Fuzzy adaptive backstepping control of chaotic roll motion of ships under input constraints

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.