Tracking Control for Nonlinear Systems With a Fuzzy Input

This paper focuses on a problem of adaptive control for a class of nonlinear strict-feedback systems with a fuzzy dead zone and immeasurable states. By using the adaptive backstepping technique, an adaptive fuzzy output-feedback controller is constructed. The proposed control method requires only one adaptive law for an $n$th-order system. Compared with the conventional deterministic dead-zone models in previous articles, the main advantage of this paper is that the proposed dead-zone model is uncertain and fuzzy.

By defuzzifying for fuzzy dead zone $tilde{Gamma }(u)$ and employing an integrated design, an integrated fuzzy controller is constructed. It is proved that, even though the dead-zone input $tilde{Gamma }(u)$ is fuzzy, the integrated fuzzycontroller can make the closed-loop system semiglobally uniformly ultimately bounded and the tracking error converge to a small neighborhood of the origin. Finally, simulation results are provided to show the effectiveness of the proposed approach.