A neural network-based anti-interference control method for a multi-ship formation at sea

Abstract

This invention belongs to the field of ship formation control technology, specifically relating to a neural network-based anti-interference control method for multi-ship formations at sea. It utilizes neural networks to approximate and compensate for uncertainties in the model, while simultaneously constructing a disturbance observer to achieve effective estimation of coupled marine environmental disturbances. To overcome the problem of traditional observers' dependence on accurate models, this method parameterizes the ship motion equations and disturbance terms to establish a canonical model of the disturbance, and uses a disturbance filter to achieve exponential convergence estimation of the disturbance state vector, thus transforming the disturbance suppression problem into an adaptive control problem. Furthermore, this method fully considers input quantization, effectively reducing propeller wear and communication burden by slowing down the rate of change of actuator output. Compared with existing technologies, the anti-interference formation control strategy proposed in this invention can achieve online estimation and suppression of unknown disturbances without relying on any prior model dynamics knowledge.

Description

Technical Field

[0001] This invention belongs to the field of ship formation control technology, specifically relating to a neural network-based anti-interference control method for multi-ship formations at sea. Background Technology

[0002] With the continuous advancement of marine technology, the focus of ship control has expanded from the motion control of single ships to the realm of multi-ship cooperative control to address increasingly complex maritime missions. For any underwater structure, unpredictable marine environmental disturbances are a fundamental challenge that must be addressed. Especially for multi-ship cooperative control systems, the propagation characteristics of external disturbances can trigger formation dynamic instability. Most disturbance suppression requires accurate models to achieve satisfactory results. However, ship motion systems are complex nonlinear and uncertain systems. Affected by changes in their own hydrodynamic parameters, environmental disturbances, or load variations, accurate modeling of ship dynamics systems is extremely difficult. Controllers based on inaccurate or outdated model parameters may experience severely degraded performance or even instability. Dynamically uncertain model parameters pose a significant challenge to robust anti-disturbance control of nonlinear systems.

[0003] Furthermore, in practical engineering applications, besides control accuracy, conserving communication resources is another bottleneck that urgently needs to be overcome. Quantizing control inputs can not only significantly reduce the burden on signal transmission but also decrease the frequency of actuator movements, thereby improving the utilization efficiency of the thruster and extending its service life.

[0004] However, existing research limits the aforementioned strategies to single-ship control systems and does not consider their simultaneous operation in a communicating fleet. This restricts the promotion and application of robust nonlinear input quantization control, which does not rely on existing experience, in multi-ship cooperative scenarios. Therefore, a neural network-based anti-interference control method for multi-ship formations at sea has significant value and promise. Summary of the Invention

[0005] To overcome the problems in the prior art, this invention proposes a neural network-based anti-interference control method for multi-ship formations at sea.

[0006] The technical solution of the present invention to solve the above-mentioned technical problems is as follows: This invention proposes a neural network-based anti-interference control method for multi-ship formations at sea, comprising the following steps: Step 100: Based on the position information and heading angle information of the leader ship, follower ship 1, and follower ship 2 in the geodetic coordinate system, as well as the velocity information in the ship's coordinate system, establish the ship's motion equations and ship kinematic model. Step 200: Parameterize the ship motion equations, model the disturbance terms as the output of an unknown exogenous system, construct the error dynamic equations, and introduce coordinate transformation matrix decoupling equations to separate the unknown parameter matrix; Step 300: Parameterize the error dynamic equation, utilize the property that the error converges to zero, and construct a linear parameterized regression equation based on the separated unknown parameter matrix; Step 400: Define the generalized position error variable, construct the Lyapunov function based on the ship kinematics model, and then design a virtual control law to stabilize the position error; Step 500: Based on the velocity error variable, construct an augmented Lyapunov candidate function that includes position error and velocity error, and design a transient control law based on the ship dynamics equations, introducing uniform quantization to slow down the rate of change of actuator output; Step 600: Use an RBF neural network to approximate the unknown complex dynamics term in the transient control law online, transform it into adjustable network weights, and obtain the neural network approximation equation; substitute the neural network approximation equation and the linear parameterized regression equation into the derivative of the augmented Lyapunov candidate function to obtain a complete error dynamic equation containing the control law to be designed. Step 700: Based on the complete error dynamic equation containing the control law to be designed, design the final anti-disturbance control law; Step 800: Design the gain matrix, interference observer observation gain matrix, neural network and input quantization design parameters in the anti-interference control law, so as to enable both follower ships to follow the leader ship in the desired formation.

[0007] Furthermore, in step 100, based on the rotation matrix, the position and heading angle information of the leader ship, follower ship 1, and follower ship 2 in the geodetic coordinate system, and the velocity information in the ship's coordinate system, the ship's motion equation, i.e., the position vector in the geodetic coordinate system, is established. The rate of change and the velocity vector in the ship's coordinate system The relationship between them: ; In the above formula, Represents position vector The rate of change of the position vector The derivative with respect to time; Indicates the first i The velocity vector of the ship in the ship's coordinate system; This represents the rotation matrix.

[0008] Furthermore, in step 100, a ship kinematics model is established: ; In the above formula, Represents a positive definite symmetric inertia matrix with hydrodynamic additional inertia; The matrix representing the Coriolis and centripetal terms; Represents the damping matrix; This represents a first-order Markov perturbation; Indicates control torque; Represents the acceleration vector in the ship's coordinate system and the velocity vector in the ship's coordinate system. The derivative with respect to time.

[0009] Further, in step 200, the disturbance term is modeled as the output of an unknown exogenous system, an error dynamic equation is constructed, and a coordinate transformation matrix decoupling equation is introduced to separate the unknown parameter matrix, including: Disturbance term Represented as the output vector of the unknown exogenous system: ; ; In the above formula, The derivative of the state vector of an exogenous system; Represents the state vector of an exogenous system; The system matrix represents the unknown exogenous system. Let represent the output matrix of the unknown exogenous system, and Form an observable pair; Define error vector The error dynamic equation is: ; ; In the above formula, Let represent the gain matrix of the interference observer, and It is required to be a Herwitz matrix; Represents the interference input matrix; This represents the true total interference; The derivative representing the true total disturbance; This represents a first-order Markov perturbation; Introducing coordinate transformation matrix The coordinate transformation is expressed as Solving for the coordinate transformation matrix using the Sylvester equations ; definition , The matrix to be solved is the matrix containing the unknown parameters. , Separated; among them, This represents a positive definite symmetric inertia matrix with hydrodynamic additional inertia.

[0010] Further, in step 300, constructing a linear parameterized regression equation includes: ; in, This represents a first-order Markov perturbation; The interference estimation attenuation term is represented as follows: , Represents the estimation error vector; Represents the perturbation parameter matrix. The regressor is represented as follows: ; ; In the above formula, Represents the main state variable; Indicates the first i The velocity vector of the ship in the ship's coordinate system; , Describe the basis functions; , These represent auxiliary state variables, corresponding to the weight coefficients of the two sets of basis functions, respectively.

[0011] Furthermore, step 400 includes: defining the generalized position error and velocity error of the design controller: ; ; In the above formula, Indicates generalized position error; Indicates speed error; Indicates the desired relative position; Represents a set of neighbors; Indicates the first i The position vector of a ship in the geodetic coordinate system; Indicates the first j The position vector of a ship in the geodetic coordinate system; Indicates the first i The velocity vector of the ship in the ship's coordinate system; This represents the vector of virtual stable functions.

[0012] Further, the uniform quantization in step 500 includes: ; In the above formula, This represents a uniform quantizer; Represents the transitional control law; It is a positive real number; This indicates the control torque.

[0013] Further, in step 600, an RBF neural network is used to approximate the unknown complex dynamic terms in the transition control law online, transforming them into adjustable network weights to obtain the neural network approximation equation, including: ; In the above formula, the input vector , Indicates the approximation error; Describe the basis functions; Represents the ideal weight vector; For virtual stable function vectors; Indicates the first i The velocity vector of the ship in the ship's coordinate system; Represents a positive definite symmetric inertia matrix with hydrodynamic additional inertia; The matrix representing the Coriolis and centripetal terms; This represents the damping matrix.

[0014] Furthermore, in step 600, the neural network approximation equation and the linear parameterized regression equation are substituted into the derivative of the augmented Lyapunov candidate function to obtain a complete error dynamic equation containing the control law to be designed: ; In the above formula, The derivative of the Lyapunov candidate function is represented by . Indicates generalized position error; Represents the rotation matrix; Indicates speed error; It is the gain matrix; Indicates the design transition control law; Indicates quantization error; This represents the interference estimation attenuation term; To represent the transpose of the perturbation parameter matrix, Indicates the regressor; Represents the basis functions.

[0015] Further, step 700: based on the complete error dynamic equation containing the control law to be designed, design the final anti-interference control law, including: ; In the above formula, Represents the gain matrix; This represents the rate of change of the weight vector.

[0016] Compared with the prior art, the present invention has the following technical effects: (1) This invention constructs a standard model of the disturbance by parametric processing of the ship motion equation and the disturbance term, and uses the disturbance filter to realize the exponential convergence estimation of the disturbance state vector, thereby transforming the disturbance suppression problem into an adaptive control problem.

[0017] (2) The present invention uses radial basis function (RBF) neural network to approximate the uncertainty of the system, and achieves effective disturbance suppression formation control under the condition that the dynamic characteristics of the model and the disturbance frequency are unknown.

[0018] (3) The present invention introduces input quantization technology into the control strategy, which significantly reduces the signal transmission burden and reduces the frequency of actuator operation. Attached Figure Description

[0019] To more clearly illustrate the technical solutions and advantages 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 only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0020] Figure 1 This is a flowchart of the control method of the present invention; Figure 2 The geodetic coordinate system and the shipboard coordinate system provided in the embodiments of the present invention; Figure 3 The simulated fleet network architecture provided in this embodiment of the invention; Figure 4 Two-dimensional perspective comparison diagrams of navigation conditions for two controllers provided in embodiments of the present invention; Figure 5 The following ship position response curve provided in the embodiments of the present invention; Figure 6 The two controllers provided in this embodiment of the invention follow the speed response curves of ship 1; Figure 7 The curve provided in this embodiment of the invention is the speed response curve of the controller following the ship 2; Figure 8 The force and torque response curves of the following ship provided in the embodiments of the present invention; Figure 9 A comparison chart of update counts with and without quantization actuators provided in this embodiment of the invention; Figure 10 The following ship interference estimation response curve provided in the embodiments of the present invention; Figure 11 The weight response curve of the following ship neural network provided in the embodiment of the present invention. Detailed Implementation

[0021] To further illustrate the technical means and effects adopted by the present invention to achieve its intended purpose, the specific implementation methods, structures, features, and effects of the technical solutions proposed according to the present invention are described in detail below with reference to the accompanying drawings and preferred embodiments. Specific features, structures, or characteristics in one or more embodiments may be combined in any suitable form. Unless otherwise defined, all technical and scientific terms used in this invention have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains.

[0022] The purpose of this invention is to provide a neural network-based anti-interference control method for multi-ship formations at sea. It optimizes the energy consumption of the control strategy under communication and actuator resource constraints through input quantization technology, forming a robust anti-interference formation control method that does not require prior model knowledge. This invention primarily addresses the research on cruise control of multi-ship formations considering unknown dynamic models and unknown time-varying marine environmental disturbances. It utilizes neural network approximation and disturbance observer estimation, disturbance parameterization and filter exponential convergence estimation, and input quantization technology to solve the model uncertainties and complex marine disturbances faced by multi-ship formations. This meets the cooperative stability control requirements of formations in unknown environments and reduces propeller wear and communication burden under input quantization. The proposed neural network-based robust anti-interference formation control method corrects the influence of uncertain dynamics and external disturbances on formation control, effectively enhancing the anti-interference capability of multi-ship cooperation. It utilizes neural networks to approximate system uncertainties, achieving disturbance suppression even when both model dynamics and disturbance frequencies are unknown. Through disturbance parameterization and disturbance filter design, the disturbance state vector is exponentially converged, transforming the disturbance suppression problem into an adaptive control problem, avoiding dependence on precise models. Input quantization techniques are employed to slow down the rate of change of actuator outputs, saving energy consumption and communication resources in the control system. The proposed anti-interference formation control strategy is completely independent of prior model dynamics knowledge, effectively improving the reliability of multi-ship formation systems and enabling the formation to achieve online estimation and suppression of unknown disturbances with optimized resource utilization strategies.

[0023] like Figures 1-2 As shown, in one embodiment of the present invention, a method for anti-interference control of multi-ship formations at sea based on neural networks is provided, comprising the following steps: Step 100: Based on the position information and heading angle information of the leader ship, follower ship 1, and follower ship 2 in the geodetic coordinate system, as well as the velocity information in the ship's coordinate system, establish the ship's motion equations and ship kinematic model. Step 200: Parameterize the ship motion equations, model the disturbance terms as the output of an unknown exogenous system, construct the error dynamic equations, and introduce coordinate transformation matrix decoupling equations to separate the unknown parameter matrix; Step 300: Parameterize the error dynamic equation, utilize the property that the error converges to zero, and construct a linear parameterized regression equation based on the separated unknown parameter matrix; Step 400: Design a robust nonlinear anti-interference control strategy using the backstepping method. The first step is to define the generalized position error variable and construct the Lyapunov function based on the ship's kinematics model, and then design a virtual control law (virtual stability function) to stabilize the position error. Step 500: The second step in designing a robust nonlinear anti-interference control strategy using the backstepping method is to construct an augmented Lyapunov candidate function that includes position error and velocity error based on the velocity error variable, and to design a transient control law based on the ship dynamics equations, introducing uniform quantization to slow down the rate of change of the actuator output. Step 600: Use an RBF neural network to approximate the unknown complex dynamics term in the transient control law online, transform it into adjustable network weights, and obtain the neural network approximation equation; substitute the neural network approximation equation and the linear parameterized regression equation into the derivative of the augmented Lyapunov candidate function to obtain a complete error dynamic equation containing the control law to be designed. Step 700: Based on the complete error dynamic equation containing the control law to be designed, design the final anti-disturbance control law; Step 800: Design the gain matrix, interference observer observation gain matrix, neural network and input quantization design parameters in the anti-interference control law, so as to enable both follower ships to follow the leader ship in the desired formation.

[0024] The following is a detailed explanation of each of the above steps: Step 100: Based on the position and heading information of the leader ship, follower ship 1, and follower ship 2 in the geodetic coordinate system, and the velocity information in the ship's coordinate system, establish a ship kinematic model.

[0025] The position and heading information of the leader ship, follower ship 1, and follower ship 2 in the geodetic coordinate system are as follows: ; In the above formula, Indicates the first i The position vector of a ship in the geodetic coordinate system; Indicates the first i The ship's position in the geodetic coordinate system; Indicates the first i The bow angle of a ship; i Indicates the ship's number index. This indicates that there are a total of [number] members in the formation. m A ship.

[0026] The speed information of the leader ship, follower ship 1, and follower ship 2 in the ship's coordinate system is as follows: ; In the above formula, Indicates the first i The velocity vector of the ship in the ship's coordinate system; Indicates surge speed; Indicates yaw rate; This represents the yaw rate.

[0027] Projecting the velocity from the ship's coordinate system to the geodetic coordinate system, the rotation matrix... for: ; Its properties are .

[0028] Based on the rotation matrix, the position and heading angle information of the leader ship, follower ship 1, and follower ship 2 in the geodetic coordinate system, and the velocity information in the ship's coordinate system, the ship's motion equations are established, i.e., the position vector in the geodetic coordinate system. The rate of change and the velocity vector in the ship's coordinate system The relationship between them: ; In the above formula, Represents position vector The rate of change of the position vector The derivative with respect to time.

[0029] Establish a ship kinematics model: ; In the above formula, Represents a positive definite symmetric inertia matrix with hydrodynamic additional inertia; The matrix representing the Coriolis and centripetal terms; Represents the damping matrix; This represents a first-order Markov perturbation; , Indicates control torque. They represent Directional control and Directional control torque; This represents the acceleration vector in the ship's coordinate system, which is also the velocity vector in the ship's coordinate system. The derivative with respect to time.

[0030] In ship motion models , and It is related to speed and hydrodynamic parameters, and is also the main reason for the high dynamic uncertainty of ship nonlinear systems.

[0031] Step 200: Parameterize the ship motion equations, model the disturbance terms as the output of an unknown exogenous system, construct the error dynamic equations, and introduce coordinate transformation matrix decoupling equations to separate the unknown parameter matrix.

[0032] To address the time-varying marine environmental disturbances experienced by maritime fleets during patrols, and to overcome the limitation of existing observers relying on precise models, the ship kinematics model is parametrically expressed. By parameterizing the ship's motion equations and modeling the total disturbance as the output of an unknown exogenous system, a dynamic model of disturbance estimation error, incorporating basis function expansion, is constructed. Furthermore, a coordinate transformation matrix decoupling equation is introduced, laying the mathematical foundation for designing an adaptive parameter law to achieve exponentially convergent estimation of the disturbance.

[0033] As an example, step 200 specifically includes: Step 210: Parameterize the ship's motion equations and classify complex dynamic terms and external disturbances as unknown terms.

[0034] Rewrite the ship's motion equations in parametric form: ; ; in: ; ; ; Here, , This indicates a known regression matrix; , Represents a vector of unknown parameters; This represents the disturbance term, which includes all external environmental disturbances (such as wind, waves, and currents).

[0035] Step 220: Model the disturbance term as the output of the unknown exogenous system.

[0036] In order to design a controller to eliminate disturbance terms Modeling the disturbance term involves introducing an exogenous system. It can be represented as the output vector of an unknown exogenous system: ; ; In the above formula, The derivative of the state vector of an exogenous system; Represents the state vector of an exogenous system; For the system matrix of an unknown exogenous system, Let represent the output matrix of the unknown exogenous system, and Forming an observable pair means that it can be observed through the output Reverse the internal state .

[0037] Step 230: , In the case of unknowns, construct the error dynamic equation.

[0038] exist , In the absence of known information, construct a dynamic system to estimate the total disturbance and define an error vector. The error dynamic equation is: ;

[0039] In the above formula, Let represent the gain matrix of the interference observer, and It is required to be a Herwitz matrix; Represents the interference input matrix; This represents the true total interference; The derivative representing the true total disturbance; This represents a first-order Markov perturbation; It is the matrix to be determined.

[0040] Step 240: Introduce the coordinate transformation matrix and decoupling equation to separate the unknown parameter matrix. , .

[0041] To obtain the interference estimation error by subtracting the parameterized interference energy from the transformed interference, a coordinate transformation matrix is ​​introduced. Coordinate transformation can be expressed as The coordinate transformation matrix is ​​solved using the Sylvester Equation. .

[0042] It is controllable, in order to ensure It is the only solution. It is defined. , It is the matrix to be determined.

[0043] Step 300: Establish a normalized interference model and use an interference filter to achieve exponential convergence estimation of the interference state vector: parameterize the error dynamic equation, utilize the property that the error converges to zero, and construct a linear parameterized regression equation based on the separated unknown parameter matrix.

[0044] A perturbation parameterization estimator based on basis function expansion is constructed, and its effectiveness in designing matrices is demonstrated. When the estimation error is the Herwitz matrix, it can converge exponentially to zero. This convergence property can then be used to transform the system equation into a linear parameterized regression form, separating the unknown parameter vector and providing a mathematical basis for designing adaptive laws for parameters.

[0045] As an example, step 300 specifically includes: Step 310: Parameterize the error dynamic equation.

[0046] Design an estimation expression vector to estimate the disturbance terms in the system online in real time: ; In the above formula, Indicates the estimation error; Represents the main state variable; , Describe the basis functions; , These represent auxiliary state variables, corresponding to the weight coefficients of the two sets of basis functions, respectively; , Index variables representing basis functions; n This indicates the number of basis functions.

[0047] As the master state variable and As an auxiliary state vector, its specific mathematical expression is as follows: ; ; .

[0048] In the above formula, The derivative of the master state variable; The derivative of the auxiliary state variable; The derivative of the auxiliary state variable; , Representing the known regression matrix respectively , The element, specifically the expression is as follows: ; .

[0049] Step 320: Derive the error dynamic equation (stability analysis).

[0050] Define the estimation error vector as: ; Estimated error vector The derivative can be obtained by the following calculation: ; because Since it is a Hurwitz matrix, the error vector is estimated. It will gradually approach 0.

[0051] Step 330: Construct a linear parameterized regression equation by utilizing the property that the error converges to zero.

[0052] By utilizing the property that the error converges to zero, the originally complex nonlinear equations can be rewritten in linear form: ; in, The interference estimation attenuation term is specifically expressed as follows: ; Here is the perturbation parameter matrix. For the regressor, specifically represented as: ; ; In the above formula, , Describe the basis functions; , This indicates the transpose of the auxiliary state variable; Represents the input matrix; It is the matrix to be determined; This represents the input matrix.

[0053] Step 400: Design a robust nonlinear anti-interference control strategy using the backstepping method. The first step is to define the generalized position error variable and construct the Lyapunov function based on the ship's kinematics model, and then design a virtual control law (virtual stability function) to stabilize the position error.

[0054] As an example, step 400 specifically includes: Step 410: Define the errors required for designing the controller, including generalized position error and velocity error.

[0055] Define the error required for the controller design: ; ; In the above formula, Indicates generalized position error; Indicates speed error; Indicates the desired relative position; Represents a set of neighbors; Indicates the first i The position vector of a ship in the geodetic coordinate system; Indicates the first j The position vector of a ship in the geodetic coordinate system; This is a virtual stable function vector.

[0056] Generalized position error The time derivative is:

[0057] Step 420: Construct the first Lyapunov function based on the generalized position error and the ship kinematics model, and find the derivative of the Lyapunov function.

[0058] The Lyapunov function is chosen as follows: ; The time derivative of the above equation is: ; Step 430: Design a virtual control law (virtual stable function) to stabilize the position error: Design a virtual stable function and rewrite the derivative of the Lyapunov function.

[0059] Design virtual stabilization function vector The specific mathematical representation is as follows: ; in, It is the first i The time derivative of the expected steady-state error between the j-th ship and the j-th ship is known. It is a design matrix.

[0060] Furthermore, the derivative of the Lyapunov function can be derived as follows: .

[0061] Step 500: The second step in designing a robust nonlinear anti-interference control strategy using the backstepping method involves constructing an augmented Lyapunov candidate function that includes position and velocity errors based on the velocity error variable, and designing a transient control law based on the ship dynamics equations, introducing uniform quantization to slow down the rate of change of the actuator output.

[0062] As an example, step 500 specifically includes: Step 510: Differentiate the velocity error, describe its variation using the ship dynamics equations, and introduce uniform input quantization to construct a transient control law that can slow down the rate of change of the actuator output.

[0063] Introduce the following uniform quantizer: ; in, This represents the transitional control law. It is a positive real number, and its physical meaning is quantization precision. Because... The error of this quantizer is bounded; This indicates a uniform quantizer.

[0064] Input quantization is designed based on a uniform quantizer, and the speed error is obtained by combining the uniform quantizer. For the time derivative, i.e., to construct a velocity error dynamics model containing quantitative error: ; In the above formula, This indicates the quantization error.

[0065] Step 520: Construct an augmented Lyapunov candidate function containing position and velocity errors based on the velocity error variable: Construct an augmented Lyapunov candidate function based on the velocity error and the Lyapunov function; Based on the velocity error dynamic model with quantified error, the derivative of the rewritten Lyapunov function, and substituting the error dynamic equation, obtain the derivative of the augmented Lyapunov candidate function.

[0066] Based on velocity error and Lyapunov function, construct augmented Lyapunov candidate function: ; Based on the velocity error dynamics model with quantification error, the derivative of the rewritten Lyapunov function, and substituting the error dynamic equation, the derivative of the augmented Lyapunov candidate function is obtained:

[0067] Step 530: Based on the analysis results of the derivative of the augmented Lyapunov function, design the transition control law.

[0068] The transition control law is as follows: .

[0069] Step 600: Use an RBF neural network to approximate the unknown complex dynamics term in the transient control law online, transform the unknown complex dynamics term into adjustable network weights, and obtain the neural network approximation equation; substitute the neural network approximation equation and the linear parameterized regression equation into the derivative of the augmented Lyapunov candidate function to obtain a complete error dynamic equation containing the control law to be designed.

[0070] As an example, step 600 specifically includes: Step 610: Use an RBF neural network to approximate the unknown complex dynamics in the transition control law online, and transform the unknown complex dynamics into adjustable network weights.

[0071] This addresses the problem of "high dynamic uncertainty" in the system model. Due to certain dynamic terms (such as...) , , The related complex coupling terms are difficult to obtain accurately, and traditional fixed parameter controllers are not effective. Therefore, RBF neural networks are used to perform online approximation on unknown complex dynamic terms, transforming the unknown terms into adjustable network weights.

[0072] An RBF neural network is used to approximate the uncertainty terms online. The neural network approximation equation is as follows: ; Wherein, input vector , To approximate the error; Describe the basis functions; This represents the ideal weight vector.

[0073] The basis function matrix is ​​represented as follows: ; Ideal weight vector: The weight coefficients that connect the basis functions and the output in a neural network.

[0074] Step 620: Substitute the neural network approximation equation and the linear parameterized regression equation into the derivative of the augmented Lyapunov candidate function to obtain a complete error dynamic equation containing the control law to be designed: .

[0075] Step 700: Design a robust anti-interference control strategy without prior knowledge, and optimize the anti-interference controller of the naval formation into a robust anti-interference controller that requires no experience accumulation.

[0076] This robust anti-interference control strategy uses neural networks to approximate the uncertainties in the model, without relying on accumulated experience or observers.

[0077] Based on the formula obtained in step 620, by letting... The specific expression of the final anti-interference control law obtained by inverse solving is as follows: ; In the above formula, This represents the estimated value of the weight vector, which is composed of column vectors, and the rate of change of the weight vector is: ; For adaptive gain; This represents the gradient term. If the velocity error... If the error is large, it means that the current estimation of the neural network is inaccurate. Therefore, the weights are adjusted significantly based on the magnitude and direction of the error until the error becomes smaller.

[0078] Step 800: Design the gain matrix, interference observer observation gain matrix, neural network and input quantization design parameters in the anti-interference control law, so as to enable both follower ships to follow the leader ship in the desired formation.

[0079] Adjusting the gain matrix of the interference observer using Young's inequality algorithm and ; Using Young's inequality algorithm, adjust the input quantization parameters ; Using Young's inequality algorithm, the gain matrix of a controller without prior knowledge is adjusted. , .

[0080] To verify the performance of the proposed neural network-based anti-interference control method for multi-ship formations at sea, the following parameters were used as a case study in a simulation experiment. The dynamic parameters of the research object are: Table 1 Hydrodynamic parameters of the simulated ship

[0081] In Table 1, Indicates the additional mass in the direction of the ship's pitch; Indicates the additional mass in the direction of sway of the ship; Indicates the additional mass in the direction of the ship's yaw; Indicates the linear damping coefficient in the oscillation direction; The linear damping coefficient representing the sway direction; This represents the linearly coupled derivative of the sway direction with respect to the yaw rate r; This represents the linearly coupled derivative of the yaw direction with respect to the lateral velocity v; Indicates the linear damping coefficient in the yaw direction; The nonlinear damping coefficient representing the sway direction with respect to the longitudinal velocity; The nonlinear damping coefficient representing the sway direction with respect to the lateral velocity; This represents the nonlinear coupling coefficient in the sway direction with respect to lateral velocity and yaw rate. It represents the nonlinear coupling coefficient between the yaw rate and the lateral velocity in the sway direction; The nonlinear damping coefficient representing the sway direction with respect to the yaw rate; This represents the nonlinear coupled derivative of the yaw direction with respect to the lateral velocity; This represents the nonlinear coupling coefficient between the yaw direction and the lateral velocity and yaw angular velocity. The nonlinear damping coefficient represents the yaw direction with respect to the yaw angular velocity; the nonlinearity of the yaw direction with respect to the yaw angular velocity; This represents the nonlinear coupling coefficient between the yaw direction and the yaw angular velocity and the lateral velocity. It is precisely the presence of numerous velocity-related hydrodynamic parameters that gives the model a high degree of dynamic uncertainty.

[0082] In maritime missions, a standard formation typically consists of three ships: a lead ship, a launch ship, and a support ship. Multi-ship formations often have network structures such as... Figure 3 As shown.

[0083] The trajectory vector of the lead ship and the formation are given by the following formula: ; ; ; In the above formula, Represents the state vector of the leader ship; , , , This indicates the expected relative positions of the lead ship, launch ship, and support ship.

[0084] All controller parameters are given in Table 2.

[0085] Table 2 Summary of Controller Parameters

[0086] In Table 2, , This represents the initial position vectors of the launching ship and the support ship; , , This represents the initial velocity vectors of the lead ship, launch ship, and support ship in the ship's coordinate system. Design parameters As the initial value of the master state variable, and Used as the initial value for the auxiliary state vector. This represents the initial value of the parametric regressor. This represents the initial value of the perturbation parameter matrix. Indicates the quantization precision. Represents the gain matrix of the interference observer; This represents the interference input matrix.

[0087] Regression Matrix and Specifically, it is expressed as follows:

[0088]

[0089] To verify its adaptability and robustness to unknown model dynamics and marine environmental disturbances, the following section will compare it with the disturbance suppression control law of existing partial model information, and conduct comparative verification using sinusoidal superposition disturbance and random disturbance respectively.

[0090] ; in, Some model information is required, including , , Apart from this, the two control strategies maintain exactly the same control conditions and all design parameters remain consistent.

[0091] Most studies simulate ocean disturbances using sine wave superposition, but this approach neglects the complexity and variability of ocean disturbances. Therefore, we employ random disturbances based on Gaussian white noise in the simulation, which can better simulate unknown, time-varying ocean disturbances in the open ocean.

[0092] Simulation results are as follows Figures 4-11 As shown. By Figure 4 It can be seen that, since there are no model parameters to rely on, the initial segment is based on The trajectory of the movement showed relatively obvious fluctuations, but it quickly surpassed the limit as the neural network approximated it. This advantage is particularly evident in its performance. When significant changes occur. From Figure 5 As can be seen from the simulation, about 30 seconds after the simulation started, both follower ships had reached the desired trajectory required for the formation. Figure 6 and Figure 7 The speed response curves for two different controllers are shown. The comparative control method is employed in this example. During the entire simulation, the velocity curve exhibited periodic spikes, which were caused by random disturbances. When the proposed neural network disturbance rejection control method was used, a similar phenomenon also existed in the first 100 seconds of the simulation. However, as the parameterized observer gradually tracked the disturbances, the velocity spike drift caused by the disturbances was significantly improved.

[0093] like Figure 8 As shown, after uniform output quantization, the output force and torque of the following vessel change from a continuous curve to a stepped form. During the horizontal holding phase of the stepped shape, the propeller speed remains constant, effectively reducing propeller wear caused by frequent speed changes. The controller with and without quantization tracks the number of changes in executed values ​​as follows... Figure 9 As shown. Figure 10 This demonstrates the tracking performance of a ship-following disturbance observer on random, unknown disturbances. In contrast, a comparative method based on partial model data... It exhibits more ideal tracking performance in the initial stage; however, as the parameter observer gradually converges, the proposed method can quickly achieve disturbance tracking and demonstrates superior performance. Figure 11 The weight change curves of the neural network are presented, which show that the approximation term itself exhibits highly dynamic numerical characteristics. This indicates that the proposed method has good approximation ability for ship models with high dynamic uncertainty.

[0094] Simulation results show that the designed neural network anti-disturbance control method can enable the naval formation to reach and maintain the desired position of the leader ship with arbitrary precision, and all signals are globally consistent and ultimately have boundaries, thus verifying the theory.

[0095] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. 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 of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention, and should all be included within the protection scope of the present invention.

Claims

1. A method for anti-interference control of multi-ship formations at sea based on neural networks, characterized in that, Includes the following steps: Step 100: Based on the position information and heading angle information of the leader ship, follower ship 1, and follower ship 2 in the geodetic coordinate system, as well as the velocity information in the ship's coordinate system, establish the ship's motion equations and ship kinematic model. Step 200: Parameterize the ship motion equations, model the disturbance terms as the output of an unknown exogenous system, construct the error dynamic equations, and introduce coordinate transformation matrix decoupling equations to separate the unknown parameter matrix; Step 300: Parameterize the error dynamic equation, utilize the property that the error converges to zero, and construct a linear parameterized regression equation based on the separated unknown parameter matrix; Step 400: Define the generalized position error variable, construct the Lyapunov function based on the ship kinematics model, and then design a virtual control law to stabilize the position error; Step 500: Based on the velocity error variable, construct an augmented Lyapunov candidate function that includes position error and velocity error, and design a transient control law based on the ship dynamics equations, introducing uniform quantization to slow down the rate of change of actuator output; Step 600: Use an RBF neural network to approximate the unknown complex dynamics term in the transient control law online, transform it into adjustable network weights, and obtain the neural network approximation equation; substitute the neural network approximation equation and the linear parameterized regression equation into the derivative of the augmented Lyapunov candidate function to obtain a complete error dynamic equation containing the control law to be designed. Step 700: Based on the complete error dynamic equation containing the control law to be designed, design the final anti-disturbance control law; Step 800: Design the gain matrix, interference observer observation gain matrix, neural network and input quantization design parameters in the anti-interference control law, so as to enable both follower ships to follow the leader ship in the desired formation.

2. The method for anti-interference control of multi-ship formations at sea based on neural networks according to claim 1, characterized in that, In step 100, based on the rotation matrix, the position and heading angle information of the leader ship, follower ship 1, and follower ship 2 in the geodetic coordinate system, and the velocity information in the ship's coordinate system, the ship's motion equation, i.e., the position vector in the geodetic coordinate system, is established. The rate of change and the velocity vector in the ship's coordinate system The relationship between them: ； In the above formula, Represents position vector The rate of change of the position vector is The derivative with respect to time; Indicates the first i The velocity vector of the ship in the ship's coordinate system; This represents the rotation matrix.

3. The method for anti-interference control of multi-ship formations at sea based on neural networks according to claim 1, characterized in that, In step 100, a ship kinematics model is established: ； In the above formula, Represents a positive definite symmetric inertia matrix with hydrodynamic additional inertia; The matrix representing the Coriolis and centripetal terms; Represents the damping matrix; This represents a first-order Markov perturbation; Indicates control torque; This represents the acceleration vector in the ship's coordinate system, which is also the velocity vector in the ship's coordinate system. The derivative with respect to time.

4. The anti-interference control method for multi-ship formations at sea based on neural networks according to claim 1, characterized in that, In step 200, the disturbance term is modeled as the output of an unknown exogenous system, an error dynamic equation is constructed, and a coordinate transformation matrix decoupling equation is introduced to separate the unknown parameter matrix, including: Disturbance term Represented as the output vector of the unknown exogenous system: ； ； In the above formula, The derivative of the state vector of an exogenous system; Represents the state vector of an exogenous system; For the system matrix of an unknown exogenous system, Let represent the output matrix of the unknown exogenous system, and Form an observable pair; Define error vector The error dynamic equation is: ； ； In the above formula, Let represent the gain matrix of the interference observer, and It is required to be a Herwitz matrix; Represents the interference input matrix; Let be the error vector, representing the true total disturbance; The derivative representing the true total disturbance; This represents a first-order Markov perturbation; Introducing coordinate transformation matrix The coordinate transformation is expressed as Solving for the coordinate transformation matrix using the Sylvester equations ; definition , The matrix to be solved is the matrix containing the unknown parameters. , Separated; among them, This represents a positive definite symmetric inertia matrix with hydrodynamic additional inertia.

5. The method for anti-interference control of multi-ship formations at sea based on neural networks according to claim 4, characterized in that, In step 300, constructing a linear parameterized regression equation includes: ； in, This represents a first-order Markov perturbation; The interference estimation attenuation term is represented as follows: , Represents the estimation error vector; Represents the perturbation parameter matrix. The regressor is represented as follows: ； ； In the above formula, Represents the main state variable; Indicates the first i The velocity vector of the ship in the ship's coordinate system; , Describe the basis functions; , These represent auxiliary state variables, corresponding to the weight coefficients of the two sets of basis functions, respectively.

6. The anti-interference control method for multi-ship formations at sea based on neural networks according to claim 1, characterized in that, Step 400 includes: defining the generalized position error and velocity error of the design controller: ； ； In the above formula, Indicates generalized position error; Indicates speed error; Indicates the desired relative position; Represents a set of neighbors; Indicates the first i The position vector of a ship in the geodetic coordinate system; Indicates the first j The position vector of a ship in the geodetic coordinate system; Indicates the first i The velocity vector of the ship in the ship's coordinate system; This represents the vector of virtual stable functions.

7. The anti-interference control method for multi-ship formations at sea based on neural networks according to claim 1, characterized in that, The uniform quantization in step 500 includes: ； In the above formula, This represents a uniform quantizer; Represents the transitional control law; It is a positive real number; This indicates the control torque.

8. The anti-interference control method for multi-ship formations at sea based on neural networks according to claim 1, characterized in that, In step 600, an RBF neural network is used to approximate the unknown complex dynamic terms in the transition control law online, transforming them into adjustable network weights to obtain the neural network approximation equation, including: ； In the above formula, the input vector , Indicates the approximation error; Describe the basis functions; Represents the ideal weight vector; Represents the vector of virtual stable functions; Indicates the first i The velocity vector of the ship in the ship's coordinate system; Represents a positive definite symmetric inertia matrix with hydrodynamic additional inertia; The matrix representing the Coriolis and centripetal terms; This represents the damping matrix.

9. A method for anti-interference control of multi-ship formations at sea based on neural networks according to claim 8, characterized in that, In step 600, the neural network approximation equation and the linear parameterized regression equation are substituted into the derivative of the augmented Lyapunov candidate function to obtain a complete error dynamic equation containing the control law to be designed: ； In the above formula, The derivative of the Lyapunov candidate function is represented by . Indicates generalized position error; Represents the rotation matrix; Indicates speed error; It is the gain matrix; This indicates a transitional control law; Indicates quantization error; This represents the interference estimation attenuation term; This represents the transpose of the perturbation parameter matrix. Indicates the regressor; Denotes the basis functions.

10. A method for anti-interference control of multi-ship formations at sea based on neural networks according to claim 9, characterized in that, Step 700: Based on the complete error dynamic equation containing the control law to be designed, design the final anti-interference control law, including: ； In the above formula, Represents the gain matrix; This represents the rate of change of the weight vector.

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