Simultaneous Auto-Tuning of Membership Functions and Fuzzy Control Rules Using Genetic Algorithms

Abstract

A novel genetic algorithm is proposed to design membership functions and to reduce the number of fuzzy control rules simultaneously since these two components are interdependent in a fuzzy logic controller. With Gaussian membership functions, the centers and the widths of these functions, the fuzzy control rules corresponding to every possible combination of input linguistic variables are chosen as parameters to be optimized. In transforming these parameters into corresponding chromosomes, a mixed coding technique is adopted. Moreover, the concept of enlarged sampling space and ranking mechanism are used to expedite the convergence of the evolutionary process. To show the feasibility and validity of the proposed method, the design of a cart-centering controller using as few as possible fuzzy control rules will be given. Simulation results will demonstrate that the designed fuzzy logic controller can drive the cart system from a given initial state to a desired final state even when the cart mass varies within a wide range.