Takagi-Sugeno fuzzy logic controller for Liu-Chen four-scroll chaotic system

Abstract

Chaos modelling, chaos control and chaos synchronisation are active areas in chaos theory, while research in these areas has potential applications in many fields like nonlinear optics, oscillations, chemical reactions, biology, neurology, secure data encryption, secure communications, robotics, neural networks, fractals and nonlinear circuits design. Especially, chaos control is an important research area, and it has a wide range of applications like control of turbulence, dynamics of lasers, plasma, chemical reactions such as Belousov-Zhabotinsky reaction, ecological systems and cardiac arrhythmias. Until now, many methods for chaos control such as open-loop control based on periodic system excitation, closed-loop control such as OGY method and time-delayed feedback control such as Pyragas method have been used. In this paper, a fuzzy logic control using fuzzy sets and fuzzy logic for the control of chaotic systems has been proposed. In more detail, this work presents a fuzzy logic controller design of a chaotic system using Takagi-Sugeno fuzzy model. The stability analysis of the fuzzy logic controller system is carried out using Barbashin-Krasovskii theorem. For the proposed fuzzy logic control, the Liu-Chen four-scroll chaotic system was used. Finally, the simulation results of the proposed control method present the effectiveness of this method.