Unmanned ship optimal tracking control method based on discrete time adaptive dynamic planning and dynamic event triggering
Through the discrete-time adaptive dynamic programming dynamic event triggering method, the problems of high energy consumption and large errors in unmanned ship tracking control are solved, and high-precision trajectory tracking and resource saving are achieved.
Patent Information
- Application Number
- CN202510903746.1
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-07-01
- Publication Date
- 2025-10-03
AI Technical Summary
The energy consumption during unmanned ship tracking control is high and there is a large minimum tracking error. The existing control strategy update mechanism is triggered in a fixed period, resulting in high resource usage.
The discrete-time adaptive dynamic programming dynamic event triggering method is adopted to obtain the optimal value function and control strategy, design the actuator-evaluator neural network, and utilize the dynamic event triggering mechanism to update the neural network parameters only when the conditions are met, thereby reducing energy consumption.
The accuracy of unmanned ship trajectory tracking is improved, the consumption of communication and computing resources is significantly reduced, and the adaptability and scalability of the system are enhanced.
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Abstract
Description
Technical Field
[0001] The present invention relates to the field of control technology, and in particular to an optimal tracking control method for an unmanned ship triggered by discrete-time adaptive dynamic programming and dynamic events. Background Art
[0002] Unmanned vessels (UAVs) are highly efficient, capable of continuous operation, economical, safe, flexible, and environmentally friendly, and have been widely used in military, civilian, and scientific research fields. Trajectory tracking using UAVs offers advantages such as improved navigation accuracy, reduced labor costs, and self-adaptation and intelligent capabilities.
[0003] For the unmanned ship trajectory tracking problem, the adaptive dynamic programming method formed by the combination of reinforcement learning, dynamic programming, and neural networks can solve the optimal control problem of the system. Through the actuator-evaluator structure and the use of iterative methods, it can achieve system stability and ensure that the preset cost function is minimized.
[0004] Since the error system value function does not tend to zero in the above method, there is a problem of large minimum tracking error. In addition, the control strategy update mechanism is triggered at a fixed period, resulting in high energy consumption requirements and resource occupation.
[0005] Existing technical problems and considerations:
[0006] How to solve the technical problem of high energy consumption during unmanned ship tracking and control. Summary of the Invention
[0007] The present invention provides an optimal tracking control method for an unmanned ship triggered by a discrete-time adaptive dynamic programming dynamic event, which solves the technical problem.
[0008] In order to solve the above technical problems, the technical solutions adopted by the present invention are as follows:
[0009] A discrete-time adaptive dynamic programming unmanned vessel optimal tracking control method triggered by dynamic events includes the following steps:
[0010] Step S1: Obtain the unmanned ship dynamics model and obtain the optimal value function of the error system that can make the minimum tracking error approach zero;
[0011] Step S2: Based on the dynamic event triggering mechanism, obtain the optimal control strategy for dynamic event triggering;
[0012] Step S3: Based on the optimal control strategy and the optimal value function, an actuator-evaluator neural network is designed;
[0013]
[0014] In formula (15), is the optimal value function, i.e., the judging neural network. is the optimal weight vector, φ c (·) is the activation function, is the weight vector, is the tracking error, θ k is the reference tracking trajectory, c represents an arbitrarily small reconstruction error;
[0015]
[0016] In formula (16), For the optimal control strategy, i.e., executing the neural network, is the optimal weight vector, φ a (·) is the activation function, is the weight vector, is the trigger moment state, a represents an arbitrarily small reconstruction error;
[0017] The judge neural network and the executive neural network form an executive-judge neural network;
[0018] Step S4: Based on the optimal value function and the optimal control strategy, the triggering conditions of the dynamic triggering mechanism are obtained;
[0019]
[0020] Formula (18) is the trigger condition of the dynamic trigger mechanism. In formula (18), 0<λ<1,ω k It is a dynamic variable inside the dynamic trigger mechanism. C is a constant, e k is the state error;
[0021] Step S5: Track the trajectory of the unmanned ship based on the optimal control strategy, the optimal value function and the triggering conditions of the dynamic trigger mechanism.
[0022] A further technical solution is that: in step S1, the unmanned ship dynamics model is:
[0023]
[0024] In formula (1), f(η,v)=-M -1 (Cv+Dv)+Δ(η,v), Δ(η,v) represents the modeling error of the unmanned ship system, η=[x,y,ψ] T represents the position and heading of the unmanned ship, v = [u, ν, r] T Indicates the forward, drifting and bow rolling speeds of the unmanned boat, μ=[μu ,μ ν ,μ r ] T represents the control input of the unmanned ship, R(ψ) represents the rotation matrix of the unmanned ship, M=M T >0 is the inertia matrix, C(v)=-C(v) T is the Coriolis force matrix, D(v) is the damping matrix;
[0025] The unmanned ship dynamics model is converted into an affine system form and discretized to obtain x k+1 =f(x k )+g(x k )u k , and are the state and control input of the system, is the drift dynamic term, is the control input dynamic term; assuming the reference tracking trajectory θ k Bounded, defined error system Γ(·) represents the command generator function, represents the tracking error;
[0026] The value function is,
[0027]
[0028] In formula (2), is the value function, is the control input, represents the utility function;
[0029]
[0030] Formula (3) is the utility function;
[0031] The optimal value function,
[0032]
[0033] In formula (4), Optimal control strategy.
[0034] A further technical solution is that: in step S2, the data system sampled at the triggering moment is defined as k i is the i-th triggering moment, and k i <k i+1 The event sampling state vector is held by the zero-order holder in the controller and is expressed as Define the error as When the event is triggered, that is, k=k iWhen a new state measurement value is introduced and the error e k Reset to zero and update the control strategy at the same time. When no event is triggered, that is, When the error e k ≠0, the sampling state will not be updated, and the control strategy will be maintained;
[0035] Under the event-triggered sampling rule, the optimal control strategy is expressed as,
[0036]
[0037] In formula (6),
[0038] A further technical solution is that in step S3, a judgment neural network is used to approximate the optimal value function, the number of layers of the judgment neural network is three, and the judgment neural network is expressed as:
[0039]
[0040] In formula (7), To judge the neural network, W c1,k is the weight vector from the input layer to the hidden layer of the judging neural network, W c2,k is the weight vector from the hidden layer to the output layer of the judging neural network, and φ(·) is the activation function;
[0041] The value function is derived through the event trigger mechanism as follows:
[0042]
[0043] Formula (8) is the value function, W c1,k is the weight vector from the input layer to the hidden layer of the judging neural network, W c2,k is the weight vector from the hidden layer to the output layer of the judging neural network, φ c (·) is the activation function, i.e.
[0044] The optimal control strategy is approximated by using an execution neural network. The execution neural network has three layers, which means the iterative strategy is:
[0045]
[0046] Formula (9) is the execution of neural network, i.e. iterative strategy, is the weight vector, φ a is the activation function is the weight vector;
[0047] The control strategy is derived through the event trigger mechanism and value function:
[0048]
[0049] In formula (10),
[0050] Gradient descent is used in both evaluating neural networks and updating the weights of neural networks in executing neural networks.
[0051] A further technical solution is that in step S3, the evaluation neural network solves the weight matrix and bias vector of the neural network by minimizing the loss function, and the loss function is defined as,
[0052]
[0053] In formula (11), Gradient descent algorithm updates the weight parameters of the judgment neural network;
[0054]
[0055] In formula (12), α c Is the learning rate of the neural network;
[0056] The performance function of executing a neural network is defined as,
[0057]
[0058] The gradient descent algorithm updates the weight parameters of the neural network.
[0059]
[0060] In formula (14), α a is the learning rate for executing the neural network.
[0061] A further technical solution is: in step S4, based on Formula (7), the optimal form is expressed as,
[0062]
[0063] In formula (15), To judge the neural network, is the optimal weight vector, c represents an arbitrarily small reconstruction error;
[0064] based on The optimal form is expressed as,
[0065]
[0066] In formula (16), is the optimal weight vector, arepresents an arbitrarily small reconstruction error;
[0067] Defining weight error Dynamic trigger mechanism defines internal dynamic variables ω k satisfy,
[0068]
[0069] In formula (17),
[0070] Derive the trigger conditions,
[0071]
[0072] In formula (18), The derived trigger conditions is uniformly eventually bounded.
[0073] The beneficial effects of adopting the above technical solution are:
[0074] A discrete-time adaptive dynamic programming method for optimal tracking control of an unmanned vessel using dynamic event triggering includes the following steps: Step S1: Obtaining the unmanned vessel's dynamic model and obtaining the optimal value function of the error system that can minimize tracking error to zero; Step S2: Obtaining the optimal control strategy for dynamic event triggering based on a dynamic event triggering mechanism; Step S3: Designing an actuator-critic neural network based on the optimal control strategy and the optimal value function; Step S4: Obtaining the triggering conditions of the dynamic triggering mechanism based on the optimal value function and the optimal control strategy; Step S5: Tracking the unmanned vessel's trajectory based on the optimal control strategy, the optimal value function, and the triggering conditions of the dynamic triggering mechanism. The method improves the accuracy of the unmanned vessel's trajectory tracking by using the value function of the error system that can minimize tracking error to zero. The dynamic event triggering method updates the parameters of the actuator and criterion neural networks only when the triggering conditions are met, significantly reducing communication and computing resources and overall system energy consumption. BRIEF DESCRIPTION OF THE DRAWINGS
[0075] Figure 1 This is a three-degree-of-freedom model diagram of the unmanned ship in the present invention;
[0076] Figure 2 Flowchart of the present invention. DETAILED DESCRIPTION
[0077] The following will be combined with the drawings in the embodiments of the present application to clearly and completely describe the technical solutions in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, not all of the embodiments. The following description of at least one exemplary embodiment is actually only illustrative and is in no way intended to limit the present application and its application or use. Based on the embodiments in the present application, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of this application.
[0078] In the following description, many specific details are set forth to facilitate a full understanding of the present application. However, the present application may also be implemented in other ways different from those described herein. Those skilled in the art may make similar generalizations without violating the connotation of the present application. Therefore, the present application is not limited to the specific embodiments disclosed below.
[0079] Example 1:
[0080] like Figure 2 As shown, the present invention discloses an optimal tracking control method for an unmanned ship triggered by a discrete-time adaptive dynamic programming dynamic event, comprising the following steps:
[0081] Step S1: Based on the unmanned ship dynamics model, an error system value function is defined that allows the minimum tracking error to approach zero.
[0082] This step addresses the unmanned ship trajectory tracking problem. Based on the unmanned ship dynamics model, an error system value function is defined that allows the minimum tracking error to approach zero. Especially in complex waters, the reference trajectory of the unmanned ship can be accurately tracked, reducing the trajectory tracking error of the unmanned ship.
[0083] In order to simulate the movement of the unmanned ship, the dynamic model of the unmanned ship is established as follows:
[0084]
[0085] In formula (1), f(η,v)=-M -1 (Cv+Dv)+Δ(η,v), Δ(η,v) represents the modeling error of the unmanned ship system, η=[x,y,ψ] T represents the position and heading of the unmanned ship, v = [u, ν, r] T Indicates the forward, drifting and bow rolling speeds of the unmanned boat, μ=[μ u ,μ ν ,μ r ] T represents the control input of the unmanned ship, R(ψ) represents the rotation matrix of the unmanned ship, M=M T >0 is the inertia matrix, C(v)=-C(v) Tis the Coriolis force matrix, and D(v) is the damping matrix.
[0086] like Figure 1 As shown in the figure, the three-degree-of-freedom model of the unmanned ship in the earth coordinate system and the body coordinate system.
[0087] In order to facilitate the implementation of digital computers, the dynamic model of the unmanned ship is converted into an affine system form and discretized to obtain x k+1 =f(x k )+g(x k )u k , and are the state and control input of the system, is the drift dynamic term, Is the control input dynamic term. In order to calculate and evaluate the deviation between the actual track of the unmanned ship and the predetermined track, and adjust the system through the tracking error to ensure that the unmanned ship accurately follows the predetermined track, it is assumed that the reference tracking track θ k If bounded, the error system can be defined where Γ(·) represents the command generator function, Represents the tracking error.
[0088] Because the usual tracking error cannot converge to zero, in order to calculate the deviation between the unmanned ship and the reference trajectory in real time, so that the control system can flexibly adjust the strategy, reduce the tracking error, and optimize the control algorithm, it is necessary to redefine the value function so that the tracking error completely converges to zero. The value function is redefined as,
[0089]
[0090] In formula (2), is the value function, is the control input, represents the utility function.
[0091]
[0092] Formula (3) is the utility function.
[0093] From this, we can derive the optimal value function,
[0094]
[0095] In formula (4), Optimal control strategy.
[0096]
[0097] Step S2: Based on the dynamic event triggering mechanism, derive the optimal control strategy for dynamic event triggering.
[0098] This step can save the communication and computing resource consumption of the unmanned ship controller and reduce the number of control updates.
[0099] In order to realize the dynamic event trigger control strategy, the data system sampled at the trigger moment is defined as k i is the i-th triggering moment, and k i <k i+1 The event sampling state vector is held by the zero-order holder in the controller and is expressed as Define the error as When the event is triggered, that is, k=k i When a new state measurement value is introduced and the error e k Reset to zero and update the control strategy at the same time. When no event is triggered, that is, When the error e k ≠0, the sampling state will not be updated, and the control strategy will be maintained.
[0100] Under the event-triggered sampling rule, the optimal control strategy is expressed as,
[0101]
[0102] In formula (6),
[0103] Step S3: Based on the optimal control strategy and the optimal value function, design the actuator-judge neural network.
[0104] This step utilizes the powerful nonlinear approximation ability of neural networks. Through multi-layer structures and nonlinear activation functions, it can approximate any complex nonlinear function, thereby achieving effective approximation of the optimal value function and the optimal control strategy.
[0105] The evaluation neural network is used to approximate the optimal value function. The evaluation neural network designed this time has three layers and is expressed as:
[0106]
[0107] In formula (7), To judge the neural network, W c1,k is the weight vector from the input layer to the hidden layer of the judging neural network, W c2,k is the weight vector from the hidden layer to the output layer of the judging neural network, φ c (·) is the activation function.
[0108] The value function is derived through the event trigger mechanism as follows:
[0109]
[0110] Formula (8) is the value function, W c1,k is the weight vector from the input layer to the hidden layer of the judging neural network, W c2,k is the weight vector from the hidden layer to the output layer of the judging neural network, φ c (·) is the activation function.
[0111] The execution neural network is used to approximate the optimal control strategy. The execution neural network layer designed this time has three layers, which means the iterative strategy is:
[0112]
[0113] Formula (9) is the execution of neural network, i.e., iterative strategy.
[0114] The control strategy is derived through the event trigger mechanism and value function:
[0115]
[0116] In formula (10),
[0117] The judge neural network (Formula (7)) and the executive neural network (Formula (9)) form the executor-judge neural network. The designed judge neural network and executive neural network, as well as the neural network weight update method, all use the gradient descent method. The gradient descent method is an iterative optimization algorithm used to minimize the objective function. The basic principle is to move in the opposite direction of the objective function gradient, because the gradient represents the direction in which the function value rises fastest, and the opposite direction is the direction in which the function value falls fastest. It has the advantages of simplicity and high efficiency.
[0118] The designed judgment neural network solves the weight matrix and bias vector of the neural network by minimizing the loss function. The loss function is defined as,
[0119]
[0120] In formula (11), The gradient descent algorithm updates the weight parameters of the judgment neural network.
[0121]
[0122] In formula (12), α c Is the learning rate of the neural network.
[0123] The designed execution neural network,performance function is defined as,
[0124]
[0125] The gradient descent algorithm updates the weight parameters of the neural network.
[0126]
[0127] In formula (14), α a is the learning rate for executing the neural network.
[0128] Step S4: Based on the optimal value function and the optimal control strategy, the triggering conditions of the dynamic triggering mechanism are obtained.
[0129] based on The optimal form is expressed as,
[0130]
[0131] In formula (15), To judge the neural network, is the optimal weight vector, c represents an arbitrarily small reconstruction error.
[0132] based on The optimal form is expressed as,
[0133]
[0134] In formula (16), To execute the neural network, is the optimal weight vector, a represents an arbitrarily small reconstruction error.
[0135] Defining weight error Dynamic trigger mechanism defines internal dynamic variables ω k satisfy,
[0136]
[0137] In formula (17),
[0138] Derive the trigger conditions,
[0139]
[0140] In formula (18), The derived trigger condition is uniformly eventually bounded.
[0141] Step S5: Track the trajectory of the unmanned ship based on the optimal control strategy, the optimal value function and the triggering conditions of the dynamic trigger mechanism.
[0142] The optimal value function,
[0143]
[0144] Optimal control strategy,
[0145]
[0146] The triggering conditions of the dynamic trigger mechanism,
[0147]
[0148] The optimal control strategy and dynamic triggering conditions of dynamic events are obtained, and a discrete-time adaptive dynamic programming trajectory tracking control method triggered by dynamic events of unmanned ships is realized, which has the advantages of high trajectory tracking accuracy and saving communication and computing resources.
[0149] The beneficial technical effects of this application are described in detail as follows.
[0150] Compared with the existing technology, the unmanned ship optimal tracking control method based on discrete-time adaptive dynamic programming triggered by dynamic events proposed in this application has the following advantages.
[0151] 1. High trajectory tracking accuracy: The method proposed in this application redefines the error system value function that allows the minimum tracking error to approach zero, thereby improving the accuracy of unmanned ship trajectory tracking.
[0152] 2. Save communication and computing resources: The dynamic event triggering method proposed in this application can update the execution neural network and evaluate the neural network parameters only when the trigger conditions are met, thereby significantly reducing communication and computing resources and reducing the overall energy consumption of the system.
[0153] 3. Strong adaptability: The method proposed in this application enhances the adaptability of the system by introducing adaptive dynamic programming.
[0154] 4. Strong scalability: The discrete-time control method proposed in this application is easy to integrate with computers, easy to port to different platforms, and easy to combine with other advanced technologies.
[0155] Example 2:
[0156] The present invention discloses an unmanned vessel optimal tracking control method triggered by dynamic events using discrete-time adaptive dynamic programming, comprising: establishing an unmanned vessel dynamics model for the unmanned vessel trajectory tracking problem, utilizing the good nonlinear approximation capability of neural networks, designing an actuator-evaluator neural network, and applying the obtained optimal control strategy and dynamic system event triggering conditions to the unmanned vessel trajectory tracking control.
[0157] Further optimization based on Example 2: The dynamic model of the unmanned ship is converted into an affine system form. In order to facilitate the implementation of digital computers, discretization processing is performed to obtain x k+1 =f(x k)+g(x k )u k ,in and are the state and control input of the system, is the drift dynamic term, is the control input dynamic term.
[0158] Further optimization based on Example 2: Defining the error system where Γ(·) represents the command generator function, Represents the tracking error. In order to make the tracking error tend to zero, the value function is redefined as:
[0159]
[0160] in Represents the utility function. In order to obtain the optimal control strategy, the optimal value function and the optimal control strategy are derived based on the Bellman optimality principle.
[0161] Further optimization based on Example 2: Under the dynamic event trigger mechanism rules, the data system sampled at the trigger moment is defined as Define the error as When an event is triggered, the control strategy is updated; when an event is not triggered, the control strategy is maintained.
[0162] Further optimization based on Example 2: In order to design the actuator-judge neural network, the designed neural network layers are three layers, the neural network weight update method uses the gradient descent method, and the designed loss functions are E a , E c , execute neural network and judge neural network respectively to iterate neural network weights W a2,k , W c2,k , and obtain the approximate value function and the approximate control strategy respectively.
[0163] Further optimization based on Example 2: After iterating the value function and control strategy, the dynamic event triggering condition is derived by the Lyapunov function.
[0164]
[0165] in
[0166] Further optimization based on Example 2: Based on the obtained optimal control strategy, optimal value function and dynamic event triggering conditions, the effect of unmanned ship trajectory tracking control triggered by dynamic events of unmanned ship adaptive dynamic planning is achieved.
[0167] Example 2 can effectively improve the accuracy of unmanned vessel trajectory tracking and save system computing and communication resources.
[0168] In summary, for unmanned ship trajectory tracking, this application proposes an optimal tracking control method based on discrete-time adaptive dynamic programming triggered by dynamic events, which solves the problems of large unmanned ship trajectory tracking error and high system resource occupancy. An unmanned ship dynamics model is established. In order to solve the problem of large unmanned ship trajectory tracking error, an error system value function is defined that allows the minimum tracking error to approach zero. The optimal control strategy for unmanned ship trajectory tracking is derived. In order to solve the problem of high system resource occupancy, a dynamic event triggering mechanism is combined. The good nonlinear approximation ability of the neural network is further utilized to design an actuator-evaluator neural network. Based on the obtained optimal control strategy and dynamic system event triggering conditions, it is applied to unmanned ship trajectory tracking control. The method proposed in this application can effectively improve the accuracy of unmanned ship trajectory tracking and save system computing and communication resources.
Claims
1. A discrete-time adaptive dynamic programming method for optimal tracking control of an unmanned vessel triggered by dynamic events, characterized by: The following steps are included: Step S1: Obtain the unmanned ship dynamics model and obtain the optimal value function of the error system that can make the minimum tracking error approach zero; Step S2: Based on the dynamic event triggering mechanism, obtain the optimal control strategy for dynamic event triggering; Step S3: Based on the optimal control strategy and the optimal value function, an actuator-evaluator neural network is designed; In formula (15), is the optimal value function, i.e., the judging neural network. is the optimal weight vector, φ c (·) is the activation function, is the weight vector, is the tracking error, is the reference tracking trajectory, c represents an arbitrarily small reconstruction error; In formula (16), For the optimal control strategy, i.e., executing the neural network, is the optimal weight vector, φ a (·) is the activation function, is the weight vector, is the trigger moment state, a represents an arbitrarily small reconstruction error; The judge neural network and the executive neural network form an executive-judge neural network; Step S4: Based on the optimal value function and the optimal control strategy, the triggering conditions of the dynamic triggering mechanism are obtained; Formula (18) is the trigger condition of the dynamic trigger mechanism. In formula (18), 0<λ<1,ω k It is a dynamic variable inside the dynamic trigger mechanism. C is a constant, e k is the state error; Step S5: Track the trajectory of the unmanned ship based on the optimal control strategy, the optimal value function and the triggering conditions of the dynamic trigger mechanism.
2. The discrete-time adaptive dynamic programming dynamic event-triggered unmanned vessel optimal tracking control method according to claim 1 is characterized by: In step S1, the unmanned ship dynamics model is: In formula (1), f(η,v)=-M -1 (Cv+Dv)+Δ(η,v), Δ(η,v) represents the modeling error of the unmanned ship system, η=[x,y,ψ] T represents the position and heading of the unmanned ship, v = [u, ν, r] T Indicates the forward, drifting and bow rolling speeds of the unmanned boat, μ=[μ u ,μ ν ,μ r ] T represents the control input of the unmanned ship, R(ψ) represents the rotation matrix of the unmanned ship, M=M T >0 is the inertia matrix, C(v)=-C(v) T is the Coriolis force matrix, D(v) is the damping matrix; The unmanned ship dynamics model is converted into an affine system form and discretized to obtain x k+1 =f(x k )+g(x k )u k , and are the state and control input of the system, is the drift dynamic term, is the control input dynamic term; assuming the reference tracking trajectory Bounded, defined error system Γ(·) represents the command generator function, represents the tracking error; The value function is, In formula (2), is the value function, is the control input, represents the utility function; Formula (3) is the utility function; The optimal value function, In formula (4), Optimal control strategy.
3. The discrete-time adaptive dynamic programming dynamic event-triggered unmanned vessel optimal tracking control method according to claim 1, characterized in that: In step S2, the data system sampled at the triggering moment is defined as k i is the i-th triggering moment, and k i <k i+1 The event sampling state vector is held by the zero-order holder in the controller and is expressed as Define the error as When the event is triggered, that is, k=k i When a new state measurement value is introduced and the error e k Reset to zero and update the control strategy at the same time. When no event is triggered, that is, When the error e k ≠0, the sampling state will not be updated, and the control strategy will be maintained; Under the event-triggered sampling rule, the optimal control strategy is expressed as, In formula (6), 4. The discrete-time adaptive dynamic programming dynamic event-triggered unmanned vessel optimal tracking control method according to claim 1 is characterized by: In step S3, the optimal value function is approximated using a judgment neural network, the number of layers of the judgment neural network is three, and the judgment neural network is expressed as: In formula (7), To judge the neural network, W c1,k is the weight vector from the input layer to the hidden layer of the judging neural network, W c2,k is the weight vector from the hidden layer to the output layer of the judging neural network, and φ(·) is the activation function; The value function is derived through the event trigger mechanism as follows: Formula (8) is the value function, W c1,k is the weight vector from the input layer to the hidden layer of the judging neural network, W c2,k is the weight vector from the hidden layer to the output layer of the judging neural network, φ c (·) is the activation function, i.e. The optimal control strategy is approximated by using an execution neural network. The execution neural network has three layers, which means the iterative strategy is: Formula (9) is the execution of neural network, i.e., iterative strategy. is the weight vector, φ a is the activation function is the weight vector; The control strategy is derived through the event trigger mechanism and value function: In formula (10), Gradient descent is used in both evaluating neural networks and updating the weights of neural networks in executing neural networks.
5. The discrete-time adaptive dynamic programming dynamic event-triggered unmanned vessel optimal tracking control method according to claim 4 is characterized by: In step S3, the evaluation neural network solves the weight matrix and bias vector of the neural network by minimizing the loss function. The loss function is defined as: In formula (11), Gradient descent algorithm updates the weight parameters of the judgment neural network; In formula (12), α c Is the learning rate of the neural network; The performance function of executing a neural network is defined as, The gradient descent algorithm updates the weight parameters of the neural network. In formula (14), α a is the learning rate for executing the neural network.
6. The discrete-time adaptive dynamic programming dynamic event-triggered unmanned vessel optimal tracking control method according to claim 4, characterized in that: In step S4, based on The optimal form is expressed as, In formula (15), To judge the neural network, is the optimal weight vector, c represents an arbitrarily small reconstruction error; based on The optimal form is expressed as, In formula (16), is the optimal weight vector, a represents an arbitrarily small reconstruction error; Defining weight error Dynamic trigger mechanism defines internal dynamic variables ω k satisfy, In formula (17), Derive the trigger conditions, In formula (18), The derived trigger conditions is uniformly eventually bounded.