Adaptive Tracking Control for A Class of Nonlinear Systems With a Fuzzy Dead-Zone 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 <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">n</tex></formula> 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 <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">Γ ̃(u)</tex> </formula> and employing an integrated design, an integrated fuzzy controller is constructed. It is proved that, even though the dead-zone input <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">Γ ̃(u)</tex></formula> is fuzzy, the integrated fuzzy controller 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.