Direct adaptive control using dynamic structure fuzzy systems

This article presents a direct adaptive control scheme for adaptive tracking of a class of continuous time nonlinear systems. We use structurally dynamic Takagi-Sugeno fuzzy systems as online function approximators and a gradient method for adaptation. It is shown that if the rules have finite support then the structure adaptation will not add any extra uncertainty to the system. We show that if the zero dynamics of the system are exponentially stable, the control strategy guarantees the convergence of the tracking error to the origin. Then we show how the stabilizing term could be smoothed to prevent high frequency chattering. However, the smoothed control action only guarantees ultimate boundedness. We provide an aircraft wing rock control problem as an illustrative example.