Self-adaptive tracking control method for autonomous underwater vehicle with input hysteresis characteristic

Abstract

The invention relates to a preset time self-adaptive tracking control method for an autonomous underwater vehicle, which comprises the following steps of: firstly, introducing a Bouc-Wen hysteresis model aiming at the hysteresis input problem encountered when the vehicle runs in a complex marine environment, and carrying out linear decomposition on the model to weaken the constraint of hysteresis nonlinearity on the design of a controller and reduce the influence of the hysteresis nonlinearity on the stability of a system; secondly, the accuracy of three-dimensional position tracking of the aircraft is improved by considering dynamic multi-target constraints; the problem of multiple time-varying asymmetric constraints is solved by designing a unified asymmetric time-varying obstacle function for the three-dimensional position of an aircraft and designing novel coordinate transformation; and finally, combining the time-varying scaling function with a multi-dimensional Taylor network approximation technology to design a controller and an adaptive law of the system. The method achieves the preset time tracking control of the autonomous underwater vehicle under the dynamic multi-target constraint, and guarantees that the tracking error can be converged to the vicinity of an original point within any preset time. A simulation result proves the effectiveness of the designed controller.

Description

Technical Field

[0001] This invention relates to the field of autonomous underwater vehicle (AUV) control technology, specifically a preset-time adaptive tracking control method for AUVs under input hysteresis and dynamic multi-objective constraints. Background Technology

[0002] In recent years, with the increasing demands for precision, efficiency, and safety in fields such as marine scientific research, environmental monitoring, and rescue, the control problem of autonomous underwater vehicles (AUVs) has gradually become a research hotspot. However, AUVs face numerous challenges in practical applications. On the one hand, trajectory tracking control, as a core task, must simultaneously address time and space constraints, directly affecting mission performance. On the other hand, the existence of hysteresis also severely impacts control accuracy. Furthermore, when operating in complex environments, AUVs must cope with multiple constraints to ensure mission safety and accuracy. These problems make traditional control strategies insufficient to meet the operational needs of today's complex marine environments.

[0003] To address the complex and ever-changing marine environment and mission requirements, while simultaneously considering the three core indicators of time efficiency, control precision, and system safety, an innovative trajectory tracking control strategy for autonomous underwater vehicles (AUVs) is urgently needed. Current traditional control strategies generally have limitations: they either struggle to effectively handle the interference of hysteresis input on control precision, or they cannot guarantee mission stability under dynamic multi-objective constraints, and they are even less able to achieve high-precision trajectory tracking within a preset timeframe, resulting in insufficient adaptability in complex marine operational scenarios. Therefore, the new strategy needs to overcome existing technological bottlenecks, simultaneously meeting the timeliness requirements of a preset timeframe and the high-precision requirements of trajectory tracking under the dual influence of hysteresis input and dynamic multi-objective constraints, providing core technological support for the efficient and safe operation of AUVs in key areas such as marine scientific research, environmental monitoring, and emergency rescue. Based on this, researching trajectory tracking control of AUVs under dynamic multi-objective constraints not only fills current technological gaps but also has significant practical implications for promoting the intelligent development of marine engineering equipment. Summary of the Invention

[0004] The purpose of this invention is to provide a preset time adaptive tracking control method for autonomous underwater vehicles (AUVs), which aims to solve the problems of existing technologies that are difficult to effectively handle the interference of hysteresis input on control accuracy, cannot ensure mission stability under dynamic multi-objective constraints, and are difficult to achieve high-precision trajectory tracking within a preset time, resulting in insufficient adaptability in complex marine environments and failure to meet the requirements of efficient and safe AUV operations.

[0005] This invention is implemented as follows: an adaptive tracking control method for an autonomous underwater vehicle under input hysteresis and dynamic multi-objective constraints, comprising the following steps: Step 1: Based on the dynamic model of the autonomous underwater vehicle (AUV), and considering the Bouc-Wen type hysteresis effect, construct the AUV control equations with hysteresis input; Step 2: Perform linear decomposition on the Bouc-Wen hysteresis model in the control equations to reduce the impact of hysteresis nonlinearity on controller design and system stability; Step 3: Define the multi-objective function ,satisfy ,in and To construct a unified asymmetric time-varying barrier function for asymmetric time-varying constraint functions. The dynamic multi-objective constraint problem is transformed into Boundedness problem; Step 4: For the desired trajectory vector Design a new coordinate transformation based on dynamic multi-objective constraints and ;in, They represent surges respectively. ,swing and undulations The three-degree-of-freedom velocity vector, They are respectively in The desired trajectory components on the axis, , , and For design parameters, , , , , , It is a virtual control signal vector that urgently needs to be designed; Step 5: Based on Step 4, construct the Lyapunov function. and By combining backstepping technology and multi-dimensional Taylor network (MTN) approximation technology, an adaptive preset-time virtual control signal with input hysteresis and dynamic multi-objective constraints is designed. Actual controller And adaptive law ; Step 6: Based on Step 5, construct the Lyapunov function for the entire control system, including tracking error and adaptive estimation error. Combining the preset time controller and adaptive law designed in step 5, the Lyapunov function is used... time derivative The closed-loop system state is regulated; the unified asymmetric time-varying obstacle function introduced in step 3 is synchronously associated with the coordinate transformation result in step 4, so that the position, velocity, control input and adaptive estimate of the autonomous underwater vehicle are all bounded within a preset time, and the tracking error converges to the neighborhood of the origin and satisfies multiple dynamic target constraints.

[0006] In this invention, the model diagram of the AUV is as follows: Figure 1 As shown.

[0007] As a further improvement to the present invention, step 1 specifically comprises: The control equations for the AUV with hysteresis input are described as follows: (1) in, This represents the position vector of an autonomous underwater vehicle in a geofixed reference frame. Earth-fixed reference system The actual position 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 ;

[0008] 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 They represent surges respectively. ,swing and undulations The three-degree-of-freedom velocity vector; Represents the system's inertia matrix; where, It refers to the mass of the underwater vehicle itself. , and These represent the additional mass generated by the vehicle during surges, rolls, and undulations due to the presence of surrounding fluids. Let be the fluid dynamic damping matrix, where and They represent the linear damping coefficients, , and These are the secondary damping coefficients for surge, sway, and undulation, respectively. It is the restoring force vector, where, and They are gravity and buoyancy, respectively. It controls the force vector and hysteresis input. For system control input and hysteresis output, This represents marine disturbance.

[0009] As a further improvement of the present invention, step 2 specifically includes: The Bouc-Wen hysteresis model is linearly decomposed into the following form: (2) in, It is a hysteresis input. Hysteresis output, and It is a parameter that satisfies , These are three-dimensional auxiliary variables that satisfy the following equation: (3) in, , , and Let be the hysteresis coefficient, and have and This is valid. Additionally, three-dimensional vectors... Conditions met: (4) in, It is a constant. Representing vectors Or matrix The 2-norm.

[0010] As a further improvement to the present invention, step 3 specifically comprises: Defined multi-objective function for , , Its satisfaction ,and These are the weighting coefficients. It is an integer; and All are asymmetric time-varying constraint functions; Constructing a unified asymmetric time-varying barrier function Its specific expression is: (5) in, , and The design parameters must satisfy the following: and .if or ,So It tends to infinitesimal; therefore when When it is bounded, The constraints will be satisfied. Therefore, the dynamic multi-objective constraint problem is transformed into The problem of boundedness.

[0011] As a further improvement to the present invention, step 5 specifically comprises: Construct the first Lyapunov function The virtual control signal vector is designed as follows: ; in, The design matrix is ​​positive definite. The preset time-invariant scaling function is expressed as follows: And there are , For preset time, constant satisfy: .

[0012] Construct a second Lyapunov function, in the following form: (6) in, For design parameters, ,and for The estimate, To approximate the error; right Taking the time derivative yields And using the inequality scaling technique, we obtain: (7) in, ; For an unknown continuous nonlinear function, It can be approximated by a multidimensional Taylor network MTN. ,in, For function terms And Multidimensional Taylor Network Approximation error between them; for The upper realm, Let be the weight vector of MTN. This represents the intermediate input layer of MTN; Based on backstepping technology, an adaptive preset time controller with input hysteresis and dynamic multi-objective constraints is designed. And adaptive law The specific expression is as follows: (8) (9) in, The design constant matrix is ​​positive definite. , For design parameters; As a further improvement to the present invention, step 6 specifically comprises: Construct the Lyapunov function for the entire control system : (10) For Lyapunov functions Find the time derivative and use the inequality scaling technique to obtain: (11) in, ; Given a third-order identity matrix; combining this with a preset time scale function, solving the above equation yields: (12) Based on the above formula, we can conclude that... , and All within the preset time The system remains bounded; consequently, all signals in the closed-loop system remain bounded within a preset time period.

[0013] Compared with the prior art, the beneficial effects of the present invention are: 1. This invention first addresses the hysteresis input problem faced by autonomous underwater vehicles (AUVs) operating in complex marine environments by innovatively introducing the Bouc-Wen hysteresis model and performing linear decomposition, which facilitates the design of a tracking controller and significantly reduces the impact of hysteresis on system stability. Secondly, to improve the accuracy of three-dimensional position tracking for AUVs, dynamic multi-objective constraints are considered. A unified asymmetric time-varying obstacle function is designed for the AUV's three-dimensional position, and combined with a novel coordinate transformation, the problem of multiple time-varying asymmetric constraints is successfully solved.

[0014] 2. This invention combines time-varying scaling functions with time-varying multidimensional Taylor network approximation techniques to develop an adaptive preset time trajectory tracking control method. This method not only achieves preset time trajectory tracking control of autonomous underwater vehicles under dynamic multi-objective constraints, but also ensures that the tracking error converges to near the origin within any preset time. Simulation results verify the effectiveness of the designed controller, demonstrating its applicability and superior performance in complex marine environments. Attached Figure Description

[0015] Figure 1 This is a model diagram of the AUV in this invention.

[0016] Figure 2 This is a tracking error diagram for case 1 of the present invention with a preset time of 2 seconds.

[0017] Figure 3 This is a tracking error diagram for scenario 2 in this invention, where the preset time is 2 seconds.

[0018] Figure 4 This is a tracking error diagram for scenario 3 of the present invention with a preset time of 2 seconds.

[0019] Figure 5 This is a tracking effect diagram for scenario 1 of the present invention with a preset time of 2 seconds.

[0020] Figure 6 This is a tracking effect diagram for scenario 2 in this invention, where the preset time is 2 seconds.

[0021] Figure 7 This is a tracking effect diagram for scenario 3 of the present invention with a preset time of 2 seconds.

[0022] Figure 8 In this invention The dynamic multi-objective constraint curve diagram.

[0023] Figure 9 In this invention The dynamic multi-objective constraint curve diagram.

[0024] Figure 10 In this invention The dynamic multi-objective constraint curve diagram.

[0025] Figure 11 The diagram shows the control input signal and hysteresis output curves for case 1. Figure 12 The control input signal and hysteresis output curves are shown in case 2. Figure 13 The control input signal and hysteresis output curves are shown in case 3. Figure 14 The response diagrams of the velocity vectors are shown for three different conditions; Figure 15 This is a tracking error diagram for scenario 1 of the present invention with a preset time of 5 seconds; Figure 16 This is a tracking error diagram for scenario 2 of the present invention with a preset time of 5 seconds; Figure 17 This is a tracking error diagram for scenario 3 in this invention with a preset time of 5 seconds; Figure 18 This is a tracking effect diagram for scenario 1 of the present invention with a preset time of 5 seconds; Figure 19This is a tracking effect diagram for scenario 2 of the present invention with a preset time of 5 seconds; Figure 20 This is a tracking effect diagram for scenario 3 of the present invention with a preset time of 5 seconds.

[0026] Figure 21 This is a comparison chart of the tracking effects under constrained and unconstrained conditions in this invention. Detailed Implementation

[0027] The following description, in conjunction with the accompanying drawings and specific embodiments, provides further details: An adaptive tracking control method for an autonomous underwater vehicle under input hysteresis and dynamic multi-objective constraints includes the following steps: Step 1: Based on the dynamic model of the autonomous underwater vehicle (AUV), and considering the Bouc-Wen type hysteresis effect, construct the AUV control equations with hysteresis input; Step 2: Perform linear decomposition on the Bouc-Wen hysteresis model in the control equations to reduce the impact of hysteresis nonlinearity on controller design and system stability; Step 3: Define the multi-objective function ,satisfy ,in and For non Symmetric time-varying constraint functions, constructing a unified asymmetric time-varying barrier function The dynamic multi-objective constraint problem is transformed into Boundedness problem; Step 4: For the desired trajectory vector A novel coordinate transformation is designed based on dynamic multi-objective constraints. and ;in, They represent surges respectively. swing and undulations The three-degree-of-freedom velocity vector, They are respectively in The desired trajectory components on the axis, , , , and For design parameters, , , , , , , , It is a virtual control signal vector that urgently needs to be designed; Step 5: Based on Step 4, construct the Lyapunov function. and By combining backstepping technology and multi-dimensional Taylor network (MTN) approximation technology, an adaptive preset-time virtual control signal with input hysteresis and dynamic multi-objective constraints is designed. Actual controller And adaptive law ; Step 6: Based on Step 5, construct the Lyapunov function for the entire control system, including tracking error and adaptive estimation error. Combining the preset time controller and adaptive law designed in step 5, the Lyapunov function is used... time derivative The closed-loop system state is regulated; the unified asymmetric time-varying obstacle function introduced in step 3 is synchronously associated with the coordinate transformation result in step 4, so that the position, velocity, control input and adaptive estimate of the autonomous underwater vehicle are all bounded within a preset time, and the tracking error converges to the neighborhood of the origin and satisfies multiple dynamic target constraints.

[0028] 1. Step 1 includes: The control equations for an AUV with hysteresis input are described as follows: (1) in, This represents the position vector of an autonomous underwater vehicle in a geofixed reference frame. Earth-fixed reference system The actual position 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, which is a positive definite matrix and satisfies They represent surges respectively. swing and undulations The three-degree-of-freedom velocity vector; Represents the system's inertia matrix; where, It refers to the mass of the underwater vehicle itself. , and These represent the additional mass generated by the vehicle during surges, rolls, and undulations due to the presence of surrounding fluids. Let be the fluid dynamic damping matrix, where and They represent the linear damping coefficients, , and These are the secondary damping coefficients for surge, sway, and undulation, respectively. It is the restoring force vector, where, and They are gravity and buoyancy, respectively. It controls the force vector and hysteresis input. Hysteresis output, This represents marine disturbance.

[0029] 2. In step 2: The Bouc-Wen hysteresis model can be used to describe hysteresis nonlinearity, and it can be linearly decomposed into the following form: in, It is a hysteresis input. Hysteresis output, and It is a parameter that satisfies , These are three-dimensional auxiliary variables that satisfy the following equation: (3) in, , , and Let be the hysteresis coefficient, and have and This is valid. Additionally, three-dimensional vectors... Conditions met: (4) in, It is a constant. Representing vectors Or matrix The 2-norm.

[0030] 3. In step 3: Defined multi-objective function for , , Its satisfaction ,and These are the weighting coefficients. It is an integer; and All are asymmetric time-varying constraint functions; Constructing a unified asymmetric time-varying barrier function Its specific expression is: (5) in, , and The design parameters must satisfy the following: and .if or ,So It tends to infinitesimal; therefore when When it is bounded, The constraints will be satisfied. Therefore, the dynamic multi-objective constraint problem is transformed into The problem of boundedness.

[0031] The actual output of the system is recorded as So for For the time derivative, the following equation holds: (13) in, , , .

[0032] 4. Step 4 specifically involves: For the desired trajectory vector A novel coordinate transformation is designed based on dynamic multi-objective constraints. and ;in, They represent surges respectively. swing and undulations The three-degree-of-freedom velocity vector, They are respectively in The desired trajectory components on the axis, , , , and For design parameters, , , , , , , , It is a virtual control signal vector that urgently needs to be designed; 5. Step 5 specifically involves: Step 1: Construct the first Lyapunov function The format is as follows: (14) Taking the time derivative of equation (14), the following equation holds: (15) in, .

[0033] Now, to ensure the feasibility of the control strategy, the following virtual control signal vector is designed. : (16) in, It is a positive definite design matrix.

[0034] right Find the time derivative, and combining it with equation (15), the following equation holds: (17) Substituting equation (16) into equation (17), The time derivative can be expressed in the following form: (18) Step 2: Construct the second Lyapunov function, in the following form: (6) in, For design parameters, ,and for The estimate, This is the approximation error.

[0035] right By taking the time derivative, we can obtain the following equation: (19) in, .

[0036] Obviously, It is a nonlinear function, therefore, It can be approximated by a multidimensional Taylor network, i.e., by the following expression: (20) in, For function terms And Multidimensional Taylor Network The approximation error between them.

[0037] Combination We can obtain the following formula: (twenty one) in, These are design parameters.

[0038] Therefore, the following inequality holds: (twenty two) and then, The time derivative is transformed into the following form: (twenty three) The controller is designed based on the Backstepping method, as detailed below: (8) in, It is a positive definite design constant matrix.

[0039] It can be transformed into the following form: (twenty four) Based on the above derivation, we design an adaptive law of the following form: (9) in, These are design parameters.

[0040] then, It can be transformed into the following form: (25) According to the Cauchy-Schwarz inequality, for ,have If this holds true, we can obtain the following inequality: (26) Item Perform the following processing: (27) It can be rewritten in the following form: (28) 6. Step 6 includes: We choose a Lyapunov function of the following form. : (10) Therefore, for the Lyapunov function To find the time derivative, we have the following inequality: (29) According to the relevant lemmas, the following inequalities hold: (30) The time derivative is expressed in the following form: (31) in, , , It is a third-order identity matrix.

[0041] If the Lyapunov function satisfy ,So exist It is bounded on top. Within it, For preset time, , It is a constant. The preset time scale function satisfies the following equation: (32) And there are and constants satisfy: .

[0042] Based on the above-preset time scale function, we solve for it and obtain: (12) Thus we can conclude that , and All within the preset time The system remains bounded, and consequently, all signals in the closed-loop system remain bounded within a preset time period.

[0043] because If this condition is met, then by simply selecting appropriate control parameters, the tracking error can converge to the origin within a preset time. Furthermore, the controller can simultaneously implement dynamic multi-objective constraints.

[0044] Example Analysis: This invention conducted two experiments: the first was a simulation experiment based on an autonomous underwater vehicle system, aimed at verifying the feasibility of the proposed control method and the rationality of the preset time mechanism; the second was a comparative experiment, aimed at demonstrating that multi-objective constraints can further improve the control performance of the system.

[0045] 1. Verification including the preset time mechanism: To demonstrate the effectiveness of the preset time adaptive tracking control method for the autonomous underwater vehicle (AUV) system, the designed virtual controller and actual controller were applied to the AUV. The detailed model parameters of the system AUV are as follows: The initial value is .

[0046] The required trajectory vector is: ; External ocean disturbances are set as follows: ; The dynamic constraint functions are set as follows: ; The other parameter values ​​are: . Objective function for three-dimensional position Defined in The expressions above are set as follows in the simulation: Scenario 1: ; Scenario 2: ; Scenario 3: .

[0047] Simulation results are as follows Figures 2 to 21 As shown. First, in order to verify the rationality of the preset time mechanism proposed in this invention, different preset times ( The tracking performance under different conditions was compared and analyzed. The tracking error and tracking effect are as follows: Figures 2 to 7 As shown, The tracking error and tracking effect are as follows: Figures 15 to 20 As shown in the simulation diagram, the tracking error converges to near the origin under both preset time settings, indicating that the preset time mechanism is effective. Figures 8 to 10 They explained respectively , and Dynamic multi-objective constraint curves under three conditions. Figures 11-14 The control input and velocity vector are displayed. Clearly, all of the above signals are bounded. Simulation results demonstrate the effectiveness of the control method proposed in this invention.

[0048] 2. Comparative Experiment: A comparative experiment was proposed to evaluate the tracking performance under dynamic multi-objective constraints and without them. The experimental results are as follows: Figure 21 As shown.

[0049] Figure 21 It is clearly shown that although the controller exhibits good tracking performance in both constrained and unconstrained cases, its tracking performance under multi-objective constraints is significantly better than that without constraints. This indicates that considering multi-objective constraints is meaningful for optimizing tracking performance.

[0050] The above are merely preferred embodiments of the present invention and are not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. An adaptive tracking control method for an autonomous underwater vehicle under input hysteresis and dynamic multi-objective constraints, characterized in that, Includes the following steps: Step 1: Based on the dynamic model of the autonomous underwater vehicle (AUV), considering the Bouc-Wen type hysteresis effect, construct the AUV control equation with hysteresis input; Step 2: Perform linear decomposition on the Bouc-Wen hysteresis model in the control equations to reduce the impact of hysteresis nonlinearity on controller design and system stability; Step 3: Define the multi-objective function ,satisfy ,in and For non Symmetric time-varying constraint functions, constructing a unified asymmetric time-varying barrier function The dynamic multi-objective constraint problem is transformed into Boundedness problem; Step 4: For the desired trajectory vector A novel coordinate transformation is designed based on dynamic multi-objective constraints. and ;in, They represent surges respectively. swing and undulations The three-degree-of-freedom velocity vector, They are respectively in The desired trajectory components on the axis, , , , and For design parameters, , , , , , , , It is a virtual control signal vector that urgently needs to be designed; Step 5: Based on Step 4, construct the Lyapunov function. and By combining backstepping technology and multi-dimensional Taylor network (MTN) approximation technology, an adaptive preset-time virtual control signal with input hysteresis and dynamic multi-objective constraints is designed. Actual controller And adaptive law ; Step 6: Based on Step 5, construct the Lyapunov function for the entire control system, including tracking error and adaptive estimation error. Combining the preset time controller and adaptive law designed in step 5, the Lyapunov function is used... time derivative The closed-loop system state is regulated; the unified asymmetric time-varying obstacle function introduced in step 3 is synchronously associated with the coordinate transformation result in step 4, so that the position, velocity, control input and adaptive estimate of the autonomous underwater vehicle are all bounded within a preset time, and the tracking error converges to the neighborhood of the origin and satisfies multiple dynamic target constraints.

2. The adaptive tracking control method for an autonomous underwater vehicle under input hysteresis and dynamic multi-objective constraints according to claim 1, characterized in that, In step 1, the control equations for the AUV with hysteresis input are described as follows: (1) in, This represents the position vector of an autonomous underwater vehicle in a geofixed reference frame. Earth-fixed reference system The actual position 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, which is a positive definite matrix and satisfies They represent surges respectively. swing and undulations The three-degree-of-freedom velocity vector; Represents the system's inertia matrix; where, It refers to the mass of the underwater vehicle itself. , and These represent the additional mass generated by the vehicle during surges, rolls, and undulations due to the presence of surrounding fluids. Let be the fluid dynamic damping matrix, where and They represent the linear damping coefficients, , and These are the secondary damping coefficients for surge, sway, and undulation, respectively. It is the restoring force vector, where, and They are gravity and buoyancy, respectively. It controls the force vector and hysteresis input. It is a hysteresis output. This represents marine disturbance.

3. The adaptive tracking control method for an autonomous underwater vehicle under input hysteresis and dynamic multi-objective constraints according to claim 1, characterized in that, In step 2, the Bouc-Wen hysteresis model is linearly decomposed into the following form: (2) in, It is a hysteresis input. It is a hysteresis output. and It is a parameter that satisfies , These are three-dimensional auxiliary variables that satisfy the following equation: (3) in, , , and Let be the hysteresis coefficient, and have and This is valid. Additionally, three-dimensional vectors... Conditions met: (4) in, It is a constant. Representing vectors or matrix The 2-norm.

4. The adaptive tracking control method for an autonomous underwater vehicle under input hysteresis and dynamic multi-objective constraints according to claim 1, characterized in that, In step 3, the defined multi-objective function for , , Its satisfaction ,and These are the weighting coefficients. It is an integer; and All are asymmetric time-varying constraint functions; Constructing a unified asymmetric time-varying barrier function Its specific expression is: (5) in, and The design parameters must satisfy the following: and .if or ,So It tends to infinitesimal; therefore when When it is bounded, The constraints will be satisfied. Therefore, the dynamic multi-objective constraint problem is transformed into The problem of boundedness.

5. The adaptive tracking control method for an autonomous underwater vehicle under input hysteresis and dynamic multi-objective constraints according to claim 1, characterized in that, The specific steps of step 5 include: Construct the first Lyapunov function The virtual control signal vector is designed as follows: ; in, , , , , , , , , , The design matrix is ​​positive definite. The preset time-invariant scaling function is expressed as follows: And there are , For preset time, constant satisfy: ; Construct a second Lyapunov function, in the following form: (6) in, For design parameters, ,and for The estimate, To approximate the error; right Taking the time derivative yields And using the inequality scaling technique, we obtain: (7) in, ; For an unknown continuous nonlinear function, It can be approximated by a multidimensional Taylor network MTN. ,in, For function terms And Multidimensional Taylor Network The approximation error between them for The upper realm, Let be the weight vector of MTN. This represents the intermediate input layer of MTN; Based on backstepping technology, an adaptive preset time controller with input hysteresis and dynamic multi-objective constraints is designed. And adaptive law The specific expression is as follows: (8) (9) in, The design constant matrix is ​​positive definite. , These are design parameters.

6. The adaptive tracking control method for an autonomous underwater vehicle under input hysteresis and dynamic multi-objective constraints according to claim 1, characterized in that, In step 6, the Lyapunov function of the entire control system is constructed. : (10) For Lyapunov functions Find the time derivative and use the inequality scaling technique to obtain: (11) in, , ; Given a third-order identity matrix; combining this with a preset time scale function, solving the above equation yields: (12) Based on the above formula, we can conclude that... , and All within the preset time The system remains bounded; consequently, all signals in the closed-loop system remain bounded within a preset time and satisfy multiple dynamic objective constraints.

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