\) represents the number of hidden - layer nodes of the output - layer neural network; represents an \(L\) - dimensional vector space; \(W\) *T represents \(W\) * 's transpose; represents the unknown bounded ideal activation - function vector; represents the pre - trained deep neural network, represents the bounded unknown function reconstruction error related to the ideal output - layer weight, the ideal activation function, and the pre - trained deep neural network; \(T\) represents the transpose; S23: According to the final approximation of the unknown nonlinear dynamics, obtain the estimated value of the final approximation of the unknown nonlinear dynamics.

3. The unmanned ship tracking control method based on offline iteration and online adjustment of a deep network according to claim 2, characterized in that In the above S23, the method for obtaining the estimated value of the final approximation of the unknown nonlinear dynamics is as follows: Define: In the formula, represents the unknown bounded output layer weight vector, that is, the ideal output layer weight; is the estimated value of the ideal output layer weight W * ; represents the estimation error of the ideal output layer weight; Then, the formula used to obtain the estimated value of the final approximation of the unknown nonlinear dynamics is as follows: where ε represents the estimation error of the deep neural network, represents the estimated value of the pre-trained deep neural network for the unknown nonlinear dynamics f′(x2(t)) in the i-th iteration; i represents the index number of the iteration times; is the estimated value of the ideal output layer weight W * ; represents the i-th estimated value of σ * ; represents the i-th estimated value of φ * (x2(t)); where, Among them, represents the estimated value of the weights of the k-th hidden layer of the deep neural network in the i-th iteration; represents the activation function of the k-th hidden layer of the deep neural network in the i-th iteration.

4. A method for unmanned ship tracking control based on offline iteration and online adjustment of a deep network according to claim 1, characterized in that In the above S1, the continuous-time nonlinear dynamic system of the unmanned ship is obtained as follows: S11: Establish the mathematical model expression of the heading tracking control of the unmanned ship considering the influence of wind, waves and currents, including uncertain disturbance terms, as follows: δ w = α r + β r where: φ represents the course angle of the unmanned ship, i.e., the output signal of the autopilot; represents the first derivative of φ; represents the second derivative of φ; represents the time constant of ship maneuverability; represents a nonlinear function with respect to the yaw angular velocity of the ship; α and β both represent the nonlinear coefficients of the yaw angular velocity of the ship; represents the unmanned ship rudder gain maneuverability index; δ represents the rudder angle of the unmanned ship and the control input of the course control system; δ w represents the equivalent rudder angle caused by uncertain environmental disturbances; α r represents the wind drift angle; β r represents the current drift angle; S12: According to the mathematical model of the unmanned ship heading tracking control, obtain the expression of the continuous-time nonlinear dynamic system of the unmanned ship as follows: Where, x1(t) = φ where: \(x_1(t)\) represents the state vector of the heading angle \(\varphi\) of the unmanned ship; \(x_2(t)\) represents the state vector of the heading angular velocity of the unmanned ship ; \(\Omega\) represents a subset of and is a compact set, * \(\mathbb{R}\) represents the set of all real numbers; \(f(x_2(t))\) represents a differentiable nonlinear dynamics with respect to \(x_2(t)\), that is, an unknown nonlinear dynamics; \(g\) represents a positive constant regarding the ship's maneuverability; \(u(t)\) represents the control input vector; \(d(t)\) represents the uncertain environmental disturbance, where \(\|d(t)\|\leq d\) * , \(d\) represents the upper bound of the uncertain environmental disturbance \(d(t)\); \(t\) represents the time variable; \(\|d(t)\|\) represents the two - norm of \(d(t)\).

5. A method for unmanned ship tracking control based on offline iteration and online adjustment of a deep network according to claim 1, characterized in that, It also includes S4: According to the Lyapunov theory, prove that according to the control input vector u(t) and the output layer weight adaptive law, the semi-global asymptotic tracking of the trajectory tracking error can be ensured, and the method is as follows: S41: Define Construct a non-smooth Lyapunov function: where: vec(·) represents the vectorization operation; denotes an augmented vector; denotes equivalent to; denotes a non-smooth Lyapunov function; tr(·) represents the trace of a matrix; S42: According to the continuous-time nonlinear dynamic system of the unmanned ship, the first tracking error and the second tracking error, obtain the dynamics of the first tracking error e1(t) and the dynamics of the second tracking error e2(t); Among them, the dynamics of the first tracking error e1(t) is expressed as follows: Wherein: is the first-order differential of e1(t), representing the dynamics of the first tracking error e1(t); The dynamics of the second tracking error e2(t) is expressed as follows: In the formula: is the first-order differential of e2(t), representing the dynamics of the second tracking error e2(t); S43: According to the virtual controller x 2d (t), the dynamics of the first tracking error e1(t), the control input vector u(t), and the dynamics of the second tracking error e2(t) The non-smooth Lyapunov function The derivative of is expressed as S42: Define as the Filippov solution that contains ; where the non-smooth Lyapunov function along the Filippov trajectory has the generalized time derivative as In the formula: represents the Filippov solution; K[·] represents the algorithm for calculating the Filippov differential inclusion; represents the differential of; represents the Clarke generalized gradient of, since for is continuously differentiable, so represents the gradient operation; Therefore, according to the non-smooth Lyapunov function the derivative of the non-smooth Lyapunov function along the Filippov trajectory satisfies the following generalized time derivative: According to the operational properties of the matrix trace, for a real column matrix the trace of the outer product is equal to the inner product, that is, tr(ba T ) = a T b; where represents an n-dimensional vector space; Therefore, it can be obtained that S43: Since there exist positive constants and satisfying and thus, according to Young's inequality, we have Where, sup represents the supremum; ‖·‖ represents the two-norm; Therefore, Therefore, there must exist Therefore, when c s , d * , τ, meet when Thus, it is proved that according to the control input vector and the output layer weight adaptive law, the semi-global asymptotic tracking of the trajectory tracking error can be ensured; where \(c = [c_1\ c_2]\) and \(e=\begin{bmatrix}e_1(t)\\e_2(t)\end{bmatrix}\) T , \(c\) represents a row vector composed of \(c_1\) and \(c_2\); \(e\) represents a column vector composed of \(e_1(t)\) and \(e_2(t)\).

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