Stabilization of Rössler chaotic dynamical system using fuzzy logic control algorithm

Abstract

This paper proposes a fuzzy logic control algorithm (FLCA) to stabilize the Rössler chaotic dynamical system. The fuzzy logic control system is based on a Takagi-Sugeno-Kang inference engine and the stability analysis in the sense of Lyapunov is carried out using Lyapunov’s direct method. The new FLCA is formulated to offer sufficient inequality stability conditions. The asymptotic complexity of our algorithm is analyzed and proved to be lower in comparison with that of linear matrix inequality-based FLCAs. A set of simulation results illustrates the effectiveness of the proposed FLCA.

Keywords:

• asymptotic complexity
• fuzzy logic control algorithm
• Lyapunov’s direct method
• Rössler chaotic dynamical system
• stabilization

Acknowledgments

This work was supported by a grant of the Romanian National Authority for Scientific Research, CNCS – UEFISCDI, project number PN-II-ID-PCE-2011-3-0109, by a grant in the framework of the Partnerships in priority areas – PN II program of the Romanian National Authority for Scientific Research ANCS, CNDI – UEFISCDI, project number PN-II-PT-PCCA-2011-3.2-0732, and by the cooperation between the Óbuda University, Budapest, Hungary, the University of Ljubljana, Slovenia, and the Politehnica University of Timisoara, Romania, in the framework of the Hungarian-Romanian and Slovenian-Romanian Intergovernmental Science & Technology Cooperation Programs.