Switching fuzzy model construction based on optimal dividing planes

Abstract

This paper presents switching fuzzy model construction based on optimal dividing planes. In our previou papers, we proposed the switching fuzzy model with arbitrary dividing planes. However, dividing planes have been selected by controller designers before constructing the switching fuzzy model. Unfortunately, it is difficult to find suitable dividing planes for complicated nonlinear systems. Moreover, the switching fuzzy models constructed from different dividing planes are different. Therefore, the model construction affects the stability analysis results. In this paper, we propose switching fuzzy model construction method using multi-dimensional sector nonlinearity concept based on optimal dividing planes. The linear consequent parts of the switching fuzzy model based on optimal dividing planes are constructed from sectors which have minimum distance between a nonlinear system and sectors, and have richer information of the nonlinear system than the consequent parts of the ordinary Takagi-Sugeno fuzzy model. Two examples are provided to illustrate the validity of this approach.