Optimal Fuzzy Synchronization of Generalized Lorenz Chaotic Systems

Volume 2, Issue 1, pp 27--36 http://dx.doi.org/10.22436/jmcs.002.01.04

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Authors

Davood Babaei Pourkargar - Chemical and Petroleum Engineering Department, Sharif University of Technology Mohammad Shahrokhi - Chemical and Petroleum Engineering Department, Sharif University of Technology

Abstract

In this article two identical generalized Lorenz systems have been synchronized by a fuzzy controller based on mamdani approach and stability of the proposed scheme has been established by the Lyapunov stability theorem. Controller parameters have been optimized by the genetic algorithm. Effectiveness of proposed method has been demonstrated through computer simulation.

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Keywords

• Fuzzy controller
• Synchronization
• Generalized Lorenz system
• Genetic Algorithm.

MSC

•  37D45
•  37N35
•  93C42
•  34D06

References

• [1] L. M. Pecora, T. L. Carroll, Synchronization in chaotic systems, Phys. Rev. Lett., 64 (1990), 821--824
  • View Article
  • MathSciNet
  • Google Scholar


• [2] V. V. Astakhov, V. S. Anishchenko, T. Kapitaniak, A. V. Shabunin, Synchronization of chaotic oscillators by periodic parametric perturbations, Phys. D, 109 (1997), 11--16
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [3] G. Chen, X. Dong, From Chaos to Order: Methodologies, Perspectives and Applications, World Scientific Publishing Co., Singapore (1998)
  • Google Scholar
  • MATH


• [4] L. O. Chua, T. Yang, G. Q. Zhong, C. W. Wu, Adaptive synchronization of Chua’s oscillators, Int. J. Bifurcation Chaos, 6 (1996), 189--201
  • View Article
  • Google Scholar


• [5] E. E. Escultura, Dynamic modeling of chaos and turbulence, Nonlinear Anal., 63 (2005), 519--532
  • View Article
  • Google Scholar
  • MATH


• [6] J. Q. Fang, Y. Hong, G. Chen, Switching manifold approach to chaos synchronization, Phys. Rev. E, 59 (1999), 2523--2526
  • View Article
  • Google Scholar


• [7] G. Feng, G. R. Chen, Adaptive control of discrete-time chaotic systems: a fuzzy control approach, Chaos Solitons Fractals, 23 (2005), 459--467
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [8] C. L. Kuo, T. H. Li, N. Guo, Design of a novel fuzzy sliding-mode control for magnetic ball levitation system, J. Intell. Robotic Syst., 42 (2005), 295--316
  • View Article
  • Google Scholar


• [9] K. Y. Lian, P. Liu, T. S. Chiang, C. S. Chiu, Adaptive synchronization design for chaotic systems via a scalar Driving signal, IEEE Trans. Circuits Syst. I, 49 (2002), 17--27
  • View Article
  • Google Scholar


• [10] T. L. Liao, Adaptive synchronization of two Lorenz systems, Chaos Solitons Fractals, 9 (1998), 1555--1561
  • View Article
  • Google Scholar
  • MATH


• [11] J. Lu, S. Zhang, Controlling Chen’s chaotic attractor using backstepping design based on parameters identification, Phys. Lett. A, 286 (2001), 145--149
  • View Article
  • Google Scholar
  • MATH


• [12] A. H. Nayfeh, B. Balachandran, Applied Nonlinear Dynamics, John Wiley \& Sons, New York (1995)
  • View Article
  • MathSciNet
  • Google Scholar


• [13] J. H. Park, Synchronization of Genesio chaotic system via backstepping approach, Chaos Solitons Fractals, 27 (2006), 1369--1375
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [14] H. N. Agiza, Chaos synchronization of Lü dynamical system, Nonlinear Anal., 58 (2004), 11--20
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [15] C. S. Shieh, Nonlinear rule-based controller for missile terminal guidance, IEE Proc. Control Theory Appl., 150 (2003), 45--48
  • View Article
  • Google Scholar


• [16] J. E. Slotine, W. Li, Applied Nonlinear Control, Prentice-Hall, New Jersey (1991)
  • View Article
  • Google Scholar


• [17] J. A. K. Suykens, P. F. Curran, J. Vandewalle, Robust nonlinear H/sub/spl infin//synchronization of chaotic Lur'e systems, IEEE Trans. Circuits Syst. I, 44 (1997), 891--904
  • View Article
  • Google Scholar


• [18] F. Takeo, Chaos and hypercyclicity for solution semigroups to some partial differential equations, Nonlinear Anal., 63 (2005), 1943--1953
  • View Article
  • Google Scholar
  • MATH


• [19] K. Tanaka, T. Ikeda, H. O. Wang, A unified approach to controlling chaos via LMI-based fuzzy control system design, IEEE Trans Circuits Syst. I, 45 (1998), 1021--1040
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [20] C. Wang, S. S. Ge, Adaptive synchronization of uncertain chaotic systems via backstepping design, Chaos Solitons Fractals, 12 (2001), 199--206
  • View Article
  • Google Scholar
  • MATH


• [21] Y. Wang, Z. H. Guan, X. Wen, Adaptive synchronization for Chen chaotic system with fully unknown parameters, Chaos Solitons Fractals, 19 (2004), 899--903
  • View Article
  • Google Scholar
  • MATH


• [22] L. A. Zadeh, Fuzzy logic, IEEE Comput., 21 (1988), 83--93
  • View Article
  • Google Scholar