Adaptive fuzzy controller for non-affine systems with zero dynamics

Abstract

In this article, the direct adaptive fuzzy control problem is investigated for a class of general non-linear systems with zero dynamics. The direct adaptive fuzzy controller is developed based on a unified observer which is used to estimate the time derivatives of the output. 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-based observers, namely for the usual high-gain observers and the sliding-mode observers together with their implementable versions. By using a general error function, and without resorting to the famous strictly positive real condition or the filtering of the observation error, a general proportional–integral (PI) law for updating the fuzzy parameters is proposed. Ultimately boundedness of the error signals is shown through Lyapunov's direct method. Theoretical results are illustrated through two simulation examples.

Keywords:

• fuzzy control
• adaptive control
• non-affine systems
• zero dynamics
• adaptation PI law
• observer