Difference State Feedback Fuzzy Control of Nonlinear Discrete-Time Ship Steering System in Descriptor Form

Abstract

This paper addresses the fuzzy controller design issue of nonlinear ship steering system in terms of the Discrete-Time (D-T) Takagi-Sugeno (T-S) Fuzzy Descriptor Model (T-SFDM). Throughout history, ship steering systems have always played a significant role, as they greatly influence the efficiency of ship navigation and affect the economic system. It is necessary to develop a more appropriate control method for enhancing navigating performance and safety. However, the ship steering systems usually serve as nonlinear systems due to the complicated working environment. Considering the increasing number of control systems are implemented using computers nowadays, discretizing the nonlinear system allows for the development of a D-T control approach. Moreover, the mathematical modeling in descriptor form offers a more comprehensive expression of ship dynamic behaviors. The perturbations, viewed as modeling errors or uncertain ship dynamics, are also considered. To solve the control problem using the T-SFDM, difference state feedback is employed to establish the fuzzy controller following the concept of the Parallel Distributed Compensator (PDC). The Lyapunov theory is applied with the free-weighting matrix to further reduce the conservativeness of the stability analysis process. A robust control method is also considered to solve the analysis problem with perturbations. In addition, the guaranteed cost constraint is incorporated into the analysis to ensure the cost-effective control force while maintaining control performance. Ultimately, the simulation is conducted for a ship steering system to verify the developed fuzzy control approach.