Fuzzy identification method for nonlinear systems

In this paper, two mathematical ways of building a fuzzy model of both linear and nonlinear systems are presented and compared. In order to determine a model for a nonlinear system, the phase plane is divided into sub-regions and a linear model is assigned for each of these regions. This linear model is represented either in state-space or ARX model form. To determine the pre-selected parameters of the linear system model under study, least-square identification method is used. Then these linear models are arranged in a fuzzy manner to characterize the overall system behavior. The results show that this method can identify linear systems exactly and nonlinear ones quite satisfactorily with both system representations, assuming that the input-output data is not corrupted by noise.