Fuzzy model-reference adaptive control

Abstract

This paper proposes a fuzzy model-reference adaptive control (Fuzzy-MRAC) to deal with controlling a plant with unknown parameters which are dependent on known variables. The proposed method uses the fuzzy basis function expansion (FBFE) to represent the unknown parameters and change the identification problem from identifying the original unknown parameters to identifying the coefficients of the FBFE. That is, the dependency property of unknown parameters is absorbed into the fuzzy basis functions and their linear combination coefficients. This data representation is substantiated by the Stone Weierstrass theorem which indicates that any continuous function can be represented by the FBFE. With the aid of the FBFE, the unknown parameters can be estimated more precisely and better performance can be expected from the fuzzy-MRAC than the traditional MRAC. Furthermore, the adaptation scheme of the proposed fuzzy-MRAC is based on both the tracking error and the prediction error. Combining these two sources of error information, the proposed fuzzy-MRAC will provide more adaptation power than a traditional adaptive control. Since the proposed fuzzy-MRAC can be considered as an extension of the traditional MRAC, its stability and convergence properties are preserved. Computer simulations were conducted to show the validity and the performance of the proposed fuzzy-MRAC and its improvements over the traditional MRAC.