AUV control method based on neural network and port controlled Hamiltonian system

Abstract

The invention discloses an AUV control method based on a neural network and a port controlled Hamiltonian system, and belongs to the technical field of automatic control. The method comprises the following steps: firstly, converting a dynamics and kinematics model of the four-degree-of-freedom AUV into a PCH system model, and designing a state error PCH trajectory tracking controller of the AUV based on a passivity method under the condition that model parameter uncertainty, time-varying ocean current interference and control input saturation are not considered; then, the RBFNN is used for processing model parameter uncertainty and time-varying ocean current interference; in addition, in order to effectively cope with control input saturation, an auxiliary system is introduced, and therefore the trajectory tracking controller suitable for the complex underwater environment is invented. By adopting the method, high-precision three-dimensional trajectory tracking control can be realized in a complex underwater environment, and the method has relatively high robustness and good stability performance.

Description

Technical Field

[0001] The invention belongs to the technical field of automatic control, and relates to three-dimensional high-precision robust control of an AUV, and in particular to an AUV control method based on a neural network and a port-controlled Hamiltonian system. Background Art

[0002] The ocean covers 71% of the earth's total area. Compared with land operations, marine development faces many challenges, including huge water pressure, insufficient light, communication difficulties, ocean current interference, unknown landforms, etc. Underwater robots are robots specially designed to perform various tasks in underwater environments. They are usually used in marine scientific research, seabed resource exploration, submarine pipeline maintenance, underwater archaeology, diving rescue, national defense and military industries. Underwater robots can be divided into cable underwater robots (ROVs), cable-free underwater robots (AUVs) and manned submersibles (HOVs). In comparison, AUVs have the advantages of large range of activities, mobility, safety, and intelligence. They have become an important tool for various underwater operation tasks and have been widely used in marine environment observation, resource surveys and other fields.

[0003] When performing a mission, the AUV usually needs to move along a pre-planned trajectory, that is, trajectory tracking. The trajectory tracking task requires not only control stability, but also sufficient control accuracy and efficiency. AUV faces many challenges when performing tracking tasks in complex underwater environments. For example, time-varying ocean current interference and model parameter uncertainty will cause the tracking accuracy and robustness of the AUV to decrease. At the same time, in practical applications, the controller design is limited by structural strength and material properties, and control input saturation needs to be considered to ensure the simplicity of engineering implementation and energy saving. These factors make the design of trajectory tracking controllers very complicated. Therefore, while ensuring the accuracy and robustness of the AUV's three-dimensional trajectory tracking mission, considering control input saturation and anti-interference ability is a very challenging task. Summary of the invention

[0004] In view of the shortcomings of the prior art, the present invention proposes an AUV control method based on a neural network and a port-controlled Hamiltonian system, transforms the dynamic and kinematic models of the actual operating AUV into a PCH system model, and designs a state error PCH trajectory tracking controller of the AUV based on a passive method without considering the uncertainty of model parameters, time-varying ocean current interference and control input saturation; and uses RBFNN to process the uncertainty of model parameters and time-varying ocean current interference; at the same time, an auxiliary system is introduced to deal with the control input saturation, thereby realizing high-precision three-dimensional trajectory tracking control in a complex underwater environment, and having strong robustness and good steady-state error.

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

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

[0007] The saturation phenomenon caused by the AUV control input being limited by the structural strength and material properties can be described as:

[0008] (1)

[0009] in, is the control force on the i-th degree of freedom after the control input saturation limit, i=1,2,…Z, Z represents the number of degrees of freedom of the AUV model. It indicates the saturation limit of the control input, defines the maximum allowable control force on each degree of freedom, and prevents excessive control input from damaging the device; It represents the input signal of the controller, which is the control force expected to be applied to each degree of freedom without considering saturation; is the hyperbolic tangent function, represents a natural constant, is a normal number.

[0010] Considering parameter uncertainty, time-varying ocean current interference and control input saturation, the multi-degree-of-freedom dynamics and kinematics model of 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: PCH system trajectory tracking controller design

[0012] For the reference trajectory tracking control task, assume that the momentum vector of the AUV and the position vector It is directly measured in real time, and the equivalent model parameter uncertainty is the sum of the time-varying ocean current disturbance Its effect on time The first derivative of are bounded, and the reference trajectory And about time The first derivative of and the second derivative All are bounded.

[0013] Leverage control The desired closed-loop system to be achieved is:

[0014] (2)

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

[0016] (3)

[0017] in, They represent the momentum tracking error and position tracking error of AUV respectively, represents the AUV mass matrix. is the positive definite constant matrix to be designed. Thus, the following state error equation is obtained:

[0018] (4)

[0019] in, , represents the momentum vector of the ideal system. represents the Coriolis centripetal force matrix of the AUV, represents the damping matrix of the AUV. is the sum of the system's parameter uncertainty and time-varying ocean current disturbances without considering The control force matrix when the control input is saturated.

[0020] Defining vectors , the momentum vector of the ideal system As filter output, the following filter is constructed:

[0021] (5)

[0022] in, , Is a normal number.

[0023] Defining Filter Error According to the state error equation, the controller of the PCH system is as follows: :

[0024] (6)

[0025] Step 3: RBFNN adaptive rate design

[0026] Use RBFNN (Radial Basis Function Neural Network) to approximate the sum of model parameter uncertainty and time-varying ocean current disturbance ,set up As the input of the neural network, given a sufficiently small positive parameter With ideal weight , so that the approximation error Satisfy any ,have ,in , , represents the radial basis function, , They are , The estimated value of . Design the following neural network adaptation rate:

[0027] (7)

[0028] in, and is a normal number to be designed, and the estimated error ,and , , is the Frobenius norm, and is a positive number, satisfying is a normal number, is the absolute value operation. The disturbance control force of the neural network fitting part is recorded as .

[0029] Step 4: Design of actuator saturation auxiliary system

[0030] In order to reduce the influence of control input saturation, the auxiliary system vector And build the following auxiliary system:

[0031] (8)

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

[0033] Step 5: Boundedness analysis of closed-loop system error

[0034] The controller of the PCH system is used to consider the uncertainty of model parameters, time-varying ocean current disturbance and control input saturation. and neural network adaptation rate , select appropriate parameter values ​​so that the tracking error of the closed-loop system converges to a small neighborhood near the origin, and obtain the corresponding controller .

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

[0036] This method combines the neural network with the state error PCH trajectory tracking controller and applies it to the trajectory tracking problem of AUV. It combines the radial basis function neural network, PCH model and auxiliary system. While ensuring the accuracy of AUV trajectory tracking control, it can effectively deal with model uncertainty, time-varying ocean current interference and control input saturation phenomenon, and can better complete the three-dimensional trajectory tracking task in complex underwater environments. In addition, the method based on the PCH model is essentially an energy-based method with clear physical meaning, and the controller design is simple and easy to implement. Compared with the traditional disturbance observer, the radial basis function neural network does not rely on accurate system modeling, and is easier to implement and adjust, especially when there is no clear disturbance model, and the radial basis function neural network performs better when facing highly nonlinear systems. At the same time, the proposed nonlinear system tracking controller design idea can be applied to other objects in addition to AUV, such as solving the control of the manipulator, the tracking control of the surface ship, and the control problem of the permanent magnet synchronous motor drive system. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] Figure 1 This is a flow chart of the AUV control method based on neural network and port-controlled Hamiltonian system.

[0038] Figure 2 Schematic diagram of the AUV's motion model.

[0039] Figure 3 Schematic diagram of the controller designed in the embodiment. DETAILED DESCRIPTION

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

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

[0042] AUV has six degrees of freedom, namely longitudinal displacement, lateral displacement, vertical displacement, roll angle, helix angle and yaw angle. In this embodiment, the roll angle and helix angle of AUV are ignored, and the parameter uncertainty, time-varying ocean current interference and control input saturation are considered. The four-degree-of-freedom dynamics and kinematics model of AUV is established, as shown in Figure 2 As shown:

[0043] (1)

[0044] in, represents the position vector of the AUV in the Earth coordinate system, are the longitudinal displacement, lateral displacement, vertical displacement and yaw angle of the AUV, respectively. represents the transpose of a matrix or vector, express -dimensional column vector; represents the velocity vector in the AUV coordinate system, They are longitudinal velocity, lateral velocity, vertical velocity, and yaw angular velocity, respectively. represents the first derivative; represents the AUV system control torque, where They are the control forces of the AUV on longitudinal velocity, lateral velocity, vertical velocity, and yaw angular velocity; represents the sum of model parameter uncertainty and time-varying ocean current disturbance, where They are the components of longitudinal velocity, lateral velocity, vertical velocity, and yaw angular velocity respectively; represents the AUV mass matrix, represents the Coriolis centripetal force matrix of the AUV, represents the damping matrix of the AUV, express dimensional real matrix. Indicates gravity and buoyancy The resultant force matrix of the longitudinal velocity, lateral velocity, and yaw angular velocity is , the vertical velocity component is . Represents a coordinate transformation matrix.

[0045] In practical applications, the AUV control input is limited by the structural strength and material properties, and the saturation phenomenon caused by this is described as:

[0046] (2)

[0047] in, , corresponding to the longitudinal velocity, lateral velocity, vertical velocity, and yaw angular velocity of the AUV, respectively. is the control force corresponding to each degree of freedom after the control input is saturated; It indicates the saturation limit of the control input, defines the maximum allowable control force on each degree of freedom, and prevents excessive control input from damaging the device; It represents the input signal of the controller, which is the control force expected to be applied to each degree of freedom without considering saturation; is the hyperbolic tangent function, represents a natural constant, is a normal number.

[0048] definition Hamiltonian system:

[0049] (3)

[0050] in, represents the state vector of the system, express About Time The derivative of represents the Hamiltonian function of the system, Represents the mapping from n-dimensional vector to scalar; Respectively dimensional input and output vectors; is an antisymmetric matrix, representing the part of the system without energy loss; is a symmetric matrix, representing the part of system energy consumption; is the coefficient matrix.

[0051] In the four-degree-of-freedom dynamics and kinematics model of the AUV shown in formula (1), a new state vector is introduced , where the state vector and 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, is the equivalent Coriolis centripetal force matrix of the AUV model, is a zero matrix with matching dimensions, is the equivalent damping matrix, , ; I represents the identity matrix with matching dimensions; , represents the system input after considering the control input saturation; is the sum of the equivalent parameter uncertainty of formula (1) and the time-varying ocean current disturbance, For the matrix The inverse of express Partial derivative of a function.

[0054] Step 2: PCH system trajectory tracking controller design

[0055] The goal of the tracking controller is to make the AUV track the reference trajectory, that is, , represents the supremum of the steady-state error. The momentum vector of the ideal system is , is the positive definite constant matrix to be designed, They represent the momentum tracking error and position tracking error of AUV respectively, , considering the initial value and reference value restrictions of the actual system model itself, there is a finite positive number satisfy , , is the Euclidean norm of the vector, represents the supremum of the norm.

[0056] For the reference trajectory tracking control task, assume that the state vector of the AUV is and It is directly measured in real time, and the uncertainty of model parameters is the sum of the time-varying ocean current disturbance and its first-order derivative with respect to time are bounded. The reference trajectory And about time The first derivative of and the second derivative are bounded, that is , , , They represent the desired longitudinal displacement, lateral displacement, vertical displacement, and yaw angle of the AUV, respectively. is a known positive constant.

[0057] In this application, the controller design of a 4-dimensional Hamiltonian system is considered, and the error state vector is defined as , is the expected vector of the system state. Using the control force To achieve the desired closed-loop system:

[0058] (5)

[0059] in, It is the part without energy loss; is the expected dissipation matrix. Therefore, we have: , thus obtaining the control law .

[0060] Based on this, the controller design of the AUV converted into a PCH system is derived, and the system state error is defined The time derivative is , using control The desired closed-loop system to be achieved is:

[0061] (6)

[0062] in, , , is an ideal non-negative definite dissipative matrix. Choose the Lyapunov function , and the expected energy function for:

[0063] (7)

[0064] in, is the positive definite constant matrix to be designed. Thus, the following state error equation is obtained:

[0065] (8)

[0066] in, is the sum of the system's parameter uncertainty and time-varying ocean current disturbances without considering The control force matrix when the control input is saturated.

[0067] Defining vectors , the momentum vector of the ideal system As filter output, the following filter is constructed:

[0068] (9)

[0069] in, , Is a normal number.

[0070] Defining Filter Error , select the Lyapunov function According to the state error equation, the controller of the PCH system is obtained as follows:

[0071] (10)

[0072] In order to analyze the nominal system, no consideration is given to The boundedness of the system error when the control input is saturated, choose the Lyapunov function ,get:

[0073] (11)

[0074] (12)

[0075] (13)

[0076] make , and satisfies ,in, is a positive constant, then:

[0077] (14)

[0078] in, is any positive constant, so:

[0079] (15)

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

[0081] Therefore, by choosing appropriate parameters ,make , Established, it can make It is uniformly ultimately bounded, that is, the tracking error of the closed-loop system can converge to a very small neighborhood near the origin.

[0082] Step 3: RBFNN adaptive rate design

[0083] RBFNN (Radial Basis Function Neural Network) can approximate any unknown smooth function, so RBFNN is used to approximate the sum of model parameter uncertainty and time-varying ocean current interference. ,set up As the input of the neural network, given a sufficiently small positive parameter With ideal weight , so that the approximation error Satisfy any ,have , , .in, represents the radial basis function, , They are , The estimated value of . Design the following neural network adaptation rate:

[0084] (16)

[0085] in, and is a normal number to be designed, and the estimated error ,and , , is the Frobenius norm, and is a positive number, satisfying is a positive constant, is the absolute value operation. The disturbance control force of the neural network fitting part is recorded as , and select the Lyapunov function , is the trace of the matrix.

[0086] Step 4: Design of actuator saturation auxiliary system

[0087] In order to reduce the influence of control input saturation, the auxiliary system vector And build the following auxiliary system:

[0088] (17)

[0089] in, Respectively The error in each degree of freedom is is a positive definite constant matrix, ,and , is a positive constant. The control force of the auxiliary system is designed to be ,in, is the positive constant matrix of the auxiliary system control force. For the auxiliary system, the Lyapunov function is selected .

[0090] Step 5: Boundedness analysis of closed-loop system error

[0091] Considering the uncertainty of model parameters, time-varying ocean current disturbance and control input saturation, the Lyapunov function is selected. . According to the controller of the PCH system and the neural network adaptation rate : (18) in, .

[0092] The AUV model in the form of the PCH system is analyzed under the conditions of model parameter uncertainty, the sum of time-varying ocean current disturbance d(x) and control input saturation, such as Figure 3 The controller shown The boundedness condition of the closed-loop system error is: Situation (1) When hour, ,remember , rewrite formula (18) as , ,and ; Situation (2): hour, , we can get: ,therefore, ,in , and there is ; In summary, by selecting parameters The value of makes the inequality , , The tracking error of the closed-loop system can be converged to a small neighborhood near the origin, that is, when the sum of the model parameter uncertainty and the time-varying ocean current disturbance d(x) and the control input are saturated, the controller designed in this application The boundedness of the closed-loop system error can be guaranteed.

Claims

1. AUV control method based on neural network and port-controlled Hamiltonian system, characterized by: The specific steps include: Step 1: Conversion of port-controlled Hamiltonian system model The saturation phenomenon caused by the AUV control input being limited by the structural strength and material properties can be described as: (1) in, is the control force on the i-th degree of freedom after the control input saturation limit, i=1,2,…Z, Z represents the number of degrees of freedom of the AUV model; represents the saturation limit of the control input, It represents the control force expected to be applied on each degree of freedom without considering saturation; is the hyperbolic tangent function, represents a natural constant, is a positive constant; Considering parameter uncertainty, time-varying ocean current interference and control input saturation, the multi-degree-of-freedom dynamics and kinematics model of AUV is established, the Hamiltonian function of the system is defined, and the AUV model is converted into the PCH system form; Step 2: PCH system trajectory tracking controller design Set the target of the PCH system trajectory tracking controller and calculate the state error equation; The controller of the PCH system is obtained according to the state error equation ; Step 3: RBFNN adaptive rate design Will As the input of RBFNN neural network, Respectively represent the momentum tracking error and position tracking error of AUV; given a positive parameter With ideal weight , so that the approximation error Satisfy any ,have , represents the equivalent sum of model parameter uncertainty and time-varying ocean current disturbance, for The estimated value of the neural network adaptation rate is designed , for An estimated value of Step 4: Design of actuator saturation auxiliary system Select auxiliary system vector And build the following auxiliary system: (2) in, represents the momentum tracking error of the AUV The error in the i-th degree of freedom; is a positive definite constant matrix, ,and , is a positive constant; the control force of the auxiliary system is designed to be ,in, is the positive definite constant matrix of the auxiliary system control force; Step 5: Boundedness analysis of closed-loop system error Select the Lyapunov function and determine the parameter value by considering the uncertainty of model parameters, time-varying ocean current disturbance and control input saturation, so that the tracking error of the PCH system trajectory tracking controller in step 2 is bounded, and the corresponding controller is obtained. .

2. The AUV control method based on a neural network and a port-controlled Hamiltonian system as claimed in claim 1, characterized in that: Considering parameter uncertainty, time-varying ocean current interference and control input saturation, a four-degree-of-freedom dynamics and kinematics model of the AUV is established: (3) in, represents the position vector of the AUV in the Earth coordinate system, are the longitudinal displacement, lateral displacement, vertical displacement and yaw angle of the AUV, respectively. represents the transpose of a matrix or vector, express dimensional column vector; represents the velocity vector in the AUV coordinate system, They are longitudinal velocity, lateral velocity, vertical velocity, and yaw angular velocity respectively; represents the AUV system control torque, where They are the control forces of the AUV on longitudinal velocity, lateral velocity, vertical velocity, and yaw angular velocity; represents the sum of model parameter uncertainty and time-varying ocean current disturbance, where They are the components of longitudinal velocity, lateral velocity, vertical velocity, and yaw angular velocity respectively; represents the AUV mass matrix, represents the Coriolis centripetal force matrix of the AUV, represents the damping matrix of the AUV, express dimensional real matrix; Indicates gravity and buoyancy The resultant force matrix of the longitudinal velocity, lateral velocity, and yaw angular velocity is , the vertical velocity component is ; Represents the coordinate transformation matrix; In the four-degree-of-freedom dynamics and kinematics model of AUV, a new state vector is introduced ,in , Respectively represent the momentum vector and position vector of the system; define Hamiltonian system and Hamiltonian function , convert the AUV model into the following PCH system form: (4) in, is the equivalent Coriolis centripetal force matrix of the AUV model, is a zero matrix with matching dimensions, is the equivalent damping matrix, , ; I represents the identity matrix with matching dimensions; , represents the system input after considering the control input saturation; is the sum of equivalent parameter uncertainty and time-varying ocean current disturbance, For the matrix The inverse of .

3. The AUV control method based on a neural network and a port-controlled Hamiltonian system as claimed in claim 2, characterized in that: Designing the Goal of a Tracking Controller , represents the supremum of the steady-state error; Assume that the momentum vector of the AUV is and the position vector is directly measured in real time, and Its effect on time The first derivative of are bounded, reference trajectory And about time The first derivative of and the second derivative are bounded, that is , , , They represent the desired longitudinal displacement, lateral displacement, vertical displacement, and yaw angle of the AUV, respectively. is a known positive constant; the momentum vector of the ideal system , is the positive constant matrix to be designed; considering the initial value and reference value restrictions of the actual system model itself, there is a finite positive constant satisfy , , is the Euclidean norm of the vector, represents the supremum of the norm; Defining system state error The time derivative is , using control The desired closed-loop system to be achieved is: (5) in, , , is an ideal non-negative definite dissipation matrix; choose the desired energy function for: (6) in, is the positive definite constant matrix to be designed; thus the following state error equation is obtained: (7) in, is the sum of the system's parameter uncertainty and time-varying ocean current disturbances without considering The control force matrix when the control input is saturated.

4. The AUV control method based on a neural network and a port-controlled Hamiltonian system as claimed in any one of claims 1 to 3, characterized in that: Defining vectors , the ideal system momentum vector As filter output, the following filter is constructed: (8) in, , is a positive constant; represents the first derivative; is the positive definite constant matrix that needs to be designed.

5. The AUV control method based on a neural network and a port-controlled Hamiltonian system as claimed in claim 4, characterized in that: Defining Filter Error , according to the state error equation, the controller of the PCH system is as follows: (9)。 6. The AUV control method based on a neural network and a port-controlled Hamiltonian system as described in any one of claims 1 to 3, characterized in that The neural network adaptation rate is: (10) in, and is the normal number to be designed, represents the radial basis function, estimating the error ,and , , is the Frobenius norm, and is a positive number, satisfying is a normal number, is the absolute value operation; the disturbance control force of the neural network fitting part is recorded as .

7. The AUV control method based on a neural network and a port-controlled Hamiltonian system as claimed in claim 3, characterized in that: Select the Lyapunov function , , , , , is the trace of the matrix; According to the controller of PCH system and neural network adaptation rate : (11) in, , To satisfy A positive constant, where ; The controller of the AUV model in the form of PCH system is analyzed under the condition of model parameter uncertainty, the sum of time-varying ocean current disturbance d(x) and control input saturation. The boundedness condition of the closed-loop system error is: Situation (1) When hour, ,remember , rewrite formula (11) as , ,and ; Situation (2): hour, , we can get: ,therefore, ,in , and there is ; In summary, by selecting parameters The value of makes the inequality , , Established, Controller Ensure the boundedness of the closed-loop system error.

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