Fuzzy system as parameter estimator of nonlinear dynamic functions

In this paper we use adaptive fuzzy systems as intelligent identification systems for nonlinear time-varying plants. A new technique to design the fuzzy system that relies on the minimization of a loss function is presented. The design technique uses the centers of the fuzzy sets (labels) at the antecedent part of the rule base as the estimated parameters. This parametrization has the Linear In The Parameters (LITPs) characteristic that allows standard parameter estimation technique to be used to estimate the parameters of the fuzzy system. The combination of the fuzzy system and the estimation method then performs as a nonlinear estimator. If several fuzzy sets are defined for the input variables at the antecedent part, the fuzzy system ("fuzzy estimator") then behaves as a collection of nonlinear estimators where different rules' regions have different parameters. The proposed scheme is potentially capable of estimating the parameters of highly nonlinear plants. Simulation examples, which use plants with highly nonlinear gain, show the power of the proposed estimation scheme in comparison to estimation using the linear model.