Interval Fuzzy Modeling Applied to Wiener Models With Uncertainties

Abstract—This correspondence addresses the problem of interval fuzzy model identification and its use in the case of the robust Wiener model. The method combines a fuzzy identification methodology with some ideas from linear programming theory. On a finite set of measured data, an optimality criterion which minimizes the maximum estimation error between the data and the proposed fuzzy model output is used. The min-max optimization problem can then be seen as a linear programming problem that is solved to estimate the parameters of the fuzzy model in each fuzzy domain. This results in lower and upper fuzzy models that define the confidence interval of the observed data. The model is called the interval fuzzy model and is used to approximate the static nonlinearity in the case of the Wiener model with uncertainties. The resulting model has the potential to be used in the areas of robust control and fault detection. Index Terms—Interval fuzzy model, linear programming, min-max opti-mization, Wiener model. I