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Stabilization of the Lorenz Chaotic Equations by Fuzzy Controller

Authors: Behrooz Rezaie, Zahra Rahmani Cherati, Mohammad Reza Jahed Motlagh, Mohammad Farrokhi


In this paper, a fuzzy controller is designed for stabilization of the Lorenz chaotic equations. A simple Mamdani inference method is used for this purpose. This method is very simple and applicable for complex chaotic systems and it can be implemented easily. The stability of close loop system is investigated by the Lyapunov stabilization criterion. A Lyapunov function is introduced and the global stability is proven. Finally, the effectiveness of this method is illustrated by simulation results and it is shown that the performance of the system is improved.

Keywords: Fuzzy Control, chaotic system, Lorenz equation

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[1] C. Wang, T. Lin, T. Lee, H. Liu, "Adaptive hybrid intelligent control for uncertain nonlinear dynamical systems", IEEE Trans. on Systems, Man and Cybernetics- part B: Cybernetics, vol. 32, no. 5, Oct. 2003.
[2] C. Park, C. Lee, M. Park, "Design of an adaptive fuzzy model based controller for chaotic dynamics in Lorenz systems with uncertainty", J. Information Sciences, vol. 147, pp. 245-266, 2002.
[3] S.Hu, Y. Liu, "Robust H∞ control of multiple time-delay uncertain nonlinear system using fuzzy model and adaptive neural network", J. Fuzzy Sets and Systems, pp. 1-18, 2003.
[4] W. Jiang, Q. Dong, D. Bin, "Observer-based robust adaptive variable universe fuzzy control for chaotic system", J. Chaos, Solitons and Fractals, vol. 23, pp. 1013-1032, 2005.
[5] X. Wang, Adaptive Fuzzy System and Control, Prentice-Hall, First Edition, New Jercy, 1994.
[6] K. Tanaka, T. Ikeda, H .O. Wang, "Controlling chaos via model-based fuzzy control system design", in Proc. of the 36th Conf. on Decision & Control, Sun Diego, California USA, Dec.1997.
[7] K. Tanaka, T. Ikeda, H.O. Wang, "A unified approach to controlling chaos Via an LMI-based fuzzy control system Design", IEEE Trans. On Circuits & Systems, vol. 45, no. 10, pp. 1021-1040, Oct.1998.
[8] L. Chen and G. Chen, "fuzzy modeling, prediction, and control of uncertain chaotic systems based on time series", IEEE Trans. On Circuits & System, vol. 47, no. 10, pp. 29-45, Oct. 2000.
[9] Z. Li, J. B. Park, Y. H. Joo, "Chaotifying continuous-time TS fuzzy systems via discretization", IEEE Trans. On Circuits & System, vol. 48, no. 10, pp. 1122-1134, Oct. 2001.
[10] G. Feng, G. Chen, "Adaptive control of discrete-time chaotic systems: a fuzzy control approach", J. Chaos, Solitons and Fractals, vol. 23, pp. 459-467, 2005.
[11] O. Castillo, P. Mellin, Soft Computing for Control of Nonlinear Dynamical Systems, First Edition, Springer-Verlag Ltd, New York, 2001.
[12] E. N. Lorenz, "Deterministic Non-Periodic Flow", J. Automata , vol. 12, pp. 130-141, 1963.