Direct adaptive fuzzy control for a class of nonlinear systems with unknown bounds

For a class of uncertain single-input single-output (SISO) nonlinear systems with unknown bound functions and unknown function control gain, a novel approach of direct adaptive fuzzy controller (AFC) without supervisory controller is proposed by Lyapunov synthesis. Based on the direct AFC with projection operator, it is developed a fuzzy approximation error estimator as adaptive compensator, which is used to estimate optimal approximation error (OAE) dynamically and reduce the influence of approximation error on system performance. In closed-loop system analysis, it is not required that the OAE is square-integrable or the OAE supremum is known. It is proved that controlled object being bounded is the sufficient condition of the OAE being bounded. The overall controller guarantees that the closed-loop system is global asymptotically stable in sense that all variables are bounded. The proposed controller is demonstrated to be simple and effective by simulation studies for inverted pendulum system. It achieves favorable performance with smooth controller output, small tracking error and strong robustness.