AUV Control Method Based on Neural Network and Port-Controlled Hamiltonian System

Abstract

This invention discloses an AUV control method based on neural networks and a port-controlled Hamiltonian system, belonging to the field of automation control technology. The method first transforms the dynamics and kinematics model of a four-degree-of-freedom AUV into a PCH system model. Then, without considering model parameter uncertainties, time-varying ocean current disturbances, and control input saturation, a passive method is used to design a PCH trajectory tracking controller for the AUV's state error. Next, RBFNN is used to handle model parameter uncertainties and time-varying ocean current disturbances. Furthermore, to effectively address control input saturation, an auxiliary system is introduced, thus inventing a trajectory tracking controller suitable for complex underwater environments. This method not only achieves high-precision three-dimensional trajectory tracking control in complex underwater environments but also exhibits strong robustness and good stability.

Description

Technical Field

[0001] This invention belongs to the field of automatic control technology and relates to three-dimensional high-precision robust control of AUVs, specifically to an AUV control method based on neural networks and port-controlled Hamiltonian systems. Background Technology

[0002] Oceans cover 71% of the Earth's surface. Compared to land-based operations, ocean development faces numerous challenges, including immense water pressure, insufficient light, communication difficulties, ocean current interference, and unknown topography. Underwater robots are robots specifically designed to perform various tasks in underwater environments, commonly used in marine scientific research, seabed resource exploration, subsea pipeline repair, underwater archaeology, diving rescue, and defense industries. Underwater robots can be categorized into tethered underwater robots (ROVs), untethered underwater robots (AUVs), and manned submersibles (HOVs). Compared to ROVs, AUVs offer advantages such as a large operating range, maneuverability, safety, and intelligence, making them crucial tools for various underwater operations and widely used in marine environmental observation and resource surveys.

[0003] In performing tasks, AUVs typically need to move along a pre-planned trajectory, a process known as trajectory tracking. Trajectory tracking requires not only stable control but also sufficient control accuracy and efficiency. AUVs face numerous challenges when performing tracking tasks in complex underwater environments. For example, time-varying ocean current disturbances and model parameter uncertainties can lead to a decrease in the tracking accuracy and robustness of the AUV. Furthermore, in practical applications, controller design is constrained by structural strength and material properties, requiring consideration of control input saturation to ensure ease of engineering implementation and energy efficiency. These factors make the design of trajectory tracking controllers extremely complex. Therefore, ensuring the accuracy and robustness of AUVs in three-dimensional trajectory tracking tasks while considering control input saturation and interference resistance is a highly challenging task. Summary of the Invention

[0004] To address the shortcomings of existing technologies, this invention proposes an AUV control method based on neural networks and a port-controlled Hamiltonian system. The dynamics and kinematics model of an actual operating AUV is transformed into a PCH system model. Without considering model parameter uncertainties, time-varying ocean current interference, and control input saturation, a passive method is used to design a PCH trajectory tracking controller for the AUV's state error. Furthermore, RBFNN is utilized to handle model parameter uncertainties and time-varying ocean current interference. An auxiliary system is also introduced to address control input saturation, thereby achieving high-precision three-dimensional trajectory tracking control in complex underwater environments, with strong robustness and good steady-state error.

[0005] The AUV control method based on neural networks and port-controlled Hamiltonian systems includes the following steps:

[0006] Step 1: Conversion of the Port-Controlled Hamiltonian (PCH) System Model

[0007] The saturation phenomenon caused by the limitation of AUV control inputs by structural strength and material properties is described as follows:

[0008] (1)

[0009] in, The control force is the control force at the i-th degree of freedom after the control input saturation constraint, i=1,2,…Z, where Z represents the number of degrees of freedom of the AUV model. It represents the saturation limit of the control input, defines the maximum permissible control force on each degree of freedom, and prevents excessive control input from damaging the equipment; The input signal of the controller represents the desired control force applied to each degree of freedom without considering saturation. It is the hyperbolic tangent function. Represents the natural constant. It is a normal number.

[0010] Considering parameter uncertainties, time-varying ocean current disturbances, and control input saturation, a multi-degree-of-freedom dynamic and kinematic model of the AUV is established, the Hamiltonian function of the system is defined, and the AUV model is converted into a PCH system form.

[0011] Step 2: Design of PCH system trajectory tracking controller

[0012] For the reference trajectory tracking control task, assume the AUV's momentum vector... and position vector The parameters are obtained directly in real time, and are the sum of the uncertainties of the equivalent model parameters and the time-varying ocean current disturbances. and its relation to time first derivative Both are bounded and refer to trajectories. and its relation to time first derivative and second derivative Both are bounded.

[0013] Utilizing control The desired closed-loop system to be implemented is:

[0014] (2)

[0015] in, Indicates system state error. Denotes the first derivative. , , , It is an ideal non-negative definite dissipation matrix. Choose the desired energy function. for:

[0016] (3)

[0017] in, These represent the momentum tracking error and position tracking error of the AUV, respectively. This represents the AUV quality matrix. Let be the positive definite constant matrix to be designed. This leads to the following state error equation:

[0018] (4)

[0019] in, , which represents the momentum vector of an ideal system. Represents the Coriolis centripetal force matrix of an AUV. This represents the damping matrix of the AUV. The system does not account for the sum of parameter uncertainties and time-varying ocean current disturbances. The control force matrix when the control input is saturated.

[0020] Define vector Momentum vector of an ideal system As the filter output, construct the following filter:

[0021] (5)

[0022] in, , It is a positive number.

[0023] Define the filtering error The controller of the PCH system is obtained based on the state error equation. :

[0024] (6)

[0025] Step 3: RBFNN Adaptive Rate Design

[0026] The sum of model parameter uncertainties and time-varying ocean current disturbances is approximated using RBFNN (Radial Basis Function Neural Network). ,set up Given a sufficiently small positive parameter as the input to the neural network. with ideal weight This makes the approximation error Satisfy any ,have ,in , , Represents radial basis functions. , They are respectively , The estimated value. The following neural network adaptive rate is designed:

[0027] (7)

[0028] in, and For the positive constants that need to be designed, estimate the error. ,and , , It is the Frobenius norm. and If it is a positive number, it satisfies For positive integers, This is an absolute value operation. The interference control force of the neural network fitting part is denoted as... .

[0029] Step 4: Design of Actuator Saturation Auxiliary System

[0030] To reduce the impact of control input saturation, the auxiliary system vector is selected. And construct the following auxiliary system:

[0031] (8)

[0032] in, Indicates the momentum tracking error of the AUV The error at the i-th degree of freedom, It is a positive definite constant matrix. ,and , It is a positive constant. The control force of this auxiliary system is designed to be... ,in, It is the positive definite constant matrix of the control force of the auxiliary system.

[0033] Step 5: Boundedness Analysis of Closed-Loop System Errors

[0034] Considering model parameter uncertainties, time-varying ocean current disturbances, and control input saturation, the controller of the PCH system is utilized. and neural network adaptive rate By selecting appropriate parameter values, the tracking error of the closed-loop system converges to a very small neighborhood around the origin, thus obtaining the corresponding controller. .

[0035] The present invention has the following beneficial effects:

[0036] This method combines neural networks with a state error PCH trajectory tracking controller for AUV trajectory tracking. By integrating radial basis function neural networks, a PCH model, and an auxiliary system, it effectively handles model uncertainties, time-varying ocean current disturbances, and control input saturation while maintaining AUV trajectory tracking control accuracy. It can successfully complete 3D trajectory tracking tasks in complex underwater environments. Furthermore, the PCH model-based method is essentially an energy-based approach with clear physical meaning, and the controller design is simple and easy to implement. Compared to traditional disturbance observers, radial basis function neural networks do not rely on precise system modeling, making them easier to implement and adjust, especially in the absence of a clear disturbance model. Moreover, radial basis function neural networks perform better when dealing with highly nonlinear systems. The proposed nonlinear system tracking controller design can be extended beyond AUVs to other applications, such as solving the control problems of robotic arms, tracking control of surface vessels, and control problems of permanent magnet synchronous motor drive systems. Attached Figure Description

[0037] Figure 1 The flowchart shows the AUV control method based on neural networks and port-controlled Hamiltonian systems.

[0038] Figure 2 This is a schematic diagram of the motion model of an AUV.

[0039] Figure 3 This is a schematic diagram of the controller designed in the embodiment. Detailed Implementation

[0040] like Figure 1 As shown, the AUV control method based on neural networks and port-controlled Hamiltonian systems specifically includes the following steps:

[0041] Step 1: Conversion of the port-controlled Hamiltonian system model

[0042] An AUV has six degrees of freedom: longitudinal displacement, lateral displacement, vertical displacement, roll angle, helix angle, and yaw angle. This embodiment ignores the roll and helix angles, while considering parameter uncertainties, time-varying ocean current interference, and control input saturation, establishing a four-degree-of-freedom dynamic and kinematic model of the AUV, such as... Figure 2 As shown:

[0043] (1)

[0044] in, This represents the position vector of the AUV in the Earth coordinate system. These represent the longitudinal displacement, lateral displacement, vertical displacement, and yaw angle of the AUV, respectively, indicated by superscript. Represents the transpose of a matrix or vector. express A column vector of dimension; This represents the velocity vector in the AUV coordinate system. These are longitudinal velocity, lateral velocity, vertical velocity, and yaw rate. Denotes the first derivative; This represents the control torque of the AUV system, where These refer to the control forces of the AUV in terms of longitudinal velocity, lateral velocity, vertical velocity, and yaw rate. This represents the sum of model parameter uncertainties and time-varying ocean current disturbances, where These are the components of longitudinal velocity, lateral velocity, vertical velocity, and yaw rate, respectively. Represents the AUV quality matrix. Represents the Coriolis centripetal force matrix of an AUV. This represents the damping matrix of the AUV. express A real matrix of dimension 1. Represents gravity and buoyancy The resultant force matrix, where the components of the force on the longitudinal velocity, lateral velocity, and yaw angular velocity are: The component of the force on the vertical velocity is . This represents the coordinate transformation matrix.

[0045] In practical applications, the control input of AUVs is limited by structural strength and material properties, and the resulting saturation phenomenon is described as follows:

[0046] (2)

[0047] in, These correspond to the longitudinal velocity, lateral velocity, vertical velocity, and yaw rate of the AUV, respectively. The control force corresponding to each degree of freedom after the control input saturation limit; It represents the saturation limit of the control input, defines the maximum permissible control force on each degree of freedom, and prevents excessive control input from damaging the equipment; The input signal of the controller represents the desired control force applied to each degree of freedom without considering saturation. It is the hyperbolic tangent function. Represents the natural constant. It is a normal number.

[0048] definition Vihamiton system:

[0049] (3)

[0050] in, Represents the state vector of the system. express Regarding time The derivative; Represents the Hamiltonian function of the system. This represents a mapping from an n-dimensional vector to a scalar; They represent 3D input and output vectors; The matrix is ​​an antisymmetric matrix, representing the part of the system without energy loss; It is a symmetric matrix, representing the portion of the system's energy consumption; It is a coefficient matrix.

[0051] In the four-degree-of-freedom dynamics and kinematics model of the AUV shown in Equation (1), a new state vector is introduced. , where the state vector and Let represent the momentum vector and position vector of the system, respectively. Define the Hamiltonian function of the system. The AUV model shown in formula (1) is converted into the following PCH system form:

[0052] (4)

[0053] in, It is the Coriolis centripetal force matrix equivalent to the AUV model. The zero matrix is ​​a dimension-matched matrix. It is the equivalent damping matrix. , ; I represents the identity matrix for dimension matching; This indicates the system input after considering control input saturation; It is the sum of the parameter uncertainty and time-varying ocean current disturbance equivalent to formula (1). For matrix The reverse; express Partial derivative operations of a function.

[0054] Step 2: Design of PCH system trajectory tracking controller

[0055] The goal of the tracking controller is to enable the AUV to track the reference trajectory, i.e. , The upper bound of the steady-state error is represented by the momentum vector of the ideal system. , Let be the positive definite constant matrix to be designed. These represent the momentum tracking error and position tracking error of the AUV, respectively. Considering the initial and reference value constraints of the actual system model itself, there exists a finite number of normal numbers. satisfy , , Let Euclidean norm be the vector. It represents the supremum of the norm.

[0056] For the reference trajectory tracking control task, assume the AUV's state vector and This is obtained directly in real time, and the model parameter uncertainty is the sum of the time-varying ocean current disturbances. and its first derivative with respect to time Both are bounded. The reference trajectory is... and its relation to time first derivative and second derivative Both are bounded, that is , , , These represent the expected longitudinal displacement, lateral displacement, vertical displacement, and yaw angle of the AUV, respectively. The given positive constant is .

[0057] In this application, the controller design of a 4D Hamiltonian system is considered, and the error state vector is defined. , This represents the desired vector of the system state. Utilizing control forces... To achieve the desired closed-loop system:

[0058] (5)

[0059] in, This is the portion with no energy loss; Let be the desired dissipation matrix. Therefore, we have: Thus, the control law is obtained. .

[0060] This leads to the controller design for an AUV converted into a PCH system, defining the system state error. The derivative with respect to time is Utilizing control The desired closed-loop system to be implemented is:

[0061] (6)

[0062] in, , , It is an ideal non-negative definite dissipation matrix. The Lyapunov function is chosen. and the expected energy function for:

[0063] (7)

[0064] in, Let be the positive definite constant matrix to be designed. This leads to the following state error equation:

[0065] (8)

[0066] in, The system does not account for the sum of parameter uncertainties and time-varying ocean current disturbances. The control force matrix when the control input is saturated.

[0067] Define vector Momentum vector of an ideal system As the filter output, construct the following filter:

[0068] (9)

[0069] in, , It is a positive number.

[0070] Define the filtering error Choose the Lyapunov function The controller for the PCH system is obtained based on the state error equation as follows:

[0071] (10)

[0072] In order to analyze the nominal system, we do not consider Given the boundedness of the system error when the control input is saturated, the Lyapunov function is chosen. ,get:

[0073] (11)

[0074] (12)

[0075] (13)

[0076] make And satisfy ,in, If the number is a positive constant, then:

[0077] (14)

[0078] in, Let be any positive constant, therefore we have:

[0079] (15)

[0080] in, Represents the smallest eigenvalue of the matrix; Let be the minimum value function. The above inequality can be expressed as .

[0081] Therefore, by selecting appropriate parameters ,make , If established, it can make It is uniformly bounded, meaning that the tracking error of the closed-loop system can converge to a very small neighborhood around the origin.

[0082] Step 3: RBFNN Adaptive Rate Design

[0083] RBFNN (Radial Basis Function Neural Network) can approximate any unknown smooth function; therefore, RBFNN is used to approximate the sum of model parameter uncertainties and time-varying ocean current disturbances. ,set up Given a sufficiently small positive parameter as the input to the neural network. with ideal weight This makes the approximation error Satisfy any ,have , , .in, Represents radial basis functions. , They are respectively , The estimated value. The following neural network adaptive rate is designed:

[0084] (16)

[0085] in, and For the positive constants that need to be designed, estimate the error. ,and , , It is the Frobenius norm. and If it is a positive number, it satisfies For positive integers, This is an absolute value operation. The interference control force of the neural network fitting part is denoted as... And select the Lyapunov function. , Let be the trace of the matrix.

[0086] Step 4: Design of Actuator Saturation Auxiliary System

[0087] To reduce the impact of control input saturation, the auxiliary system vector is selected. And construct the following auxiliary system:

[0088] (17)

[0089] in, They represent Errors in each degree of freedom It is a positive definite constant matrix. ,and , It is a positive constant. The control force of this auxiliary system is designed to be... ,in, This is the positive definite constant matrix of the control force of the auxiliary system. For the auxiliary system, the Lyapunov function is chosen. .

[0090] Step 5: Boundedness Analysis of Closed-Loop System Errors

[0091] Considering model parameter uncertainties, time-varying ocean current disturbances, and control input saturation, the Lyapunov function is chosen. According to the PCH system controller and neural network adaptive rate : (18) in, .

[0092] Analyze the AUV model in the form of a PCH system under the conditions of model parameter uncertainty, the sum of time-varying ocean current disturbances d(x), and control input saturation, such as Figure 3 The controller shown Boundedness condition for closed-loop system error: Case (1), when hour, ,remember Rewrite formula (18) as follows , ,and ; Situation (2), when hour, We can obtain: ,therefore, ,in And there are ; In summary, by selecting parameters The value of makes the inequality ... , , The design of this controller allows the tracking error of the closed-loop system to converge to a very small neighborhood around the origin. This means that, given the sum of model parameter uncertainties and time-varying ocean current disturbances (d(x)) and control input saturation, the controller designed in this application achieves this result. This ensures the boundedness of the closed-loop system error.

Claims

1. An AUV control method based on neural networks and port-controlled Hamiltonian systems, characterized in that: Specifically, the following steps are included: Step 1: Conversion of the port-controlled Hamiltonian system model The saturation phenomenon caused by the limitation of AUV control inputs by structural strength and material properties is described as follows: Where, τ i The control force is the control force at the i-th degree of freedom after the control input saturation constraint, where i = 1, 2, ..., Z, and Z represents the number of degrees of freedom of the AUV model. This indicates the saturation limit of the control input. This represents the desired control force applied to each degree of freedom without considering saturation. It is the hyperbolic tangent function. Represents the natural constant. It is a positive constant; Considering parameter uncertainties, time-varying ocean current disturbances, and control input saturation, a four-degree-of-freedom dynamic and kinematic model of the AUV is established, the Hamiltonian function of the system is defined, and the AUV model is converted into the PCH system form. Step 2: Design of PCH system trajectory tracking controller Set the target of the PCH system trajectory tracking controller and calculate the state error equation; Define vector The momentum vector of the ideal system As the filter output, construct the following filter: in, , It is a positive number; Denotes the first derivative; The positive definite constant matrix to be designed; Represents the AUV quality matrix. For matrix The reverse; Represents the system's position vector; Indicates the reference trajectory; The positive definite constant matrix to be designed; Define the filtering error The controller of the PCH system is obtained based on the state error equation. : in, , , Represents the Coriolis centripetal force matrix of an AUV. This represents the damping matrix of the AUV. It is the equivalent damping matrix. It is an ideal non-negative definite dissipation matrix; Step 3: RBFNN Adaptive Rate Design Will As input to the RBFNN neural network, These represent the momentum tracking error and position tracking error of the AUV, respectively; given positive parameters with ideal weight This makes the approximation error Satisfy any ,have , This represents the sum of the equivalent model parameter uncertainties and time-varying ocean current disturbances. for The estimated value is used to design the neural network adaptive rate. : (10) in, and For the positive constants that need to be designed, Represents the radial basis function, estimation error ,and , , It is the Frobenius norm. and If it is a positive number, it satisfies For positive integers, It is an absolute value operation; the interference control force of the neural network fitting part is denoted as... ; for The estimated value; Step 4: Design of Actuator Saturation Auxiliary System Selecting the auxiliary system vector And construct the following auxiliary system: in, Indicates the momentum tracking error of the AUV The error in the i-th degree of freedom; It is a positive definite constant matrix. ,and , It is a positive constant; the control force of this auxiliary system is designed to be... ,in, It is the positive definite constant matrix of the control force of the auxiliary system; Step 5: Boundedness Analysis of Closed-Loop System Errors By selecting the Lyapunov function and considering model parameter uncertainties, time-varying ocean current disturbances, and control input saturation, the parameter values ​​are determined to ensure that the tracking error of the PCH system trajectory tracking controller in step 2 is bounded, thus obtaining the corresponding controller. .

2. The AUV control method based on neural networks and port-controlled Hamiltonian systems as described in claim 1, characterized in that: Considering parameter uncertainties, time-varying ocean current disturbances, and control input saturation, a four-degree-of-freedom dynamic and kinematic model of the AUV is established: in, This represents the position vector of the AUV in the Earth coordinate system. These represent the longitudinal displacement, lateral displacement, vertical displacement, and yaw angle of the AUV, respectively, indicated by superscript. Represents the transpose of a matrix or vector. express A column vector of dimension; This represents the velocity vector in the AUV coordinate system. These are longitudinal velocity, lateral velocity, vertical velocity, and yaw rate, respectively. This represents the control torque of the AUV system, where These refer to the control forces of the AUV in terms of longitudinal velocity, lateral velocity, vertical velocity, and yaw rate; This represents the sum of model parameter uncertainties and time-varying ocean current disturbances, where These are the components of longitudinal velocity, lateral velocity, vertical velocity, and yaw rate, respectively. express A real matrix of dimension 1; Represents gravity and buoyancy The resultant force matrix, where the components of the force on the longitudinal velocity, lateral velocity, and yaw angular velocity are: The component of the force on the vertical velocity is ; Represents the coordinate transformation matrix; In the four-degree-of-freedom dynamics and kinematics model of the AUV, a new state vector is introduced. ,in Denotes the momentum vector of the system; Definition Vie Hamiltonian system and Hamiltonian function The AUV model is converted into the following PCH system form: in, It is the Coriolis centripetal force matrix equivalent to the AUV model. The zero matrix is ​​a dimension-matched matrix; I represents the identity matrix for dimension matching; This indicates the system input after considering control input saturation; It is the sum of equivalent parameter uncertainties and time-varying ocean current disturbances. .

3. The AUV control method based on neural networks and port-controlled Hamiltonian systems as described in claim 2, characterized in that: The goal of designing a tracking controller , It represents the upper bound of the steady-state error; Assume the momentum vector of the AUV and position vector It is obtained through direct real-time measurement, and and its relation to time first derivative Both are bounded, with reference trajectories. and its relation to time first derivative and second derivative Both are bounded, that is , , , These represent the expected longitudinal displacement, lateral displacement, vertical displacement, and yaw angle of the AUV, respectively. Given positive constants; momentum vector of the ideal system Considering the initial and reference value constraints of the actual system model itself, there exists a finite number of positive constants. satisfy , , Let Euclidean norm be the vector. Denotes the supremum of the norm; Define system state error The derivative with respect to time is Utilizing control The desired closed-loop system to be implemented is: in, , , It is an ideal nonnegative definite dissipation matrix; choose the desired energy function. for: in, The positive definite constant matrix to be designed is given; thus, the following state error equation is obtained: in, The system does not account for the sum of parameter uncertainties and time-varying ocean current disturbances. The control force matrix when the control input is saturated.

4. The AUV control method based on neural networks and port-controlled Hamiltonian systems as described in claim 3, characterized in that: Choose Lyapunov functions , , , , , The trace of the matrix; According to the controller of the PCH system and neural network adaptive rate : in, Let be any positive constant. , To meet The positive constants, of which ; Analysis of the sum of model parameter uncertainties and time-varying ocean current disturbances in the form of a PCH system AUV model When the control input is saturated, the controller Boundedness condition for closed-loop system error: In summary, by selecting parameters The value of makes the inequality ... , , Establishment, controller Ensure the boundedness of the closed-loop system error.

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