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Keywords = underactuated ship

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20 pages, 1284 KB  
Article
Practical L1-Based Guidance and Neural Path-Following Control for Underactuated Ships with Backlash Hysteresis
by Chenfeng Huang, Bingyan Zhang, Haitong Xu and Meirong Wei
J. Mar. Sci. Eng. 2026, 14(4), 402; https://doi.org/10.3390/jmse14040402 - 22 Feb 2026
Viewed by 350
Abstract
The study addresses trajectory tracking control for underactuated vessels with uncertain backlash-type hysteresis. First, an improved practical L1-based guidance strategy is developed by embedding the L1 mechanism into the virtual ship framework to eliminate steering overshoot and yaw angle error accumulation, which can [...] Read more.
The study addresses trajectory tracking control for underactuated vessels with uncertain backlash-type hysteresis. First, an improved practical L1-based guidance strategy is developed by embedding the L1 mechanism into the virtual ship framework to eliminate steering overshoot and yaw angle error accumulation, which can facilitate the smooth turning of ships along waypoint-based paths with large curvature. Next, to mitigate control performance degradation induced by backlash-like hysteresis nonlinearity, an improved quadratic function is utilized to boost the closed-loop system’s convergence capability. Moreover, system model uncertainty-induced perturbations are compensated using the resilient neural damping method, which can simplify the structure and reduce the computation burden of the proposed controller. Utilizing Lyapunov-based approaches and the special Young’s inequality, uniformly ultimately bounded stability over a semi-global domain is established. Finally, numerical simulations are executed to validate the efficacy of the developed control architecture. Full article
(This article belongs to the Special Issue New Technologies in Autonomous Ship Navigation)
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24 pages, 1303 KB  
Article
Event-Sampled Adaptive Neural Automatic Berthing Control for Underactuated Ships Under FDI Attacks
by Peng Zhang, Fangliang Xiao, Chun Li and Guibing Zhu
J. Mar. Sci. Eng. 2025, 13(9), 1636; https://doi.org/10.3390/jmse13091636 - 27 Aug 2025
Viewed by 885
Abstract
This work addresses the automatic berthing control problem of underactuated ships under false data injection (FDI) attack, and an event-sampled automatic berthing control scheme is proposed. To avoid the FDI attack signals from entering the closed-loop system through the sensor–controller channel and worsening [...] Read more.
This work addresses the automatic berthing control problem of underactuated ships under false data injection (FDI) attack, and an event-sampled automatic berthing control scheme is proposed. To avoid the FDI attack signals from entering the closed-loop system through the sensor–controller channel and worsening the berthing control performance as much as possible, a novel event-sampled adaptive neural network state observer is developed, which is independent of the controller. To solve the control design problem of berthing caused by underactuated features, an equivalent motion model of underactuated ships under FDI attack is established by differential homeomorphic transformation. Furthermore, under the backstepping design framework, using the state observer and adaptive neural network technology, a single-parameter learning-based automatic berthing control solution is developed. Meanwhile, to further reduce the network resource consumption and load caused by the transmission of control signals, an event-triggered mechanism for the controller–actuator channel is established. The theoretical analysis by Lyapunov indicates that the constructed closed-loop system for automatic berthing control is stable, and all the signals are bounded. Simulation and comparison are carried out to verify the effectiveness and superiority of proposed control scheme, and the results verify the conclusions and theoretical feasibility of this work. Full article
(This article belongs to the Special Issue Control and Optimization of Ship Propulsion System)
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17 pages, 1877 KB  
Article
Obstacle Avoidance Tracking Control of Underactuated Surface Vehicles Based on Improved MPC
by Chunyu Song, Qi Qiao and Jianghua Sui
J. Mar. Sci. Eng. 2025, 13(9), 1603; https://doi.org/10.3390/jmse13091603 - 22 Aug 2025
Viewed by 1004
Abstract
This paper addresses the issue of the poor collision avoidance effect of underactuated surface vehicles (USVs) during local path tracking. A virtual ship group control method is suggested by using Freiner coordinates and a model predictive control (MPC) algorithm. We track the planned [...] Read more.
This paper addresses the issue of the poor collision avoidance effect of underactuated surface vehicles (USVs) during local path tracking. A virtual ship group control method is suggested by using Freiner coordinates and a model predictive control (MPC) algorithm. We track the planned path using the MPC algorithm according to the known vessel state and build a hierarchical weighted cost function to handle the state of the virtual vessel, to ensure that the vessel avoids obstacles while tracking the path. In addition, the control system incorporates an Extended Kalman Filter (EKF) algorithm to minimize the state estimation error by continuously updating the ship state and providing more accurate state estimation for the system in a timely manner. In order to validate the anti-interference and robustness of the control system, the simulation experiment is carried out with the “Yukun” as the research object by adding the interference of wind and wave of level 6. The outcome shows that the algorithm suggested in this paper can accurately perform the trajectory-tracking task and make collision avoidance decisions under six levels of external interference. Compared with the original MPC algorithm, the improved MPC algorithm reduces the maximum rudder angle output value by 58%, the integral absolute error by 46%, and the root mean square error value by 46%. The control method provides a new technical choice for trajectory tracking and collision avoidance of USVs in complex marine environments, with a reliable theoretical basis and practical application value. Full article
(This article belongs to the Special Issue Control and Optimization of Ship Propulsion System)
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25 pages, 2473 KB  
Article
Predefined-Time Adaptive Neural Control with Event-Triggering for Robust Trajectory Tracking of Underactuated Marine Vessels
by Hui An, Zhanyang Yu, Jianhua Zhang, Xinxin Wang and Cheng Siong Chin
Processes 2025, 13(8), 2443; https://doi.org/10.3390/pr13082443 - 1 Aug 2025
Viewed by 930
Abstract
This paper addresses the trajectory tracking control problem of underactuated ships in ocean engineering, which faces the dual challenges of tracking error time–performance regulation and robustness design due to the system’s underactuated characteristics, model uncertainties, and external disturbances. Aiming to address the issues [...] Read more.
This paper addresses the trajectory tracking control problem of underactuated ships in ocean engineering, which faces the dual challenges of tracking error time–performance regulation and robustness design due to the system’s underactuated characteristics, model uncertainties, and external disturbances. Aiming to address the issues of traditional finite-time control (convergence time dependent on initial states) and fixed-time control (control chattering and parameter conservativeness), this paper proposes a predefined-time adaptive control framework that integrates an event-triggered mechanism and neural networks. By constructing a Lyapunov function with time-varying weights and designing non-periodic dynamically updated dual triggering conditions, the convergence process of tracking errors is strictly constrained within a user-prespecified time window without relying on initial states or introducing non-smooth terms. An adaptive approximator based on radial basis function neural networks (RBF-NNs) is employed to compensate for unknown nonlinear dynamics and external disturbances in real-time. Combined with the event-triggered mechanism, it dynamically adjusts the update instances of control inputs, ensuring prespecified tracking accuracy while significantly reducing computational resource consumption. Theoretical analysis shows that all signals in the closed-loop system are uniformly ultimately bounded, tracking errors converge to a neighborhood of the origin within the predefined-time, and the update frequency of control inputs exhibits a linear relationship with the predefined-time, avoiding Zeno behavior. Simulation results verify the effectiveness of the proposed method in complex marine environments. Compared with traditional control strategies, it achieves more accurate trajectory tracking, faster response, and a substantial reduction in control input update frequency, providing an efficient solution for the engineering implementation of embedded control systems in unmanned ships. Full article
(This article belongs to the Special Issue Design and Analysis of Adaptive Identification and Control)
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18 pages, 1451 KB  
Article
Sustainable Trajectory Tracking Control for Underactuated Ships Using Non-Singular Fast Terminal Sliding Mode Control
by Minjie Zheng, Qianqiang Chen, Yulai Su and Guoquan Chen
Sustainability 2025, 17(13), 5866; https://doi.org/10.3390/su17135866 - 26 Jun 2025
Viewed by 790
Abstract
Accurate and robust trajectory tracking is essential for ensuring the safety and efficiency of underactuated ships operating in complex marine environments. However, conventional sliding mode control (SMC) methods often suffer from issues such as chattering and slow convergence, limiting their practical application. To [...] Read more.
Accurate and robust trajectory tracking is essential for ensuring the safety and efficiency of underactuated ships operating in complex marine environments. However, conventional sliding mode control (SMC) methods often suffer from issues such as chattering and slow convergence, limiting their practical application. To address these challenges, this paper proposes a novel non-singular fast terminal sliding mode control (NFTSMC) strategy for sustainable trajectory tracking of underactuated ships. The proposed approach first designs a virtual control law based on surge and sway position errors, and then develops a non-singular fast terminal sliding mode control law using an exponential reaching strategy, guaranteeing finite-time convergence and eliminating singularities. The Lyapunov-based stability analysis proves the boundedness and convergence of tracking errors under external disturbances. The simulation results demonstrate that the proposed non-singular fast terminal sliding mode control outperforms traditional sliding mode control in terms of convergence speed, tracking accuracy, and control smoothness, especially under wind, wave, and current disturbances. Full article
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16 pages, 4542 KB  
Article
Energy-Based Adaptive Control for Variable-Rope-Length Double-Pendulum Ship-Borne Cranes: A Disturbance Rejection Stabilization Controller Without Overshoot
by Ken Zhong, Yuzhe Qian, He Chen and Shujie Wu
Actuators 2025, 14(2), 52; https://doi.org/10.3390/act14020052 - 24 Jan 2025
Cited by 1 | Viewed by 1449
Abstract
The operation process of double-pendulum ship-borne cranes with variable rope lengths is frequently complex, with numerous unpredictable circumstances, such as the swing of the load and external environmental interferences, which undoubtedly make the analysis of the swing characteristics of the system and the [...] Read more.
The operation process of double-pendulum ship-borne cranes with variable rope lengths is frequently complex, with numerous unpredictable circumstances, such as the swing of the load and external environmental interferences, which undoubtedly make the analysis of the swing characteristics of the system and the controller design more difficult. On this basis, an active disturbance rejection controller based on an energy coupling method is proposed to inhibit the double-pendulum swing angle. The controller can suppress the swing of the hook and load within 0.5 degrees under the conditions of continuous sea wave disturbances and external disturbances. Firstly, the energy function of the system is constructed by analyzing the dynamic model of the system. Then, an adaptive control method is designed by analyzing the energy function of the system. In addition, an overshoot limit term and an anti-swing term are added to limit the overshoot and swing of underactuated parts of the system. Then, the stability of the closed-loop system is strictly proven by using Lyapunov analysis. Finally, the simulation and experimental results indicate that the proposed controller ensures the accurate positioning of the jib and rope length without overshoot. Additionally, it effectively reduces the double-pendulum swing angle when there is an external interference such as waves, demonstrating strong robustness. Full article
(This article belongs to the Special Issue Modeling and Nonlinear Control for Complex MIMO Mechatronic Systems)
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25 pages, 6353 KB  
Article
Fractional-Order Controller for the Course Tracking of Underactuated Surface Vessels Based on Dynamic Neural Fuzzy Model
by Guangyu Li, Yanxin Li, Xiang Li, Mutong Liu, Xuesong Zhang and Hua Jin
Fractal Fract. 2024, 8(12), 720; https://doi.org/10.3390/fractalfract8120720 - 5 Dec 2024
Cited by 3 | Viewed by 1335
Abstract
Aiming at the uncertainty problem caused by the time-varying modeling parameters associated with ship speed in the course tracking control of underactuated surface vessels (USVs), this paper proposes a control algorithm based on the dynamic neural fuzzy model (DNFM). The DNFM simultaneously adjusts [...] Read more.
Aiming at the uncertainty problem caused by the time-varying modeling parameters associated with ship speed in the course tracking control of underactuated surface vessels (USVs), this paper proposes a control algorithm based on the dynamic neural fuzzy model (DNFM). The DNFM simultaneously adjusts the structure and parameters during learning and fully approximates the inverse dynamics of ships. Online identification and modeling lays the model foundation for ship motion control. The trained DNFM, serving as an inverse controller, is connected in parallel with the fractional-order PIλDμ controller to be used for the tracking control of the ship’s course. Moreover, the weights of the model can be further adjusted during the course tracking. Taking the actual ship data of a 5446 TEU large container ship, simulation experiments are conducted, respectively, for course tracking, course tracking under wind and wave interferences, and comparison with five different controllers. This proposed controller can overcome the influence of the uncertainty of modeling parameters, tracking the desired course quickly and effectively. Full article
(This article belongs to the Special Issue Applications of Fractional-Order Systems to Automatic Control)
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19 pages, 5629 KB  
Article
A Model-Free Adaptive Positioning Control Method for Underactuated Unmanned Surface Vessels in Unknown Ocean Currents
by Zihe Qin, Feng Zhang, Wenlin Xu, Yu Chen and Jinyu Lei
J. Mar. Sci. Eng. 2024, 12(10), 1801; https://doi.org/10.3390/jmse12101801 - 9 Oct 2024
Cited by 1 | Viewed by 1730
Abstract
Aiming to address the problem of underactuated unmanned surface vehicles (USVs) performing fixed-point operations at sea without dynamic positioning control systems, this paper introduces an original approach to positioning control: the virtual anchor control method. This method is applicable in environments with currents [...] Read more.
Aiming to address the problem of underactuated unmanned surface vehicles (USVs) performing fixed-point operations at sea without dynamic positioning control systems, this paper introduces an original approach to positioning control: the virtual anchor control method. This method is applicable in environments with currents that change slowly and does not require prior knowledge of current information or vessel motion model parameters, thus offering convenient usability. This method comprises four steps. First, a concise linear motion model with unknown disturbances is proposed. Then, a motion planning law is designed by imitating underlying principles of ship anchoring. Next, an adaptive disturbance observer is proposed to estimate uncertainties in the motion model. In the last step, based on the observer, a sliding-mode method is used to design a heading control law, and a thrust control law is also designed by applying the Lyapunov method. Numerical simulation experiments with significant disturbances and tidal current variations are conducted, which demonstrate that the proposed method has a good control effect and is robust. Full article
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19 pages, 9762 KB  
Article
Graph Search-Based Path Planning for Automatic Ship Berthing
by Xiaocheng Liu, Zhihuan Hu, Ziheng Yang and Weidong Zhang
J. Mar. Sci. Eng. 2024, 12(6), 933; https://doi.org/10.3390/jmse12060933 - 2 Jun 2024
Cited by 4 | Viewed by 2467
Abstract
Ship berthing is one of the most challenging operations for crews, involving optimal trajectory generation and intricate harbor maneuvering at low speed. In this paper, we present a practical path-planning method that generates smooth trajectories for an underactuated surface vehicle (USV) traveling in [...] Read more.
Ship berthing is one of the most challenging operations for crews, involving optimal trajectory generation and intricate harbor maneuvering at low speed. In this paper, we present a practical path-planning method that generates smooth trajectories for an underactuated surface vehicle (USV) traveling in a confined harbor environment. Our approach introduces a Generalized Voronoi Diagram (GVD)-based path planner to handle the unberthing phase. The hybrid A* search-based path finding method is used for the transportation phase. A simple planner based on a Bézier curve is proposed for the berthing phase. To track the target path, an adaptive pure pursuit method and proportional-derivative (PD) controller is used. The performance of the given method is tested numerically and experimentally on a catamaran with a pair of non-steerable thrusters. The results demonstrate that the proposed algorithm can achieve a successful berthing operation through static obstacle handling and smooth trajectory generation. Full article
(This article belongs to the Special Issue Motion Control and Path Planning of Marine Vehicles—2nd Edition)
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18 pages, 2982 KB  
Article
Cooperative Maritime Search of Multi-Ship Based on Improved Robust Line-of-Sight Guidance
by Weili Guo, Cheng Liu and Ting Sun
J. Mar. Sci. Eng. 2024, 12(1), 105; https://doi.org/10.3390/jmse12010105 - 5 Jan 2024
Cited by 5 | Viewed by 1711
Abstract
In this paper, an improved robust line-of-sight (RLOS) guidance-based fuzzy sliding mode controller is presented to control underactuated ships to conduct the cooperative maritime search operation under the presented improved creeping line search method. First, considering that the ship cannot perform turning with [...] Read more.
In this paper, an improved robust line-of-sight (RLOS) guidance-based fuzzy sliding mode controller is presented to control underactuated ships to conduct the cooperative maritime search operation under the presented improved creeping line search method. First, considering that the ship cannot perform turning with corners, an improved creeping line search method is presented by integrating the Bezier method into the traditional creeping line search method to smooth the transition points with corners and employing the cubic spline interpolation method to generate continuous reference paths. Second, an improved RLOS guidance method is presented for the first time by exploring the idea of robust adaptive control to mitigate the chattering effect of the RLOS guidance. Third, the fuzzy logic system with approximate ability is integrated into the design of sliding mode controller to handle unknown nonlinear model dynamics and environmental disturbances. Finally, an improved RLOS guidance-based fuzzy sliding mode controller is presented. The closed-loop stability is guaranteed by the Lyapunov theorem. Comparative simulations are conducted to illustrate the advantages and verify the effectiveness of the presented method. Full article
(This article belongs to the Special Issue Optimal Maneuvering and Control of Ships)
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30 pages, 7438 KB  
Review
Ship Autonomous Collision-Avoidance Strategies—A Comprehensive Review
by Hongguang Lyu, Zengrui Hao, Jiawei Li, Guang Li, Xiaofeng Sun, Guoqing Zhang, Yong Yin, Yanjie Zhao and Lunping Zhang
J. Mar. Sci. Eng. 2023, 11(4), 830; https://doi.org/10.3390/jmse11040830 - 14 Apr 2023
Cited by 57 | Viewed by 9308
Abstract
Autonomous decision-making for ships to avoid collision is core to the autonomous navigation of intelligent ships. In recent years, related research has shown explosive growth. However, owing to the complex constraints of navigation environments, the Convention of the International Regulations for Preventing Collisions [...] Read more.
Autonomous decision-making for ships to avoid collision is core to the autonomous navigation of intelligent ships. In recent years, related research has shown explosive growth. However, owing to the complex constraints of navigation environments, the Convention of the International Regulations for Preventing Collisions at Sea, 1972 (COLREGs), and the underactuated characteristics of ships, it is extremely challenging to design a decision-making algorithm for autonomous collision avoidance (CA) that is practically useful. Based on the investigation of many studies, current decision-making algorithms can be attributed to three strategies: alteration of course alone, alteration of speed alone, and alteration of both course and speed. This study discusses the implementation methods of each strategy in detail and compares the specific ways, applicable scenes, and limiting conditions of these methods to achieve alteration of course and/or speed to avoid collision, especially their advantages and disadvantages. Additionally, this study quantitatively analyzes the coupling mechanisms of alterations of course and speed for autonomous CA decision-making under different encounter situations, supplementing and optimizing the decision-making theory for ship autonomous CA. Finally, several feasible algorithms and improvement schemes for autonomous CA decision-making, combined with course and speed alterations, are discussed. Full article
(This article belongs to the Section Ocean Engineering)
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16 pages, 5205 KB  
Article
Cooperative Path Tracking for Swarm of MASSs Based on Consensus Theory
by Xuewei Li, Miao Gao, Zhen Kang, Xiangyu Chen, Xi Zeng, Shuai Chen, Haixin Sun and Anmin Zhang
J. Mar. Sci. Eng. 2023, 11(2), 312; https://doi.org/10.3390/jmse11020312 - 1 Feb 2023
Viewed by 2186
Abstract
At present, marine autonomous surface ships (MASSs) play a huge role in marine shipping, surveying and mapping, safeguarding the rights and interests of marine space, and other maritime tasks. The cooperative operation of a swarm of MASSs can extend the scope of operation [...] Read more.
At present, marine autonomous surface ships (MASSs) play a huge role in marine shipping, surveying and mapping, safeguarding the rights and interests of marine space, and other maritime tasks. The cooperative operation of a swarm of MASSs can extend the scope of operation of the MASSs, and thus allow them to carry out more complex tasks. Path tracking is an important problem for the control of a swarm of MASSs. In this paper, the control of underactuated MASSs is decoupled, to control the heading and speed, respectively. First of all, in the path tracking, the improved arc LOS guidance law is introduced, and the heading torque controller is designed, so that the MASS can track the reference path efficiently and accurately. Then the single-path guided path tracking without formation of the swarm of MASSs is studied, the reference path of the swarm center tracking is defined, and the heave thrust controller of the swarm of MASSs is designed based on consensus theory, so that the surge velocity of the MASS can tend towards consistentcy, and finally converge to the desired speed. Finally, the effectiveness of the proposed control strategy is verified by two groups of simulation experiments. Full article
(This article belongs to the Special Issue Application of Advanced Technologies in Maritime Safety)
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21 pages, 10541 KB  
Article
Finite Time Trajectory Tracking with Full-State Feedback of Underactuated Unmanned Surface Vessel Based on Nonsingular Fast Terminal Sliding Mode
by Donghao Xu, Zipeng Liu, Jiuzhen Song and Xueqian Zhou
J. Mar. Sci. Eng. 2022, 10(12), 1845; https://doi.org/10.3390/jmse10121845 - 1 Dec 2022
Cited by 13 | Viewed by 2615
Abstract
Marine transportation and operations have attracted the attention of more and more countries and scholars in recent years. A full-state finite time feedback control scheme is designed for the model parameters uncertainty, unknown ocean environment disturbances, and unmeasured system states in the underactuated [...] Read more.
Marine transportation and operations have attracted the attention of more and more countries and scholars in recent years. A full-state finite time feedback control scheme is designed for the model parameters uncertainty, unknown ocean environment disturbances, and unmeasured system states in the underactuated Unmanned Surface Vessel (USV) trajectory tracking control. The external wind, wave and current environmental disturbances and model parameters perturbation are extended by Nonlinear Extended State Observer (NESO) to the state of the system, namely complex disturbances. The complex disturbances, positions and velocities of USV can be observed by NESO and feedback to USV control system. Next, the underactuated USV error model is obtained by operating the obtained feedback information and the virtual ship model. According to the error model, a Nonsingular Fast Terminal Sliding Model surface (NFTSM) is constructed to realize finite-time control. The control law is deduced through the Lyapunov stability theory to ensure the stability of the system. The results of MATLAB numerical simulations under different disturbances show that the trajectory tracking algorithm has fast responses, and a good convergence of the errors is observed, which verifies the effectiveness of the designed scheme. Full article
(This article belongs to the Special Issue Motion Control and Path Planning of Marine Vehicles)
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12 pages, 1810 KB  
Article
Guidance-Based Path Following of an Underactuated Ship Based on Event-Triggered Sliding Mode Control
by Yuxi Zhang and Yong Liu
J. Mar. Sci. Eng. 2022, 10(11), 1780; https://doi.org/10.3390/jmse10111780 - 18 Nov 2022
Cited by 11 | Viewed by 2714
Abstract
In this paper, the path following of an underactuated ship as a fundamental application for autonomous sailing in seaways is studied. First, the guidance system based on the line of sight (LOS) method is established to handle underactuated dynamics of ship motion. Then, [...] Read more.
In this paper, the path following of an underactuated ship as a fundamental application for autonomous sailing in seaways is studied. First, the guidance system based on the line of sight (LOS) method is established to handle underactuated dynamics of ship motion. Then, path following control is converted to heading control with fewer dimensions. Second, the extended state observer (ESO) is used to observe unknown dynamics of ship motion. Third, the sliding mode control method is highly robust to external disturbance and is employed to design the controller. Fourth, the event-triggered mechanism (ETM) is included to reduce the trigger time. All the closed-loop signals are shown to be bounded by the Lyapunov theory. Simulations are carried out to verify the effectiveness of the proposed method. Full article
(This article belongs to the Special Issue Advances in Marine Vehicles, Automation and Robotics)
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25 pages, 5983 KB  
Article
Fractional-Order PIλDμ Controller Using Adaptive Neural Fuzzy Model for Course Control of Underactuated Ships
by Guangyu Li, Baojie Chen, Huayue Chen and Wu Deng
Appl. Sci. 2022, 12(11), 5604; https://doi.org/10.3390/app12115604 - 31 May 2022
Cited by 9 | Viewed by 2543
Abstract
For the uncertainty caused by the time-varying modeling parameters with the sailing speed in the course control of underactuated ships, a novel identification method based on an adaptive neural fuzzy model (ANFM) is proposed to approximate the inverse dynamic characteristics of the ship [...] Read more.
For the uncertainty caused by the time-varying modeling parameters with the sailing speed in the course control of underactuated ships, a novel identification method based on an adaptive neural fuzzy model (ANFM) is proposed to approximate the inverse dynamic characteristics of the ship in this paper. This model adjusts both its own structure and parameters as it learns, and is able to automatically partition the input space, determine the number of membership functions and the number of fuzzy rules. The trained ANFM is used as an inverse controller, in parallel with a fractional-order PIλDμ controller for the course control of underactuated ships. Meanwhile, the sine wave curve and the sawtooth wave curve are considered as the input learning samples of ANFM, respectively, and the inverse dynamics simulation experiments of the ship are carried out. Two different ANFM structures are obtained, which are connected in parallel with the fractional-order PIλDμ controller respectively to control the course of ship. The simulation results show that the proposed method can effectively overcome the influence of uncertainty of ship modeling parameters, track the desired course quickly and effectively, and has a good control effect. Finally, comparative experiments of four different controllers are carried out, and the results show that the FO PIλDμ controller using ANFM has the advantages of small overshoot, short adjustment time, and precise control. Full article
(This article belongs to the Special Issue Soft Computing Application to Engineering Design)
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