Identification of Nonlinear System Based on Fuzzy Model with Enhanced Gradient Search

Abstract

Theidentification and modeling theory of nonlinear systems has always been challengingto researchers. Fuzzy system due to its languagedescriptive way similar to human brain and deal with qualitative informationintelligently proves better choice for nonlinear system modeling over last fewdecades. The fuzzy system theory itself also has nonlinear characteristics thereforewhen establishing the fuzzy model of nonlinear system; it should be able towell describe the nonlinear characteristics. Takagi-Sugeno (TS) fuzzy systemsare not only suitable for modeling the nonlinear system due to combination ofthe good performance with the simple linear expressions, but also useful todesign the fuzzy controller. This paper proposed a new optimization algorithm namedas Enhanced Gradient Search (EGS) for identification of nonlinear system basedon TS fuzzy system. In proposed EGS, parameters of membership functions aretrained adaptively so as to calculate the gradient of cost function which isnecessary for minimizing the error. Using gradient information of costfunction, EGS applies in an innovative way such that it keeps and updates thebest search results at every training step during the optimization process. Theapplicability of EGS for TS fuzzy model shows splendid performance especially inmodeling of nonlinear system.