Fuzzy approximation-based indirect adaptive controller for multi-input multi-output non-affine systems with unknown control direction

A fuzzy approximation-based indirect adaptive control is investigated for a class of unknown non-affine non-linear systems with unknown control direction. An equivalent model in affine-like form is first derived for the original non-affine system by using a Taylor series expansion. Next, a fuzzy indirect adaptive control is designed based on this affine-like equivalent model. In this control scheme, the adaptive fuzzy systems are used to appropriately approximate the equivalent affine model's unknown non-linearities, whereas the Nussbaum gain function is used to deal with the unknown control directions (being closely related to the sign of control gain matrix). A decomposition property of the control gain matrix is fully exploited in the controller design and the stability analysis. It is proven that, under some appropriate assumptions, the proposed control scheme can achieve that all the signals in the closed-loop control system are bounded and the tracking errors converge to a small neighbourhood around zero. Effectiveness of the developed scheme is illustrated by two simulation examples.