Fuzzy model-reference adaptive control

This paper proposes a fuzzy model-reference adaptive control (fuzzy-MRAC) to deal with controlling a plant with unknown parameters. The proposed method uses the fuzzy basis function expansion to represent the unknown, slowly-varying parameters in a plant. The use of fuzzy basis function expansion (FBFE) to represent the unknown parameters changes the identification problem from identifying slowly-varying parameters to identifying constant parameters of the FBFE. That is, the varying property of unknown parameters is absorbed into the fuzzy sets. This data representation is substantiated by the Stone Weierstrass theorem which indicates that any continuous function can be represented by the FBFE. Since constant parameters are easier to estimate than varying parameters, 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 trading 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 improvement over the traditional MRAC