Generalized type-2 fuzzy logic in galactic swarm optimization: design of an optimal ball and beam fuzzy controller

In this paper we present a modification based on generalized type-2 fuzzy logic to an algorithm that is inspired on the movement of large masses of stars and their attractive force in the universe, known as galactic swarm optimization (GSO). The modification consists on the dynamic adjustment of parameters in GSO using type-1 and type-2 fuzzy logic. The main idea of the proposed approach is the application of fuzzy systems to dynamically adapt the parameters of the GSO algorithm, which is then applied to parameter optimization of the membership functions of the bar and ball fuzzy controller. The experimentation was carried out using the original GSO algorithm, and the type-1 and type-2 fuzzy variants of GSO. In addition a disturbance was added to the bar and ball fuzzy controller plant to be able to validate the effectiveness of the proposed approach in optimizing fuzzy controllers. A formal comparison of results is performed with statistical tests showing that GSO with generalized type-2 fuzzy logic is the best method for optimizing the fuzzy controller.