A preset time adaptive tracking control method of an autonomous underwater vehicle

Abstract

The present application belongs to the technical field of autonomous underwater vehicle control, and relates to a preset time adaptive tracking control method for autonomous underwater vehicle. The present application firstly establishes a three-degree-of-freedom dynamic model of the autonomous underwater vehicle, constructs a non-time-varying scale function for preset time coordinate transformation, realizes preset time control through the method of non-time-varying scale function coordinate transformation, reduces the complexity of the controller design process, and ensures that the tracking error can converge to a small neighborhood of the origin within the preset time without relying on the initial conditions; the MTN approximation technique is combined with the adaptive backstepping method to develop a novel adaptive network control scheme; the Lyapunov stability theory is used to prove that all signals in the closed-loop system remain bounded, and the rationality of the proposed scheme is verified through simulation. The method of the present application reduces the complexity of the controller design process while ensuring the stability of the system.

Description

Technical Field

[0001] This invention belongs to the field of autonomous underwater vehicle (AUV) control technology, specifically relating to a preset time adaptive tracking control method for autonomous underwater vehicles. Background Technology

[0002] In recent years, due to the increasing demand for marine resource development and marine environmental protection, autonomous underwater vehicles (AUVs), as core equipment for marine exploration and operations, have demonstrated significant technological advantages in fields such as seabed topography mapping, environmental monitoring, and resource exploration. However, due to the strong nonlinearity and time-varying characteristics of the marine environment, AUVs face severe challenges in actual operations. First, the dynamic model of the vehicle exhibits significant parameter uncertainties, and its hydrodynamic parameters are easily affected by ocean current disturbances and carrier deformation, resulting in drift. Second, in complex marine environments, the vehicle needs to achieve accurate trajectory tracking in unknown dynamic scenarios, which places extremely high demands on the real-time response capability and environmental adaptability of the control system. Traditional control methods often struggle to balance preset time constraints with computational complexity optimization, leading to significant performance bottlenecks in controllers during practical engineering applications.

[0003] To address the model uncertainties and dynamic environmental disturbances in the tracking and control of autonomous underwater vehicles, while also considering multiple performance indicators such as control accuracy, computational efficiency, and real-time performance, it is necessary to construct a preset time control strategy based on the backstepping framework.

[0004] Based on this, the present invention designs an adaptive compensation mechanism with time-varying gain characteristics and combines it with multidimensional Taylor network (MTN) approximation technology to identify and compensate for unknown dynamics online, thereby achieving controller parameter self-tuning and computational complexity optimization while ensuring global stability. Summary of the Invention

[0005] This invention addresses the tracking control problem and external disturbance problem of autonomous underwater vehicle (AUV) systems with model uncertainty and nonlinear characteristics. It proposes a preset time adaptive tracking control method for AUVs. This method is an AUV preset time tracking control method based on multidimensional Taylor network approximation technology, which breaks through the limitations of existing tracking control schemes and effectively solves the problem of comprehensive handling of system nonlinearity and uncertainty.

[0006] The technical solution of this invention is:

[0007] This invention provides a preset time adaptive tracking control method for an autonomous underwater vehicle, comprising the following steps:

[0008] (1) Based on the physical model of the autonomous underwater vehicle (AUV) and considering the multi-source interference factors in the marine environment, the three-degree-of-freedom control equations of the AUV are constructed.

[0009] (2) Construct a preset time-invariant scaling function This function implements the function from the domain. to the value range The mapping, The specific form of expression is:

[0010] ;

[0011] in, and They are preset times and any positive constants, respectively. ;

[0012] (3) For the desired trajectory vector Define the tracking error vector and Based on the backstepping technique, the first Lyapunov function is constructed. And based on the time-varying scaling function of step (2) Design virtual control signal vector ;

[0013] in, They are respectively in The desired trajectory components on the axis, This represents the position vector of the AUV in the Earth-fixed reference frame, i.e., the actual trajectory of the AUV. They are respectively in The actual trajectory components on the axis, , They represent surges respectively. ,swing and undulations The three-degree-of-freedom velocity vector, For virtual control signal vectors, Let be the Jacobian matrix from the fixed object reference frame to the Earth-fixed reference frame. For the designed positive definite matrix, The desired trajectory vector The first derivative;

[0014] (4) Based on step (3), construct the second Lyapunov function. ,Will Its first derivative is obtained by taking the derivative with respect to time. And by using the inequality scaling technique, we obtain ;

[0015] in, , For an unknown continuous nonlinear function, Represents the system's inertia matrix. For design parameters, The roll angle in the Earth-fixed reference frame. for The estimate, for The estimation error, and For the controller and adaptive law that urgently need to be designed;

[0016] (5) Based on the unknown continuous function in step (4) It is approximated using the multidimensional Taylor network (MTN) approximation technique, i.e. ;

[0017] in, These are the input vector and approximation error of the MTN, respectively. for The upper realm, Let be the weight vector of MTN. This represents the intermediate input layer of MTN;

[0018] (6) Based on step (5), design a preset time adaptive controller using backstepping technology. Preset time adaptive law ;

[0019] in, For the designed positive definite matrix, , For design constants, ;

[0020] (7) Based on step (6), construct the Lyapunov function of the entire control system. Stability analysis was performed on the autonomous underwater vehicle system to ensure that all closed-loop signals were bounded and that the tracking error converged to the vicinity of the origin within a preset time.

[0021] Furthermore, in step (1), the three-degree-of-freedom governing equations of the AUV are:

[0022] ;

[0023] in, This represents the position vector of the AUV in the Earth-fixed reference frame. They are respectively in The actual trajectory components on the axis; The attitude vector described by Euler angles, i.e., the roll angle in the ground-fixed reference frame. Pitch angle and yaw angle ; Let be the Jacobian matrix from the fixed object reference frame to the Earth-fixed reference frame. These represent the three-degree-of-freedom velocity vectors of surge u, sway v, and undulation r, respectively. Represents the system's inertia matrix. It is the bulk mass of the AUV. , ,and These represent the additional mass generated by the AUV during surge u, sway v, and undulation r, respectively. The damping matrix is ​​the fluid dynamics matrix. , , They represent the linear damping coefficients, , , These are the secondary damping coefficients for surge u, sway v, and undulation r, respectively; It is the restoring force vector; where, and These are gravity and buoyancy, respectively. It is the control force vector; This represents multiple sources of disturbance in the ocean.

[0024] Furthermore, in step (2), Given the designed preset time scale function, if the constructed entire control system is a positive definite Lyapunov function... satisfy ,So exist Bounded above; within which, and All are constants, Abbreviated as Its specific form is as follows:

[0025] ;

[0026] in, and They are preset times and any positive constants, respectively. .

[0027] Furthermore, in step (4), MTN is used to approximate an unknown continuous nonlinear function, assuming... It is defined on compact sets If an unknown continuous function is defined on a given surface, then for any constant... There exists an MTN that can approximate this unknown function. ,Right now

[0028] ;

[0029] in, and These are the input vector and weight vector of the MTN, respectively. This represents the intermediate input layer of MTN. To approximate the error and satisfy .

[0030] Furthermore, in step (7), the Lyapunov function of the entire control system is constructed. :

[0031] ;

[0032] calculate Regarding time The first derivative of is obtained using inequality techniques:

[0033] ;

[0034] in, , Let represent the smallest eigenvalue of matrix *. It is the identity matrix;

[0035] Therefore, it can be concluded that all closed-loop signals in the control system are bounded, and the tracking error... At the preset time It converges inward to near the origin.

[0036] The beneficial effects of this invention are:

[0037] (1) This invention develops a novel preset time adaptive tracking control scheme for autonomous underwater vehicles, proposing a completely new preset time scale function to achieve preset time control. The method of this invention reduces the complexity of the controller design process while ensuring the stability of the system.

[0038] (2) First, this invention innovatively adopts MTN neural network approximation technology to construct a preset time tracking control framework. Through nonlinear mapping characteristics, it performs high-precision modeling of the complex dynamic characteristics of the system, significantly reducing the controller structure complexity brought about by the traditional time-varying scale function coordinate transformation method, making the algorithm easier to implement in engineering. Second, for the three-degree-of-freedom motion coupling characteristics of autonomous underwater vehicles, an adaptive compensation mechanism is designed to offset the influence of unmodeled dynamics and external disturbances. The preset time stability and tracking error convergence of the closed-loop system are rigorously proved with the help of Lyapunov theory. Finally, simulation experiments verify the superior performance of the proposed method in terms of tracking accuracy, anti-interference ability and dynamic response speed. Its control input curve is smooth and no high-frequency chattering phenomenon occurs, verifying the actual feasibility of the scheme. Attached Figure Description

[0039] Figure 1This is a model reference diagram of the AUV in this invention.

[0040] Figure 2 This is a structural diagram of the MTN in this invention.

[0041] Figure 3 This is a three-dimensional trajectory tracking diagram of the AUV in this invention.

[0042] Figure 4 This is a tracking error diagram of the AUV in this invention.

[0043] Figure 5 This is a control input response diagram of the AUV in this invention.

[0044] Figure 6 This is a position tracking diagram under two different control schemes in this invention. Detailed Implementation

[0045] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0046] To further understand the present invention, it will be further described in conjunction with the accompanying drawings and embodiments.

[0047] Example 1

[0048] This embodiment provides a preset time adaptive tracking control method for an autonomous underwater vehicle, including the following steps:

[0049] (1) Based on the physical model of the autonomous underwater vehicle (AUV) and considering multi-source interference factors in the marine environment, a model is constructed as follows: Figure 1 The three-degree-of-freedom control equations for the AUV are shown below;

[0050] (1)

[0051] in, This represents the position vector of an autonomous underwater vehicle in a geofixed reference frame. They are respectively in The actual trajectory components on the axis; The attitude vector described by Euler angles, i.e., the roll angle in the ground-fixed reference frame. Pitch angle and yaw angle .

[0052] Let be the Jacobian matrix from the fixed object reference frame to the Earth-fixed reference frame, which is a positive definite matrix and satisfies .

[0053] These represent the three-degree-of-freedom velocity vectors for surge u, sway v, and undulation r, respectively.

[0054] Represents the system's inertia matrix; where, It refers to the mass of the underwater vehicle itself. , ,and These represent the additional mass that a vehicle generates during surges, swaying, and undulations due to the presence of surrounding fluids.

[0055] Here, is the fluid dynamics damping matrix; where, , , They represent the linear damping coefficients, , , These are the secondary damping coefficients for surge, sway, and undulation, respectively.

[0056] It is the restoring force vector; where, and These are gravity and buoyancy, respectively.

[0057] It is the control force vector. This represents multiple sources of disturbance in the ocean.

[0058] (2) Construct a preset time-invariant scaling function If a positive definite Lyapunov function satisfy ,exist It is bounded on top. Within it, Preset time scale function (PTSF). and All are constants.

[0059] To simplify the calculation process, Abbreviated as .

[0060] Preset time scale function ,Right now To from the domain to the value range A mapping, which is a constructed preset time-scale function, is as follows: Specific forms of expression:

[0061] (2)

[0062] in, and They are preset time and positive numbers respectively. .

[0063] (3) For the desired trajectory vector Define the tracking error vector and Based on the backstepping technique, the first Lyapunov function is constructed. And based on the time-varying scaling function of step (2) Design virtual control signal vector ;

[0064] in, They are respectively in The desired trajectory components on the axis, They are respectively in The actual trajectory components on the axis, , For virtual control signal vectors, For the designed positive definite matrix, The desired trajectory vector The first derivative. The specific process is as follows:

[0065] For the desired trajectory vector and tracking error vector Propose coordinate transformation

[0066] (3)

[0067] The first Lyapunov function is

[0068] (4)

[0069] Based on system (1) and coordinate transformation (3), we can obtain

[0070] (5)

[0071] calculate Regarding time The first derivative and, combined with equation (5), have

[0072] (6)

[0073] Based on the backstepping method design process, design the virtual control signal vector in the following form.

[0074] (7)

[0075] in, This is the positive definite matrix designed.

[0076] virtual control signal vector Substituting into the first derivative of the Lyapunov function From this, we can obtain

[0077] (8)

[0078] (4) Based on step (3), construct the second Lyapunov function. ,Will Its first derivative is obtained by taking the derivative with respect to time. And by using the inequality scaling technique, we obtain ;

[0079] in, , For an unknown continuous nonlinear function, for The estimate, for The estimation error, and The controller and adaptive law that urgently need to be designed are as follows:

[0080] The second Lyapunov function is

[0081] (9)

[0082] in, for The estimation error and . The 2-norm of * Let be the weight vector of MTN.

[0083] According to coordinate transformation formula (3), calculate Regarding time The derivative is

[0084] (10)

[0085] The specific calculation process of the time derivative is as follows:

[0086] (11)

[0087] in, .

[0088] calculate Regarding time The first derivative and combined with the above formula, we get

[0089] (12)

[0090] (5) Based on the unknown continuous function in step (4) The multidimensional Taylor network (MTN) approximation technique is used to approximate it. The specific steps are as follows:

[0091] From step (4), we can obtain

[0092] (13)

[0093] Obviously, For an unknown continuous nonlinear function, approximation using MTN. ,Right now

[0094] (14)

[0095] in, and These are the input vector and approximation error of the MTN, respectively. for The upper realm, Let be the weight vector of MTN. This represents the intermediate input layer of MTN;

[0096] (6) Based on step (5), design a preset time adaptive controller using backstepping technology. Preset time adaptive law The specific process is as follows:

[0097] According to equation (14) and Young's inequality, we can obtain

[0098] (15)

[0099] in, This is a design constant.

[0100] Design controller for

[0101] (16)

[0102] Substitute to get

[0103] (17)

[0104] Based on the backstepping method design process, design the adaptive law. for

[0105] (18)

[0106] in, and All are design constants.

[0107] Substituting the controller and adaptive law into the first derivative of the Lyapunov function In the middle, for

[0108] (19)

[0109] According to the Cauchy-Schwarz inequality, for ,have Therefore, combining equation (14), the following equation holds true.

[0110] (20)

[0111] Therefore, the first derivative of the second Lyapunov function can be further simplified to:

[0112] (twenty one)

[0113] Therefore, a preset time adaptive controller Preset time adaptive law They were designed as (16) and (18) respectively.

[0114] (16)

[0115] (18)

[0116] (7) Based on step (6), construct the Lyapunov function of the entire control system. Stability analysis was performed on the autonomous underwater vehicle system to ensure that all closed-loop signals were bounded and that the tracking error converged to near the origin within a preset time. The specific process is as follows:

[0117] Choose a Lyapunov function of the following form

[0118] (twenty two)

[0119] calculate Regarding time The first derivative of can be obtained

[0120] (twenty three)

[0121] According to Young's inequality and

[0122] (twenty four)

[0123] Substituting (24) into (23), we get

[0124] (25)

[0125] in, , Let represent the smallest eigenvalue of matrix *. It is an identity matrix.

[0126] According to the presupposed time theory, if a positive definite Lyapunov function satisfy ,So exist It is bounded on top. Within it... For the preset time scale function, and All are constants. The constructed preset timescale function takes the following form:

[0127] (2)

[0128] in, and They are preset times and any positive constants, respectively. .

[0129] Therefore, the tracking error of the system can be determined. Can be set at a preset time It converges inward to near the origin.

[0130] Application Example 1

[0131] System setup: To demonstrate the effectiveness of the designed preset time adaptive tracking control scheme, the virtual controller and the actual controller are applied to the autonomous underwater vehicle system.

[0132] The detailed physical parameters of the aircraft are as follows: , , , , , , , , , , , , , , .

[0133] The desired trajectory vector is The initial conditions are as follows: Ocean disturbance is The control parameters are as follows: The set time is .

[0134] Simulation results are as follows Figures 3 to 5 As shown, Figure 3 and Figure 4 The effects of position tracking and tracking error on autonomous underwater vehicles are respectively presented. Figure 5 This is a schematic diagram for controlling the input response.

[0135] in, Figure 3 This invention demonstrates that the control strategy proposed in this invention can ensure that the autonomous underwater vehicle system operates within a preset time. The internal tracking of the desired trajectory indicates that the control scheme is feasible. Figure 4 It can be seen that the tracking error can gradually approach the origin within a preset time. It should be noted that... Figure 5 The results show that the control law designed in this invention exhibits chattering. This is because, in simulations, the control gain is gradually increased to reduce trajectory tracking errors, but such gain adjustments may induce chattering behavior in the control law. However, in many practical applications, this level of chattering is acceptable, especially considering the requirement to improve trajectory tracking accuracy. In summary, the control scheme proposed in this invention ensures that the autonomous underwater vehicle system can quickly and accurately track the desired trajectory while guaranteeing the boundedness of the closed-loop signal.

[0136] Comparative Example 1

[0137] To highlight the advantages of the control strategy based on MTN approximation technology proposed in this invention, a comparative experiment was designed to compare the tracking performance of the MTN-based control scheme and the RBFNN-based control scheme. The relevant results are presented in… Figure 6 The experimental results clearly show that although both control schemes exhibit good tracking performance, the MTN-based control scheme of this invention is better and can track the desired trajectory more effectively.

[0138] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, alterations, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A preset-time adaptive tracking control method for an autonomous underwater vehicle, characterized in that, Includes the following steps: (1) Based on the physical model of the autonomous underwater vehicle (AUV) and considering the multi-source interference factors in the marine environment, the three-degree-of-freedom control equations of the AUV are constructed. (2) Construct a preset time-invariant scaling function This function implements the function from the domain. to the value range The mapping, The specific form of expression is: ； in, and They are preset times and any positive constants, respectively. ; (3) For the desired trajectory vector Define the tracking error vector and Based on the backstepping technique, the first Lyapunov function is constructed. And based on the time-varying scaling function of step (2) Design virtual control signal vector ; in, They are respectively in The desired trajectory components on the axis, This represents the position vector of the AUV in the Earth-fixed reference frame, i.e., the actual trajectory of the AUV. They are respectively in The actual trajectory components on the axis, They represent surges respectively. ,swing and undulations The three-degree-of-freedom velocity vector, For virtual control signal vectors, Let be the Jacobian matrix from the fixed object reference frame to the Earth-fixed reference frame. For the designed positive definite matrix, The desired trajectory vector The first derivative; (4) Based on step (3), construct the second Lyapunov function. ,Will Its first derivative is obtained by taking the derivative with respect to time. And by using the inequality scaling technique, we obtain ; in, , For an unknown continuous nonlinear function, Represents the system's inertia matrix. For design parameters, The roll angle in the Earth-fixed reference frame. for The estimate, for The estimation error, and For the controller and adaptive law that urgently need to be designed; (5) Based on the unknown continuous function in step (4) It is approximated using the multidimensional Taylor network (MTN) approximation technique, i.e. ; in, These are the input vector and approximation error of the MTN, respectively. for The upper realm, Let be the weight vector of MTN. This represents the intermediate input layer of MTN; (6) Based on step (5), design a preset time adaptive controller using backstepping technology. Preset time adaptive law ; in, For the designed positive definite matrix, , For design constants, ; (7) Based on step (6), construct the Lyapunov function of the entire control system. Stability analysis was performed on the autonomous underwater vehicle system to ensure that all closed-loop signals were bounded and that the tracking error converged to the vicinity of the origin within a preset time.

2. The preset time adaptive tracking control method for autonomous underwater vehicles according to claim 1, characterized in that, In step (1), the three-degree-of-freedom governing equations for the AUV are: ； in, This represents the position vector of the AUV in the Earth-fixed reference frame. They are respectively in The actual trajectory components on the axis; The attitude vector described by Euler angles, i.e., the roll angle in the ground-fixed reference frame. Pitch angle and yaw angle ; Let be the Jacobian matrix from the fixed object reference frame to the Earth-fixed reference frame. They represent surges respectively. u ,swing v and undulations r The three-degree-of-freedom velocity vector; Represents the system's inertia matrix. It is the bulk mass of the AUV. These represent the AUV's surge protection. u ,swing v and undulations r The additional mass generated in the process; Here is the fluid dynamics damping matrix. They represent the linear damping coefficients, surge u ,swing v and undulations r The secondary damping coefficient; It is the restoring force vector; where, and These are gravity and buoyancy, respectively. It is the control force vector; This represents multiple sources of disturbance in the ocean.

3. The preset time adaptive tracking control method for autonomous underwater vehicles according to claim 1, characterized in that, In step (2), Given the designed preset time scale function, if the constructed entire control system is a positive definite Lyapunov function... satisfy ,So exist Bounded above; within which, and All are constants, Abbreviated as Its specific form is: ； in, and They are preset times and any positive constants, respectively. .

4. The preset time adaptive tracking control method for autonomous underwater vehicles according to claim 1, characterized in that, In step (5), MTN is used to approximate the norm of an unknown continuous nonlinear function, assuming... It is defined on compact sets If an unknown continuous function is defined on a given surface, then for any constant... There exists an MTN that can approximate this unknown continuous function. ,Right now ； in, and These are the input vector and weight vector of the MTN, respectively. This represents the intermediate input layer of MTN. To approximate the error and satisfy .

5. The preset time adaptive tracking control method for autonomous underwater vehicles according to claim 1, characterized in that, In step (7), the Lyapunov function of the entire control system is constructed. : ； calculate Regarding time The first derivative of is obtained using inequality techniques: ； in, Let represent the smallest eigenvalue of matrix *. It is the identity matrix; Therefore, it can be concluded that all closed-loop signals in the control system are bounded, and the tracking error... At the preset time It converges inward to near the origin.

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