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

Abstract

The invention provides an unmanned ship practical predefined time fault-tolerant tracking control method considering faults and saturation, and the method comprises the steps: inputting an expected trajectory of a USV into a predefined time fault-tolerant controller, and then providing command control input to an actuator; the USV forms a track under the action of disturbance and actual input; after force and torque caused by the fault and an estimated value in fault detection are subjected to fault detection judgment through a threshold value, a total uncertainty model, interference and a fault d are obtained and serve as input of an observer to be used for calculation of a self-adaptive law in a predefined time fault-tolerant controller; a ship operation state is acquired by a sensor and then is calculated with an expected trajectory to obtain a dynamic tracking error which is used for calculating a control rate in a predefined time fault-tolerant controller.

Description

Technical Field

[0001] The present invention belongs to the technical fields 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 Art

[0002] In practical engineering applications, timely fault detection and estimation are often crucial, while a time-consuming fault detection process may cause 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 the system can continue to operate normally or quickly recover to a normal state when a fault or error occurs. The goal of fault-tolerant control is to minimize the impact of faults on system performance through effective design and implementation strategies, thereby improving the reliability and availability of the system. This involves the use of advanced control theory and technology. In addition, research and development of related control methods are essential to improve the safety and efficiency of ship transportation. In actual ship control, actuator and sensor failures may occur simultaneously within the same system. Typical event scenarios include sudden equipment failures, significant deterioration of system capabilities, and extreme environmental changes such as wind, waves, currents, and tides that may affect the stability of the ship. These situations may cause oscillations, slamming, surfing, and speed loss, ultimately hindering operational efficiency. In order to improve the control performance of such systems, it is crucial to further investigate and analyze the various uncertainties and unstable factors (including faults) found during the controller design process.

[0004] Recent advances in unmanned vessels have had a significant impact on the maritime and shipbuilding industries, especially because they are able to operate continuously in complex deep-sea environments. This capability has facilitated future deep-sea exploration and innovation in global marine equipment. Previous studies have provided solutions to this area. However, they rely on the assumption that all necessary state information can be accurately measured by sensors. In fact, in actual engineering scenarios, some state information is often difficult to measure, so it is necessary to estimate input saturation, uncertain models, faults, and disturbances. 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 and cannot be adjusted with its parameters. But practical applications usually require an adjustable settling time. In contrast, the settling time of a predefined-time controller can be calculated. Therefore, studying methods to achieve practical predefined-time convergence has become a key research area.

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

[0006] However, in practical engineering, the time allocated to fault detection is often limited due to task requirements. The time-consuming fault detection process may lead to system instability or significant performance degradation because there is not enough time to take compensatory measures for the impact of the fault during the detection period. However, existing fault estimation algorithms may not be able to provide results within the specified time frame. Summary of the invention

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

[0008] The technical solution specifically adopted by the present invention to solve the technical problem is:

[0009] A practical predefined time fault-tolerant tracking control method for an unmanned ship considering failure and saturation, characterized in that: the desired trajectory η of the USV is set d After entering the predefined time fault-tolerant controller, the command control input τ is provided 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 caused by the fault a and the estimated value of υ in fault detection After fault detection and discrimination by threshold ε, the total uncertainty model, interference and fault d are obtained as the observer The input is used to calculate the adaptive law in the predefined time fault-tolerant controller; the ship's operating state is collected by the sensor and compared with the expected trajectory η d After calculation, the dynamic tracking error is obtained Used for calculation of control ratio in predefined time fault-tolerant controller.

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

[0011]

[0012] η=[x,y,ψ] T ,υ=[u,v,r] T (4)

[0013] in Indicates 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 set of real numbers, Represents n as a vector; τ1 represents the disturbance:

[0014] τ1=F w +F s (5)

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

[0016] The uncertainty modeling △M, △C and △D 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] Furthermore, the dynamic tracking error between the USV trajectory and the desired trajectory is given by:

[0021]

[0022] where η d is the expected trajectory;

[0023] The command input τ acting on the ship c And the actual input τ is modeled as follows:

[0024] τ=(I3-E)τ c +τ a (10)

[0025] in 0≤e i ≤1, e i = 0 means the participant is normal, and e i =1 means the participant fails completely; τ a represents the force and torque caused by the fault, τ c Indicates command control input; diag{a1,a2,…,an} represents a diagonal matrix;

[0026] Therefore, formula (2) can be written as:

[0027]

[0028] Expressed as the estimated value of υ in fault detection, the estimation error is defined as follows:

[0029]

[0030] get:

[0031]

[0032] Where K is the gain matrix;

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

[0034]

[0035] set up Satisfies the Lipschitz condition, that is:

[0036]

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

[0038] Construct the following formula:

[0039]

[0040] The derivative of V0 is:

[0041]

[0042] If there is no fault, the critical state is However, if a failure occurs, the critical state becomes The threshold is set to when When it is greater than the threshold, it is determined that a fault is detected; min (A) represents the minimum eigenvalue of matrix A.

[0043] Furthermore, formula (11) can be written as:

[0044]

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

[0046] To estimate uncertain models, input saturation errors, disturbances, and faults, an observer is used. 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 adaptation law in the predefined time fault-tolerant controller is as follows:

[0053]

[0054] where 0 < p < 1 and K0 is the gain coefficient.

[0055] Furthermore, denote:

[0056] x1 = η (24)

[0057]

[0058] u = RM -1 τ c (27)

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

[0060]

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

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

[0068]

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

[0070]

[0071] Where α is an auxiliary variable:

[0072]

[0073] Where 0 <p<1,k2> 0,ω>0;

[0074] The derivative of α is:

[0075]

[0076] The control rate in the predefined 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: an unmanned ship practical predefined time fault-tolerant tracking control method considering failures and saturation as described above is adopted during operation.

[0082] An electronic device comprises a memory, a processor and a computer program stored in the memory and executable on the processor. When the processor executes the program, the steps of the practical predefined time fault-tolerant tracking control method for an unmanned ship considering faults and saturation as described above are implemented.

[0083] A non-transitory computer-readable storage medium stores a computer program, which, when executed by a processor, implements the steps of the practical predefined time fault-tolerant tracking control method for an unmanned ship considering failures and saturation as described above.

[0084] Compared with the prior art, the present invention and its preferred embodiment provide a predefined time convergence mechanism. The mechanism is first based on fault detection and then performs a predefined time fault estimation. It also provides a predefined time fault-tolerant controller and a 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. The effectiveness of this method is verified by applying it to the trajectory tracking of unmanned surface vessels, and the method is superior to traditional fixed time and predefined time controllers. Its main features include simple operation, significant effect, and intuitive display. Ultimately, this study improves the transient stability and robustness of the control of unmanned ships under non-ideal conditions and environments. BRIEF DESCRIPTION OF THE DRAWINGS

[0085] The present invention is further described in detail below with reference to the accompanying drawings and specific embodiments:

[0086] Figure 1 This is a control algorithm framework diagram of an embodiment of the present invention;

[0087] Figure 2 This is a tracking trajectory diagram of scenario 1 of an embodiment of the present invention;

[0088] Figure 3 This is a tracking speed diagram of scenario 1 of an embodiment of the present invention;

[0089] Figure 4 is a tracking error diagram of scenario 1 of an embodiment of the present invention;

[0090] Figure 5 This is a tracking uncertainty model diagram of scenario 1 of an embodiment of the present invention;

[0091] Figure 6 This is a tracking command control input diagram of scenario 1 of an embodiment of the present invention;

[0092] Figure 7 This is a diagram of the tracking fault detection result of scenario 1 of an embodiment of the present invention;

[0093] Figure 8 This is a diagram of the tracking output result of scenario 1 of an embodiment of the present invention;

[0094] Fig. 9 This is a tracking trajectory diagram of scenario 2 of an embodiment of the present invention;

[0095] Fig.10 This is a tracking speed diagram of scenario 2 of an embodiment of the present invention;

[0096] Fig.11 is a tracking error diagram of scenario 2 of an embodiment of the present invention;

[0097] Fig.12 This is a tracking uncertainty model diagram of scenario 2 of an embodiment of the present invention;

[0098] Fig.13 This is a tracking command control input diagram of scenario 2 of an embodiment of the present invention;

[0099] Fig.14 This is a diagram of the tracking fault detection result of scenario 2 of an embodiment of the present invention;

[0100] Fig.15 This is a diagram of the tracking output result of scenario 2 of an embodiment of the present invention;

[0101] Fig.16 Graph showing the tracking error and command control torque under different k3 in an embodiment of the present invention;

[0102] Fig.17 1 is a command control input diagram of tracking error and command control torque under different k3 in an embodiment of the present invention;

[0103] Fig.18 : is a tracking error diagram of the tracking error and command control input under different τM of the embodiment of the present invention;

[0104] Fig.19 3 is a diagram of the tracking error and command control torque input under different τM according to an embodiment of the present invention.

[0105] Fig. 20 The tracking error and command control input test result diagram under different p of the embodiment of the present invention;

[0106] Fig.21 4 is a comparison diagram of different algorithms according to the embodiments of the present invention. DETAILED DESCRIPTION

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

[0108] It should be noted that the following detailed descriptions are illustrative and are intended to provide further explanation of the present application. Unless otherwise specified, all technical and scientific terms used in this specification have the same meanings as those commonly understood by those skilled in the art to which the present application belongs.

[0109] It should be noted that the terms used herein are only for describing specific embodiments and are not intended to limit the exemplary embodiments according to the present application. As used herein, unless the context clearly indicates otherwise, the singular form is also intended to include the plural form. In addition, it should be understood that when the terms "comprise" and / or "include" are used in this specification, it indicates the presence of features, steps, operations, devices, components and / or combinations thereof.

[0110] In order to cope with the practical challenges of fault estimation, the embodiments of the present invention design a new predefined time observer for estimating input saturation, uncertain models, actuator faults, disturbances, and sensor faults within a predefined time. It avoids the time-consuming fault detection process that may cause system instability or significant performance degradation. A new practical predefined time fault-tolerant control is developed and an upper limit is provided for its stabilization time. Sufficient conditions for predefined time convergence have been established. In order to address potential problems related to singularities, a new singularity avoidance scheme is introduced. This non-singular property ensures that the tracking error does not approach infinity near the origin.

[0111] like Figure 1 As shown, the expected trajectory η d After entering the predefined time fault-tolerant controller, the command control input τ is provided c to the actuator; the USV forms a trajectory η under the action of the disturbance τ1 and the actual input τ. On the other hand, the force and torque τ caused by the fault a and the estimated value of υ in fault detection After fault detection and discrimination by threshold ε, the total uncertainty model, interference and fault d are obtained as the observer The input is used to feed back to the predefined time fault-tolerant controller for the calculation of the adaptive law; in addition, the ship's operating state is collected by the sensor and compared with the expected trajectory η d After calculation, the dynamic tracking error is obtained Used for calculation of control ratio in predefined time fault-tolerant controller.

[0112] The specific steps of implementing and designing the embodiment of the present invention include:

[0113] The first step is system modeling

[0114]

[0115] η=[x,y,ψ] T ,υ=[u,v,r] T (4)

[0116] in Indicates 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 set of real numbers, Represents n as a vector. τ1 represents the disturbance:

[0117] τ1=F w +F s (5)

[0118] Where Fw =[F wx ,F wy ,N w ] T is the wind resistance. s =[F sx ,F sy ,N s ] T is the wave resistance.

[0119] The uncertainty modeling △M, △C and △D and the nominal models M, C and D are defined as follows:

[0120] M1=M+ΔM (6)

[0121] C1=C+ΔC (7)

[0122] D1=D+ΔD (8)

[0123] Step 2: Fault Detection

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

[0125]

[0126] where η d is the expected trajectory.

[0127] The command input τ acting on the ship c And the actual input τ is modeled as follows:

[0128] τ=(I3-E)τ c +τ a (10)

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

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

[0131]

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

[0133]

[0134] We can get:

[0135]

[0136] Where K is the gain matrix.

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

[0138]

[0139] set up Satisfies the Lipschitz condition (i.e., the Lipschitz continuity condition, which is a stronger smoothness condition than uniform continuity), namely:

[0140]

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

[0142] Construct the following formula:

[0143]

[0144] The derivative of V0 is:

[0145]

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

[0147] The third step is fault estimation.

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

[0149]

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

[0151] In order to estimate the uncertain model, input saturation error, disturbance and fault, this embodiment constructs an observer The estimated 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 adaptation law is designed as follows:

[0159]

[0160] where 0 < p < 1 and K0 is the gain coefficient.

[0161] Step 4: Control law design.

[0162] Denote:

[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 follows:

[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 the non-singularity, ensuring It does not go to infinity near the origin.

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

[0190] The above scheme and design provided by the present invention are verified by examples as follows:

[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 value is η(0)=[-60m,1.39m,-71.33°] T and υ(0)=[0.005,0.006,0.004] T , the perturbation is τ d1 =-0.005sin(t),τ d2 =0.005sin(t),andτ d3 =-0.005sin(t), the expected trajectory state is [0m, 0m, 0°] T , the main parameters are k1 = 0.1, p = 0.9, τ M =100, andε=0.002, at t=20s, a fault occurs, e1=0.1, e2=0.3and e3=0.1. The test results are as follows Figure 2-Figure 8 shown.

[0192] Scenario 2: When t = 5s, a 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 as follows Figure 9-Figure 15 shown.

[0193] This embodiment also conducts 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 comparative tests of different algorithms, proving that the scheme of the present invention can achieve the above-mentioned effects and the effects are better than the existing schemes.

[0194] It should be noted that, unless otherwise defined, the technical terms or scientific terms used in the present invention should be understood by people with ordinary skills in the field to which the present invention belongs. The "first", "second" and similar words used in the present invention do not indicate any order, quantity or importance, but are only used to distinguish different components. "Include" or "comprise" and similar words mean that the elements or objects appearing before the word include the elements or objects listed after the word and their equivalents, without excluding other elements or objects. "Connect" or "connected" and similar words are not limited to physical or mechanical connections, but may include electrical connections, whether direct or indirect. "Up", "down", "left", "right" and the like are only used to indicate relative positional relationships. When the absolute position of the described object changes, the relative positional relationship may also change accordingly.

[0195] The above is only a preferred embodiment of the present invention, and does not limit the present invention in other forms. Any technician familiar with the profession may use the above disclosed technical content to change or modify it into an equivalent embodiment with equivalent changes. However, any simple modification, equivalent change and modification made to the above embodiment according to the technical essence of the present invention without departing from the technical solution of the present invention still belongs to the protection scope of the technical solution of the present invention.

[0196] This patent is not limited to the above-mentioned optimal implementation mode. Anyone can derive other forms of practical predefined time fault-tolerant tracking control methods for unmanned ships taking into account faults and saturation under the inspiration of this patent. All equal changes and modifications made within the scope of the patent application of the present invention shall fall within the scope of coverage of this patent.

Claims

1. A practical predefined time fault-tolerant tracking control method for an unmanned ship considering failure and saturation, characterized by: The desired trajectory of the USV η d After entering the predefined time fault-tolerant controller, the command control input τ is provided 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 caused by the fault a and the estimated value of υ in fault detection After fault detection and discrimination by threshold ε, the total uncertainty model, interference and fault d are obtained as the observer The input is used to calculate the adaptive law in the predefined time fault-tolerant controller; the ship's operating state is collected by the sensor and compared with the expected trajectory η d After calculation, the dynamic tracking error is obtained Used for calculation of control ratio in predefined time fault-tolerant controller.

2. The practical predefined-time fault-tolerant tracking control method for an unmanned surface vehicle (USV) considering faults and saturation according to claim 1, characterized in that: The USV is modeled as follows: η=[x,y,ψ] T ,υ=[u,v,r] T (4) in Indicates 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 set of real numbers, Represents n as a vector; τ1 represents the disturbance: τ1=F w +F s (5) Where F w =[F wx ,F wy ,N w ] T is wind resistance; F s =[F sx ,F sy ,N s ] T is the 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).

3. The practical predefined-time fault-tolerant tracking control method for an unmanned surface vehicle (USV) considering faults and saturation according to claim 2, characterized in that: The dynamic tracking error between the USV trajectory and the desired trajectory is given by the following formula: where η d is the expected trajectory; The command input τ acting on the ship c And the actual input τ is modeled as follows: τ=(I3-E)τ c +t a (10) in 0≤e i ≤1, e i = 0 means the participant is normal, and e i =1 means the participant fails completely; τ a represents the force and torque caused by the fault, τ c Indicates command control input; diag{a1,a2,…,a n } represents a diagonal matrix; Thus, equation (2) is written as: Expressed as the estimated value of υ in fault detection, the estimation error is defined as follows: Obtain: where K is the gain matrix; According to equations (11) and (13), there is: set up Satisfies the Lipschitz condition, that is: where L > 0 is the Lipschitz constant; Construct the following formula: The derivative of V0 is: If there is no fault, the critical state is However, if a failure occurs, the critical state becomes The threshold is set to when When it is greater than the threshold, it is determined that a fault is detected; min (A) represents the minimum eigenvalue of matrix A.

4. The practical predefined-time fault-tolerant tracking control method for an unmanned surface vehicle (USV) considering faults and saturation according to claim 3, characterized in that: Equation (11) is written as: where d represents the total uncertain model, disturbance, and fault; To estimate uncertain models, input saturation errors, disturbances, and faults, an observer is used. The estimated error is: Equation (18) is written as: set up Based on Young's inequality, we have: where a > 0; The calculation of the adaptation law in the predefined-time fault-tolerant controller is as follows: where 0 < p < 1 and K0 is the gain coefficient.

5. The practical predefined-time fault-tolerant tracking control method for an unmanned surface vehicle (USV) considering faults and saturation according to claim 4, characterized in that: Denote: x1 = η (24) u=RM -1 τ c (27) The system state equation is expressed as follows: Considering actuator saturation, a smooth model is defined 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, the following auxiliary variable is constructed: Let auxiliary vector 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.

6. An unmanned ship, characterized in that: During operation, the practical predefined-time fault-tolerant tracking control method for an unmanned surface vehicle (USV) considering faults and saturation according to any one of claims 1-5 is adopted.

7. 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, the steps of the practical predefined-time fault-tolerant tracking control method for an unmanned surface vehicle (USV) considering faults and saturation according to any one of claims 1-5 are implemented.

8. 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, the steps of the practical predefined-time fault-tolerant tracking control method for an unmanned surface vehicle (USV) considering faults and saturation according to any one of claims 1-5 are implemented.

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