28 - Adaptive Fuzzy Logic Control Synthesis without a Fuzzy Rule Base

Abstract

This chapter discusses the adaptive fuzzy logic control synthesis without using a fuzzy rule base. The positions of centers of output fuzzy sets are determined by introducing an analytic function of input variables, instead of the definition of the fuzzy rule base. The analytic activation function is used instead of min–max operators. It supports analytic procedures in an fuzzy logic control (FLC) system and makes possible the elimination of any fuzzy rule base. The number of input variables and the number of input fuzzy sets of the FLC system are not limited because there are no rules of the present approach. Thus, the chapter solves the vexing problem of fuzzy logic. New adaptive input and output fuzzy sets for the FL system are developed with the ɛ-β distribution of input fuzzy membership states and with the ɛ-β distribution of output fuzzy membership states. The chapter develops a parameter β-adaptation algorithm for the synthesis of the adaptive FLC system. The optimal, heuristic, and combined parameter β-adaptation schemes are employed. Finally, the proposed adaptive FLC synthesis procedures are applied to the adaptive FLC system of a robot of rotation, rotation, translation, and rotation (RRTR) structure.