Fin Stabilizer-Based Finite-Time H<sub>??/sub> Interval Type-2 Fuzzy Synthesis for Ship Rolling Motion With Bouc-Wen Hysteresis Under Imperfect Premise Matching

Abstract

When a ship operates at sea, it undergoes noticeable motions caused by waves and winds, with rolling being the most pronounced. Nowadays, fin stabilizers remain the most widely adopted devices for roll stabilization. However, they often exhibit hysteresis due to variations in hydrodynamic forces. To better address the control problem of ship rolling motion under nonlinearities, uncertainties, and hysteresis, this article proposes an Interval Type-2 (IT2) fuzzy controller design method that incorporates a novel Bouc-Wen (B-W) hysteresis estimator within the Takagi-Sugeno fuzzy model (TSFM) framework. The main contribution of this research lies in developing a B-W hysteresis state estimator within the IT2 TSFM framework to accurately capture the nonlinear hysteresis behavior. An IT2 fuzzy controller corresponding to the IT2 TSFM is developed using the imperfect premise matching method to improve the flexibility of controller design in practical applications. By combining with finite-time control theory, the IT2 fuzzy controller guarantees finite-time boundedness (FTB) and achieves performance index under the finite-time H-infinity criterion. According to Lyapunov theory, a new set of sufficient conditions is formulated using LMIs to guarantee the FTB for the ship rolling system. Finally, the simulation results of the nonlinear ship rolling system using the fin stabilizers are presented to verify the performance of the proposed IT2 fuzzy control approach.