Observer-based direct adaptive fuzzy control for single-input single-output non-linear systems with unknown gain sign

This study presents an observer-based direct adaptive fuzzy control for a class of uncertain single-input single-output non-linear systems with unknown gain sign. A state observer is designed to estimate the unmeasured state, the direct adaptive fuzzy controller is designed in the presence of only system output is available for measurement, and the parameter adaptive laws are updated by fuzzy basis functions rather than by its filtering. A robust controller is designed to compensate for the lumped errors, and a Nussbaum gain function is incorporated in the robust controller to estimate the unknown gain sign. The proposed scheme guarantees that all of the signals in the resulting closed-loop systems are bounded and that the tracking errors converge asymptotically to zero. A simulation example is used to demonstrate the effectiveness of the proposed scheme.