An iterative learning approach to identify fractional order KiBaM model

Abstract

This paper discusses the parameter and differentiation order identification of continuous fractional order KiBaM models in ARX U+0028 autoregressive model with exogenous inputs U+0029 and OE U+0028 output error model U+0029 forms. The least squares method is applied to the identification of nonlinear and linear parameters, in which the Gr U+00FC nwald-Letnikov definition and short memory principle are applied to compute the fractional order derivatives. An adaptive P-type order learning law is proposed to estimate the differentiation order iteratively and accurately. Particularly, a unique estimation result and a fast convergence speed can be arrived by using the small gain strategy, which is unidirectional and has certain advantages than some state-of-art methods. The proposed strategy can be successfully applied to the nonlinear systems with quasi-linear characteristics. The numerical simulations are shown to validate the concepts.