Unmanned ship tracking control method based on deep network offline iteration and online adjustment

Abstract

The invention discloses an unmanned ship tracking control method based on off-line iteration and on-line adjustment of a deep network. The method comprises the following steps: acquiring a first-step approximate value of unknown nonlinear dynamic through a pre-trained deep neural network; performing online adjustment on the unknown nonlinear dynamic first-step approximate value to obtain an estimated value of the unknown nonlinear dynamic final approximate value; and obtaining a controller and an output layer weight adaptive law to ensure that the state vector of the course angle of the unmanned ship can track an expected smooth time-varying trajectory. And tracking control of the unmanned ship based on offline iteration and online adjustment of the deep network is realized. According to the method, by combining the deep neural network, the approximation performance of the function is potentially improved, so that the method has a better approximation effect on an unknown dynamic state with more complex features.

Description

Technical Field

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

[0002] With the development of automatic control technology in the field of marine engineering, unmanned surface vessels (USV) and deep neural networks have undoubtedly become the focus of scholars. Unmanned ships can replace humans to perform some dangerous and boring special operations at sea, and have extremely high research value in protecting the safety of human lives at sea. At present, they have been widely used in resource exploration, coastal surveillance, military patrol and reconnaissance. As a more complex neural network, deep neural networks have better approximation performance for unknown dynamics with more complex characteristics. They have stronger approximation capabilities for the complex dynamic characteristics of unmanned ships such as wind, waves, and currents during navigation.

[0003] Due to the influence of complex sea conditions such as wind, waves and ocean currents, the heading tracking control performance of unmanned ships has been severely challenged. Therefore, in order to ensure the safety and efficiency of navigation, it is necessary to improve the heading tracking control of unmanned ships. Compared with general situations, the navigation dynamics of unmanned ships will have more complex characteristics under severe sea conditions, and the traditional heading tracking control based on single hidden layer artificial neural network has 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 deep network offline iteration and online adjustment to overcome the above technical problems.

[0005] In order to achieve the above object, the technical solution of the present invention is:

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

[0007] S1: Establishing a mathematical model of unmanned ship heading tracking control including uncertain interference terms under the influence of wind, waves and current, so as to transform the mathematical model of unmanned ship heading tracking control into a second-order state space equation, thereby obtaining a continuous-time nonlinear dynamic system of the unmanned ship;

[0008] S2: According to the continuous-time nonlinear dynamic system of the unmanned ship, based on the pre-trained deep neural network, offline iterate the unknown nonlinear dynamics in the nonlinear dynamic system to obtain a first-step approximation of the unknown nonlinear dynamics; online adjust the first-step approximation of the unknown nonlinear dynamics to obtain a 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 approximate value of the unknown nonlinear dynamic, the controller and the output layer weight adaptation law are obtained to ensure that the state vector of the heading angle of the unmanned ship can track the 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.

[0010] Beneficial effects: The unmanned ship tracking control method based on offline iteration and online adjustment of a deep network of the present invention obtains the first step approximation of unknown nonlinear dynamics through a pre-trained deep neural network; the first step approximation of the unknown nonlinear dynamics is adjusted online to obtain an estimate of the final approximation of the unknown nonlinear dynamics; and then the controller and output layer weight adaptive law are obtained to ensure that the state vector of the heading angle of the unmanned ship can track the 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. The present invention potentially improves the approximation performance of the function by combining a deep neural network, so that it has a better approximation effect on unknown dynamics with more complex features. BRIEF DESCRIPTION OF THE DRAWINGS

[0011] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. 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.

[0012] Figure 1 It is a flow chart of the unmanned ship tracking control method based on deep network offline iteration and online adjustment of the present invention;

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

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

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

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

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

[0018] Figure 7 This is a control input simulation diagram provided in this embodiment. DETAILED DESCRIPTION

[0019] 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.

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

[0021] S1: Establishing a mathematical model of unmanned ship heading tracking control including uncertain interference terms under the influence of wind, waves and current, so as to transform the mathematical model of unmanned ship heading tracking control into a second-order state space equation, thereby obtaining a continuous-time nonlinear dynamic system of the unmanned ship;

[0022] Specifically, this embodiment first obtains a mathematical model of the unmanned ship heading tracking control under the influence of sea conditions such as wind, waves, and currents, and then converts the mathematical model of the unmanned ship heading tracking control into a second-order state space equation as a 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: The mathematical model of the unmanned ship heading tracking control including uncertain interference terms under the influence of wind, waves, currents, etc. is established as follows:

[0025]

[0026] δ w =α r +β r

[0027] Where: φ represents the heading angle of the unmanned ship, i.e. the output signal of the autopilot; represents the first derivative of φ; represents the second-order derivative of φ; A time constant that represents the maneuverability of a ship; represents the nonlinear function of the ship's bow angular velocity; α, β both represent the nonlinear coefficients of the ship's bow angular velocity; represents the maneuverability index of the unmanned ship rudder gain; δ represents the control input of the unmanned ship rudder angle and heading control system; δ w represents the equivalent rudder angle caused by uncertain environmental disturbance; α r represents the wind pressure difference angle; β r Represents the flow pressure difference angle.

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

[0029]

[0030] in,

[0031] x1(t)=φ

[0032]

[0033] Where: x1(t) represents the state vector of the heading angle φ of the unmanned ship; x2(t) represents the heading angular velocity of the unmanned ship The state vector of Ω represents A subset of and is a compact set, represents the set of all real numbers; f(x2(t)) represents the differentiable nonlinear dynamics about x2(t), that is, the unknown nonlinear dynamics; g represents a positive constant about the ship's maneuverability; u(t) represents the control input vector; d(t) represents the uncertain environmental disturbance, 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 binary norm of d(t).

[0034] S2: According to the continuous-time nonlinear dynamic system of the unmanned ship, the unknown nonlinear dynamics are iterated offline based on the pre-trained deep neural network to obtain a first-step approximation value of the unknown nonlinear dynamics; the first-step approximation value of the unknown nonlinear dynamics is adjusted online to obtain an estimated value of the final approximation value of the unknown nonlinear dynamics;

[0035] Preferably, the method for obtaining an estimate of the final approximation of the unknown nonlinear dynamics is as follows:

[0036] S21: according to historical experimental and simulation data, in this embodiment, the historical heading angular velocity of the ship and the unknown nonlinear dynamics, based on the pre-trained deep neural network, obtain the first step approximation of the unknown nonlinear dynamics;

[0037] Specifically, this embodiment first performs offline iteration. The collected data from past experiments and simulations are used to pre-train the deep neural network to make the first step approximation of the unknown nonlinear dynamic f(x2(t)). The pre-trained deep neural network Φ * (x2(t)) is expressed as

[0038] The formula used to obtain a first approximation to the unknown nonlinear dynamics is as follows:

[0039]

[0040] Among them, W k represents the weight of the kth 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 kth hidden layer of a deep neural network; Represents composite operations of functions; represents a pre-trained deep neural network; represents the set of all real numbers; f1(2(t)) represents the first step approximation of the unknown nonlinear dynamics; x2(t) represents the angular velocity of the unmanned ship The state vector of

[0041] S22: According to the first step approximation value of the unknown nonlinear dynamics, based on a single-layer neural network constructed by an ideal output layer weight and an ideal activation function, online adjusting the first step approximation value of the unknown nonlinear dynamics to obtain a final approximation value of the unknown nonlinear dynamics;

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

[0043] Preferably, the formula used for online adjustment of the first step approximation of the unknown nonlinear dynamics is as follows: Then the final approximation value f′(x2(t)) of the unknown nonlinear dynamics obtained after 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 hidden layer nodes of the output layer neural network; represents an L-dimensional vector space; W * The transpose of represents the unknown bounded ideal activation function vector; represents a pre-trained deep neural network, represents the bounded unknown function reconstruction error associated with the ideal output layer weights, ideal activation function, and pre-trained deep neural network; T represents the transpose.

[0046] S23: According to the final approximate value of the unknown nonlinear dynamics, obtain an estimated value of the final approximate value 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 to train the deep neural network. The online adjustment strategy of the output layer weight based on Lyapunov has significant flexibility in data training.

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

[0048] definition

[0049]

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

[0051] Then, the formula used to obtain the estimated value of the final approximate value of the unknown nonlinear dynamics is as follows:

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

[0053]

[0054] Among them, ε d represents the deep neural network estimation error, represents the estimated value of the unknown nonlinear dynamic f′(x2(t)) by the pre-trained deep neural network in the i-th iteration; i represents the index number of the iteration number; is the ideal output layer weight W * The estimated value of Represents σ * The i-th estimated value of ; Representative Φ * the i-th estimate of (x2(t));

[0055] in,

[0056]

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

[0058] S3: Based on the estimated value of the final approximate value of the unknown nonlinear dynamic system of the unmanned ship, the backstepping method is used to design the controller and the output layer weight adaptation law to ensure that the system state x1(t) can track the expected smooth time-varying trajectory x 1d (t); Realize tracking control of unmanned ship based on deep network offline iteration and online adjustment.

[0059] Preferably, the controller and the output layer weight adaptive law acquisition method are as follows:

[0060] S31: In order to quantify the control target, a tracking error is defined, and a first tracking error related to the heading angle of the unmanned ship and a second tracking error related to the heading angular velocity of the unmanned ship are obtained;

[0061] The first tracking error is the difference between the state vector of the heading angle of the unmanned ship and the expected 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] Among them, 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 1de2(t) represents the second tracking error, that is, the difference between x2(t) and x 2d (t) the difference between; It means equivalent to;

[0065] S32: According to the first tracking error, a virtual controller is established using a backstepping method:

[0066] The designed virtual controller is established as follows:

[0067]

[0068] Where c1 is a positive constant used to design the virtual controller;

[0069] S33: Estimates of the final approximation of the unknown nonlinear dynamics and the ideal output layer weights W * The estimated value of , the controller is obtained as follows;

[0070]

[0071] Where 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 related to the ship's maneuverability; e1(t) represents the first tracking error, i.e., the difference between x1(t) and x 1d e2(t) represents the second tracking error, that is, the difference between x2(t) and x 2d (t) The difference between 2d (t) is the virtual controller; represents the estimate of the final approximation of the unknown nonlinear dynamics by the pre-trained deep neural network in the i-th iteration; is the ideal output layer weight W * The estimated value of ; u(t) represents the control input vector; Representative Φ * the i-th estimate of (x2(t)); Represents σ * The i-th estimated value of ;

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

[0073]

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

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

[0076] Specifically, the offline iterative update of the inner features of the deep neural network will introduce 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, this embodiment adopts a more rigorous non-smooth Lyapunov analysis to fully consider the time segmentation discontinuities 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, it is only necessary to prove that the non-smooth Lyapunov function constructed next is less than zero to prove that the designed tracking controller u(t) and the adaptive law are effective when appropriate parameters are selected. Semi-global asymptotic tracking that ensures trajectory tracking error.

[0077] S41: Definition Construct a nonsmooth Lyapunov function:

[0078]

[0079] Where: vec(·) represents vectorized operation; z(t) represents an augmented vector; It is equivalent to; V L (z) represents the non-smooth Lyapunov function; tr(·) represents the trace of the 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 expressed as follows, thereby obtaining the dynamics of the first tracking error e1(t) and the dynamics of the second tracking error e2(t);

[0081] The dynamic expression of the first tracking error e1(t) is 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 dynamic expression of the second tracking error e2(t) is 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 non-smooth Lyapunov function V L The derivative of (z) is expressed as

[0087]

[0088] S42: Define z to contain The Filippov solution of . In which, the non-smooth Lyapunov function V is defined L (z) Along the Filippov track The generalized time derivative of is

[0089]

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

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

[0092]

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

[0094] Therefore, it is possible to obtain

[0095]

[0096] Specifically, when using the approximate properties of universal functions in this embodiment, there are often some known constants that can ensure that some of the variables under consideration have upper bounds. and satisfy and

[0097] S43: Since there are positive constants and satisfy and Therefore, according to Young's inequality, we have

[0098]

[0099] Among them, sup represents the supremum; ‖·‖ represents the two-norm;

[0100] Therefore, it can be seen that along the Filippov trajectory Almost everywhere (ae) belong Expressed as

[0101]

[0102] Therefore, combined with the inequality relationship obtained in S43, there must be

[0103]

[0104] Therefore, when c s , d * ,τ, satisfy hour,

[0105]

[0106] This proves that under the condition of selecting appropriate parameters, according to the control input vector u(t) and the output layer weight adaptive law It can ensure the semi-global progressive tracking of 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, the more complex structure of the deep neural network compared with the single hidden layer neural network can potentially improve the function approximation performance, and the hidden layer weights are updated through the back propagation 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 uncertain interference.

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

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

[0111] The simulation object is the Dalian Maritime University's "Yukun" ship, the ship parameters are: the length between the two columns is 105m, the ship width is 18m, the rudder blade area is 11.46m 2 , full load speed 16.7kn, full load midship draft 5.2m, full load displacement 5735.5m 3 , square coefficient 0.5595. Take the unmanned ship rudder gain maneuverability index Time constant of ship maneuverability The nonlinear coefficients of the ship's bow angular velocity are α=100, β=200. The marine environment interference parameters are set as follows: wind direction ψ wind =30°, wind level S=5, flow direction ψ current =30°, flow velocity v current =5kn. Set the ideal course of the unmanned ship to Select 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, the learning rate is fixed at 0.1, and 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 verification, and 15% for testing.

[0113] The simulation experiment results are shown in the figure: Figure 2This is the mean square error simulation diagram of the deep neural network offline training. It can be seen that the mean square error finally converges to 0.08; Figure 3 This is a simulation diagram of the loss of the deep neural network offline training. The final loss converges to 3.3×10 -3 ; Figure 4 The trajectory simulation diagram of the ship heading and the reference heading provided in this embodiment shows that the designed controller has a good control effect on the ship and can quickly track the ship heading; Figure 5 The simulation diagram of the ship heading tracking error result provided in this embodiment shows that the tracking error is bounded and stable under the action of the designed controller; Figure 6 This is a simulation diagram of the convergence result of the output layer weights provided in this embodiment. The output layer weights finally converge stably; Figure 7 The control input simulation diagram provided in this embodiment shows 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 based on deep network offline iteration and online adjustment in this embodiment can well realize 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 unknown dynamics with more complex features, and the controller designed based on the Lyapunov method can ensure excellent tracking control performance, and the system control input curve is more in line with navigation practice. The effectiveness and rationality of the unmanned ship tracking control method based on deep neural network offline iteration and online adjustment proposed in this embodiment are further verified.

[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 takes into account that the navigation dynamics of the unmanned ship will have more complex characteristics under extremely severe sea conditions. The traditional heading tracking control based on a single hidden layer artificial neural network does not have a good effect on the approximation of the dynamics of more complex characteristics. Compared with the single hidden layer neural network, the more complex structure of the deep neural network can potentially improve the function approximation performance, and update the hidden layer weights through the back propagation algorithm, so that it has a better approximation effect on the unknown dynamics of more complex characteristics. Therefore, by utilizing the superior approximation ability of the deep neural network and training based on previous navigation data, it is possible to predict the dynamic characteristics of the unmanned ship under complex sea conditions, add an online adjustment strategy, and design the output layer weight adaptive law, thereby improving the flexibility of data training.

[0117] 2. This embodiment constructs a non-smooth Lyapunov function 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 will introduce discontinuities into the adaptive algorithm, these discontinuities will propagate into the closed-loop error system. The general smooth Lyapunov-based stability analysis cannot achieve the ideal proof effect. Therefore, a more rigorous non-smooth Lyapunov analysis is used to fully consider the time segment discontinuity in the dynamics, so as to achieve the purpose of semi-global asymptotic tracking proof, thereby ensuring that the designed heading tracking controller has good tracking performance.

[0118] 3. This embodiment carried out simulation experiments based on the MATLAB platform, considered the offline training strategy of deep neural networks, used previous navigation data training to predict unknown dynamics with complex characteristics, adopted an online adjustment strategy, and designed the output layer weight adaptation law to improve the flexibility of data training. In addition, the heading tracking controller designed based on Lyapunov can 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 deep neural networks 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 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. An unmanned ship tracking control method based on deep network offline iteration and online adjustment, characterized in that: The following steps are involved: S1: Establishing a mathematical model of unmanned ship heading tracking control including uncertain interference terms under the influence of wind, waves and current, so as to transform the mathematical model of unmanned ship heading tracking control into a second-order state space equation, thereby obtaining a 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, offline iteration is performed on the unknown nonlinear dynamics in the nonlinear dynamic system to obtain a first step approximation of the unknown nonlinear dynamics; By performing online adjustment on the first step approximation of the unknown nonlinear dynamics to obtain a final approximation of the unknown nonlinear dynamics, an estimate of the final approximation of the unknown nonlinear dynamics is obtained; S3: according to the continuous-time nonlinear dynamic system of the unmanned ship, an estimated value of the final approximate value of the unknown nonlinear dynamics, obtaining a controller and an 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 tracking control of unmanned ships based on deep network offline iteration and online adjustment.

2. According to claim 1, the unmanned ship tracking control method based on deep network offline iteration and online adjustment is characterized in that: In S2, the method for obtaining an estimated value of the final approximate value of the unknown nonlinear dynamics is as follows: S21: According to the historical heading angular velocity of the ship and the unknown nonlinear dynamics, a first step approximation of the unknown nonlinear dynamics is obtained based on a pre-trained deep neural network; The formula used to obtain a first approximation to the unknown nonlinear dynamics is as follows: Among them, W k represents the weight of the kth 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 kth hidden layer of a deep neural network; Represents composite operations of functions; represents a pre-trained deep neural network; represents the set of all real numbers; f1(x2(t)) represents the first step approximation of the unknown nonlinear dynamics; x2(t) represents the angular velocity of the unmanned ship The state vector of S22: obtaining a final approximate value of the unknown nonlinear dynamics according to the first step approximate value of the unknown nonlinear dynamics; The formula used is as follows: where f′(x2(t)) represents the final approximation of the unknown nonlinear 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 * The transpose of represents the unknown bounded ideal activation function vector; represents a pre-trained deep neural network, ε(x2(t))∈ represents the bounded unknown function reconstruction error associated with the ideal output layer weights, ideal activation function, and pre-trained deep neural network; T represents transpose; S23: Obtain an estimated value of the final approximate value of the unknown nonlinear dynamics according to the final approximate value of the unknown nonlinear dynamics.

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

4. The unmanned ship tracking control method based on deep network offline iteration and online adjustment according to claim 1 is characterized in that: In S3, the method for obtaining the adaptive law of the controller and output layer weights is as follows: S31: Acquire a first tracking error related to the heading angle of the unmanned ship and a 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 expected 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; Among them, 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 e2(t) represents the second tracking error, that is, the difference between x2(t) and x 2d (t) the difference between; It means equivalent to; S32: According to the first tracking error, a virtual controller is established using a backstepping method: The designed virtual controller is established as follows: Where c1 is a positive constant used to design the virtual controller; S33: Based on the estimated value of the final approximation of the unknown nonlinear dynamics and the estimated value of the ideal output layer weight, a controller is obtained as follows; Where 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 related to the ship's maneuverability; e1(t) represents the first tracking error, i.e., the difference between x1(t) and x 1d e2(t) represents the second tracking error, that is, the difference between x2(t) and x 2d (t) The difference between 2d (t) is the virtual controller; represents the estimate of the final approximation of the unknown nonlinear dynamics by the pre-trained deep neural network in the i-th iteration; is the ideal output layer weight W * The estimated value of ; u(t) represents the control input vector; Represents Φ * the i-th estimate of (x2(t)); Represents σ * The i-th estimated value of ; The output layer weight adaptation law is obtained as follows: Where Γ represents an adaptive positive definite matrix, and t is a positive constant used to adjust the adaptive law.

5. The unmanned ship tracking control method based on deep network offline iteration and online adjustment according to claim 1 is characterized in that: In S1, the continuous-time nonlinear dynamic system of the unmanned ship is obtained as follows: S11: The mathematical model of the unmanned ship heading tracking control including uncertain interference terms under the influence of wind, waves, currents, etc. is established as follows: d w =a r +b r Where: φ represents the heading angle of the unmanned ship, i.e. the output signal of the autopilot; represents the first derivative of φ; represents the second-order derivative of φ; A time constant that represents the maneuverability of a ship; represents the nonlinear function of the ship's bow angular velocity; α, β both represent the nonlinear coefficients of the ship's bow angular velocity; represents the maneuverability index of the unmanned ship rudder gain; δ represents the control input of the unmanned ship rudder angle and heading control system; δ w represents the equivalent rudder angle caused by uncertain environmental disturbance; α r represents the wind pressure difference angle; β r represents the flow pressure difference angle; S12: According to the unmanned ship heading tracking control mathematical model, the continuous-time nonlinear dynamic system expression of the unmanned ship is obtained as follows: in, x1(t)=φ Where: x1(t) represents the state vector of the heading angle φ of the unmanned ship; x2(t) represents the heading angular velocity of the unmanned ship The state vector of , x1(t), Ω represents A subset of and is a compact set, represents the set of all real numbers; f(x2(t)) represents the differentiable nonlinear dynamics about x2(t), that is, the unknown nonlinear dynamics; g represents a positive constant about the ship's maneuverability; u(t) represents the control input vector; d(t) represents the uncertain environmental disturbance, 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 binary norm of d(t).

6. The unmanned ship tracking control method based on deep network offline iteration and online adjustment according to claim 1 is characterized in that: Also included is S4: According to Lyapunov theory, it is proved that according to the control input vector u(t) and the output layer weight adaptation law, the semi-global progressive tracking of the trajectory tracking error can be ensured, and the method is as follows: S41: Definition Construct a nonsmooth Lyapunov function: Where: vec(·) represents vectorization operation; z(t) represents an augmented vector; It is equivalent to; V L (z) represents the non-smooth Lyapunov function; tr(·) represents the trace of the matrix; S42: acquiring the dynamics of the first tracking error e1(t) and the dynamics of the second tracking error e2(t) according to the continuous-time nonlinear dynamic system of the unmanned ship and the first tracking error and the second tracking error; The dynamic expression of the first tracking error e1(t) is as follows: Where: is the first-order differential of e1(t), representing the dynamics of the first tracking error e1(t); The dynamic expression of the second tracking error e2(t) is as follows: Where: 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 V L The derivative of (z) is expressed as S42: Define z to contain The Filippov solution of L (z) Along the Filippov locus The generalized time derivative of is Where: z represents the Filipov solution; K[·] represents the algorithm for calculating the Filipov differential inclusion; represents the differential of z(t); V L (z) Clarke generalized gradient, due to V L (z) is continuously differentiable with respect to z, so represents the gradient operation; Therefore, according to the non-smooth Lyapunov function V L The derivative of (z) Get the non-smooth Lyapunov function V L (z) Along the Filippov locus The generalized time derivative of satisfies: According to the operational properties of matrix trace, for real column matrix The trace of the outer product is equal to the inner product, that is, tr(ba T )=a T b; among which, represents an n-dimensional vector space; Therefore, it is possible to obtain S43: Since there is a positive constant and satisfy and Therefore, according to Young's inequality, we have Among them, sup represents the supremum; ‖·‖ represents the two-norm; therefore, Therefore, there must be Therefore, when satisfy hour, It is thus proved that according to the control input vector and the output layer weight adaptation law, the semi-global progressive tracking of the trajectory tracking error can be ensured; Where c = [c1c2], 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).

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