Adaptive output-feedback stabilization for planar nonlinear systems with unknown control directions

Abstract

This paper considers the global adaptive stabilization via output-feedback for a class of uncertain planar nonlinear systems. Different from the existing related literature, the systems under investigation are subjected to unknown control directions, and simultaneously allow linear unmeasured states dependent growth. To solve the problem, an adaptive output-feedback scheme is proposed, not only to deal with the uncertainties, but also to achieve the global stabilization of the systems. First, a state transformation is introduced to bring the unknown control directions together, and subsequently, a state observer is designed with one dynamic gain. Then, we recursively design an output-feedback controller by using backstepping method and adaptive scheme. In this procedure, the Nussbaum-type function is introduced to compensate the unknown control directions. It is shown that all the signals of the resulting closed-loop system are bounded, and the states of the original system and designed observer converge to zero.