Methodology for fuzzy identification in a noisy environment

Abstract

An approach to non-linear discrete time systems identification based on the Instrumental Variable (IV) method and the Takagi–Sugeno (TS) fuzzy model is proposed. In this approach, the chosen instrumental variables, statistically uncorrelated with noise, are mapped to fuzzy sets, partitioning the input space in subregions to define unbiased estimates of the TS fuzzy model consequent parameters in a noisy environment. The Fuzzy Instrumental Variable (FIV) concept is proposed; consistency and unbias of the FIV algorithm are derived. Simulation results show the efficiency of the FIV algorithm.