Unmanned ship practical predefined time fault-tolerant tracking control method considering fault and saturation

Abstract

The application provides a practical predefined time fault-tolerant tracking control method for unmanned surface vehicle (USV) considering faults and saturation, which comprises the following steps: after the desired trajectory of the USV is input into a predefined time fault-tolerant controller, a command control input is provided to an actuator; the USV forms a trajectory under the action of a disturbance and an actual input; after the estimated value of the force and torque caused by the fault and the fault detection is distinguished by a threshold value in the fault detection, a total uncertain model, a disturbance and a fault are obtained d , which is used as an input of an observer and for the calculation of an adaptive law in the predefined time fault-tolerant controller; and a dynamic tracking error is obtained by operating the running state of the ship collected by a sensor with the desired trajectory, which is used for the calculation of a control rate in the predefined time fault-tolerant controller.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of unmanned ships, fault detection, etc., and specifically relates to a practical predefined time fault-tolerant tracking control method for unmanned ships considering faults and saturation. BACKGROUND

[0002] In practical engineering applications, timely fault detection and estimation are often crucial, and time-consuming fault detection processes can lead to system instability or significant performance degradation.

[0003] Fault-tolerant control refers to a series of measures and strategies adopted in the design and operation of a system to ensure that it can continue to function normally or quickly recover to normal state in the event of a fault or error. The goal of fault-tolerant control is to minimize the impact of faults on system performance through effective design and implementation of strategies, thereby improving system reliability and availability. This involves the use of advanced control theory and technology. In addition, research and development of related control methods are crucial for improving the safety and efficiency of ship transportation. In actual ship control, faults in actuators and sensors can occur simultaneously within the same system. Typical event scenarios include sudden equipment failure, significant deterioration of system capabilities, and extreme environmental changes such as wind, wave, current, and tide that can affect ship stability. These situations can cause oscillation, slamming, surfing, and speed loss, ultimately hindering operational efficiency. To improve the control performance of such systems, it is essential to further investigate and analyze various uncertainties and instabilities discovered during the controller design process, including faults.

[0004] Recent advances in unmanned ships have had a significant impact on maritime and shipbuilding industries, particularly because they can operate continuously in complex deep-sea environments. This capability has facilitated innovation in future deep-sea exploration and global marine equipment. Previous research has provided solutions for this field. However, they depend on the assumption that all necessary state information can be accurately measured by sensors. In fact, in practical engineering scenarios, certain state information is often difficult to measure, so input saturation, uncertain models, faults, and disturbances need to be estimated. Some existing methods have adopted a fault-tolerant control strategy using integral sliding mode state feedback control for unmanned surface vessels, but this method does not include fault detection. However, the settling time of a fixed-time controller is a fixed value that cannot be adjusted with its parameters. But practical applications usually require adjustable settling time. In contrast, the settling time of a predefined time controller can be calculated. Therefore, researching methods to achieve practical predefined time convergence has become a key research area.

[0005] Despite the significant progress made, there is still room for improvement and further exploration in this field. First, many studies assume that all necessary state information can be accurately measured by sensors. However, in real engineering scenarios, some state information may be difficult to obtain. In addition, in order to achieve robust motion control of electric ships under disturbance, the ship system must be stable within a predetermined time. The ability to adjust the convergence time is a key issue.

[0006] However, in real engineering, the time allocated to fault detection is often limited due to task requirements. A time-consuming fault detection process can cause the system to become unstable or significantly degrade performance, as there is not enough time to take compensatory measures for the effects of the fault during detection. However, existing fault estimation algorithms may not be able to provide results within the specified time range. SUMMARY

[0007] In view of the defects and deficiencies of the prior art, the present application provides a practical predefined time fault-tolerant tracking control method for unmanned ships considering faults and saturation, aiming to provide a practical predefined time fault-tolerant tracking control method for unmanned surface vehicles (USVs) or unmanned ships affected by faults.

[0008] The technical solutions adopted by the present application to solve its technical problems are as follows:

[0009] A practical predefined time fault-tolerant tracking control method for unmanned ships considering faults and saturation, characterized in that the desired trajectory η d of the USV is input into the predefined time fault-tolerant controller, which provides a command control input τ c to the actuator; the USV forms a trajectory η under the action of the disturbance τ1 and the actual input τ; the force and torque τ a caused by the fault and the estimated value of υ in the fault detection are input into the observer , which is used to calculate the adaptive law in the predefined time fault-tolerant controller; the operating state of the ship is collected by the sensor and operated with the desired trajectory η d to obtain the dynamic tracking error , which is used to calculate the control rate in the predefined time fault-tolerant controller.

[0010] Further, the USV is modeled as follows:

[0011]

[0012] η=[x,y,ψ] T ,υ=[u,v,r] T (4)

[0013] wherein denotes the trajectory; denotes the velocity vector; M1is the inertia matrix, C1is the Coriolis matrix, and D1is the damping matrix; is the input vector; is the real set, denotes n is the vector; τ1denotes the disturbance:

[0014] τ1= F w +F s (5)

[0015] wherein F w = [F wx , F wy , N w ] T is the wind resistance; F s = [F sx , F sy , N s ] T is the wave resistance;

[0016] The uncertainties modeling ΔM, ΔC and ΔD and the nominal models M, C and D are defined as follows:

[0017] M1= M + ΔM (6)

[0018] C1= C + ΔC (7)

[0019] D1= D + ΔD (8).

[0020] Further, the dynamic tracking error between the USV trajectory and the desired trajectory is given by:

[0021]

[0022] wherein η d is the desired trajectory;

[0023] The commanded input τ c and the actual input τ acting on the ship are modeled as follows:

[0024] τ = (I3-E)τ c + τ a (10)

[0025] wherein 0≤e i ≤1, e i = 0 indicates a normal participant, while e i = 1 indicates a complete failure of the participant; τ a denotes the fault induced forces and torques, τ c denotes the commanded control input; diag{a1,a2,…,an} denotes a diagonal matrix;

[0026] Thus, equation (2) is written as:

[0027]

[0028] is an estimate of υ in fault detection, and the estimation error is defined as:

[0029]

[0030] Obtained:

[0031]

[0032] where K is a gain matrix;

[0033] According to equations (11) and (13), we have:

[0034]

[0035] Let satisfy the Lipschitz condition, i.e.:

[0036]

[0037] where L > 0 is the Lipschitz constant;

[0038] The following equation is constructed:

[0039]

[0040] The derivative of V0is:

[0041]

[0042] If there is no fault, the critical state is However, if a fault occurs, the critical state will change to The threshold is set to When is greater than the threshold, it is determined that a fault is detected; λ min (A) denotes the smallest eigenvalue of matrix A.

[0043] Further, equation (11) is written as:

[0044]

[0045] Its d represents the total uncertain model, disturbance and fault;

[0046] In order to estimate the uncertain model, input saturation error, disturbance and fault, an observer The estimation error is:

[0047] Equation (18) is written as:

[0048]

[0049] Let Based on Young's inequality, we have:

[0050]

[0051] where a > 0;

[0052] The calculation of the adaptive law in the predefined time fault-tolerant controller is as follows:

[0053]

[0054] where 0 < p < 1, K0 is a gain coefficient.

[0055] Further, let:

[0056] x1 = η (24)

[0057]

[0058] u = RM -1 τ c (27)

[0059] The system state equation is represented as follows:

[0060]

[0061] Considering actuator saturation, a smooth model is defined to describe the nonlinear model of saturation:

[0062]

[0063] where τ M is the upper limit of the actuator input;

[0064] The error of input saturation is determined as follows:

[0065] Δτ = u - τ s (30)

[0066] where |△τ| ≤ Λ;

[0067] In order to compensate for saturation, the following auxiliary variable is constructed:

[0068]

[0069] Let the auxiliary vector s = [s1, s2, s3] T :

[0070]

[0071] where a is an auxiliary variable:

[0072]

[0073] where 0 < p < 1, k2 > 0, ω > 0;

[0074] The derivative of a is:

[0075]

[0076] The control rate in the pre-defined time fault-tolerant controller is:

[0077]

[0078] where c > 0; ξ is calculated as follows:

[0079]

[0080] where k3 > 0, for sig p (x) = [sgn(x1) | x1 p , sgn(x2) | x2 p ,..., sgn(x n ) | x n | p ] T , where sgn is the sign function.

[0081] And, an unmanned ship: in operation, the unmanned ship practical pre-defined time fault-tolerant tracking control method considering faults and saturation as described above is adopted.

[0082] An electronic device comprising a memory, a processor, and a computer program stored on the memory and executable on the processor, the processor implementing the steps of the unmanned ship practical pre-defined time fault-tolerant tracking control method considering faults and saturation as described above when executing the program.

[0083] A non-transitory computer-readable storage medium having stored thereon a computer program, the computer program being executable by a processor to implement the steps of the unmanned ship practical pre-defined time fault-tolerant tracking control method considering faults and saturation as described above.

[0084] Compared with the prior art, the present application and its preferred schemes provide a predefined time convergence mechanism. The mechanism is first based on fault detection, and then a predefined time fault estimation is performed. It also provides a predefined time fault-tolerant controller, and theoretical proof of the proposed control algorithm. It also introduces a new singularity avoidance scheme to ensure that the tracking error does not approach infinity near the origin. By applying the method to the trajectory tracking of an unmanned surface vehicle, its effectiveness is verified, which is superior to the traditional fixed-time and predefined-time controllers. Its main features include simple operation, significant effect, and intuitive display. Finally, this research improves the transient stability and robustness of the unmanned ship control under non-ideal conditions and environments. BRIEF DESCRIPTION OF DRAWINGS

[0085] The present application will be further described in detail below in combination with the drawings and specific embodiments:

[0086] Figure 1 The control algorithm framework diagram for the embodiments of the present application is shown in Figure 1.

[0087] Figure 2 The tracking trajectory graph for scenario 1 of the embodiments of the present application is shown in Figure 2.

[0088] Figure 3 The tracking speed graph for scenario 1 of the embodiments of the present application is shown in Figure 3.

[0089] Figure 4 The tracking error graph for scenario 1 of the embodiments of the present application is shown in Figure 4.

[0090] Figure 5 The tracking uncertain model graph for scenario 1 of the embodiments of the present application is shown in Figure 5.

[0091] Figure 6 The tracking command control input graph for scenario 1 of the embodiments of the present application is shown in Figure 6.

[0092] Figure 7 The tracking fault detection result graph for scenario 1 of the embodiments of the present application is shown in Figure 7.

[0093] Figure 8 The tracking output result graph for scenario 1 of the embodiments of the present application is shown in Figure 8.

[0094] Figure 9 The tracking trajectory graph for scenario 2 of the embodiments of the present application is shown in Figure 9.

[0095] Figure 10 The tracking speed graph for scenario 2 of the embodiments of the present application is shown in Figure 10.

[0096] Figure 11 The tracking error graph for scenario 2 of the embodiments of the present application is shown in Figure 11.

[0097] Figure 12 The tracking uncertain model graph for scenario 2 of the embodiments of the present application is shown in Figure 12.

[0098] Figure 13 Tracking command control input graph for scenario 2 of the embodiment of the present application;

[0099] Figure 14 Tracking fault detection result graph for scenario 2 of the embodiment of the present application;

[0100] Figure 15 Tracking output result graph for scenario 2 of the embodiment of the present application;

[0101] Figure 16 Tracking error and command control torque tracking error graph for different k3 of the embodiment of the present application;

[0102] Figure 17 Tracking error and command control torque command control input graph for different k3 of the embodiment of the present application;

[0103] Figure 18 Tracking error and command control input tracking error graph for different τΜ of the embodiment of the present application;

[0104] Figure 19 Tracking error and command control input command control torque graph for different τΜ of the embodiment of the present application.

[0105] Figure 20 Tracking error and command control input test result graph for different p of the embodiment of the present application;

[0106] Figure 21 Comparison graph for different algorithms of the embodiment of the present application. DETAILED DESCRIPTION

[0107] In order to make the features and advantages of the patent more obvious and easy to understand, the following specific examples are described in detail as follows:

[0108] It should be noted that the following detailed description is exemplary and is intended to provide further explanation of the present application. Unless otherwise indicated, all technical and scientific terms used in the specification have the same meaning as commonly understood by one of ordinary skill in the art to which the present application pertains.

[0109] It should be noted that the terms used herein are only for the purpose of describing specific embodiments, and are not intended to limit the exemplary embodiments according to the present application. As used herein, the singular form is intended to include the plural form unless the context clearly indicates otherwise, and furthermore, it should be understood that when the terms "comprise" and / or "include" are used in the specification, they indicate the presence of a feature, step, operation, device, component, and / or combination thereof.

[0110] The embodiment of the application is designed to cope with the actual challenge of fault estimation, a new pre-defined time observer is designed to estimate input saturation, uncertain model, actuator fault, disturbance and sensor fault within a pre-defined time. It avoids time-consuming fault detection process which may lead to system instability or significant performance degradation. A new practical pre-defined time fault-tolerant control is developed and an upper bound of its stable time is provided. The sufficient condition of pre-defined time convergence has been established. In order to solve the potential problem related to singularity, a new singularity avoidance scheme is introduced. This non-singularity feature ensures that the tracking error will not approach infinity near the origin.

[0111] As shown in Figure 1 , the desired trajectory η d is input into the pre-defined time fault-tolerant controller, and the command control input τ c is provided to the actuator; the USV forms the trajectory η under the action of the disturbance τ1 and the actual input τ, on the other hand, the fault causes the force and torque τ a and the estimated value of υ in the fault detection are obtained after the fault detection is distinguished by the threshold ε, and the total uncertain model, disturbance and fault d are obtained as the input of the observer , which is used for feedback to the pre-defined time fault-tolerant controller for adaptive law calculation; in addition, the ship running state is collected by the sensor and operated with the desired trajectory η d to obtain the dynamic tracking error which is used for control rate calculation in the pre-defined time fault-tolerant controller.

[0112] The specific steps of the embodiment of the application include:

[0113] First, system modeling

[0114]

[0115] η=[x,y,ψ] T ,υ=[u,v,r] T (4)

[0116] wherein represents the trajectory. represents the velocity vector. M1 is the inertia matrix, C1 is the Coriolis matrix, and D1 is the damping matrix. is the input vector. is the real set, represents n is a vector. τ1 represents disturbance:

[0117] τ1=F w +F s (5)

[0118] wherein Fw =[F wx ,F wy N w ] T For wind resistance. F s =[F sx ,F sy N s ] T For wave resistance.

[0119] Uncertainty modeling ΔM, ΔC, and ΔD, as well as the nominal model M, C, and D, are defined as follows:

[0120] M1=M+ΔM (6)

[0121] C1=C+ΔC (7)

[0122] D1=D+ΔD (8)

[0123] The second step is fault detection.

[0124] The dynamic tracking error between the unmanned surface vehicle (USV) or unmanned vessel and the desired trajectory is given by the following formula:

[0125]

[0126] Where η d This represents the desired trajectory.

[0127] Command input τ applied on the ship c The modeling of the actual input τ is as follows:

[0128] τ=(I3-E)τ c +τ a (10)

[0129] in 0≤e i ≤1, e i =0 indicates that the participant is normal, while e i =1 indicates that the participant has completely failed. Furthermore, τ a τ represents the force and torque caused by the fault. c This indicates command control input. diag{a1,a2,…,a n} represents a diagonal matrix.

[0130] Therefore, equation (2) can be written as:

[0131]

[0132] This represents the estimated value of υ in fault detection. Its estimation error is defined as follows:

[0133]

[0134] Available:

[0135]

[0136] where K is a gain matrix.

[0137] Referring to equations (11) and (13), we have:

[0138]

[0139] Let satisfy the Lipschitz condition (i.e. Lipschitz continuity, which is a stronger smoothness condition than uniform continuity), i.e.:

[0140]

[0141] where L > 0 is the Lipschitz constant.

[0142] Construct the following equation:

[0143]

[0144] The derivative of V0 is:

[0145]

[0146] If there is no fault, the critical state is However, if a fault occurs, the critical state will become This means It can exceed Therefore, the threshold value can be set as When is greater than the threshold value, it is determined that a fault is detected. λ min (A) represents the minimum eigenvalue of matrix A.

[0147] Step 3, fault estimation.

[0148] Equation (11) can be written as:

[0149]

[0150] Its d represents the total uncertain model, disturbance, and fault.

[0151] In order to estimate the uncertain model, input saturation error, disturbance, and fault, the present embodiment constructs an observer The estimation error is:

[0152]

[0153] Equation (18) can be written as:

[0154]

[0155] Let Based on Young's inequality, we have:

[0156]

[0157] where a > 0.

[0158] The adaptive law is designed as follows:

[0159]

[0160] where 0 < p < 1, K0is the gain coefficient.

[0161] Step 4: Control law design.

[0162] Let

[0163] x1= η (24)

[0164]

[0165] u = RM -1 τ c (27)

[0166] The system state equation can be expressed as follows:

[0167]

[0168] Considering actuator saturation, a smooth model is defined to describe the saturated nonlinear model:

[0169]

[0170] where τ M is the upper limit of the actuator input.

[0171] The error of input saturation is determined as follows:

[0172] Δτ = u - τ s (30)

[0173] where |△τ|≤Λ;

[0174] To compensate for saturation, the following auxiliary variables are constructed:

[0175]

[0176] Let the auxiliary vector s = [s1, s2, s3] T :

[0177]

[0178] where α is an auxiliary variable:

[0179]

[0180] where 0 < p < 1, k2 > 0, ω > 0;

[0181] The derivative of α is:

[0182]

[0183] The control input is designed as:

[0184]

[0185] where c > 0. ξ is calculated as:

[0186]

[0187] where k3 > 0, for sig p (x) = [sgn(x1)|x1| p , sgn(x2)|x2| p ,..., sgn(x n )|x n | p ] T , where sgn is the sign function.

[0188] Equation (35) guarantees nonsingularity, ensuring that it does not tend to infinity near the origin.

[0189] The system achieves actual predefined time convergence stability, and the convergence time is k1 = min{k2, k3}.

[0190] The above scheme and design provided by the present application are verified by the following examples:

[0191] In scenario 1, the ship model parameters are as follows: d 11 = 0.7225 + 1.3274|u| + 5.8664u 2 , d 22 = 0.8612 + 36.2823|v| + 8.05|r|, d 23 = -0.1079 + 0.845|v| + 3.45|r|, d 32 = -0.1025 - 5.0437|v| - 0.13|r|, d 33= 1.9 - 0.08 |u| + 0.75 |r|, η d = [0, 0, 0] T , the initial state is η(0) = [-60 m, 1.39 m, -71.33°] T and υ(0) = [0.005, 0.006, 0.004] T , the disturbance is τ d1 = -0.005 sin(t), τ d2 = 0.005 sin(t), and τ d3 = -0.005 sin(t), the desired trajectory state is [0 m, 0 m, 0°] T , the main parameters are k1 = 0.1, p = 0.9, τ M = 100, and ε = 0.002, at t = 20 s, the fault occurs, e1 = 0.1, e2 = 0.3 and e3 = 0.1. The test results are shown in Figures 2-8 .

[0192] Scenario 2: when t = 5 s, the fault occurs e1 = 0.2, e2 = 0.4 and e3 = 0.2, τ M = 3, and other parameters are the same as those in scenario 1. The test results are shown in Figures 9-15 .

[0193] The embodiment also carries out tracking error and command control torque under different k3, tracking error and command control input under different τM, tracking error and command control input under different p, and comparison test of different algorithms, which proves that the scheme of the present application can realize the above-mentioned effects and the effects are better than those of the prior art.

[0194] It should be noted that, unless otherwise defined, the technical terms or scientific terms used in the present application should be understood as the usual meaning understood by those skilled in the art to which the present application belongs. The words "first", "second" and the like used in the present application do not represent any order, number or importance, but are only used to distinguish different components. The words "include" or "contain" and the like mean that the elements or objects before the words cover the elements or objects listed after the words and their equivalents, without excluding other elements or objects. The words "connect" or "connected" and the like are not limited to physical or mechanical connection, but can include electrical connection, whether direct or indirect. The words "up", "down", "left", "right" and the like are only used to represent relative positional relationship, when the absolute position of the described object changes, the relative positional relationship may also change accordingly.

[0195] The above merely describes preferred embodiments of the present application, and is not intended to limit the present application in other forms. Any person skilled in the art can make changes or modifications to the above disclosed technical contents to obtain equivalent embodiments. However, any simple modification, equivalent change and modification made to the above embodiments without departing from the technical solution of the present application and according to the technical essence of the present application shall still fall within the protection scope of the present application.

[0196] The present patent is not limited to the above preferred embodiments, and anyone can derive other various forms of unmanned ship practical predefined time fault and saturation considering fault and saturation unmanned ship practical predefined time fault and saturation considering fault and saturation unmanned ship practical predefined time fault and saturation considering fault and saturation unmanned ship practical predefined time fault and saturation considering fault and saturation unmanned ship practical predefined time fault and saturation considering fault and saturation unmanned ship practical predefined time fault and saturation considering fault and saturation unmanned ship practical predefined time fault and saturation considering fault and saturation unmanned ship practical predefined time fault and saturation considering fault and saturation unmanned ship practical predefined time fault and saturation considering fault and saturation unmanned ship practical predefined time fault and saturation considering fault and saturation unmanned ship practical predefined time fault and saturation considering fault and saturation unmanned ship practical predefined time fault and saturation considering fault and saturation unmanned ship practical predefined time fault and saturation considering fault and saturation unmanned ship practical predefined time fault and saturation considering fault and saturation unmanned ship practical predefined time fault and saturation considering fault and saturation unmanned ship practical predefined time fault and saturation considering fault and saturation unmanned ship practical predefined time fault and saturation considering fault and saturation unmanned ship practical predefined time fault and saturation considering fault and saturation unmanned ship practical predefined time fault and saturation considering fault and saturation unmanned ship practical predefined time fault and saturation considering fault and saturation unmanned ship practical predefined time fault and saturation considering fault and saturation unmanned ship practical predefined time fault and saturation considering fault and saturation unmanned ship practical predefined time fault and saturation considering fault and saturation unmanned ship practical predefined time fault and saturation considering fault and saturation unmanned ship practical predefined time fault and saturation considering fault and saturation unmanned ship practical predefined time

Claims

1. A practical predefined time-tolerant fault-tolerant tracking control method for unmanned surface vessels considering faults and saturation, characterized in that: The expected trajectory η of the USV d After inputting the predefined time-tolerant controller, provide the command control input τ. c The actuator; the USV forms a trajectory η under the action of disturbance τ1 and actual input τ; the force and torque τ caused by the fault. a And the estimated value of υ in fault detection After fault detection and discrimination based on the threshold ε, the total uncertainty model, disturbance, and fault d are obtained and used as the observer. The input is used to calculate the adaptive law in the predefined time-tolerant controller; the ship's operating status is collected by sensors and compared with the desired trajectory η. d The dynamic tracking error is obtained after calculation. Used for calculating control laws in predefined time-tolerant controllers; Model the USV as follows: η=[x,y,ψ] T ,υ=[u,v,r] T (4) in Represents the trajectory; M1 represents the velocity vector; C1 is the inertia matrix; D1 is the Coriolis matrix; The input vector; For the set of real numbers, Represents an n-dimensional vector; τ1 represents a perturbation: τ1=F w +F s (5) In the formula F w =[F wx ,F wy N w ] T For wind resistance; F s =[F sx ,F sy N s ] T For wave resistance; The uncertainty models ΔM, ΔC, and ΔD and the nominal models M, C, and D are defined as follows: M1 = M + ΔM (6) C1 = C + ΔC (7) D1 = D + ΔD (8) The dynamic tracking error between the USV trajectory and the desired trajectory is given by: Where η d For the desired trajectory; Command input τ applied on the ship c The modeling of the actual input τ is as follows: τ=(I3-E)τ c +t a (10) in 0≤e i ≤1, e i =0 indicates that the participant is normal, while e i =1 indicates that the participant has completely failed; τ a τ represents the force and torque caused by the fault. c Indicates command control input; diag{a1,a2,…,a n } represents a diagonal matrix; Therefore, rewrite Equation (2) as: This represents the estimated value of υ in fault detection, and the estimation error is defined as follows: Obtain: where K is the gain matrix; According to Equations (11) and (13), we have: set up It satisfies the Lipschitz condition, that is: where L > 0 is the Lipschitz constant; Construct the following: The derivative of V0 is: If there is no fault, the critical state is: However, if a fault occurs, the critical state will become Threshold set to when When the value exceeds the threshold, a fault is detected; λ min (A) represents the smallest eigenvalue of matrix A; Rewrite Equation (11) as: where d represents the total uncertain model, disturbance, and fault; To estimate uncertainties, input saturation errors, disturbances, and faults, an observer is used. The estimation error is: Rewrite Equation (18) as: set up Based on Young's inequality, we have: where a > 0; The calculation of the adaptive law in the predefined-time fault-tolerant controller is as follows: where 0 < p < 1 and K0 is the gain coefficient.

2. The practical predefined-time fault-tolerant tracking control method for an unmanned surface vehicle considering faults and saturation according to Claim 1, characterized in that: Denote: x1 = η (24) u=RM -1 τ c (27) The system state equation is expressed as follows: Considering actuator saturation, define a smooth model to describe the saturated nonlinear model: Where τ M The upper limit of the actuator input; The error of input saturation is determined as follows: Δτ=u-τ s (30) where |Δτ| ≤ Λ; To compensate for saturation, construct the following auxiliary variable: Let the auxiliary vector be s = [s1, s2, s3]. T : where α is the auxiliary variable: where 0 < p < 1, k2 > 0, ω > 0; The derivative of α is: The control law in the predefined-time fault-tolerant controller is: where c > 0; ξ is calculated as follows: Where k3>0, for sig p (x)=[sgn(x1)|x1| p ,sgn(x2)|x2| p ,...,sgn(x n )|x n | p ] T , where sgn is the sign function.

3. An unmanned surface vessel, characterized in that: Adopt the practical predefined-time fault-tolerant tracking control method for an unmanned surface vehicle considering faults and saturation according to Claim 1 or 2 during operation.

4. An electronic device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the steps of the practical predefined-time fault-tolerant tracking control method for an unmanned surface vehicle considering faults and saturation according to Claim 1 or 2.

5. A non-transitory computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the steps of the practical predefined-time fault-tolerant tracking control method for an unmanned surface vehicle considering faults and saturation according to Claim 1 or 2.

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