Direct robust adaptive fuzzy control (DRAFC) for uncertain nonlinear systems using small gain theorem

A novel direct robust adaptive fuzzy control (DRAFC) is proposed for a class of nonlinear systems with uncertain system and gain functions, which both are unstructured (or non-repeatable) state-dependent unknown nonlinear functions. Takagi-Sugeno type fuzzy logic systems are used to approximate the uncertain system function and the DRAFC algorithm is designed by use of input-to-state stability (ISS) approach and small gain theorem. The resulting closed-loop system is proven to be semi-globally uniformly ultimately bounded. In addition, the possible controller singularity problem in some of the existing adaptive control schemes met with feedback linearization techniques can be removed and the adaptive mechanism with only one learning parameterization can be achieved. The control performance of the closed-loop system is guaranteed by appropriately choosing the design parameters. An example illustrating the proposed method is included for a ship autopilot system to maintain the ship on a pre-determined heading. Simulation results show the effectiveness of the control scheme.