A multi-unmanned ship cooperative output feedback adaptive fault-tolerant optimization control method

Abstract

The application discloses a kind of multi-unmanned ship cooperative output feedback adaptive fault-tolerant optimization control methods, including according to the mathematical model of multi-unmanned ship system design neural network state observer;According to the definition of composite Lyapunov function of cooperative tracking error variable in combination with neural network state observer, the feedforward fault-tolerant controller containing parameter online adaptive update law is designed based on backstepping method;Based on nominal error affine system definition infinite time domain performance cost function to construct Hamilton-Jacobi-Bellman equation;Based on Hamilton-Jacobi-Bellman equation in combination with evaluation neural network, obtain optimization feedback controller;According to the composite optimization control instruction of feedforward fault-tolerant controller and optimization feedback controller, to realize multi-unmanned ship cooperative output feedback adaptive fault-tolerant optimization control.The technical problem that existing multi-unmanned ship control method cannot effectively resist intermittent failure and external disturbance at the same time, control precision and energy consumption are considered, and the calculation complexity is high.

Description

Technical Field

[0001] This invention relates to the field of fault-tolerant control technology for multiple unmanned vessels, and in particular to a collaborative output feedback adaptive fault-tolerant optimization control method for multiple unmanned vessels. Background Technology

[0002] In recent years, with the deepening of marine resource development and utilization, unmanned surface vessels (USVs), with their core characteristics of intelligence and autonomy, have played an increasingly important role in marine exploration, environmental monitoring, and security patrols. Compared with traditional manned vessels, USVs can adapt to long-term, high-intensity continuous operations, greatly expanding human capabilities in exploring the ocean. However, USV platforms are typically small in size, resulting in limited energy carrying capacity. Therefore, optimizing energy consumption during control has become a key technological bottleneck for extending their operational endurance and improving mission efficiency.

[0003] However, unmanned surface vessels (USVs) face numerous challenges in actual deployment: First, external disturbances such as wind, waves, and currents in the marine environment, as well as the unknown nonlinearities of the hull hydrodynamic model, bring serious uncertainties to the control system; second, in practical applications, due to sensor limitations, it is often difficult to accurately measure the full speed state of the USV; and more seriously, the USV's propulsion system is prone to intermittent failures in harsh environments, which can severely reduce formation tracking performance and even damage system stability.

[0004] Currently, although there is considerable research on fault-tolerant control for multiple unmanned vessels, most solutions focus only on satisfying stability constraints, neglecting optimality issues in the control process (such as energy consumption). Optimal control of nonlinear systems typically requires solving complex HJB equations, traditionally approximated using adaptive dynamic programming, such as an "actuator-evaluator" dual-network architecture. However, for multi-unmanned vessel tracking tasks with extremely high real-time requirements, the iterative learning of the dual network incurs a massive computational burden. Therefore, designing an optimal tracking control method for multi-unmanned vessels that can effectively resist intermittent faults and external disturbances while balancing control accuracy and energy consumption, and with low computational complexity, is a pressing technical challenge. Summary of the Invention

[0005] This invention provides a multi-unmanned vessel cooperative output feedback adaptive fault-tolerant optimization control method to overcome the above-mentioned technical problems.

[0006] To achieve the above objectives, the technical solution of the present invention is as follows: A collaborative output feedback adaptive fault-tolerant optimization control method for multiple unmanned surface vessels includes the following steps: S1: Construct a mathematical model for a multi-unmanned surface vessel system that includes a propeller intermittent failure model; S2: Design a neural network state observer based on the mathematical model of a multi-unmanned vessel system; S3: Based on the preset reference signal and the mathematical model of the multi-unmanned vessel system, define the cooperative tracking error variable; based on the cooperative tracking error variable and the neural network state observer, define the composite Lyapunov function, and design a feedforward fault-tolerant controller with online adaptive update law of parameters based on the backstepping method. S4: Construct a nominal error affine system based on the cooperative tracking error variable, define an infinite time-domain performance cost function based on the nominal error affine system to construct the Hamilton-Jacobi-Bellman equation; combine the Hamilton-Jacobi-Bellman equation with an evaluation neural network to obtain an optimized feedback controller; S5: Based on the feedforward fault-tolerant controller and the optimized feedback controller, obtain composite optimized control commands, and then realize the optimized control of multi-unmanned vessel cooperative output feedback adaptive fault tolerance.

[0007] Furthermore, the mathematical model of the multi-unmanned vessel system constructed in S1 is as follows:

[0008]

[0009]

[0010]

[0011]

[0012] In the formula: Indicates the first The state vector of the ship in the geodetic coordinate system and ; Indicates the first The ship's position and heading angle; Denotes the velocity vector in the attached coordinate system and ; Indicates longitudinal velocity, lateral velocity, and bow roll rate; Represents the transformation rotation matrix; Represents the inertia matrix; Represents the Coriolis and centripetal force matrix; Represents the hydrodynamic damping matrix; Indicates unknown dynamic items in the system; Represents the velocity vector in the geodetic coordinate system; express The first derivative; Represents the lumped dynamics of an unknown nonlinear system; This indicates the actual actuator control commands output, taking into account the possibility of intermittent thruster failures. Represents the ideal input instruction and ; express Element; Indicates the unknown fault time interval Intermittent faults occur within the actuator, and the corresponding actuator efficiency factor is... ; express The lower bound; Represents an unknown bias fault vector; express The first derivative; This indicates transpose.

[0013] Furthermore, step S2 specifically includes the following steps: S21: Based on the mathematical model of the multi-unmanned vessel system, the subsystem state vector is defined as follows: and ; S22: Based on the state vector of the subsystem, design the neural network state observer as follows:

[0014]

[0015]

[0016] In the formula: express The estimate; express The estimate; express The estimate; express The estimate; express The estimate; express The estimate; Represents the parameter matrix and , ; Indicates the observer gain; Indicates correspondence of The estimated value; express , , The first derivative.

[0017] Furthermore, step S3 specifically includes the following steps: S31: Define the reference signal as... and ; Indicates the desired position and desired heading angle; S32: Based on the mathematical model of the multi-unmanned surface vessel system and the aforementioned reference signal, Define the collaborative tracking error variable as:

[0018]

[0019]

[0020] In the formula: Indicates the first Local expected reference signal of an unmanned surface vessel; Represents the desired position offset vector and ; The x and y coordinates represent the positional offset; This represents the position tracking error vector; Represents the speed tracking error vector; This indicates that the state observer is used to... The estimated velocity-state value is obtained; Represents a virtual control law; S33: Define the virtual control law as... ; The signal represents the virtual feedforward controller; This indicates the signal of the virtual feedback optimization controller; Furthermore, based on the position tracking error vector, the virtual feedforward controller is designed as follows:

[0021] In the formula: Indicate design parameters and ; express The first derivative; S34: Construct the Lyapunov function based on the position tracking error vector for:

[0022] Based on Lyapunov functions Based on the velocity tracking error vector and the neural network, a composite Lyapunov function is defined. for:

[0023] In the formula: This represents the positive definite design parameters used to adjust the adaptive convergence rate; Indicates adaptive parameters and ; Represents the error variable and = ; express The estimated value; = ; express The estimated value; Indicates the error in neural network weight estimation and ; Represents the weights of the neural network; express The estimated value; S35: For composite Lyapunov functions Differentiate to obtain the composite Lyapunov function. The derivative of the composite Lyapunov function is used to ensure that... Since the derivative is less than or equal to 0, a feedforward fault-tolerant controller with an online adaptive update law for parameters is designed using the backstepping method, combining the virtual control law with the velocity tracking error vector and the position tracking error vector.

[0024]

[0025]

[0026]

[0027]

[0028] In the formula: This indicates a feedforward fault-tolerant controller; Indicates adaptive parameters; The basis functions of a neural network; express The first derivative; This represents the positive definite design parameters used to adjust the adaptive convergence rate; express The first derivative; express The first derivative; express The first derivative; This represents the positive definite design parameters used to adjust the adaptive convergence rate.

[0029] Furthermore, step S4 specifically includes the following steps: S41: Define the optimal feedback term as and ;and The signal represents the optimized feedback controller signal; the nominal error affine system is constructed based on the cooperative tracking error variable and the optimal feedback term as follows:

[0030] In the formula: Describes the augmented error vector and ; Represents the control gain matrix and ; Indicates the drift term and ; Represents the parameter matrix; This represents a nonlinear function used to compensate for the speed tracking error vector; express The first derivative; S42: Defining an Infinite Time-Domain Performance Cost Function Based on a Nominal Error Affine System for:

[0031] In the formula: This represents the infinite time-domain performance metrics of the design; Indicates time; This represents a positive definite weight matrix; This represents the control energy penalty matrix; S43: Based on optimal control theory and the performance cost function in the infinite time domain Define the Hamiltonian function for:

[0032] In the formula: Represents the infinite time-domain performance cost function gradient and ; express The abbreviated form; S44: Order To obtain the theoretically optimal feedback control law for:

[0033] In the formula: The gradient of the optimal cost function is represented. express The abbreviated form; The theoretical optimal feedback control law Substituting back the Hamiltonian function, we obtain the Hamilton-Jacobi-Bellman equation, i.e., the HJB equation:

[0034] S45: Considering the nonlinear partial differential properties of the HJB equation, the optimal cost function is approximated using an evaluation neural network as follows:

[0035] In the formula: This represents the optimal cost function after approximation; Represents the basis functions for evaluating neural networks; This represents the transpose of the weight estimates for evaluating a neural network. And the gradient of the optimal cost function after approximation Represented as:

[0036] In the formula: express The abbreviated form; According to the gradient Obtain the approximate optimal control law for:

[0037] S46: Define the Hamiltonian function Approximate Hamiltonian function residual In order to make weight The objective function converges to the optimal value and is minimized by using gradient descent to minimize the squared error. and Therefore, an online adaptive update law for evaluating network weights is designed. for:

[0038] In the formula: Indicates the direction of the search gradient for the weights; This represents the drift term obtained by approximation using a neural network. The estimated value; This represents the current Bellman residual value; By evaluating the online adaptive update law of network weights Update and obtain the optimal feedback controller in the optimal control law. .

[0039] Furthermore, the composite optimization control command, i.e. the ideal input command, obtained in S5 is:

[0040] In the formula: The signal represents the feedforward fault-tolerant controller; This represents the signal of the optimal feedback controller in the optimal control law.

[0041] Beneficial Effects: This invention provides a collaborative output feedback adaptive fault-tolerant optimization control method for multiple unmanned surface vessels (USVs). Based on the backstepping method, a feedforward fault-tolerant controller incorporating an online adaptive update law for parameters is designed to compensate for the effects of system nonlinear dynamics and actuator failures. For unpredictable intermittent thruster failures, this invention designs an adaptive feedforward fault-tolerant compensation mechanism, i.e., a feedforward fault-tolerant controller, ensuring closed-loop system stability under actuator efficiency decay and bias failures. An infinite time-domain performance cost function is defined based on the nominal error affine system to construct the Hamilton-Jacobi-Bellman equation. An evaluation neural network is combined with the Hamilton-Jacobi-Bellman equation to obtain an optimized feedback controller. Unlike traditional fault-tolerant control that only guarantees stability, this invention introduces an optimization objective, i.e., the infinite time-domain performance cost function, and actively adjusts the trade-off between tracking error and energy consumption through adaptive dynamic programming, making it highly suitable for long-term deployment of USVs. This invention transforms the complex tracking optimization problem into a stabilization problem of collaborative tracking error variables, avoiding the computational burden of traditional dual-network adaptive dynamic programming algorithms and improving the real-time performance of the control algorithm. Attached Figure Description

[0042] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0043] Figure 1 The flowchart is a process for the multi-unmanned vessel cooperative output feedback adaptive fault-tolerant optimization control method of the present invention; Figure 2 This is a block diagram of the core technology of the multi-unmanned vessel cooperative output feedback adaptive fault-tolerant optimization control method in this embodiment; Figure 3 This is a curve showing the unmanned vessel's navigation trajectory in this embodiment; Figure 4 This is a graph showing the relationship between the unmanned vessel's forward direction and position and the tracking error in this embodiment. Figure 5 This is a graph showing the lateral position and tracking error of the unmanned vessel in this embodiment; Figure 6 This is a graph showing the heading angle and error curve of the unmanned vessel in this embodiment; Figure 7 For the unmanned vessel thruster output in this embodiment A curve graph; Figure 8 For the unmanned vessel thruster output in this embodiment A curve graph; Figure 9For the unmanned vessel thruster output in this embodiment The curve graph. Detailed Implementation

[0044] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0045] This embodiment provides a multi-unmanned surface vessel cooperative output feedback adaptive fault-tolerant optimization control method, such as Figures 1 to 2 As shown, the specific steps include: S1: Construct a mathematical model for a multi-unmanned surface vessel system that includes a propeller intermittent failure model; Specifically, establish by The unmanned vessel formation model consisting of 10 follower ships, the first The mathematical model of an unmanned vessel in its own attached coordinate system is represented as follows:

[0046]

[0047]

[0048]

[0049] In the formula: Indicates the first The state vector of the ship in the geodetic coordinate system and ; Indicates the first The ship's position and heading angle; Denotes the velocity vector in the attached coordinate system and ; Indicates longitudinal velocity, lateral velocity, and bow roll rate; Represents the transformation rotation matrix; Represents the inertia matrix; Represents the Coriolis and centripetal force matrix; Represents the hydrodynamic damping matrix; Indicates unknown dynamic items in the system; Represents the velocity vector in the geodetic coordinate system; express The first derivative; Represents the lumped dynamics of an unknown nonlinear system; The intermittent failure model of the thruster is as follows:

[0050] In the formula: This indicates the actual actuator control commands output, taking into account the possibility of intermittent thruster failures. Represents the ideal input instruction and ; express Element; Indicates the unknown fault time interval Intermittent faults occur within the actuator, and the corresponding actuator efficiency factor is... ; express The lower bound; Represents an unknown bias fault vector; express The first derivative; This indicates transpose.

[0051] S2: Design a neural network state observer based on the mathematical model of the multi-unmanned surface vessel system, specifically including: S21: Due to the velocity vector Unable to be directly measured, using neural networks to measure unknown functions Online approximation is performed, decoupling the system dynamics into three independent subsystems, with state observers designed for longitudinal, lateral, and bow directions respectively. In this embodiment, the subsystem state vector is defined based on the mathematical model of the multi-unmanned surface vessel system. and ; S22: Based on the state vector of the subsystem, design the neural network state observer as follows:

[0052]

[0053]

[0054] In the formula: express The estimate; express The estimate; express The estimate; express The estimate; express The estimate; express The estimate; Represents the parameter matrix and , ; Indicates the observer gain; Indicates correspondence of The estimated value; express , , The first derivative. In this embodiment, to ensure the asymptotic stability of the observation errors of each subsystem, the observer gain is selected. Make ( All of them are matrix, ; S3: Based on the preset reference signal and the mathematical model of the multi-unmanned vessel system, define the cooperative tracking error variable; based on the cooperative tracking error variable and the neural network state observer, define the composite Lyapunov function, and design a feedforward fault-tolerant controller with online adaptive update law of parameters based on the backstepping method. The specific steps include: S31: In the multi-unmanned vessel cooperative formation control framework, this embodiment employs a pilot-follower method to maintain the system's formation configuration and track its trajectory. To characterize the macroscopic motion trend of the formation during mission execution and the geometric constraints between vessels, a virtual pilot is introduced as a global reference benchmark. The reference signal is defined based on the ideal motion trajectory of the virtual pilot in the geodetic coordinate system. and ; Indicates the desired position and desired heading angle; S32: Considering the first The unmanned vessels following the formation need to maintain a specific relative geometric position, and the desired position offset vector is defined as follows: To accurately describe the real-time target position of the following ship in the geodetic coordinate system, a rotation matrix is ​​used. Mapping the relative offset in the attached coordinate system to the geodetic coordinate system, thereby constructing the first... Local expected reference signal of an unmanned vessel Based on the mathematical model of the multi-unmanned surface vessel system and combined with the reference signal, Define the collaborative tracking error variable as:

[0055]

[0056]

[0057] In the formula: Indicates the first Local expected reference signal of an unmanned surface vessel; Represents the desired position offset vector and ; The x and y coordinates represent the positional offset; This represents the position tracking error vector; Represents the speed tracking error vector; This indicates that the state observer is used to... The estimated velocity-state value is obtained; The virtual control law is represented; the position tracking error vector not only reflects the tracking performance of a single ship to the navigator, but is also the core input for the subsequent design of the adaptive feedforward fault-tolerant controller and the ADP (Adaptive Dynamic Programming) feedback optimization controller. This embodiment also includes... Differentiating, we get:

[0058] In the formula: The observation error of the state observer is represented by... ; S33: Define the virtual control law as... ; The signal represents the virtual feedforward controller; This indicates the signal of the virtual feedback optimization controller; Furthermore, based on the position tracking error vector, the virtual feedforward controller is designed as follows:

[0059] In the formula: Indicate design parameters and ; express The first derivative; This embodiment also includes... Taking the derivative and substituting it into the intermittent failure model of the actuator, we get:

[0060] In the formula: This represents the dynamic equations of the unknown system obtained through neural network approximation. The estimated value To offset the efficiency loss caused by the failure and unknown bias Define parameters To construct a composite Lyapunov function: S34: Construct the Lyapunov function based on the position tracking error vector for:

[0061] Based on Lyapunov functions Based on the velocity tracking error vector and the neural network, a composite Lyapunov function is defined. for:

[0062] In the formula: This represents the positive definite design parameters used to adjust the adaptive convergence rate; Indicates adaptive parameters and ; Represents the error variable and = ; express The estimated value; = ; express The estimated value; Indicates the error in neural network weight estimation and ; Represents the weights of the neural network; express The estimated value; S35: For composite Lyapunov functions Differentiate to obtain the composite Lyapunov function. The derivative of the composite Lyapunov function is used to ensure that... Since the derivative is less than or equal to 0, a feedforward fault-tolerant controller with an online adaptive update law for parameters is designed using the backstepping method, combining the virtual control law with the velocity tracking error vector and the position tracking error vector.

[0063]

[0064]

[0065]

[0066]

[0067] In the formula: This indicates a feedforward fault-tolerant controller; Indicates adaptive parameters; The basis functions of a neural network; express The first derivative; This represents the positive definite design parameters used to adjust the adaptive convergence rate; express The first derivative; express The first derivative; express The first derivative; This represents the positive definite design parameters used to adjust the adaptive convergence rate.

[0068] S4: Construct a nominal error affine system based on the cooperative tracking error variable, define an infinite time-domain performance cost function based on the nominal error affine system to construct the Hamilton-Jacobi-Bellman equation; combine the Hamilton-Jacobi-Bellman equation with an evaluation neural network to obtain an optimized feedback controller; The specific steps include: S41: In the feedforward term After completing the decoupling compensation for system nonlinearity and faults, the next step is to design the optimal feedback term. To optimize performance; in this embodiment, the optimal feedback term is defined as and ;and The signal represents the optimized feedback controller signal; the nominal error affine system after feedforward compensation is constructed based on the cooperative tracking error variable and the optimal feedback term:

[0069] In the formula: Describes the augmented error vector and ; Represents the control gain matrix and ; Indicates the drift term and ; Represents the parameter matrix; This represents a nonlinear function used to compensate for the speed tracking error vector; express The first derivative; S42: Defining an Infinite Time-Domain Performance Cost Function Based on a Nominal Error Affine System for:

[0070] In the formula: This represents the infinite time-domain performance metrics of the design; Indicates time; This represents a positive definite weight matrix; This represents the control energy penalty matrix; S43: Based on optimal control theory and the performance cost function in the infinite time domain Define the Hamiltonian function for:

[0071] In the formula: Represents the infinite time-domain performance cost function gradient and ; express The abbreviated form; S44: Take the partial derivative of the Hamiltonian function with respect to the control input and set it to zero, that is, let To obtain the theoretically optimal feedback control law for:

[0072] In the formula: The gradient of the optimal cost function is represented. express The abbreviated form; The theoretical optimal feedback control law Substituting back the Hamiltonian function, we obtain the Hamilton-Jacobi-Bellman equation, i.e., the HJB equation:

[0073] S45: Considering the nonlinear partial differential characteristics of the HJB equation, which makes it difficult to obtain an analytical solution, this embodiment uses an evaluation neural network to approximate the optimal cost function as follows:

[0074] In the formula: This represents the optimal cost function after approximation; Represents the basis functions for evaluating neural networks; This represents the transpose of the weight estimates for evaluating a neural network. And the gradient of the optimal cost function after approximation Represented as:

[0075] In the formula: express The abbreviated form; According to the gradient Obtain the approximate optimal control law for:

[0076] S46: Define the Hamiltonian function Approximate Hamiltonian function residual In order to make weight The objective function converges to the optimal value and is minimized by using gradient descent to minimize the squared error. and Therefore, an online adaptive update law for evaluating network weights is designed. for:

[0077] In the formula: Indicates the direction of the search gradient for the weights; This represents the drift term obtained by approximation using a neural network. The estimated value; This represents the current Bellman residual value; By evaluating the online adaptive update law of network weights Update and obtain the optimal feedback controller in the optimal control law. This embodiment ensures the accuracy of feedback terms through real-time online learning using the online adaptive update law. It can continuously adjust the control strategy, thereby bringing the system closer to the theoretical optimal state.

[0078] S5: Based on the feedforward fault-tolerant controller and the optimized feedback controller, the composite optimized control command, i.e., the ideal input command, is obtained as follows:

[0079] In the formula: The signal represents the feedforward fault-tolerant controller; This represents the signal of the optimal feedback controller in the optimal control law.

[0080] By applying composite optimization control commands to the controller of the unmanned vessel, adaptive fault-tolerant optimization control with collaborative output feedback of multiple unmanned vessels can be achieved.

[0081] To verify the technical effectiveness of the method described in this embodiment, a multi-unmanned vessel formation consisting of five unmanned vessels was used as the control object. A formation trajectory tracking experiment was conducted in a simulation environment, and intermittent faults were introduced into the thrusters of each unmanned vessel. The occurrence times of these intermittent faults are shown in Table 1 (unit: seconds). The experimental results are attached. Figure 2 To be continued Figure 9 As shown.

[0082] Table 1. Time periods of intermittent failures of unmanned surface vessels in simulation experiments

[0083] like Figure 3 The figure shows the navigation trajectory of a multi-unmanned surface vessel (USV) formation. As can be seen from the figure, in a complex dynamic environment, all following vessels can quickly converge and accurately maintain the preset formation configuration, proving that the method described in this invention has excellent cooperative tracking and control accuracy.

[0084] like Figures 4 to 6The figures show the tracking error curves of the unmanned surface vessel in the three degrees of freedom: longitudinal position, lateral position, and heading angle. It can be seen that after the control method is activated, despite the presence of unmeasured velocity states and external disturbances, all errors can be quickly suppressed and stably converge to a very small bounded region near zero, indicating that the method described in this embodiment has the characteristics of fast response and high robustness.

[0085] like Figures 7 to 9 The figures show the actual output torque of the unmanned surface vessel (USV) under intermittent thruster failures in three degrees of freedom: longitudinal position, lateral position, and bow angle. As can be seen from the figures, even if sudden actuator failures occur at different times during the entire control process, the output torque can still achieve fault-tolerant control of the USV system through adaptive system adjustment. This fully verifies that the "feedforward fault tolerance + optimal feedback" composite mechanism designed in this embodiment can effectively handle thruster failure problems, ensuring the physical reliability and operational economy of the control system.

[0086] Experimental results show that the method described in this embodiment can achieve high-precision, high-stability, and energy-optimal trajectory tracking control for multi-unmanned vessel formations under complex conditions such as unmeasurable velocity state and intermittent thruster failures.

[0087] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A multi-unmanned surface vessel cooperative output feedback adaptive fault-tolerant optimization control method, characterized in that, The specific steps include: S1: Construct a mathematical model for a multi-unmanned surface vessel system that includes a propeller intermittent failure model. Its expression is: In the formula: Indicates the first The state vector of the ship in the geodetic coordinate system and ; Indicates the first The ship's position and heading angle; Denotes the velocity vector in the attached coordinate system and ; Indicates longitudinal velocity, lateral velocity, and bow roll rate; Represents the transformation rotation matrix; Represents the inertia matrix; Represents the Coriolis and centripetal force matrix; Represents the hydrodynamic damping matrix; Indicates unknown dynamic items in the system; Represents the velocity vector in the geodetic coordinate system; express The first derivative; Represents the lumped dynamics of an unknown nonlinear system; This indicates the actual actuator control commands output, taking into account the possibility of intermittent thruster failures. Represents the ideal input instruction and ; express Element; Indicates the unknown fault time interval Intermittent faults occur within the actuator, and the corresponding actuator efficiency factor is... ; express The lower bound; Represents an unknown bias fault vector; express The first derivative; Indicates transpose; S2: Design a neural network state observer based on the mathematical model of a multi-unmanned vessel system; The specific steps include: S21: Based on the mathematical model of the multi-unmanned vessel system, the subsystem state vector is defined as follows: and ; S22: Based on the state vector of the subsystem, design the neural network state observer as follows: In the formula: express The estimate; express The estimate; express The estimate; express The estimate; express The estimate; express The estimate; Represents the parameter matrix and , ; Indicates the observer gain; Indicates correspondence of The estimated value; express , , The first derivative; S3: Based on the preset reference signal and the mathematical model of the multi-unmanned vessel system, define the cooperative tracking error variable; A composite Lyapunov function is defined based on the collaborative tracking error variable combined with a neural network state observer, and a feedforward fault-tolerant controller containing an online adaptive update law for parameters is designed based on the backstepping method. S4: Construct a nominal error affine system based on the cooperative tracking error variable, define an infinite time-domain performance cost function based on the nominal error affine system to construct the Hamilton-Jacobi-Bellman equation; combine the Hamilton-Jacobi-Bellman equation with an evaluation neural network to obtain an optimized feedback controller; S5: Based on the feedforward fault-tolerant controller and the optimized feedback controller, obtain composite optimized control commands, and then realize the optimized control of multi-unmanned vessel cooperative output feedback adaptive fault tolerance.

2. The multi-unmanned vessel cooperative output feedback adaptive fault-tolerant optimization control method according to claim 1, characterized in that, S3 specifically includes the following steps: S31: Define the reference signal as... and ; Indicates the desired position and desired heading angle; S32: Based on the mathematical model of the multi-unmanned surface vessel system and the aforementioned reference signal, Define the collaborative tracking error variable as: In the formula: Indicates the first Local expected reference signal of an unmanned surface vessel; Represents the desired position offset vector and ; The x and y coordinates represent the positional offset; This represents the position tracking error vector; Represents the speed tracking error vector; This indicates that the state observer is used to... The estimated velocity-state value is obtained; Represents a virtual control law; S33: Define the virtual control law as... ; The signal represents the virtual feedforward controller; This indicates the signal of the virtual feedback optimization controller; Furthermore, based on the position tracking error vector, the virtual feedforward controller is designed as follows: In the formula: Indicate design parameters and ; express The first derivative; S34: Construct the Lyapunov function based on the position tracking error vector for: Based on Lyapunov functions Based on the velocity tracking error vector and the neural network, a composite Lyapunov function is defined. for: In the formula: This represents the positive definite design parameters used to adjust the adaptive convergence rate; Indicates adaptive parameters and ; Represents the error variable and = ; express The estimated value; = ; express The estimated value; Indicates the error in neural network weight estimation and ; Represents the weights of the neural network; express The estimated value; S35: For composite Lyapunov functions Differentiate to obtain the composite Lyapunov function. The derivative of the composite Lyapunov function is used to ensure that... Since the derivative is less than or equal to 0, a feedforward fault-tolerant controller incorporating an online adaptive update law for parameters is designed using the backstepping method, based on the virtual control law and the velocity tracking error vector and the position tracking error vector: In the formula: This indicates a feedforward fault-tolerant controller; Indicates adaptive parameters; The basis functions of a neural network; express The first derivative; This represents the positive definite design parameters used to adjust the adaptive convergence rate; express The first derivative; express The first derivative; express The first derivative; This represents the positive definite design parameters used to adjust the adaptive convergence rate.

3. The multi-unmanned surface vessel cooperative output feedback adaptive fault-tolerant optimization control method according to claim 2, characterized in that, S4 specifically includes the following steps: S41: Define the optimal feedback term as and ;and The signal represents the optimized feedback controller signal; the nominal error affine system is constructed based on the cooperative tracking error variable and the optimal feedback term as follows: In the formula: Describes the augmented error vector and ; Represents the control gain matrix and ; Indicates the drift term and ; Represents the parameter matrix; This represents a nonlinear function used to compensate for the speed tracking error vector; express The first derivative; S42: Defining an Infinite Time-Domain Performance Cost Function Based on a Nominal Error Affine System for: In the formula: This represents the infinite time-domain performance metrics of the design; Indicates time; This represents a positive definite weight matrix; This represents the control energy penalty matrix; S43: Based on optimal control theory and the performance cost function in the infinite time domain Define the Hamiltonian function for: In the formula: Represents the infinite time-domain performance cost function gradient and ; express The abbreviated form; S44: Order To obtain the theoretically optimal feedback control law for: In the formula: The gradient of the optimal cost function is represented. express The abbreviated form; The theoretical optimal feedback control law Substituting back the Hamiltonian function, we obtain the Hamilton-Jacobi-Bellman equation, i.e., the HJB equation: S45: Considering the nonlinear partial differential properties of the HJB equation, the optimal cost function is approximated using an evaluation neural network as follows: In the formula: This represents the optimal cost function after approximation; Represents the basis functions for evaluating neural networks; This represents the transpose of the weight estimates for evaluating a neural network. And the gradient of the optimal cost function after approximation Represented as: In the formula: express The abbreviated form; According to the gradient Obtain the approximate optimal control law for: S46: Define the Hamiltonian function Approximate Hamiltonian function residual In order to make weight The objective function converges to the optimal value and is minimized by using gradient descent to minimize the squared error. and Therefore, an online adaptive update law for evaluating network weights is designed. for: In the formula: Indicates the direction of the search gradient for the weights; This represents the drift term obtained by approximation using a neural network. The estimated value; This represents the current Bellman residual value; By evaluating the online adaptive update law of network weights Update and obtain the optimal feedback controller in the optimal control law. .

4. The multi-unmanned vessel cooperative output feedback adaptive fault-tolerant optimization control method according to claim 3, characterized in that, The composite optimization control command, i.e., the ideal input command, obtained in S5 is: In the formula: The signal represents the feedforward fault-tolerant controller; This represents the signal of the optimal feedback controller in the optimal control law.

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