Skip to main content
SpringerLink
Log in

Synchronization of two different chaotic systems using novel adaptive interval type-2 fuzzy sliding mode control

  • Original Paper
  • Published:
Nonlinear Dynamics Aims and scope Submit manuscript

Abstract

In this paper, we use sliding mode control integrated with an interval type-2 fuzzy system for synchronization of two different chaotic systems in presence of system unmodeling and external disturbances. To reduce the chattering and improve the robustness of reaching phase of the Sliding Mode Control (SMC), an interval fuzzy type-2 logic controller is used. In addition, an adaptive interval type-2 fuzzy inference approximator is proposed (as equivalent control part of SMC) to approximate the unknown parts of the uncertain chaotic system. Using type-2 fuzzy systems makes more effective synchronization results in presence of system uncertainty and disturbances in comparison with type-1 fuzzy approximators. The stability analysis for the proposed control scheme is provided, and simulation results compare the performance of interval type-2 fuzzy and type-1 fuzzy controllers to verify the effectiveness of the proposed method.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Ott, E., Grebogi, C., Yorke, J.A.: Controlling chaos. Phys. Rev. Lett. 64(11), 1196–1199 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  2. Pecora, L.M., Carroll, T.L.: Synchronization in chaotic systems. Phys. Rev. Lett. 64(8), 821–824 (1990)

    Article  MathSciNet  Google Scholar 

  3. Boccaletti, S., Kurthsv, J., Osiper, G.: The synchronization of chaotic systems. Phys. Rep. 366, 1–101 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  4. Chen, G., Dong, X.: From Chaos to Order Methodologies, Perspectives and Applications. Singapore, World Scientific (1998)

    Book  MATH  Google Scholar 

  5. Schuster, H.G.: Handbook of Chaos Control. Wiley-VCH, New York-Weinheim (1999)

    Book  MATH  Google Scholar 

  6. Sprott, J.C.: Chaos and Time-Series Analysis. Oxford University Press, London (2003)

    MATH  Google Scholar 

  7. Naschie, M.E.: Transfinite physics treading the path of Cantor and Einstein. Chaos Solitons Fractals 25(4), 765–933 (2005)

    Article  Google Scholar 

  8. Carroll, T., Pecora, L.: Cascading synchronized chaotic. Physica D 67, 126–140 (1993)

    Article  MATH  Google Scholar 

  9. Zhan, M., Hu, G., Yang, J.Z.: Synchronization of chaos in coupled systems. Phys. Rev. 62, 2963–2966 (2002)

    Google Scholar 

  10. Wang, S.H., Xiao, J.H., Wang, X.G., Hu, B., Hu, G.: Spatial orders appearing at instabilities of synchronous chaos of spatiotemporal systems. Eur. Phys. J. B 30, 571–575 (2002)

    Article  Google Scholar 

  11. Guan, S.G., Lai, C.-H., Wei, G.W.: Bistable chaos without symmetry in generalized synchronization. Phys. Rev. 71, 036209 (2005)

    MathSciNet  Google Scholar 

  12. Pisarchik, A.N., Pisarchik, A.N., Jaimes-Reátegui, R., Villalobos-Salazar, J.R., García-López, J.H., Boccaletti, S.: Synchronization of chaotic systems with coexisting attractors. Phys. Rev. Lett. 96, 244102 (2006)

    Article  Google Scholar 

  13. Lai, Y.-C., Andrade, V.: Catastrophic bifurcation from riddled to fractal basins. Phys. Rev. E 64, 056228 (2001)

    Article  MathSciNet  Google Scholar 

  14. Barahona, M., Pecora, L.M.: Synchronization in Small-World Systems. Phys. Rev. Lett. 89, 054101 (2002)

    Article  Google Scholar 

  15. Zhou, C.S., Kurths, J.: Dynamical weights and enhanced synchronization in adaptive complex networks. Phys. Rev. Lett. 96, 164102 (2006)

    Article  Google Scholar 

  16. Zhou, C.S., Motter, A.E., Kurths, J.: Universality in the synchronization of weighted random networks. Phys. Rev. Lett. 96, 034101 (2006)

    Article  Google Scholar 

  17. Astakhov, V.V., Anishchenko, V.S., Kapitaniak, T., Shabunin, A.V.: Synchronization of chaotic oscillators by periodic parametric perturbations. Physica D 109, 11–16 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  18. Yang, X.S., Duan, C.K., Liao, X.X.: A note on mathematical aspects of drive-response type synchronization. Chaos Solitons Fractals 10, 1457–1462 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  19. Wang, Y., Guan, Z.H., Wen, X.: Adaptive synchronization for Chen chaotic system with fully unknown parameters. Chaos Solitons Fractals 19, 899–903 (2004)

    Article  MATH  Google Scholar 

  20. Chua, L.O., Yang, T., Zhong, G.Q., Wu, C.W.: Adaptive synchronization of Chua’s oscillators. Int. J. Bifurc. Chaos 6, 189–201 (1966)

    Google Scholar 

  21. Liao, T.L.: Adaptive synchronization of two Lorenz systems. Chaos Solitons Fractals 9, 1555–1561 (1998)

    Article  MATH  Google Scholar 

  22. Lian, K.Y., Liu, P., Chiang, T.-S., Chiu, C.-S.: Adaptive synchronization design for chaotic systems via a scalar driving signal. IEEE Trans. Circuits Syst. 49, 17–27 (2002)

    Article  Google Scholar 

  23. Wu, C.W., Yang, T., Chua, L.O.: On adaptive synchronization and control of nonlinear dynamical systems. Int. J. Bifurc. Chaos 6, 455–471 (1996)

    Article  MATH  Google Scholar 

  24. Fang, J.Q., Hong, Y., Chen, G.: Switching manifold approach to chaos synchronization. Phys. Rev. 59, 2523–2526 (1999)

    Google Scholar 

  25. Yin, X., Ren, Y., Shan, X.: Synchronization of discrete spatiotemporal chaos by using variable structure control. Chaos Solitons Fractals 14, 1077–1082 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  26. Yu, X., Song, Y.: Chaos synchronization via controlling partial state of chaotic systems. Int. J. Bifurc. Chaos 11, 1737–1741 (2001)

    Article  Google Scholar 

  27. Lu, J., Zhang, S.: Controlling Chen’s chaotic attractor using backstepping design based on parameters identification. Phys. Lett. 286, 145–149 (2001)

    Google Scholar 

  28. Wang, C., Ge, S.S.: Adaptive synchronization of uncertain chaotic systems via backstepping design. Chaos Solitons Fractals 12, 196–206 (2001)

    Article  MathSciNet  Google Scholar 

  29. Suykens, J.A.K., Curran, P.F., Vandewalle, J., Chua, L.O.: Robust nonlinear H∞ synchronization of chaotic Lur’e systems. IEEE Trans. Circuits Syst. 44, 891–904 (1997)

    Article  MathSciNet  Google Scholar 

  30. Tanaka, K., Ikeda, T., Wang, H.O.: A unified approach to controlling chaos via LMI-based fuzzy control system design. IEEE Trans. Circuits Syst. 45, 1021–1040 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  31. Zadeh, L.A.: Fuzzy sets. Inf. Control 8(3), 338–353 (1965)

    Article  MathSciNet  MATH  Google Scholar 

  32. Kuo, C.L., Li, T.H., Guo, N.: Design of a novel fuzzy sliding-mode control for magnetic ball levitation system. Journal of Intelligent and Robotic Systems 1–22 (2004)

  33. Feng, G., Chen, G.: Adaptive control of discrete-time chaotic systems: a fuzzy control approach. Chaos Solitons Fractals 23, 459–467 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  34. Xue, Y.J., Yang, S.Y.: Synchronization of generalized Henon map by using adaptive fuzzy controller. Chaos Solitons Fractals 17, 717–722 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  35. Mendel, J.M.: Computing derivatives in interval type-2 fuzzy logic systems. IEEE Trans. Fuzzy Syst. 12(1), 84–98 (2004)

    Article  Google Scholar 

  36. Wang, J.S., Lee, C.S.G.: Self-adaptive neuro-fuzzy inference systems for classification application. IEEE Trans. Fuzzy Syst. 10(6), 790–802 (2002)

    Article  Google Scholar 

  37. Kovacic, Z., Balenovic, M., Bogdan, S.: Sensitivity based self learning fuzzy logic control for a servo system. IEEE Control Syst. Mag. 18(3), 41–51 (1998)

    Article  Google Scholar 

  38. Golea, N., Golea, A., Benmahammed, K.: Fuzzy model reference adaptive control. Fuzzy Sets and Systems 137(3), 353–366 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  39. Hojati, M., Gazor, S.: Hybrid adaptive fuzzy identification and control of nonlinear systems. IEEE Trans. Fuzzy Syst. 10(2), 198–210 (2002)

    Article  Google Scholar 

  40. Lee, H., Tomizuka, M.: Robust adaptive control using a universal approximator for SISO nonlinear systems. IEEE Trans. Fuzzy Syst. 8, 95–106 (2001)

    Google Scholar 

  41. Wang, C.H., Lee, C.S.: Dynamical optimal training for interval type-2 fuzzy neural network (T2FNN) Part B. IEEE Trans. Syst. Man Cybern. 34(3), 1462–1477 (2004)

    Article  Google Scholar 

  42. Zadeh, L.A.: The concept of a linguistic variable and its application to approximate reasoning-I. Inf. Sci. 8, 199–249 (1975)

    Article  MathSciNet  Google Scholar 

  43. Zarandi, M.H.F., Burhan Türksen, I., Sobhani, J., Ramezanianpour, A.A.: Fuzzy polynomial neural networks for approximation of the compressive strength of concrete. Appl. Soft. Comput. 8(1), 488–498 (2008)

    Article  Google Scholar 

  44. Mendoza, O., Melin, P., Licea, G.: A hybrid approach for image recognition combining type-2 fuzzy logic, modular neural networks and the Sugeno integral. Inf. Sci. 179(13), 2078–2101 (2009)

    Article  Google Scholar 

  45. Doctor, F., Hagras, H., Callaghan, V.: A type-2 fuzzy embedded agent to realise ambient intelligence in ubiquitous computing environments. Inf. Sci. 171(4), 309–334 (2005)

    Article  Google Scholar 

  46. Mitchell, H.B.: Pattern recognition using type-II fuzzy sets. Inf. Sci. 170(2–4), 409–418 (2005)

    Article  Google Scholar 

  47. Choi, B.I., Rhee, F.C.H.: Interval type-2 fuzzy membership function generation methods for pattern recognition. Inf. Sci. 179(13), 2102–2122 (2009)

    Article  MATH  Google Scholar 

  48. Martínez, R., Castillo, O., Aguilar, L.T.: Optimization of interval type-2 fuzzy logic controllers for a perturbed autonomous wheeled mobile robot using genetic algorithms. Inf. Sci. 179(13), 2158–2174 (2009)

    Article  MATH  Google Scholar 

  49. Jamaludin, J., Rahim, N.A., Hew, W.P.: Development of a self-tuning fuzzy logic controller for intelligent control of elevator systems. Eng. Appl. Artif. Intell. 22(8), 1167–1178 (2009)

    Article  Google Scholar 

  50. Lin, T.C., Liu, H.L., Kuo, M.J.: Direct adaptive interval type-2 fuzzy control of multivariable nonlinear systems. Eng. Appl. Artif. Intell. 22(3), 420–430 (2009)

    Article  Google Scholar 

  51. Park, J.H.: Synchronization of Genesio chaotic system via backstepping approach. Chaos Solitons Fractals 27, 369–375 (2006)

    Google Scholar 

  52. Slotine, E., Li, W.: Applied Nonlinear Control. Englewood Cliffs, Prentice-Hall (1991)

    MATH  Google Scholar 

  53. Mendel, J.M.: Computing derivatives in interval type-2 fuzzy logic systems. IEEE Trans. Fuzzy Syst. 12(1), 84–98 (2004)

    Article  Google Scholar 

  54. Edwards, C., Spurgeon, S.K.: Sliding Mode Control: Theory and Applications. CRC Press, Boca Raton (1998)

    Google Scholar 

  55. Yau, T., Chen, C.L.: Chattering-free fuzzy sliding-mode control strategy for uncertain chaotic systems. Chaos Solitons Fractals 30, 709 (2006)

    Article  Google Scholar 

  56. Roopaei, M., Zolghadri Jahromi, M.: Synchronization of two different chaotic systems using novel adaptive fuzzy sliding mode control. Chaos 18, 033133 (2008)

    Article  MathSciNet  Google Scholar 

  57. Wang, B., Wen, G.: On the synchronization of a class of chaotic systems based on backstepping method. Phys. Lett. A 370(1), 35–39 (2007)

    Article  MATH  Google Scholar 

  58. Liu, B., Zhou, Y., Jiang, M., Zhang, Z.: Synchronizing chaotic systems using control based on tridiagonal structure. Chaos Solitons Fractals 39(5), 2274–2281 (2009)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Electrical and Computer Engineering, Shiraz University, Shiraz, Iran

    Mehdi Roopaei, Mansoor Zolghadri Jahromi & Bijan Ranjbar-Sahraei

  2. Department of Electronic Engineering, Feng-Chia University, Taichung, Taiwan

    Tsung-Chih Lin

Authors
  1. Mehdi Roopaei
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Mansoor Zolghadri Jahromi
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Bijan Ranjbar-Sahraei
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Tsung-Chih Lin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mehdi Roopaei.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Roopaei, M., Zolghadri Jahromi, M., Ranjbar-Sahraei, B. et al. Synchronization of two different chaotic systems using novel adaptive interval type-2 fuzzy sliding mode control. Nonlinear Dyn 66, 667–680 (2011). https://doi.org/10.1007/s11071-010-9939-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-010-9939-4

Keywords

Search

Navigation