Identification of interval fuzzy models using recursive least square method

In this paper, we present a new method of interval fuzzy model identification. Unlike the previously introduced methods, this method uses recursive least square methods to estimate the parameters. The idea behind interval fuzzy systems is to introduce optimal lower and upper bound fuzzy systems that define the band which contains all the measurement values.

This results in lower and upper fuzzy models or a fuzzy model with a set of lower and upper parameters. The model is called the interval fuzzy model (INFUMO). This type of modeling has various applications such as nonlinear circuits modeling. There has been tremendous amount of activities to use linear matrix inequality based techniques to design a controller for this type of fuzzy systems.

The fact that the actual desired data must lie between upper and lower fuzzy systems, introduces some constrains on the identification process of the lower and upper fuzzy systems. We would introduce a cost function which includes the violation of constrains and try to find an adaptation law which minimizes this cost function and at the same time tries to be less conservative.