H∞ estimation for optimization of rational-powered membership functions

Determination of membership functions of a fuzzy logic system to achieve the best performance is of great importance. Constraining the membership functions to a specific shape which is parameterized by a few variables and then applying a parameter optimization method can be a solution. The H_∞ filter has been applied to optimize only parameters of triangular membership functions. In this study, the H_∞ filter is extended to optimize the input rational-powered membership functions and output singletons. The corresponding equations and derivatives are given and finally the simulation results are shown and compared with Gradient Descent and extended Kalman filtering methods to discuss the efficiency of this approach.