Polynomial fuzzy model-based approach for underactuated surface vessels

The main goal of this study is to introduce a new polynomial fuzzy model-based structure for a class of marine systems with non-linear and polynomial dynamics. The suggested technique relies on a polynomial Takagi–Sugeno (T–S) fuzzy modelling, a polynomial dynamic parallel distributed compensation and a sum-of-squares (SOS) decomposition. The new proposed approach is a generalisation of the standard T–S fuzzy models and linear matrix inequality which indicated its effectiveness in decreasing the tracking time and increasing the efficiency of the robust tracking control problem for an underactuated surface vessel (USV). Additionally, in order to overcome the USV control challenges, including the USV un-modelled dynamics, complex nonlinear dynamics, external disturbances and parameter uncertainties, the polynomial fuzzy model representation is adopted. Moreover, the USV-based control structure is formulated in terms of SOS conditions. Unlike the conventional approaches, the proposed approach can be easily implemented in the real-time and applied to a reasonably wide class of non-linear systems. Finally, the extensive studies and hardware-in-the-loop simulations are presented, which prove the effectiveness of the novel proposed method.