Modeling of extremal fuzzy dynamic systems. Part Ⅵ. Problems of states estimation (filtration) of extremal fuzzy process

摘要

A fuzzy-integral model of an extremal fuzzy process (EFP) is considered. The model describes the evolution of one class of weakly structurable fuzzy dynamic systems (Klir 1985), i.e. of the so-called extremal fuzzy dynamic systems, which have been constructed in Part Ⅲ of this work. In the present paper, problems of an optimal filtering of continuous as well as of discrete EFP are solved by means of "past" evaluating information. Sufficient conditions are established for the existence of an optimal estimating fuzzy process. Using only one "past" evaluating fuzzy state of the considered system, variants of fuzzy observers (representations of an optimal estimating EFP) are constructed in terms of approximation of piecewise-constant and extremally measurable filtration functions for continuous and discrete extremal fuzzy dynamic systems. The results obtained are illustrated by a numerical example.