Unmanned ship target surrounding tracking control method with global fixed time stability

Abstract

The invention discloses a global fixed time stable unmanned ship target surrounding tracking control method. The control scheme comprises the steps of designing a fixed time heading and longitudinal speed dual guidance law, designing a fixed time observer, designing a fixed time auxiliary saturation system, designing a fixed time control law and triggering a fixed threshold event. The existing target surrounding control technology can only realize asymptotic stability, exponential stability or finite time stability of a system state, and is difficult to ensure high efficiency, flexibility and strong robustness when the unmanned ship executes a task, while the fixed time control technology is utilized in the method, so that the proposed control scheme has higher flexibility and higher robustness. According to the method, all error signals in the unmanned surface vehicle path tracking control system can be converged to zero within fixed time, the convergence time is independent of the initial state of the system while the error convergence speed is increased, and a powerful guarantee is provided for the unmanned surface vehicle to execute a fast, efficient and stable target surrounding control task.

Description

Technical Field

[0001] This invention belongs to the field of unmanned surface vessel (USV) motion control, and specifically relates to a globally fixed-time stable USV target encirclement and tracking control method. Background Technology

[0002] The increasing complexity and diversification of tasks such as marine scientific research, resource exploration, and marine security have made the intelligent and automated exploration of the marine environment a key research direction. As a crucial vehicle for marine exploration and operations, unmanned surface vessels (USVs), with their high maneuverability, autonomy, and safety, demonstrate broad application prospects in military reconnaissance, marine mapping, resource monitoring, environmental protection, and disaster relief. Compared to traditional manned vessels, USVs can not only perform high-risk missions in harsh environments but also achieve long-term autonomous navigation and multi-vessel collaborative operations. Therefore, motion control technology for USVs has become a research hotspot in the field of intelligent marine equipment, and target encirclement, as a key component of USV motion control technology, plays a vital role in the autonomous navigation of USVs.

[0003] Most unmanned surface vessels (USVs) have an underactuated structure, with their kinematic power derived from the propeller and rudder at the stern. Existing USV target encirclement control methods mostly employ indirect design, i.e., designing the guidance subsystem and control subsystem separately. Line-of-sight (LOS) guidance law, due to its simplicity, is applied to the design of USV target encirclement control systems, and most existing guidance subsystem research is based on LOS guidance. However, existing LOS guidance strategies typically only guarantee asymptotic or exponential convergence of system errors, with an infinite convergence time. Furthermore, current technologies usually only consider bow-oriented guidance, defining the desired speed as a constant, resulting in a lack of system flexibility and failing to meet the requirement of rapid system error convergence.

[0004] In the research of control subsystems, methods such as PID control, backstepping control, sliding mode control, adaptive control, intelligent control, and reinforcement learning control, or combinations of several of these methods, are widely used. However, existing technologies typically achieve asymptotically stable or exponentially stable control effects, with theoretically infinite convergence times. Furthermore, external unknown disturbances and actuator saturation during navigation pose significant challenges to achieving safe and rapid unmanned surface vessel (USV) path tracking. Summary of the Invention

[0005] To address the aforementioned problems, there is an urgent need to invent and design a globally stable, time-fixed unmanned surface vessel (USV) target encirclement control method. This would significantly improve the speed and flexibility of USV target encirclement operations while perfectly handling unknown interferences and actuator saturation issues during navigation. The technical means employed in this invention are as follows: Define the distance tracking error and the orbiting angle error when the target is surrounded by an unmanned surface vessel; Design of an orbital line-of-sight guidance law for a fixed-time target unmanned surface vessel based on fixed-time control theory; Design a fixed-time observer based on the kinematic equations of the target unmanned surface vessel; Design a fixed-time dynamic auxiliary saturation system; Based on a fixed-time observer and a fixed-time dynamic auxiliary saturation system, a fixed-threshold event-triggered controller is designed to control the lumped unknown disturbances and actuator saturation phenomena encountered by the unmanned surface vessel (USV) during navigation. This design constructs a robust control scheme, which is then used to encircle and control the USV target.

[0006] Furthermore, when defining the distance tracking error and orbiting angle error for target unmanned surface vessels (USVs) surrounding them: assuming the target USV is a cooperative target in a communication transition state or a neutral target without escape capability, its dynamic description is as follows:

[0007] The relative distance between the following unmanned surface vessel and the target unmanned surface vessel and relative angle The definition is as follows:

[0008] Surround angle Defined as the angle between the longitudinal heading of the following unmanned surface vessel (USV) and the line connecting the two USVs, its range is mapped to an interval. Inside:

[0009] For a single following unmanned surface vessel (USV) performing orbital control over a target USV, the distance tracking error and orbital angle error are defined as follows:

[0010] in, For the desired circumference, The desired orbital angle is set in the guidance law; The derivatives of distance error and angle error are expressed as:

[0011] in

[0012] in .

[0013] Furthermore, when designing the orbital line-of-sight guidance law for a fixed-time target unmanned surface vessel: Based on fixed-time control theory, a dual guidance law is designed as follows:

[0014] in, and These represent the desired heading angle and longitudinal velocity, respectively. and For fixed-time auxiliary items, the definition is as follows: , in, , , , All are positive constants. It is the forward line of sight of the unmanned surface vessel during navigation. , Represents a symbolic function.

[0015] Furthermore, when designing a fixed-time observer: First, a fixed-time perturbation observer is designed, and the kinematic equations following the unmanned surface vessel are described as follows:

[0016] in, Represents the position and heading vector in the inertial coordinate system; This represents the velocity vector in the ship's coordinate system. For bow angle Defined rotation matrix; Design the following fixed-time velocity observer:

[0017] in, The matrix to be designed is a positive definite matrix. The diagonal element should be greater than The corresponding upper bound, constant and All are positive numbers and satisfy the following conditions: , , With a fixed-time lumped uncertainty observer, the dynamic equations of the unmanned surface vessel can be rewritten as follows:

[0018] Design the following fixed-time perturbation observer:

[0019] in, The positive definite gain matrix to be designed is... The diagonal elements should be greater than Upper bounds of each corresponding component, constants and It is a positive number and satisfies ; Define auxiliary variables as follows:

[0020] Design a fixed-time high-dimensional extended state observer:

[0021] in

[0022] in, , , Measurable states , , The estimated value; , , They are unknowns , , The estimated value, the observer gain satisfies ( ).

[0023] Furthermore, the fixed-time dynamic auxiliary saturation system is designed as follows:

[0024] Piecewise continuous smooth function The definition is as follows:

[0025] in , , , and To meet Two small positive constants.

[0026] Furthermore, when encircling and controlling unmanned surface vessels: Design a fixed-time longitudinal velocity dynamics controller, and design the longitudinal velocity controller as follows:

[0027] in, It is a positive number, and has , Defined as the error between the actual longitudinal velocity of the unmanned surface vessel and the desired longitudinal velocity given in the guidance law, i.e. ; It is the estimate from a fixed-time lumped disturbance observer in the direction; ; Design a fixed-time bow dynamics controller, and design the bow dynamics controller as follows:

[0028] in, It is a positive number, and has ; Defined as the error between the actual bow angle of the unmanned surface vessel and the desired bow angle given in the guidance law, i.e., ... ; It is the estimate from a fixed-time lumped disturbance observer in the direction;

[0029] Furthermore, the following fixed-threshold event trigger controller is designed:

[0030] The measurement error is defined as:

[0031] In event-triggered control strategies This represents the controller's output value at the last trigger moment, while Using a zero-order hold in the interval The value remains constant. Until the next trigger time. arrival; Define a fixed threshold trigger law

[0032] in, When in the first Secondary trigger interval hour .

[0033] This invention discloses a globally fixed-time stable unmanned surface vessel (USV) target encirclement and tracking control method. In the control framework, firstly, an unknown disturbance and unknown velocity in the system are accurately estimated based on a fixed-time disturbance observer, and compensation is completed within a fixed time. Since the convergence time of the observer is fixed, the system's ability to suppress disturbances remains consistent and efficient globally, and is not weakened by adverse initial conditions, thus ensuring high-precision formation maintenance and strong anti-interference robustness under complex sea conditions. Simultaneously, the constructed dynamic auxiliary saturation subsystem effectively solves the actuator saturation problem existing in the actual operation of the USV, avoiding the impact of control command exceeding limits on system performance and stability. Furthermore, the control subsystem's function is to ensure that the actual bow and longitudinal velocities of the USV accurately track the expected values ​​given by the guidance subsystem within a fixed time, thereby ensuring that the USV can achieve fast, stable, and reliable target encirclement control within a finite time.

[0034] This invention is not only suitable for encircling stationary targets, but also highly efficient in dealing with high-speed moving targets. The system can track, approach, and form a stable encirclement of dynamic targets within a known time, providing a feasible technical solution for challenging tasks such as dynamic maritime encirclement and pursuit and coordinated surveillance of moving targets.

[0035] This invention, through a systematic innovation of a globally fixed-time stabilization framework, achieves a comprehensive and leapfrog improvement in unmanned surface vessel (USV) target encirclement control in terms of convergence time determinism, dynamic response speed, anti-interference robustness, engineering practicality, and mission flexibility. It provides a significantly superior and practical advanced control method for solving the problem of efficient, reliable, and coordinated encirclement control tasks for USV swarms in complex marine environments. Attached Figure Description

[0036] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0037] Figure 1 This is a framework diagram of the global fixed-time stable target encirclement control system of the present invention; Figure 2 This is a schematic diagram of the target encirclement geometry principle of the unmanned surface vessel involved in this invention; Figure 3 This is a diagram showing the target encirclement effect of the unmanned surface vessel under the control algorithm described in this invention; Figure 4This is a convergence diagram of distance error and angle error of the unmanned surface vessel under the control algorithm described in this invention and the ordinary algorithm; Figure 5 This is an image showing the estimation effect of the unmanned surface vessel using the speed observer described in this invention; Figure 6 This is an estimation effect diagram of the unmanned surface vessel using the lumped disturbance observer described in this invention; Figure 7 This is an estimation effect diagram of the unmanned surface vessel using the high-dimensional state observer and the ordinary state observer described in this invention; Figure 8 This is a diagram of the control force and control torque of the unmanned surface vessel under the control algorithm described in this invention; Figure 9 This is a diagram showing the trigger times of event triggers for the unmanned surface vessel under the control algorithm described in this invention. Detailed Implementation

[0038] To enable those skilled in the art to better understand the present invention, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. 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 should fall within the scope of protection of the present invention.

[0039] It should be noted that the terms "first," "second," etc., in the specification, claims, and accompanying drawings of this invention are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that the embodiments of the invention described herein can be implemented in orders other than those illustrated or described herein. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover a non-exclusive inclusion; for example, a process, method, system, product, or apparatus that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0040] The mathematical model of the unmanned surface vessel described in this invention is a split model, comprising kinematic equations and dynamic equations, wherein the kinematic equations are:

[0041] in, This indicates the three positional status information of the unmanned surface vessel: longitudinal, lateral, and bow angle. This represents three velocity state information: longitudinal velocity, lateral drift velocity, and bow angular velocity. All of these state information are continuously differentiable.

[0042] The aforementioned dynamic equation is:

[0043] in, It is the system's control input. It is the longitudinal thrust provided by the propeller at the stern of the unmanned surface vessel during navigation. The steering torque is provided by the unmanned surface vessel's servo motor system; This represents the viscous drag term experienced by the unmanned surface vessel (USV) in the three directions of motion. Specifically, the drag term includes unknown disturbances that vary with the environment, unknowns in the USV modeling, and parameter perturbations. This is a known term in the modeling of unmanned surface vessels. Specifically, its expression is as follows:

[0044] These represent unmanned surface vessels in Mass parameters and hydrodynamic damping coefficients in three directions; The global fixed-time stable target encirclement tracking control method includes the following steps; Step 1: Define the distance tracking error and the surrounding angle error of the target enclosure. The target unmanned surface vessel is either a cooperative target capable of communication or a neutral target without the ability to escape; its dynamic description is as follows:

[0045] The relative distance between the following unmanned surface vessel and the target unmanned surface vessel and relative angle The definition is as follows:

[0046] Surround angle Defined as the angle between the longitudinal heading of the following unmanned surface vessel (USV) and the line connecting the two USVs, its range is mapped to an interval. Inside:

[0047] To achieve orbital control of a single following unmanned surface vessel (USV) around a target USV, the distance tracking error and orbital angle error are defined as follows:

[0048] in, For the desired circumference, The desired orbital angle is set in the guidance law.

[0049] The derivatives of distance error and angle error can be expressed as:

[0050] in

[0051] in

[0052] Step 2: Design a fixed-time target orbital line-of-sight guidance law Based on fixed-time control theory, a dual guidance law is designed as follows:

[0053] in, and These represent the desired heading angle and longitudinal velocity, respectively. and For fixed-time auxiliary items, the definition is as follows: , in, , , , All are positive constants. It is the forward line of sight of the unmanned surface vessel during navigation. , Represents a symbolic function; Under the aforementioned dual guidance law of fixed-time bow and longitudinal velocity, the unmanned surface vessel's distance error... With angle error It will converge to zero within a fixed time, and due to the presence of longitudinal velocity guidance, the stabilization speed of the unmanned surface vessel is further accelerated.

[0054] Consider the following Lyapunov candidate function (LCF):

[0055] Differentiate the LFC above and substitute the guidance law designed in Step 2 into it.

[0056] in

[0057] The proof results show that the guidance subsystem is stable at a fixed time.

[0058] Step 3: Design a fixed-time observer The kinematic equations of a following unmanned surface vessel (USV) are described as follows:

[0059] in, Represents the position and heading vector in the inertial coordinate system; This represents the velocity vector in the ship's coordinate system. For bow angle Defined rotation matrix.

[0060] Design the following fixed-time velocity observer:

[0061] in, This is the positive definite matrix that needs to be designed. The diagonal element should be greater than The corresponding upper bound. Constant. and All are positive numbers and satisfy the following conditions: , .

[0062] make As an auxiliary variable, it is defined as follows:

[0063] Define the velocity observation error as: For auxiliary variables Taking the derivative, we get:

[0064] The above formula shows that as long as A velocity observer that can converge within a fixed time. The error can then converge within a fixed time. Consider the following LCF:

[0065] Differentiating the above LCF yields:

[0066] in

[0067] The proof shows that the velocity observer is stable at a fixed time. B proposes a fixed-time lumped uncertainty observer, and the dynamic equations of the unmanned surface vessel can be rewritten as:

[0068] Design the following fixed-time perturbation observer:

[0069] in, This is the positive definite gain matrix that needs to be designed. The diagonal elements should be greater than Upper bounds of corresponding components. Constants. and It is a positive number and satisfies .

[0070] Define auxiliary variables as follows:

[0071] For auxiliary variables Taking the derivative, we get:

[0072] The above formula shows that as long as If convergence is possible within a fixed time, then the lumped disturbance observer error will also converge within a fixed time. Consider the following LCF:

[0073] Differentiating the above LCF yields:

[0074] in

[0075] The proof shows that the lumped disturbance observer is stable at a fixed time. Design a fixed-time high-dimensional extended state observer in C:

[0076] in

[0077] in, , , Measurable states , , The estimated value; , , They are unknowns , , The estimated value. The observer gain satisfies ( ).

[0078]

[0079] Consider the following LCF:

[0080] in

[0081]

[0082] Similarly, we can obtain:

[0083]

[0084] The final result is:

[0085] in

[0086] The proof shows that the higher-order state observer is stable over a fixed time. Step 4: Design a fixed-time dynamic auxiliary saturation system The fixed-time assisted saturation system is designed as follows:

[0087] Piecewise continuous smooth function The definition is as follows:

[0088] in , , , and To meet Two small positive constants.

[0089] Step 5: Design of Fixed-Time Control Law By using a fixed-time observer and a dynamic auxiliary saturation system, the lumped unknown disturbances and actuator saturation problems faced by unmanned surface vessels during navigation are addressed, thereby designing a control law with higher robustness, ultimately ensuring accurate and rapid target encirclement control of the unmanned surface vessel. A. Design of a fixed-time longitudinal velocity dynamics controller Specifically, the longitudinal speed controller is designed as follows:

[0090] in, It is a positive number, and has ; Defined as the error between the actual longitudinal velocity of the unmanned surface vessel and the desired longitudinal velocity given in the guidance law, i.e. ; It is the estimate from a fixed-time lumped disturbance observer in the direction; ; B. Design of a fixed-time bow dynamics controller Specifically, the bow dynamics controller is designed as follows:

[0091] in, It is a positive number, and has ; Defined as the error between the actual bow angle of the unmanned surface vessel and the desired bow angle given in the guidance law, i.e. ; It is the estimate from a fixed-time lumped disturbance observer in the direction; ; Step 6: Design of Fixed Threshold Event Trigger Controller Design a fixed threshold event trigger controller as follows:

[0092] The measurement error is defined as:

[0093] In event-triggered control strategies This represents the controller's output value at the last trigger moment, while Using a zero-order hold in the interval The value remains constant. Until the next trigger time. arrival.

[0094] Define a fixed threshold trigger law

[0095] in, When in the first Secondary trigger interval hour .

[0096] Consider the following LCF:

[0097] Differentiating the above LCF and substituting the system described in steps 4 and 6, we get:

[0098] After sorting, we can obtain:

[0099] in

[0100] Through proof and analysis, it can be concluded that the designed control law is stable at a fixed time.

[0101] The following section presents some lemmas used in proving the stability of the system using this method; Lemma 1 for nonlinear systems If a constant exists and as well as , making Then the system It converges in a fixed time; the system state can converge to 0 within a fixed time. Lemma 2 for nonlinear systems If a constant exists and as well as , making Then the system It converges in a fixed time; the system state can converge to 0 within a fixed time. Lemma 3 For any and any vector The following inequalities always hold true:

[0102] Where, constant Satisfying the relation ,therefore ; Lemma 4 For any real number , and any positive real number The following inequalities always hold true: in , and satisfy ; Example Figure 1 This is a system framework diagram of the present invention; Figure 2 This is a schematic diagram illustrating the geometric principles of unmanned surface vessel (USV) path tracking. (Comprehensive) Figure 1 and Figure 2 The effectiveness of the control method described in this invention is illustrated through simulation experiments using a specific unmanned surface vessel (USV) as an example. The specific model parameters of the USV are as follows: , , , , ,

[0103] The initial position and velocity of the target unmanned surface vessel are: , , Following the initial position and speed of the unmanned surface vessel , , ; The interference designed for unmanned surface vessels performing tracking missions is as follows:

[0104] The other main parameters are:

[0105]

[0106] Figure 3 This is a rendering of a target encirclement following an unmanned surface vessel. Figure 4 This is a convergence plot of distance and angle errors following the unmanned surface vessel (USV). It can be seen that, under the control method described in this invention, the USV can achieve rapid, smooth, and precise encirclement of the target USV. Furthermore, the fixed convergence time of this invention is faster than that of ordinary algorithms, demonstrating that this method has good speed and accuracy.

[0107] Figures 5 to 7 This is a comparison chart of the observation results and actual results of the three observers described in this invention. It can be seen that all three observers achieve the observation effect very well and quickly.

[0108] Figure 8 It follows the longitudinal thrust input and the bow torque input of the unmanned surface vessel.

[0109] Figure 9 The diagram shows the event triggering times of the unmanned surface vessel under the control algorithm described in this invention. It can be seen that the fixed threshold event trigger works well and reduces the number of actuator operations.

[0110] The sequence numbers of the above embodiments of the present invention are for descriptive purposes only and do not represent the superiority or inferiority of the embodiments.

[0111] In the above embodiments of the present invention, the descriptions of each embodiment have different focuses. For parts not described in detail in a certain embodiment, please refer to the relevant descriptions of other embodiments.

[0112] In the several embodiments provided in this application, it should be understood that the disclosed technical content can be implemented in other ways. The device embodiments described above are merely illustrative; for example, the division of units can be a logical functional division, and in actual implementation, there may be other division methods. For instance, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the displayed or discussed mutual coupling, direct coupling, or communication connection may be through some interfaces; the indirect coupling or communication connection between units or modules may be electrical or other forms.

[0113] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple units. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.

[0114] Furthermore, the functional units in the various embodiments of the present invention can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit.

[0115] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A globally time-stabilized unmanned surface vessel (USV) target encirclement tracking control method, characterized in that: Define the distance tracking error and the orbiting angle error when the target is surrounded by an unmanned surface vessel; Design of an orbital line-of-sight guidance law for a fixed-time target unmanned surface vessel based on fixed-time control theory; Design a fixed-time observer based on the kinematic equations of the target unmanned surface vessel; Design a fixed-time dynamic auxiliary saturation system; Based on a fixed-time observer and a fixed-time dynamic auxiliary saturation system, a fixed-threshold event-triggered controller is designed to control the lumped unknown disturbances and actuator saturation phenomena encountered by the unmanned surface vessel (USV) during navigation. This design constructs a robust control scheme, which is then used to encircle and control the USV target.

2. The globally fixed-time stable unmanned surface vessel target encirclement tracking control method according to claim 1, characterized in that: When defining the range tracking error and orbiting angle error for target unmanned surface vessels (USVs) surrounding a target: assuming the target USV is a cooperative target in a communication transition state or a neutral target without escape capability, its dynamic description is as follows: The relative distance between the following unmanned surface vessel and the target unmanned surface vessel and relative angle The definition is as follows: Surround angle Defined as the angle between the longitudinal heading of the following unmanned surface vessel (USV) and the line connecting the two USVs, its range is mapped to an interval. Inside: A single following unmanned surface vessel (USV) is used to perform orbital control of the target USV. The distance tracking error and orbital angle error are defined as follows: in, For the desired circumference, The desired orbital angle is set in the guidance law; The derivatives of distance error and angle error are expressed as: in in 。 3. The globally fixed-time stable unmanned surface vessel target encirclement tracking control method according to claim 1, characterized in that: When designing the orbital line-of-sight guidance law for a fixed-time target unmanned surface vessel: Based on fixed-time control theory, a dual guidance law is designed as follows: in, and These represent the desired heading angle and longitudinal velocity, respectively. and For fixed-time auxiliary items, the definition is as follows: , in, , , , All are positive constants. It is the forward line of sight of the unmanned surface vessel during navigation. , Represents a symbolic function.

4. The globally fixed-time stable unmanned surface vessel target encirclement tracking control method according to claim 1, characterized in that: When designing a fixed-time observer: First, design a fixed-time disturbance observer. The kinematic equations for following the unmanned surface vessel are described as follows: in, Represents the position and heading vector in the inertial coordinate system; This represents the velocity vector in the ship's coordinate system. For bow angle Defined rotation matrix; Design the following fixed-time velocity observer: in, The matrix to be designed is a positive definite matrix. The diagonal element should have a value greater than The corresponding upper bound, constant and All are positive numbers and satisfy the following conditions: , , With a fixed-time lumped uncertainty observer, the dynamic equations of the unmanned surface vessel can be rewritten as follows: Design the following fixed-time perturbation observer: in, The positive definite gain matrix to be designed is... The diagonal elements should be greater than Upper bounds of each corresponding component, constants and It is a positive number and satisfies ; Define auxiliary variables as follows: Design a fixed-time high-dimensional extended state observer: in in, , , Measurable states , , The estimated value; , , They are unknowns , , The estimated value, the observer gain satisfies ( ).

5. The globally fixed-time stable unmanned surface vessel target encirclement tracking control method according to claim 1, characterized in that: The design of a fixed-time dynamic auxiliary saturation system is as follows: Piecewise continuous smooth function The definition is as follows: in , , , and To meet Two small positive constants.

6. The globally fixed-time stable unmanned surface vessel target encirclement tracking control method according to claim 1, characterized in that: When encircling and controlling unmanned surface vessel targets: Design a fixed-time longitudinal velocity dynamics controller, and design the longitudinal velocity controller as follows: in, It is a positive number, and has , Defined as the error between the actual longitudinal velocity of the unmanned surface vessel and the desired longitudinal velocity given in the guidance law. ; It is the estimate from a fixed-time lumped disturbance observer in the direction; ; Design a fixed-time bow dynamics controller, and design the bow dynamics controller as follows: in, It is a positive number, and has ; Defined as the error between the actual bow angle of the unmanned surface vessel and the desired bow angle given in the guidance law, i.e. , It is the estimate from a fixed-time lumped disturbance observer in the direction; .

7. The globally fixed-time stable unmanned surface vessel target encirclement tracking control method according to claim 1, characterized in that: Design a fixed threshold event trigger controller as follows: The measurement error is defined as: In event-triggered control strategies This represents the controller's output value at the last trigger moment, while Using a zero-order hold in the interval The value remains constant. Until the next trigger time. arrival; Define a fixed threshold trigger law in, When in the first Secondary trigger interval hour .

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