Notes on the approximation rate of KH controllers 1

This paper investigates the approximation behaviour of the KH interpolative fuzzy controllers. First, in accordance with the remarks in [20], it is pointed out that it is a fuzzy generalization of the Shepard operator. Shepard operator has thoroughly studied by approximation theorist since the mid 70s. Exploiting the aforementioned relationship, we establish analog results on the approximation rate of KH controllers. The optimal order and class of approximation (saturation problem) are determined for certain values of the exponent λ. Corresponding results on the MACI method, being a modification of the KH interpolator, are also provided.