A method and system for adaptive repetitive learning fault-tolerant control of high-order internal model of unmanned surface vessels

Abstract

This invention belongs to the field of intelligent control technology for marine vehicles, and discloses a high-order internal model adaptive repetitive learning fault-tolerant control method and system for unmanned surface vessels (USVs). The method first establishes a mathematical model of the USV, including actuator multiplicative failure faults, based on its dynamics and actuator fault characteristics. Then, it designs an observer to achieve full-state measurability of the USV system. Simultaneously, it uses an adaptive law to approximate the fault coefficients to estimate the actuator multiplicative failure faults. Next, for USV systems with periodic non-repeating trajectories, a high-order internal model repetitive learning fault-tolerant controller is designed. Under the condition of ensuring safe and stable system operation, the repetitive learning control gain and feedback control gain are obtained. Finally, trajectory tracking control of the USV system is achieved. The control method proposed in this invention can ensure stable and accurate tracking of time-varying periodic trajectories by the USV under conditions of partial state unmeasurability and actuator multiplicative failure faults.

Description

Technical Field

[0001] This invention belongs to the field of intelligent control technology for marine vehicles, specifically relating to a high-order internal model adaptive repetitive learning fault-tolerant control method and system for unmanned surface vessels. Background Technology

[0002] Unmanned Marine Vehicles (UMVs) have been widely used in marine environmental monitoring, resource exploration, search and rescue, and waterway management due to their superior maneuverability, environmental adaptability, high automation, and low cost. Achieving high-precision trajectory tracking is fundamental to completing various operational tasks; however, unmodeled dynamics and complex marine environmental disturbances often affect tracking performance. To address this, researchers have proposed various strategies such as sliding mode control and model predictive control. However, existing methods generally fail to effectively learn and utilize the potential temporal periodicity of the desired trajectory itself. When UMVs perform periodic tasks, repetitive learning control, which uses historical operational experience to correct current control commands, holds promise for further improving accuracy. Such methods have already been successfully applied in systems such as robotic arms.

[0003] However, applying repetitive learning control to UMVs still faces several prominent challenges: First, the system state is not fully measurable. Under harsh marine conditions, sensors are prone to damage or performance degradation, resulting in some states being unmeasurable. Existing solutions are mostly designed based on the assumption of full state measurability, and direct application when the state is unmeasurable can lead to performance degradation or even instability.

[0004] Second, there is the non-repetitive nature of the desired trajectory. In real-world tasks, the desired trajectory may change during different cycles as needed. Traditional repetitive learning control assumes that the desired trajectory is strictly repeated, making it difficult to handle this type of tracking problem with non-repetitive cycles.

[0005] Thirdly, there is the issue of actuator failure. The marine environment easily leads to multiplicative failures in actuators, severely weakening maneuverability. Most existing control strategies lack effective online fault-tolerance mechanisms, threatening system safety and reliability.

[0006] Furthermore, the idea of ​​using higher-order internal models to handle changing reference trajectories in iterative learning control provides inspiration for handling periodic non-repeating trajectories, but there are no reports on combining it with repetitive learning control for use in UMVs.

[0007] In summary, there is a lack of high-precision trajectory tracking solutions capable of simultaneously handling multiple complex situations such as unpredictable states, non-repeating trajectory changes, and actuator failures. Therefore, there is an urgent need to research an adaptive repetitive learning fault-tolerant control strategy that can simultaneously estimate the state, describe the non-repeating trajectory, and compensate for faults. Summary of the Invention

[0008] The purpose of this invention is to propose a high-order internal model adaptive repetitive learning fault-tolerant control method for unmanned surface vessels (USVs). This method can solve the problem of high-precision trajectory tracking control of USVs under complex operating conditions such as unmeasurable system state, periodic non-repetitive changes in the desired trajectory, and multiplicative failure of actuators.

[0009] To achieve the above objectives, the present invention adopts the following technical solution: A method for adaptive repetitive learning fault-tolerant control of high-order internal models of unmanned surface vessels includes the following steps: Step 1. Based on the dynamics and actuator failure characteristics of the unmanned surface vessel (USV), establish a mathematical model of the USV containing multiplicative actuator failures, providing a foundation for the subsequent design of the observer and the high-order internal model repetitive learning fault-tolerant controller; Step 2. To address the unmeasurability of the unmanned surface vessel (USV) system's state, an observer is designed to make the full state of the USV system measurable; an adaptive law is used to approximate the fault coefficients in order to estimate the multiplicative failure faults of the actuators. Step 3. For unmanned surface vessel systems with periodic non-repeating trajectories, design a high-order internal model repetitive learning fault-tolerant controller. Under the condition of ensuring safe and stable operation of the system, obtain the repetitive learning control gain and the feedback control gain. Step 4. Based on the fault coefficient, repetitive learning control gain, and feedback control gain, a high-order internal model repetitive learning fault-tolerant controller is used to realize trajectory tracking control of the unmanned surface vessel system.

[0010] Furthermore, based on the adaptive repetitive learning fault-tolerant control method for high-order internal models of unmanned surface vessels (USVs), this invention also proposes a corresponding high-order internal model adaptive repetitive learning fault-tolerant control system for USVs, the technical solution of which is as follows: A high-order internal model adaptive repetitive learning fault-tolerant control system for unmanned surface vessels includes: The model building module is used to build a mathematical model of the unmanned surface vessel (USV) containing multiplicative failure faults of the actuators, based on the dynamics and actuator failure characteristics of the USV, so as to provide a basis for the design of the subsequent observer and high-order internal model repetitive learning fault-tolerant controller. The observer design module is used to make the full state of the unmanned surface vessel system measurable by designing an observer to address the unmeasurability of the unmanned surface vessel system's state; and to approximate the fault coefficients using an adaptive law to estimate the multiplicative failure faults of the actuators. The controller design module is used to design a high-order internal model repetitive learning fault-tolerant controller for unmanned surface vessel systems with periodic non-repeating trajectories. Under the condition of ensuring the safe and stable operation of the system, the repetitive learning control gain and feedback control gain are obtained. And a trajectory tracking control module, which is used to achieve trajectory tracking control of the unmanned surface vessel system based on the fault coefficient, repetitive learning control gain and feedback control gain, using a high-order internal model repetitive learning fault-tolerant controller.

[0011] The present invention has the following advantages: As described above, this invention discloses a high-order internal model adaptive repetitive learning fault-tolerant control method for unmanned surface vessels (USVs). This method addresses complex operating conditions such as partially unmeasurable states, partial actuator failures, and periodically non-repeating trajectories. By constructing a state observer to estimate the unmeasurable states, it achieves full-state measurability of the USV system. Furthermore, this invention utilizes a high-order internal model to describe the trajectory's variation over a periodic period to handle periodically non-repeating desired trajectories. Additionally, this invention designs an adaptive law to approximate and compensate for actuator fault coefficients online, addressing multiplicative actuator failures, thereby achieving fault estimation and compensation. Finally, this invention synthesizes observation information to design a high-order internal model repetitive learning fault-tolerant controller, enabling the system to safely and stably track the ideal trajectory even under actuator multiplicative failures and periodically non-repeating trajectories, thus ensuring high-precision trajectory tracking with full-state control even under complex operating conditions. Attached Figure Description

[0012] Figure 1 This is a flowchart of the high-order internal model adaptive repetitive learning fault-tolerant control method for unmanned surface vessels in an embodiment of the present invention.

[0013] Figure 2 This is a control block diagram of the high-order internal model adaptive repetitive learning fault-tolerant control method for unmanned surface vessels in an embodiment of the present invention.

[0014] Figure 3 The tracking effect obtained by using the control method proposed in this invention Figure 1 .

[0015] Figure 4 The tracking effect obtained by using the control method proposed in this invention Figure 2 .

[0016] Figure 5 The tracking effect obtained by using the control method proposed in this invention Figure 3 .

[0017] Figure 6 The tracking effect obtained by using the control method proposed in this invention Figure 4 .

[0018] Figure 7 The tracking effect obtained by using the control method proposed in this invention Figure 5 .

[0019] Figure 8The tracking effect obtained by using the control method proposed in this invention Figure 6 . Detailed Implementation

[0020] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments: Example 1 This embodiment discloses a high-order internal model adaptive repetitive learning fault-tolerant control method for unmanned surface vessels (USVs). The general idea of ​​this method includes: building an USV test simulation system; establishing a mathematical model of the USV including actuator multiplicative failure faults based on the dynamics and actuator fault characteristics of the USV; designing a state observer to estimate the system state, providing support for precise control; using the high-order internal model to accurately describe the periodic non-repetitive expected trajectory; designing an adaptive law to approximate the actuator multiplicative failure fault coefficient in real time, providing a basis for fault compensation; and finally, constructing a high-order internal model repetitive learning fault-tolerant controller to ensure stable and accurate tracking of the time-varying periodic trajectory of the USV under conditions of partial state unpredictability and actuator multiplicative failure faults.

[0021] like Figure 1 As shown, an adaptive repetitive learning fault-tolerant control method for high-order internal models of unmanned surface vessels includes the following steps: Step 1. Based on the dynamics and actuator failure characteristics of the unmanned surface vessel (USV), establish a mathematical model of the USV including multiplicative actuator failures. This model provides a foundation for the subsequent design of the observer and the high-order internal model repetitive learning fault-tolerant controller. The multiplicative actuator failure is specifically a propulsion component failure.

[0022] In this embodiment, step 1 specifically includes: In step 1 of this embodiment, based on the dynamics and actuator failure characteristics of the unmanned surface vessel (USV), a mathematical model of the USV with multiplicative actuator failure is established, resulting in the system state equations for the USV with multiplicative actuator failure: (1) in, Indicates the first time, and For vectors, For rotation matrix, This indicates the yaw angle relative to Earth. Represents an invertible matrix. Represents the damping matrix. Represents the mooring force matrix. Indicates propulsion force including malfunctions; Represents an external disturbance that satisfies , It is a constant.

[0023] vector Defined as: .

[0024] in, , and These represent the longitudinal speed, rolling speed, and yaw rate of the hull, respectively.

[0025] vector Defined as: .

[0026] in, and These represent the x-coordinate and y-coordinate of the position relative to Earth.

[0027] Rotation matrix Defined as: .

[0028] Propulsion with faults The description is in the following form: (2) in, Indicates system control input, This is a matrix of fault coefficient pairs.

[0029] ,in Represents the notation of a diagonal matrix. Indicates the first The failure coefficient of each actuator satisfies , , and They are respectively The upper and lower bounds, Time indicates the first Each actuator is fault-free. The smaller the value, the more severe the fault. Time indicates the first An actuator experiences a multiplicative failure, meaning the actuator itself is experiencing a multiplicative failure, rather than a complete failure.

[0030] In step 1 of this embodiment, the unmanned surface vessel system is also included. Linearization is performed at the point, and an auxiliary state vector is constructed simultaneously. for: .

[0031] The unmanned surface vessel system is described as follows: (3) in, , , Indicates the measurement output. This is the measurement matrix.

[0032] Step 2. Addressing the unmeasurability of the unmanned surface vessel (USV) system's state, an observer is designed to make the system's full state measurable. An adaptive law is used to approximate the fault coefficients, enabling accurate estimation of multiplicative actuator failures, thus providing a foundation for compensating for multiplicative failures.

[0033] In step 2 of this embodiment, the observer is designed as follows: (4) in, express The estimated value, This represents the ideal control input vector. , , , Indicates control input, Represents the observer gain matrix. express The estimated value.

[0034] In step 2 of this embodiment, to eliminate the impact of multiplicative failure faults, the following controller is designed: (5) in, for The estimate, , It is generated by the following adaptive law: (6) in, For adaptive parameters, ; As a scalar, ; It is a matrix.

[0035] Constructing a matrix for: The multiplicative failure coefficient can be estimated using the adaptive law.

[0036] In step 2 of this embodiment, the definition of an error vector is also included. and : , .

[0037] The error system for the unmanned surface vessel is derived as follows: (7) in, .

[0038] In step 2 of this embodiment, the following method is also used to construct a Lyapunov function of the following form for the error system shown in formula (7): (8) in, It is a positive definite matrix. .

[0039] The constructed Lyapunov function Regarding time Taking the derivative, we get: (9) function Represented as: ,in Represents a matrix.

[0040] According to the adaptive law shown in formula (6), we get: (10) in, This indicates the system output error.

[0041] based on and Then we have: (11) Formula (9) can be rewritten as: (12) definition , As a scalar, Formula (12) can be rewritten as: (13) It can guarantee the consistent eventual boundedness of the state estimation error, that is, satisfy: (14) (15) in, For a matrix, It is the identity matrix. It is a scalar.

[0042] Obtain the observer gain matrix for: .

[0043] Step 3. For unmanned surface vessel systems with periodic non-repeating trajectories, design a high-order internal model repetitive learning fault-tolerant controller. Under the condition of ensuring safe and stable operation of the system, obtain the repetitive learning control gain and the feedback control gain.

[0044] The desired trajectory is not always repeated, but varies between periods, exhibiting the characteristics of a periodic non-repeating trajectory. To solve this problem and improve the control effect, a repetitive learning controller and a feedback controller are designed.

[0045] In step 3 of this embodiment, the ideal model of the unmanned surface vessel system is described as follows: (16) in, , and These represent the ideal state, ideal input, and ideal output of the unmanned surface vessel system, respectively.

[0046] The desired trajectory of an unmanned surface vessel (USV) is not always periodic, but often varies continuously between periods, which can be achieved through the following: The internal model form of the order represents a periodically changing non-repeating trajectory, i.e., a periodically non-repeating trajectory: (17) in, It is a constant. Indicates the period length. , , Representing the first, second, and third orders of an ideal respectively. Order state vector.

[0047] To facilitate convergence analysis in the discrete periodic domain, a shift operator is introduced. Its satisfaction Then formula (17) can be rewritten as: (18) in, .

[0048] To achieve full-state trajectory tracking, the following high-order internal model repetitive learning fault-tolerant controller is proposed: (19) in, This represents the repetitive learning control law. This indicates the control law that was repeatedly learned in the previous cycle; Indicates a feedback controller; For system estimation error, ; This indicates the system estimation error in the previous period; This indicates the system output error of the previous cycle; This is the feedback control gain matrix.

[0049] Defined as: .

[0050] Defined as: .

[0051] Defined as: .

[0052] in, , and This represents the repeated learning control gain matrix. .

[0053] Based on formulas (4), (16), and (19), the system fault error is calculated as follows: (20) in, For the input error vector, Defined as: .

[0054] According to formula (18), we get: (twenty one) in, This represents the input error vector of the previous cycle.

[0055] make , ,get: (twenty two) in, Indicates the first period of the previous cycle Order of input error vector.

[0056] Therefore, we get: (twenty three) in, It is a constant. It is the Euclidean norm.

[0057] In order to make ,in , For the first One cycle, At the initial moment, ,get: (twenty four) Using formula (24), the repetitive learning control gain matrix is ​​designed under the condition of ensuring the safe and stable operation of the system. .

[0058] In step 3 of this embodiment, a Lyapunov function is constructed for the high-order internal model repetitive learning fault-tolerant controller. for: (25) in, It is a symmetric positive definite matrix. for The inverse matrix.

[0059] Lyapunov function Taking the derivative with respect to time, we get: (26) Using inequalities ,in and For a matrix, and Each is a matrix sum matrix Transpose of the given value, we get: (27) in, and It is a scalar, and , .

[0060] .

[0061] Based on formula (24), we obtain It eventually converges to 0, which can be obtained from formula (27): (28) For the state tracking error to eventually become uniformly bounded, the following inequality must be satisfied: (29) in, For auxiliary matrix, .

[0062] The feedback control gain of the high-order internal model repetitive learning fault-tolerant controller is obtained as follows: (30) The repetitive learning control gain of the high-order internal model repetitive learning fault-tolerant controller is: (31) (32) Based on formulas (30), (31), and (32), the design of the high-order internal model repetitive learning fault-tolerant controller shown in formula (19) is completed, and the observer gain of the system is finally obtained. Feedback control gain and repetitive learning control gain , and .

[0063] The method of this invention enables the unmanned surface vessel system to still have good control and tracking performance even when there are some actuator failures and disturbances.

[0064] Thus, the method of this invention effectively overcomes the impact of missing information by designing an observer to accurately estimate the multiplicative failure faults and disturbances of the unmanned surface vessel actuators. On this basis, the method of this invention also designs a high-order internal model repetitive learning fault-tolerant controller for the system to realize composite disturbance-resistant fault-tolerant control of the unmanned surface vessel power system, and provides the design of the observer and controller that makes the unmanned surface vessel system eventually uniform and bounded.

[0065] Step 4. Based on the fault coefficient, repetitive learning control gain, and feedback control gain, a high-order internal model repetitive learning fault-tolerant controller is used to realize trajectory tracking control of the unmanned surface vessel system.

[0066] like Figure 2 The control block diagram of the high-order internal model adaptive repetitive learning fault-tolerant control method for unmanned surface vessels proposed in this invention is shown. Sensors are used to measure the actual output of the system and convert the output signal into the signal required for subsequent analysis. Observers are used to obtain all system states, approximate multiplicative failure faults using an adaptive law, estimate the fault coefficient, compensate for the fault based on the fault coefficient, compare the trajectory information described by the high-order internal model with the feedback information, and send it to the repetitive learning controller. The trajectory information of the previous cycle, i.e., the ideal trajectory of the previous cycle, is stored in the memory. The controller inputs control signals to the actuators to precisely control the system. The repetitive learning fault-tolerant control mainly includes feedback control and repetitive learning control.

[0067] The method of this invention can ensure that the unmanned surface vessel system can still operate safely and stably with high precision even when the actuators experience multiplicative failures, some states are unmeasurable, and the trajectory period is not repeated.

[0068] In addition, to verify the effectiveness of the method proposed in this invention, the following specific experiments are also provided: like Figures 3 to 8 As shown, state , , , , , These are longitudinal position, lateral position, position yaw angle, longitudinal speed, yaw speed, and yaw rate, respectively. , , , , , They are respectively states , , , , , The target being tracked.

[0069] Initial moment hour, , , , , , In the case of partial thruster failure, the simulation effect with a period of 4 seconds obtained by using the control method proposed in this invention is as follows: Figures 3 to 8 As shown, after two cycles, all state trajectories were well tracked. Furthermore, with the help of a feedback controller, the tracking error converges over time, ensuring good transient behavior during the learning process. The high-order internal model adaptive repetitive learning fault-tolerant control method for unmanned surface vessels proposed in this invention can correctly perform the tracking of periodic non-repetitive trajectories.

[0070] Example 2 This embodiment 2 describes an adaptive repetitive learning fault-tolerant control system for high-order internal models of unmanned surface vessels. This system is based on the same inventive concept as the adaptive repetitive learning fault-tolerant control method for high-order internal models of unmanned surface vessels in embodiment 1.

[0071] Specifically, the high-order internal model adaptive repetitive learning fault-tolerant control system for the unmanned surface vessel includes the following modules: The model building module is used to establish a mathematical model of the unmanned surface vessel (USV) including multiplicative failure faults of the actuators, based on the dynamics and actuator failure characteristics of the USV. This provides a foundation for the design of subsequent observers and high-order internal model repetitive learning fault-tolerant controllers.

[0072] The observer design module is used to make the full state of the unmanned surface vessel (USV) system measurable by designing an observer; and to approximate the fault coefficients using an adaptive law to estimate the multiplicative failure faults of the actuators.

[0073] The controller design module is used to design a high-order internal model repetitive learning fault-tolerant controller for unmanned surface vessel systems with periodic non-repeating trajectories. Under the condition of ensuring safe and stable operation of the system, the repetitive learning control gain and feedback control gain are obtained.

[0074] And a trajectory tracking control module, which is used to achieve trajectory tracking control of the unmanned surface vessel system based on the fault coefficient, repetitive learning control gain and feedback control gain, using a high-order internal model repetitive learning fault-tolerant controller.

[0075] It should be noted that the implementation process of the functions and roles of each functional module in the high-order internal model adaptive repetitive learning fault-tolerant control system of unmanned surface vessels is detailed in the implementation process of the corresponding steps in the method of Example 1, and will not be repeated here.

[0076] Of course, the above description is only a preferred embodiment of the present invention. The present invention is not limited to the above-described embodiments. It should be noted that any equivalent substitutions or obvious modifications made by those skilled in the art under the guidance of this specification fall within the scope of this specification and should be protected by the present invention.

Claims

1. A high-order internal model adaptive repetitive learning fault-tolerant control method for unmanned surface vessels, characterized in that, Includes the following steps: Step 1. Based on the dynamics and actuator failure characteristics of the unmanned surface vessel (USV), establish a mathematical model of the USV containing multiplicative actuator failures, providing a foundation for the subsequent design of the observer and the high-order internal model repetitive learning fault-tolerant controller; Step 2. To address the unmeasurability of the unmanned surface vessel (USV) system's state, an observer is designed to make the full state of the USV system measurable; an adaptive law is used to approximate the fault coefficients in order to estimate the multiplicative failure faults of the actuators. Step 3. For unmanned surface vessel systems with periodic non-repeating trajectories, design a high-order internal model repetitive learning fault-tolerant controller. Under the condition of ensuring safe and stable operation of the system, obtain the repetitive learning control gain and the feedback control gain. Step 4. Based on the fault coefficient, repetitive learning control gain, and feedback control gain, a high-order internal model repetitive learning fault-tolerant controller is used to realize trajectory tracking control of the unmanned surface vessel system.

2. The unmanned surface vessel high-order internal model adaptive repetitive learning fault-tolerant control method according to claim 1, characterized in that, In step 1, based on the dynamics and actuator failure characteristics of the unmanned surface vessel (USV), a mathematical model of the USV with multiplicative actuator failure is established, resulting in the system state equations for the USV with multiplicative actuator failure: (1) in, Indicates the first time, and For vectors, For rotation matrix, This indicates the yaw angle relative to Earth. Represents an invertible matrix. Represents the damping matrix. Represents the mooring force matrix. Indicates propulsion force including malfunctions; Represents an external disturbance that satisfies , It is a constant; vector Defined as: ; in, , and These represent the longitudinal speed, rolling speed, and yaw rate of the hull, respectively. vector Defined as: ; in, and These represent the x-coordinate and y-coordinate of the position relative to Earth; Rotation matrix Defined as: ; Propulsion with faults The description is in the following form: (2) in, Indicates system control input, This is a matrix of fault coefficient pairs; ,in Represents the notation of a diagonal matrix. Indicates the first The failure coefficient of each actuator satisfies , , and They are respectively The upper and lower bounds, Time indicates the first Each actuator is fault-free. Time indicates the first A multiplicative failure of an actuator.

3. The unmanned surface vessel high-order internal model adaptive repetitive learning fault-tolerant control method according to claim 2, characterized in that, Step 1 also includes the unmanned surface vessel system in Linearization is performed at the point, and an auxiliary state vector is constructed simultaneously. for: ; The unmanned surface vessel system is described as follows: (3) in, , , Indicates the measurement output. This is the measurement matrix.

4. The unmanned surface vessel high-order internal model adaptive repetitive learning fault-tolerant control method according to claim 3, characterized in that, In step 2, the observer is designed in the following form: (4) in, express The estimated value, This represents the ideal control input vector. , , , Indicates control input, Represents the observer gain matrix. express The estimated value.

5. The unmanned surface vessel high-order internal model adaptive repetitive learning fault-tolerant control method according to claim 4, characterized in that, In step 2, to eliminate the impact of multiplicative failure, the following controller is designed: (5) in, for The estimate, , It is generated by the following adaptive law: (6) in, For adaptive parameters, ; As a scalar, ; It is a matrix; Constructing a matrix for: .

6. The unmanned surface vessel high-order internal model adaptive repetitive learning fault-tolerant control method according to claim 5, characterized in that, Step 2 also includes defining an error vector. and : , ; The error system for the unmanned surface vessel is derived as follows: (7) in, .

7. The unmanned surface vessel high-order internal model adaptive repetitive learning fault-tolerant control method according to claim 6, characterized in that, Step 2 also includes constructing a Lyapunov function of the form shown in formula (7) for the error system. : (8) in, It is a positive definite matrix. ; The constructed Lyapunov function Regarding time Taking the derivative, we get: (9) function Represented as: ,in Represents a matrix; According to the adaptive law shown in formula (6), we get: (10) in, Indicates the system output error; based on and Then we have: (11) Formula (9) can be rewritten as: (12) definition , As a scalar, Formula (12) can be rewritten as: (13) It can guarantee the consistent eventual boundedness of the state estimation error, that is, satisfy: (14) (15) in, For a matrix, It is the identity matrix. It is a scalar; Obtain the observer gain matrix for: .

8. The unmanned surface vessel high-order internal model adaptive repetitive learning fault-tolerant control method according to claim 7, characterized in that, In step 3, the ideal model of the unmanned surface vessel system is described as follows: (16) in, , and These represent the ideal state, ideal input, and ideal output of the unmanned surface vessel system, respectively. Through the following The internal model form of the order represents a periodically changing non-repeating trajectory, i.e., a periodically non-repeating trajectory: (17) in, It is a constant. Indicates the period length. , , Representing the first, second, and third orders of an ideal respectively. Order state vector; Introducing shift operators Its satisfaction Then formula (17) can be rewritten as: (18) in, ; To achieve full-state trajectory tracking, the following high-order internal model repetitive learning fault-tolerant controller is proposed: (19) in, This represents the repetitive learning control law. This indicates the control law that was repeatedly learned in the previous cycle; Indicates a feedback controller; For system estimation error, ; This indicates the system estimation error in the previous period; This indicates the system output error of the previous cycle; For feedback control gain matrix; Defined as: ; Defined as: ; Defined as: ; in, , and This represents the repeated learning control gain matrix. ; Based on formulas (4), (16), and (19), the system fault error is calculated as follows: (20) in, For the input error vector, Defined as: ; According to formula (18), we get: (21) in, This represents the input error vector from the previous cycle; make , ,get: (22) in, Indicates the first period of the previous cycle Order of input error vector; Therefore, we get: (23) in, It is a constant. It is the Euclidean norm; In order to make ,in , For the first One cycle, At the initial moment, ,get: (24) Using formula (24), the repetitive learning control gain matrix is ​​designed under the condition of ensuring the safe and stable operation of the system. .

9. The high-order internal model adaptive repetitive learning fault-tolerant control method for unmanned surface vessels according to claim 8, characterized in that, In step 3, a Lyapunov function is constructed for the high-order internal model repetitive learning fault-tolerant controller. for: (25) in, It is a symmetric positive definite matrix. for The inverse matrix; Lyapunov function Taking the derivative with respect to time, we get: (26) Using inequalities ,in and For a matrix, and Each is a matrix sum matrix Transpose of the given value, we get: (27) in, and It is a scalar, and , ; ； Based on formula (24), we obtain It eventually converges to 0, which can be obtained from formula (27): (28) For the state tracking error to eventually become uniformly bounded, the following inequality must be satisfied: (29) in, For auxiliary matrix, ; The feedback control gain of the high-order internal model repetitive learning fault-tolerant controller is obtained as follows: (30) The repetitive learning control gain of the high-order internal model repetitive learning fault-tolerant controller is: (31) (32)。 10. A high-order internal model adaptive repetitive learning fault-tolerant control system for unmanned surface vessels, characterized in that, include: The model building module is used to build a mathematical model of the unmanned surface vessel (USV) containing multiplicative failure faults of the actuators, based on the dynamics and actuator failure characteristics of the USV, so as to provide a basis for the design of the subsequent observer and high-order internal model repetitive learning fault-tolerant controller. The observer design module is used to make the full state of the unmanned surface vessel (USV) system measurable by designing an observer; and to approximate the fault coefficients using an adaptive law to estimate the multiplicative failure faults of the actuators. The controller design module is used to design a high-order internal model repetitive learning fault-tolerant controller for unmanned surface vessel systems with periodic non-repeating trajectories. Under the condition of ensuring the safe and stable operation of the system, the repetitive learning control gain and feedback control gain are obtained. And a trajectory tracking control module, which is used to achieve trajectory tracking control of the unmanned surface vessel system based on the fault coefficient, repetitive learning control gain and feedback control gain, using a high-order internal model repetitive learning fault-tolerant controller.

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