Adaptive fuzzy control of a class of SISO nonaffine nonlinear systems

This paper presents a direct adaptive fuzzy control scheme for a class of uncertain continuous-time single-input single-output (SISO) nonaffine nonlinear dynamic systems. Based on the implicit function theory, the existence of an ideal controller, that can achieve control objectives, is firstly shown. Since the implicit function theory guarantees only the existence of the ideal controller and does not provide a way for constructing it, a fuzzy system is employed to approximate this unknown ideal control law. The adjustable parameters in the used fuzzy system are updated using a gradient descent adaptation algorithm. This algorithm is designed in order to minimize a quadratic cost function of the error between the unknown ideal implicit controller and the used fuzzy control law. The stability analysis of the closed-loop system is performed using a Lyapunov approach. In particular, it is shown that the tracking error converges to a neighborhood of zero. The effectiveness of the proposed adaptive control scheme is demonstrated through the simulation of a simple nonaffine nonlinear system.