H∞ Heading Control Method Based on Nonlinear Variable-parameter Unmanned Ship Model

Abstract

The present invention proposes an H∞ heading control method based on a non - linear variable - parameter unmanned ship model. Considering the complex and variable impact of water flow on the ship, the circulation force acting on the ship is obtained by using the low - aspect - ratio wing theory, and then a non - linear variable - parameter heading control model is established. For the established non - linear variable - parameter heading control model, through a parameter - dependent Lyapunov function, the non - linear matrix inequality conditions for the H∞ robust stability of the system are derived, and the non - linear variable - parameter H∞ robust controller is obtained by solving the non - linear matrix inequality conditions using the SOS toolbox in MATLAB.

Description

Technical Field

[0001] The present invention belongs to the technical field of unmanned ship heading control, and particularly relates to an H∞ heading control method based on a non-linear variable parameter unmanned ship model. Background Art

[0002] With the development of ocean and river-related commerce and military affairs, unmanned ships have become an important platform for performing tasks such as search and rescue, reconnaissance, and monitoring due to their advantages of small size, high speed, low cost, and no risk of personnel going online. Heading control is one of the key technologies for unmanned ships to achieve autonomous, reliable, and safe navigation. However, during the navigation of an unmanned ship, the state of the unmanned ship is often time-varying, such as time-varying speed, which causes the hydrodynamic forces received by the unmanned ship to constantly change, destroying the stable structure of the system. The change in hydrodynamic forces is mainly reflected in the uncertainty of the unmanned ship model parameters, and this phenomenon results in the unmanned ship system having strong time-varying non-linearity.

[0003] In the current field of unmanned ship heading control, the unmanned ship models mainly used are Fossen, Norrbin, and Nomoto, etc. For the convenience of model parameter identification and system control, these models have been simplified into simple forms, or even only exhibit linear time-invariant characteristics. However, during the actual navigation of an unmanned ship, there are various time-varying factors such as ship speed, wind and waves, and water flow that cause model parameter uncertainty, which will destroy the stable structure of the unmanned ship system. Moreover, due to the inherent non-linear characteristics of the unmanned ship model itself, it is difficult for the linear time-invariant characteristic model to represent the actual situation of the unmanned ship, thus further increasing the difficulty of unmanned ship heading control. On the other hand, to design a heading controller for an unmanned ship model with non-linear time-varying characteristics to suppress external disturbances and parameter uncertainties, sliding mode control, backstepping method, and H∞ robust control can be used. However, the sliding mode control method has the fatal drawback of chattering during the switching of the system. The backstepping method requires accurate information about the model of the ship heading control system and its varying parameters, which is very difficult in practical applications. The H∞ robust control method achieves the purpose of suppressing disturbances and uncertainties by suppressing the maximum gain of the transfer function between the disturbance and the desired output, and has the advantages of strong robustness, good control effect, and independence from the disturbance model. When designing an H∞ robust controller, the model needs to be substituted into the control framework of a linear variable parameter system to describe the non-linear time-varying characteristics of the controlled model. However, its essence is to linearize the model around a specific operating point of the model time-varying parameters. Therefore, the control framework of the linear variable parameter system cannot reflect the complete dynamic characteristics of the controlled model, especially the non-linear characteristics. Summary of the Invention

[0004] To solve the problems of defects and deficiencies existing in the prior art, the present invention proposes an H∞ heading control method based on a non-linear variable parameter unmanned ship model. For a small underactuated unmanned ship, a non-linear variable parameter heading control model is established, and a non-linear variable parameter H∞ robust controller is designed to enable the system to obtain disturbance rejection and robust performance, realizing fast and high-precision tracking of the heading.

[0005] Considering the complex and variable impact of water flow on the ship, the circulation force acting on the ship is obtained by using the low aspect ratio wing theory, and then a non-linear variable parameter heading control model is established. For the established non-linear variable parameter heading control model, through a parameter-dependent Lyapunov function, the non-linear matrix inequality conditions for the H∞ robust stability of the system are derived, and the non-linear matrix inequality conditions are solved by the SOS toolbox in MATLAB to obtain a non-linear variable parameter H∞ robust controller. The non-linear variable parameter heading control model is established based on the low aspect ratio wing theory, and the hydrodynamic terms have relatively clear physical meanings, which can fully describe the hydrodynamic forces acting on the ship and reflect the non-linear time-varying characteristics of the unmanned ship. The non-linear variable parameter H∞ robust controller can well suppress external disturbances on the premise of ensuring system stability, and by including the non-linear state and time-varying parameters of the system, it overcomes the parameter perturbation phenomenon caused by the inherent non-linearity and time-varying parameters of the system, thereby realizing the tracking of the heading angle of the given unmanned ship and ensuring fast, smooth and high-precision heading tracking performance. The present invention endows the unmanned ship with a new non-linear variable parameter heading control model, and at the same time proposes a non-linear variable parameter H∞ robust control solution for the heading control problem of this model.

[0006] The technical solution adopted by the present invention to solve its technical problems is:

[0007] An H∞ heading control method based on a non-linear variable parameter unmanned ship model, characterized in that it is used for the control system of a small underactuated unmanned ship, and based on a non-linear variable parameter heading control model and a non-linear variable parameter H∞ robust controller, specifically includes the following steps:

[0008] Step S1: Establish a ship dynamics model under the Fossen framework. During the establishment process, heaving, rolling and pitching motions are ignored, and the six-degree-of-freedom unmanned ship is simplified into a three-degree-of-freedom dynamics model related to surge, sway and yaw motions;

[0009] Step S2: According to the low aspect ratio wing theory, decompose the hydrodynamic damping matrix in the established three-degree-of-freedom dynamics model into the circulation force and cross-flow resistance matrix acting on the ship, and obtain a three-degree-of-freedom unmanned ship model based on the low aspect ratio wing;

[0010] Step S3: According to the actual physical characteristics of the small underactuated unmanned boat, ignoring the sway motion and cross-flow resistance, the maneuvering dynamics model is obtained by decomposing the three-degree-of-freedom unmanned boat model based on the low aspect ratio wing.

[0011] Step S4: According to the relationship between the heading angle and the heading angular velocity, the heading angle state variable is introduced into the maneuvering dynamics model, and the heading angle error is used as the feedback to obtain the nonlinear variable parameter heading error model.

[0012] Step S5: Substitute the assumed nonlinear state feedback controller into the nonlinear variable parameter heading error model to establish a nonlinear variable parameter heading control closed-loop system.

[0013] Step S6: Construct a Lyapunov function related to the state and parameters, prove the H∞ robust performance and stability of the nonlinear variable parameter heading control closed-loop system, and deduce the conditions for the system to have H∞ robust stability.

[0014] Step S7: The H∞ robust stability condition can be transformed into a polynomial linear matrix inequality by using lemmas such as Schur complement and SOS.

[0015] Step S8: Solve the polynomial linear matrix inequality through the SOS toolbox in MATLAB software to obtain the assumed nonlinear state feedback controller in Step S5 as the nonlinear variable parameter H∞ robust controller.

[0016] Step S9: The unmanned boat system takes the measured heading angle and heading angular velocity as feedback, analyzes the obtained heading angle error and inputs it into the H∞ robust controller to achieve tracking of the given heading angle, suppression of external disturbances and parameter perturbations.

[0017] Furthermore, the three-degree-of-freedom dynamics model obtained in Step S1 is:

[0018]

[0019] where \(v = [u, v, r]\) T is the unmanned boat state vector, and \(u\), \(v\), \(r\) are the surge velocity, sway velocity and yaw velocity respectively; \(M\in R\) 3×3 is the inertia matrix; \(C(v)\in R\) 3×3 is the Coriolis centripetal force matrix; \(D(v)\in R\) 3×3 is the hydrodynamic damping matrix; \(\tau = [\tau\) u , \(\tau\) v , \(\tau\) r T is the propeller output torque, and \(\tau\) u , \(\tau\) v , \(\tau\) r are the torques for surge, sway and yaw motions respectively; \(\tau\)​w = [τ uw , τ vw , τ rw T is the external interference, τ uw , τ vw , τ rw are respectively the external interferences of surge, sway and yaw motions.

[0020] Furthermore, step S2 is specifically as follows: According to the low aspect ratio wing theory, the hydrodynamic damping matrix in the ship model is replaced by the circulation and cross-flow forces acting on the ship, that is, let:

[0021] D(v) = F LD (v) + F cf (v)

[0022] where, F cf (v) is the cross-flow resistance acting on the ship; F LD (v) = F L (v) + F D (v) is the circulation force acting on the ship, F L (v) = [X L , Y L , N L T is the circulation lift force acting on the ship, F D (v) = [X D , Y D , N D T is the circulation resistance acting on the ship; X L and X D are respectively the circulation lift force and resistance of the surge motion, Y L and Y D are respectively the circulation lift force and resistance of the sway motion, N L and N D are respectively the circulation lift moment and resistance moment of the yaw motion.

[0023] Furthermore, the maneuvering dynamics model of step S3 is specifically:

[0024]

[0025] where, are system parameters, m is the mass of the ship, x g is the distance from the center of gravity to the origin of the ship coordinate system on the x-axis, is the added mass coefficient, N (u,v,r) is the yaw circulation moment coefficient.

[0026] Furthermore, in step S4, the non-linear variable parameter heading error model is: ​​​

[0027]

[0028] where x = [r, ψ e T is the state variable; u τ = c4τ r is the actuator output; w = c4τ rw is the total external disturbance; z = ψ e is the controlled output, and the surge velocity u is a time-varying parameter denoted as u(t); B1 = B2 = [1, 0] T , and C = [0, 1] are the system matrices of the nonlinear time-varying parameter model.

[0029] Furthermore, in step S5, the assumed nonlinear state feedback controller is specifically: for the unmanned ship heading control system, if there exists a symmetric positive definite polynomial matrix P(u(t)) that depends on the time-varying parameter, and a polynomial matrix such that the polynomial linear matrix inequality:

[0030]

[0031]

[0032] holds, then the control system is asymptotically stable, and the H∞ norm for the external disturbance w is less than γ, where γ is the H∞ performance index. At this time, the form of the state feedback controller of the closed-loop system is:

[0033]

[0034] Furthermore, in step S8, for the polynomial linear matrix inequality, it is transformed into the sum-of-squares form and solved through the SOS toolbox in the MATLAB software to obtain a symmetric positive definite polynomial matrix P(u(t)) and a polynomial matrix thus designing the control law u τ .

[0035] Compared with the prior art, the present invention and its preferred embodiments have the following beneficial effects:

[0036] 1. The provided nonlinear time-varying parameter heading control model establishes a hydrodynamic mechanism model of the ship at the physical level, replacing the previous hydrodynamic empirical model, and has a relatively clear physical meaning;

[0037] 2. Compared with other heading control models, the provided nonlinear time-varying parameter heading control model not only has a simple form, but also fully restores the nonlinear time-varying characteristics of the unmanned ship system, which is helpful for designing a controller that can accurately adjust the heading;

[0038] ​3. The provided non - linear variable - parameter H∞ robust controller incorporates the system state, time - varying parameters, and their derivatives, eliminating the need for system linearization. As a result, it no longer conceals the non - linear time - varying characteristics of the system, reduces the conservatism in controller design, and improves the dynamic performance and robustness of the unmanned ship heading control system.

[0039] 4. Transforming the design of the non - linear variable - parameter H∞ robust controller into a problem of solving polynomial linear matrix inequality conditions allows for the use of the SOS toolbox in MATLAB software for solution, reducing the computational complexity and facilitating engineering implementation. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] The present invention will be further described in detail below in conjunction with the drawings and specific embodiments:

[0041] Figure 1 It is the structure diagram of the H∞ heading control method based on the non - linear variable - parameter unmanned ship model in the embodiment of the present invention;

[0042] Figure 2 It is the flow chart for establishing the non - linear variable - parameter unmanned ship model in the embodiment of the present invention;

[0043] Figure 3 It is the flow chart for designing the non - linear variable - parameter H∞ robust controller in the embodiment of the present invention;

[0044] Figure 4 It is the heading tracking simulation diagram in the embodiment of the present invention;

[0045] Figure 5 It is the simulation diagram of the actual error of the tracking heading angle in the embodiment of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0046] To make the features and advantages of this patent more obvious and understandable, specific embodiments are given below for detailed description as follows:

[0047] It should be noted that the following detailed description is exemplary and is intended to provide further explanation of the present application. Unless otherwise specified, all technical and scientific terms used in this specification have the same meaning as commonly understood by those of ordinary skill in the technical field to which this application belongs.

[0048] It should be noted that the terms used herein are only for describing specific embodiments and are not intended to limit the exemplary embodiments according to the present application. As used herein, unless the context clearly indicates otherwise, the singular forms are also intended to include the plural forms. In addition, it should be understood that when the terms "comprise" and / or "include" are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or combinations thereof.

[0049] Please refer to Figure 1, the present invention provides an H∞ heading control method based on a non-linear variable parameter unmanned ship model. According to the low aspect ratio wing theory, the circulation and cross-flow forces acting on the ship are obtained, a non-linear variable parameter heading control model is established, and polynomial linear matrix inequalities are derived. Then, the SOS toolbox in MATLAB software is used to solve them, and finally a non-linear variable parameter H∞ robust controller is obtained. Based on the establishment of a model that fully describes the non-linear time-varying characteristics of the unmanned ship, this method designs a non-linear variable parameter H∞ robust controller, providing good stability and strong robustness for the unmanned ship heading control system. The specific steps are as follows:

[0050] Step 1: As Figure 2 shown, according to the ship theory of the Fossen framework, a three-degree-of-freedom dynamic model of surge, sway, and yaw motions is established:

[0051]

[0052] where, v = [u, v, r] T is the state vector of the unmanned ship, and u, v, and r are the surge velocity, sway velocity, and yaw velocity respectively; M ∈ R 3×3 is the inertia matrix; C(v) ∈ R 3×3 is the Coriolis centripetal force matrix; D(v) ∈ R 3×3 is the hydrodynamic damping matrix; τ = [τ u , τ v , τ r T is the output torque of the thruster, and τ u , τ v , τ r are the torques of surge, sway, and yaw motions respectively; τ w = [τ uw , τ vw , τ rw T is the external disturbance, and τ uw , τ vw , τ rw are the external disturbances of surge, sway, and yaw motions respectively.

[0053] Step 2: As Figure 2 shown, regarding the ship as a low aspect ratio wing, according to the low aspect ratio wing theory, the hydrodynamic damping matrix in the ship model is replaced by the circulation and cross-flow forces acting on the ship, that is, let:

[0054] D(v) = F LD (v) + F cf (v)

[0055] where, F cf (v) is the cross-flow resistance acting on the ship; FLD $(v)=F$ L $(v)+F$ D $(v)$ is the circulation force acting on the ship, $F$ L $(v)=[X$ L ,Y L ,N L $ T is the circulation lift acting on the ship, $F$ D $(v)=[X$ D ,Y D ,N D $ T is the circulation drag acting on the ship; $X$ L and $X$ D are the circulation lift and drag in the surge motion respectively, $Y$ L and $Y$ D are the circulation lift and drag in the sway motion respectively, $N$ L and $N$ D are the circulation lift moment and drag moment in the yaw motion respectively.

[0056] Step 3: As shown in Figure 2 , perform a force analysis on the circulation and cross-flow forces acting on the ship in different motion directions of the ship to obtain a dynamic model of the unmanned ship based on a low aspect ratio wing, and decompose the dynamic model of the unmanned ship based on the low aspect ratio wing according to the characteristics of the underactuated small unmanned ship to obtain a maneuvering dynamic model:

[0057]

[0058] Among them, is the system parameter, $m$ is the mass of the ship, $x$ g is the distance from the center of gravity to the origin of the ship's coordinate system on the x-axis, is the added mass coefficient, $N$ (u,v,r) is the yaw circulation moment coefficient.

[0059] Step 4: As shown in Figure 3 , introduce the yaw angle variable into the maneuvering dynamic model according to the physical relationship between the yaw angle and the yaw angular velocity, obtain a nonlinear variable parameter yaw control model, and consider that the yaw angle is given as constant within a yaw sampling step. According to the yaw angle error $\psi$ e $=\psi$ d $-\psi$, establish a nonlinear variable parameter yaw error model:

[0060]

[0061] Among them, $x = [r,\psi$ e $ T is the state variable; $u$ τ $=c4\tau$ r is the actuator output; $w = c4\tau$rw is the total external interference; z = ψ e is the controlled output, and the surge velocity u is a time-varying parameter denoted as u(t); B1 = B2 = [1, 0] T , C = [0, 1] is the system matrix of the nonlinear time-varying parameter model.

[0062] Step 5: As Figure 3 shown, for the nonlinear time-varying parameter heading error model, construct the Lyapunov function V(x, t) = x T P -1 (u(t))x. According to the system H∞ stability condition: (1) V(x, u, t) > 0; It is deduced that the solution condition for the H∞ robust stability controller of the unmanned ship heading control system is: for the unmanned ship heading control system, if there exists a symmetric positive definite polynomial matrix P(u(t)) that depends on the time-varying parameter, a polynomial matrix such that the polynomial linear matrix inequality:

[0063]

[0064]

[0065] holds, then the control system is asymptotically stable, and the H∞ norm for the external disturbance w is less than γ, where γ is the H∞ performance index. At this time, the form of the state feedback controller of the closed-loop system is:

[0066]

[0067] Step 6: As Figure 3 shown, transform the polynomial linear matrix inequality into the sum of squares form and solve it through the SOS toolbox in the MATLAB software to obtain a symmetric positive definite polynomial matrix P(u(t)) and a polynomial matrix so as to design the control law u with H∞ robust performance τ .

[0068] Step 7: As Figure 1 , Figure 3 shown, set the given heading angle ψ of the system according to the requirements d , the heading angular velocity r and the heading angle error ψ of the unmanned ship e as the state feedback, so as to build the unmanned ship heading control simulation system. Substitute the obtained control law into u τ simulation system, and optimize the parameters to achieve the expected control performance, and finally realize the tracking of the given heading angle. The simulation results are as Figure 4 , Figure 5 shown.

[0069] Those skilled in the art should understand that the embodiments of the present application can be provided as a method, a system, or a computer program product. Therefore, the present application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Moreover, the present application can take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk memory, CD-ROM, optical memory, etc.) that contain computer-usable program code.

[0070] The present application is described with reference to the flowcharts and / or block diagrams of methods, devices (systems), and computer program products according to the embodiments of the present application. It should be understood that each flow and / or block in the flowchart and / or block diagram can be implemented by computer program instructions, and the combination of the flows and / or blocks in the flowchart and / or block diagram can also be implemented. These computer program instructions can be provided to the processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing devices to generate a machine, such that the instructions executed by the processor of the computer or other programmable data processing devices generate means for implementing the functions specified in Figure 1 one flow or multiple flows and / or blocks Figure 1 one block or multiple blocks.

[0071] These computer program instructions can also be stored in a computer-readable memory that can direct a computer or other programmable data processing devices to work in a specific manner, such that the instructions stored in the computer-readable memory generate a manufactured article including instruction means that implement the functions specified in Figure 1 one flow or multiple flows and / or blocks Figure 1 one block or multiple blocks.

[0072] These computer program instructions can also be loaded onto a computer or other programmable data processing devices, such that a series of operation steps are executed on the computer or other programmable devices to generate a computer-implemented process, so that the instructions executed on the computer or other programmable devices provide steps for implementing the functions specified in Figure 1 one flow or multiple flows and / or blocks Figure 1 one block or multiple blocks.

[0073] As mentioned above, it is only the preferred embodiment of the present invention, and it is not a limitation to the present invention in other forms. Any person skilled in the art may use the disclosed technical content to make changes or modifications into equivalent embodiments with equivalent changes. However, any simple modifications, equivalent changes, and modifications made to the above embodiments based on the technical essence of the present invention without departing from the technical content of the present invention still fall within the protection scope of the technical solution of the present invention.

[0074] This patent is not limited to the above-mentioned best implementation mode. Anyone inspired by this patent can derive various other forms of H∞ heading control methods based on the non-linear variable parameter unmanned ship model. All equivalent changes and modifications made according to the scope of the patent application of the present invention shall fall within the scope covered by this patent.

Claims

1. A method for H∞ heading control based on a non-linear variable parameter unmanned ship model, characterized in that, A control system for a small underactuated unmanned ship, based on a nonlinear variable-parameter heading control model and a nonlinear variable-parameter H∞ robust controller, specifically includes the following steps: Step S1: Establish a ship dynamics model under the Fossen framework. During the establishment process, the heaving, rolling, and pitching motions are ignored, and the six-degree-of-freedom unmanned ship is simplified into a three-degree-of-freedom dynamics model related to surge, sway, and yaw motions; Step S2: According to the low aspect ratio wing theory, decompose the hydrodynamic damping matrix in the established three-degree-of-freedom dynamics model into the circulation force and cross-flow resistance matrix suffered by the ship, and obtain a three-degree-of-freedom unmanned ship model based on the low aspect ratio wing; Step S3: According to the actual physical characteristics of the small underactuated unmanned ship, ignore the sway motion and cross-flow resistance, and decompose the three-degree-of-freedom unmanned ship model based on the low aspect ratio wing to obtain a maneuvering dynamics model; Step S4: According to the relationship between the heading angle and the heading angular velocity, introduce the heading angle state variable into the maneuvering dynamics model, and use the heading angle error as feedback to obtain a nonlinear variable-parameter heading error model; Step S5: Substitute the assumed nonlinear state feedback controller into the nonlinear variable-parameter heading error model to establish a nonlinear variable-parameter heading control closed-loop system; Step S6: Construct a Lyapunov function related to the state and parameters, prove the H∞ robust performance and stability of the nonlinear variable-parameter heading control closed-loop system, and derive the conditions for the system to have H∞ robust stability; Step S7: Convert the H∞ robust stability conditions into polynomial linear matrix inequalities; Step S8: Solve the polynomial linear matrix inequalities through the SOS toolbox in the MATLAB software to obtain the nonlinear state feedback controller assumed in Step S5, as the nonlinear variable-parameter H∞ robust controller; Step S9: The unmanned ship system takes the measured heading angle and heading angular velocity as feedback, analyzes and obtains the heading angle error and inputs it into the H∞ robust controller to achieve the tracking of the given heading angle, and the suppression of external disturbances and parameter perturbations.

2. The H∞ heading control method based on the non-linear variable parameter unmanned ship model according to claim 1, characterized in that: The three-degree-of-freedom dynamics model obtained in Step S1 is: where \(v = [u, v, r]\) T is the state vector of the unmanned ship, and \(u\), \(v\), and \(r\) are the surge velocity, sway velocity, and yaw velocity respectively; \(M\in R\) 3×3 is the inertia matrix; \(C(v)\in R\) 3×3 is the Coriolis centripetal force matrix; \(D(v)\in R\) 3×3 is the hydrodynamic damping matrix; \(\tau = [\tau\) u , \(\tau\) v , \(\tau\) r T is the output torque of the thruster, and \(\tau\) u , \(\tau\) v , \(\tau\) r are the torques of surge, sway, and yaw motions respectively; \(\tau\) w = [\tau\) uw , \(\tau\) vw , \(\tau\) rw T is the external disturbance, and \(\tau\) uw , \(\tau\) vw , \(\tau\) rw are the external disturbances of surge, sway, and yaw motions respectively.​​ 3. The H∞ heading control method based on the non-linear variable parameter unmanned ship model according to claim 2, characterized in that: Step S2 is specifically: According to the low aspect ratio wing theory, replace the hydrodynamic damping matrix in the ship model with the circulation and cross-flow forces suffered by the ship, that is, let: D(v) = F LD (v) + F cf (v) Among them, F cf (v) is the cross-flow resistance suffered by the ship; F LD (v) = F L (v) + F D (v) is the circulation force suffered by the ship, and F L (v) = [X L , Y L, N L T is the circulation lift suffered by the ship, and F D (v) = [X D , Y D , N D T is the circulation resistance suffered by the ship; X L and X D are respectively the circulation lift and resistance of the surge motion, Y L and Y D are respectively the circulation lift and resistance of the sway motion, and N L and N D are respectively the circulation lift moment and resistance moment of the yaw motion.​​ 4. The H∞ heading control method based on the non-linear variable parameter unmanned ship model according to claim 3, characterized in that: The maneuvering dynamics model in Step S3 is specifically: Among them, is a system parameter, m is the mass of the ship, and x g is the distance from the center of gravity to the origin of the ship's coordinates along the x-axis, is the added mass coefficient, and N (u,v,r) is the yaw circulation moment coefficient.

5. The H∞ heading control method based on the non-linear variable parameter unmanned ship model according to claim 4, characterized in that: In Step S4, the nonlinear variable-parameter heading error model is: where \(x = [r,\psi e \) T is the state variable; \(u τ = c4\tau r is the actuator output; \(w = c4\tau rw is the total external disturbance; \(z=\psi e is the controlled output, and the surge velocity \(u\) is a time-varying parameter denoted as \(u(t)\); \(B1 = B2 = [1,0] T , C = [0,1]\) are the system matrices of the nonlinear time-varying parameter model.

6. The H∞ heading control method based on the non-linear variable parameter unmanned ship model according to claim 5, characterized in that: In step S5, the assumed non-linear state feedback controller is specifically: for the unmanned ship heading control system, if there exists a symmetric positive definite polynomial matrix P(u(t)) that depends on time-varying parameters, and a polynomial matrix such that the polynomial linear matrix inequality: If it holds, then the control system is asymptotically stable, and the H∞ norm for the external disturbance w is less than γ, where γ is the H∞ performance index. At this time, the form of the state feedback controller of the closed-loop system is:

7. The H∞ heading control method based on the non-linear variable parameter unmanned ship model according to claim 6, characterized in that: In step S8, for the polynomial linear matrix inequality, it is transformed into the sum-of-squares form and solved through the SOS toolbox in MATLAB software to obtain a symmetric positive definite polynomial matrix P(u(t)) and a polynomial matrix so as to design the control law u τ .

Images