To address the risk of progressive capsizing caused by the chaotic roll motion of ships induced by parametric excitation in complex sea conditions, and to enhance the navigational safety, this paper proposes a fuzzy adaptive backstepping control method for regulating chaotic roll motion of ships under input constraints.

Based on the backstepping control framework combined with fuzzy adaptive control technology, this method addresses the strong nonlinearity inherent in the chaotic roll motion of ships. Recognizing that critical state variables, such as roll angular velocity and roll angular acceleration, are difficult to measure directly in real-world applications, a fuzzy state observer is designed to estimate these unmeasurable states in real time, thereby enhancing system observability and reliability. To handle the unknown complex nonlinear functions present in the model, a fuzzy logic system is introduced to provide effective approximation, mitigating the impact of model uncertainty. Additionally, considering the mechanical amplitude limitations of the fin stabilizer in practical engineering, an auxiliary control system is constructed to constrain the control input, ensuring that the control commands remain within the physical execution capabilities of the fin stabilizer and preventing system instability due to input saturation. Finally, Lyapunov-based stability analysis is conducted, and it is rigorously proven that all signals in the closed-loop system are semi-globally uniformly ultimately bounded, guaranteeing that the tracking error converges to a neighborhood of the origin.

The simulation experiments show that, compared with existing control methods in the literature, the controller proposed in this paper achieves notable improvements in suppressing chaotic oscillations, reducing energy consumption, and accelerating response speed. The mean absolute error (MAE) is reduced by 47.28%, the mean integrated absolute (MIA) by 17.74%, the mean total variation (MTV) by 57.20%, and the convergence time by 44.62%.

The proposed method effectively suppresses the chaotic roll motion induced by parametric excitation, significantly enhances the robustness of the control system under model uncertainties and input constraints, and effectively reduces the risk of progressive capsizing. This provides reliable technical support for ensuring the safe navigation of ships.

This study investigates how to effectively address path-dependent constraints during the path-following of unmanned surface vessels in complex waterways while ensuring navigation safety and stability.

First, performance and feasibility constraints are established for the vessel's navigation based on the precision and safety requirements of autonomous ships in shallow waters. Next, to address the issues of the path parameter representation and convergence requirements of the controller, a barrier Lyapunov function (BLF) combined with a fixed-time convergence strategy is applied. A path-dependent controller capable of converging within a fixed time is then designed, and radial basis function neural networks (RBFNN) and adaptive robust terms are used to handle nonlinearities and environmental disturbances. Finally, the intelligent unmanned surface vehicle model "Dazhi" is used to simulate shallow water effects, and the controller's performance is analyzed through simulations.

The simulation results show that the path tracking error converges rapidly to the desired region without violating the constraints. Compared to the unconstrained case, the controller demonstrates clear advantages in convergence speed and precision, verifying its effectiveness and robustness.

The proposed control strategy is innovative and significant in addressing path-dependent constraints for ship navigation, ensures precise path tracking within a fixed time, and has significant theoretical and practical application value. Future research may further optimize the control strategy to address more complex water environments and higher-precision path tracking tasks.

To solve the problems of communication resource limitations and parameter uncertainty in the dynamic positioning control tasks of fully driven ships in marine engineering applications, this paper presents a robust event-triggered control algorithm for ship dynamic positioning that considers the dynamic characteristics of the actuators.

The algorithm uses a radial basis function (RBF) neural network to approximate system uncertainty. At the same time, a novel event-triggering mechanism in the sensor-controller channel is designed by introducing a zero-order hold which reduces the signal transmission frequency in the sensor−controller and controller−actuator channels, thus greatly saving the communication resources of the system. In addition, the adaptive parameters are updated online and designed to compensate for the gain uncertainty of the actuators, which reduces the computational load and ensures that the ship can perform dynamic positioning tasks stably.

The Lyapunov stability theory is used to prove that all error variables in the closed-loop control system satisfy semi-global uniformly ultimately bounded (SGUUB) stability, and the effectiveness of the proposed algorithm is verified through comparison with a simulation.

The results of this study can provide useful references for promoting the development of intelligent ship equipment.

This paper seeks to solve the problem of excessive energy consumption caused by the excessive amplitude of the rudder angle and high frequency of rudder angle change during ship course-keeping.

A closed-loop gain shaping algorithm (CGSA) is used to design the controller; a double nonlinear feedback algorithm is introduced; the steering amplitude and frequency are reduced by a combination of the bipolar S-function and arc-tangent function; and the whole control system is controlled by the positive feedback method.

The simulation results show that the proposed double nonlinear feedback algorithm improves the comprehensive energy-saving evaluation index of steering gear energy consumption by 31.53% and 18.63% under Beaufort No. 6 and Beaufort No. 8 respectively.

It is verified that the double nonlinear feedback method has a positive effect on saving the power consumption of the steering gear and reducing carbon emissions in the course of ship navigation, and an equivalent control effect of positive feedback and negative feedback, providing valuable references for the study of ship course-keeping control.

A robust adaptive course-keeping control algorithm is designed to deal with the course-keeping problem for under-actuated ships with rudder faults, gain uncertainty and marine disturbances.

By combining the robust neural damping technique and adaptive approach, numerous neural network (NN) weights can be compressed horizontally, and only two gain-related adaptive learning parameters need to be designed to compensate for both the gain uncertainty and unknown fault parameters. The proposed controller is proven to be semi-global uniform and ultimately bounded (SGUUB) through Lyapunov analysis. Finally, the Nomoto mathematical model is established using "Yukun", and the effectiveness and superiority of the course-keeping algorithm is illustrated by carrying out comparison experiments under marine interference conditions.

The results show that the average rudder angle of "Yukun" under rudder failure is reduced by 51%, significantly improving control performance.

The results of this study can provide references for tackling the course-keeping control problem of under-actuated ships.