A unified approach for design of indirect adaptive output-feedback fuzzy controller

摘要

In this paper, an indirect adaptive fuzzy output-feedback control based on the observer is presented for Single-Input Single-Output (SISO) uncertain non-linear systems. On the basis of the estimation of the tracking error, and without resorting to the famous Strictly Positive Real condition or the filtering of the observation error, a Proportional-Integral law for updating the adjustable parameters is proposed. Then, a unified observer is used to estimate the tracking error. Indeed, the corrective term of the proposed observer involves a well-defined design function which is shown to be satisfied by the commonly used High-Gain (HG)-based observers, namely, for the usual HG observers and the Sliding Modes observers together with their implementable versions. The Lyapunov synthesis approach is used to guarantee a Uniformly Ultimately Bounded property of the observation and tracking errors, as well as of all other signals in a closed-loop system. The viability and the efficiency of the obtained fundamental results are clearly illustrated through a numerical simulation involving the usual benchmark example of the fuzzy control community.