Stable fuzzy logic control of a general class of chaotic systems

Abstract

This paper proposes a new approach to the stable design of fuzzy logic control systems that deal with a general class of chaotic processes. The stable design is carried out on the basis of a stability analysis theorem, which employs Lyapunov's direct method and the separate stability analysis of each rule in the fuzzy logic controller (FLC). The stability analysis theorem offers sufficient conditions for the stability of a general class of chaotic processes controlled by Takagi---Sugeno---Kang FLCs. The approach suggested in this paper is advantageous because inserting a new rule requires the fulfillment of only one of the conditions of the stability analysis theorem. Two case studies concerning the fuzzy logic control of representative chaotic systems that belong to the general class of chaotic systems are included in order to illustrate our stable design approach. A set of simulation results is given to validate the theoretical results.