Direct adaptive fuzzy control with a self-structuring algorithm

This paper presents a direct self-structuring adaptive fuzzy control (DSAFC) scheme for affine nonlinear single-input–single-output systems. We show that the only restriction on the control gain is that it be positive. No upper bound on this gain nor its derivative needs to be known. From an initial fuzzy system with a small number of rules, the self-structuring algorithm adds membership functions and rules when needed. To limit the size of the fuzzy system from growing indefinitely, the self-structuring algorithm replaces old membership functions by new ones instead of adding more membership functions so that the number of rules never exceeds a predefined upper bound. The stability of the closed loop system is guaranteed using the Lyapunov synthesis approach. The proposed control scheme is demonstrated by application to an inverted pendulum and a magnetic levitation system.