Advertisement

Nonlinear Dynamics

, Volume 85, Issue 2, pp 1105–1117 | Cite as

Finite-time synchronization between two complex-variable chaotic systems with unknown parameters via nonsingular terminal sliding mode control

  • Junwei Sun
  • Yan Wang
  • Yanfeng Wang
  • Yi Shen
Original Paper

Abstract

Based on the synchronization of real-variable chaotic systems, the problem of synchronization between two complex-variable chaotic systems with unknown parameters is investigated via nonsingular terminal sliding mode control in a finite time. On the basic of the adaptive laws and finite-time stability theory, a nonsingular terminal sliding mode control is developed to guarantee the synchronization between two complex-variable chaotic systems in a given finite time. It is theoretically proved that the introduced sliding mode technique has finite-time convergence and stability in both reaching and sliding mode phases. Numerical simulation results are shown to verify the effectiveness and applicability of the finite-time synchronization.

Keywords

Compound synchronization  Combination synchronization  Combination system  Mixed system 

Notes

Acknowledgments

The authors thank the editor and the anonymous reviewers for their resourceful and valuable comments and constructive suggestions. The work was supported by the State Key Program of the National Natural Science Foundation of China (Grant No. 61134012), the National Natural Science Foundation of China (Grant Nos. 61472371, 61472372 and 61572446), China Postdoctoral Science Foundation funded project (Grant No. 2015M570641), Basic and Frontier Technology Research Program of Henan Province (Grant No. 162300410220), and the Science Foundation of for Doctorate Research of Zhengzhou University of Light Industry (Grant No. 2014BSJJ044).

References

  1. 1.
    Ott, E., Grebogi, C., Yorke, J.A.: Controlling chaos. Phys. Rev. Lett. 64(11), 1196–1199 (1990)MathSciNetCrossRefMATHGoogle Scholar
  2. 2.
    Zhang, Q., Lu, J., Lü, J., Tse, C.: Adaptive feedback synchronization of a general complex dynamical network with delayed nodes. IEEE Trans. Circuits Syst. II Express Briefs 55(2), 183–187 (2008)CrossRefGoogle Scholar
  3. 3.
    Karimi, H.R., Gao, H.: New delay-dependent exponential synchronization for uncertain neural networks with mixed time delays. IEEE Trans. Syst. Man Cybern. B 40(1), 173–185 (2010)CrossRefGoogle Scholar
  4. 4.
    Vincent, U.E.: Synchronization of identical and non-identical 4-D chaotic systems using active control. Chaos Solitons Fractals 37(4), 1065–1075 (2008)MathSciNetCrossRefMATHGoogle Scholar
  5. 5.
    Yu, Y., Li, H.: Adaptive hybrid projective synchronization of uncertain chaotic systems based on backstepping design. Nonlinear Ana. RWA 12(1), 388–393 (2011)MathSciNetCrossRefMATHGoogle Scholar
  6. 6.
    Dedieu, H., Ogorzalek, M.J.: Identifiability and identification of chaotic systems based on adaptive synchronization. IEEE Trans. Circuits Syst. I Fundam. Theory Appl. 44(10), 948–962 (1997)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Zhang, H., Xie, Y., Wang, Z., Zheng, C.: Adaptive synchronization between two different chaotic neural networks with time delay. IEEE Trans. Neural Netw. 18(6), 1841–1845 (2007)CrossRefGoogle Scholar
  8. 8.
    Liu, X., Cao, J.: Exponential stability of anti-periodic solutions for neural networks with multiple discrete and distributed delays, IMechE, Part I. J. Syst. Control Eng. 223(3), 299–308 (2009)Google Scholar
  9. 9.
    Liu, X., Cao, J.: Complete periodic synchronization of delayed neural networks with discontinuous activations. Int. J. Bifurcat. Chaos 20(7), 2151–2164 (2010)MathSciNetCrossRefMATHGoogle Scholar
  10. 10.
    Sun, J., Shen, Y., Zhang, G., Xu, C., Cui, G.: Combination-combination synchronization among four identical or different chaotic systems. Nonlinear Dyn. 73(3), 1211–1222 (2013)MathSciNetCrossRefMATHGoogle Scholar
  11. 11.
    Sun, J., Shen, Y., Yin, Q., Xu, C.: Compound synchronization of four memristor chaotic oscillator systems and secure communication. Chaos 22, 1–11 (2013)MathSciNetMATHGoogle Scholar
  12. 12.
    Sun, J., Yin, Q., Shen, Y.: Compound synchronization for four chaotic systems of integer order and fractional order. Europhys. Lett. 106, 40005 (2014)CrossRefGoogle Scholar
  13. 13.
    Sun, J., Shen, Y.: Quasi-ideal memory system. IEEE Trans. Cybern. 45(7), 1353–1362 (2016)CrossRefGoogle Scholar
  14. 14.
    Yang, T., Chua, L.: Impulsive stabilization for control and synchronization of chaotic systems: theory and application to secure communication. IEEE Trans. Circuits Syst. I Fundam. Theory Appl. 44(10), 976–988 (1997)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Zhang, H., Ma, T., Huang, G., Wang, Z.: Robust global exponential synchronization of uncertain chaotic delayed neural networks via dual-stage impulsive control. IEEE Trans. Syst. Man Cybern. B 40(3), 831–844 (2010)CrossRefGoogle Scholar
  16. 16.
    Sun, D.: Position synchronization of multiple motion axes with adaptive coupling control. Automatica 39(6), 997–1005 (2003)MathSciNetCrossRefMATHGoogle Scholar
  17. 17.
    Grosu, I., Banerjee, R., Roy, P.K., Dana, S.K.: Design of coupling for synchronization of chaotic oscillators. Phys. Rev. E 80(3), 016212 (2009)CrossRefGoogle Scholar
  18. 18.
    Ghosh, D., Grosu, I., Dana, S.K.: Design of coupling for synchronization in time-delayed systems. Chaos 22(3), 033111 (2012)MathSciNetCrossRefMATHGoogle Scholar
  19. 19.
    Feki, M.: Sliding mode control and synchronization of chaotic systems with parametric uncertainties. Chaos Solitons Fractals 41(3), 1390–1400 (2009)MathSciNetCrossRefMATHGoogle Scholar
  20. 20.
    Liu, X., Su, H., Chen, M.Z.Q.: A switching approach to designing finite-time synchronization controllers of coupled neural networks. IEEE Trans. Neural Netw. Learn. Syst., In Press.doi: 10.1109/TNNLS.2015.2448549
  21. 21.
    Liu, X., Lam, J., Yu, W., Chen, G.: Finite-time consensus of multiagent systems with a switching protocol. IEEE Trans. Neural Netw. Learn. Syst., In: Press. doi: 10.1109/TNNLS.2015.2425933
  22. 22.
    Su, H., Chen, M.Z.Q., Wang, X.: Global coordinated tracking of multi-agent systems with disturbance uncertainties via bounded control inputs. Nonlinear Dyn. 82(4), 2059–2068 (2015)MathSciNetCrossRefGoogle Scholar
  23. 23.
    Su, H., Chen, M.Z.Q.: Multi-agent containment with input saturation on switching topologies. IET Con. Theory Appl. 9(3), 399–409 (2015)MathSciNetCrossRefGoogle Scholar
  24. 24.
    Konishi, K., Hirai, M., Kokame, H.: Sliding mode control for a class of chaotic systems. Phys. Lett. A 245(6), 511–517 (1998)CrossRefGoogle Scholar
  25. 25.
    Aghababa, M.P., Khanmohammadi, S., Alizadeh, G.: Finite-time synchronization of two different chaotic systems with unknown parameters via sliding mode technique. Appl. Math. Model 35(6), 3080–3091 (2011)MathSciNetCrossRefMATHGoogle Scholar
  26. 26.
    Peng, Y.F.: Robust intelligent sliding model control using recurrent cerebellar model articulation controller for uncertain nonlinear chaotic systems. Chaos Solitons Fractals 39(1), 150–167 (2009)MathSciNetCrossRefMATHGoogle Scholar
  27. 27.
    Jang, M.J., Chen, C.L., Chen, C.K.: Sliding mode control of hyperchaos in Rössler systems. Chaos Solitons Fractals 14(9), 1465–1476 (2002)MathSciNetCrossRefMATHGoogle Scholar
  28. 28.
    Bhat, S.P., Bernstein, D.S.: Finite-time stability of continuous autonomous systems. SIAM J. Control Optim. 38(3), 751–766 (2000)MathSciNetCrossRefMATHGoogle Scholar
  29. 29.
    Yu, X.H., Man, Z.H.: Fast terminal sliding-mode control design for nonlinear dynamical systems. IEEE Trans. Circuits Syst. I Fundam. Theory Appl 49(2), 261–264 (2002)MathSciNetCrossRefGoogle Scholar
  30. 30.
    Wang, H., Han, Z., Xie, Q., Zhang, W.: Finite-time chaos control via nonsingular terminal sliding mode control. Commun. Nonlinear Sci. Numer. Simul. 14(6), 2728–2733 (2009)MathSciNetCrossRefMATHGoogle Scholar
  31. 31.
    Mei, J., Jiang, M., Wang, B., Long, B.: Finite-time parameter identification and adaptive synchronization between two chaotic neural networks. J. Frankl. Inst. 350(6), 1617–1633 (2013)MathSciNetCrossRefMATHGoogle Scholar
  32. 32.
    Mei, J., Jiang, M., Wang, J.: Finite-time structure identification and synchronization of drive-response systems with uncertain parameter. Commun. Nonlinear Sci. Numer. Simul. 18(4), 999–1015 (2013)MathSciNetCrossRefMATHGoogle Scholar
  33. 33.
    Zhao, H., Li, L., Peng, H., Xiao, J., Yang, Y., Zheng, M.: Impulsive control for synchronization and parameters identification of uncertain multi-links complex network. Nonlinear Dyn. 83(3), 1437–1451 (2016)Google Scholar
  34. 34.
    Luo, C., Wang, X.: Hybrid modified function projective synchronization of two different dimensional complex nonlinear systems with parameters identification. J. Franklin Inst. 350(9), 2646–2663 (2011)MathSciNetCrossRefMATHGoogle Scholar
  35. 35.
    Wang, X., Zhao, H., Lin, X.: Module-phase synchronization in hyperchaotic complex Lorenz system after modified complex projection. Appl. Math. Comput. 232, 91–96 (2014)MathSciNetCrossRefGoogle Scholar
  36. 36.
    Luo, C., Wang, X.: Chaos in the fractional-order complex Lorenz system and its synchronization. Nonlinear Dyn. 71(1–2), 241–257 (2013)MathSciNetCrossRefMATHGoogle Scholar
  37. 37.
    Sun, J., Shen, Y., Zhang, X.: Modified projective and modified function projective synchronization of a class of real nonlinear systems and a class of complex nonlinear systems. Nonlinear Dyn. 78(3), 1755–1764 (2014)MathSciNetCrossRefGoogle Scholar
  38. 38.
    Shen, J., Cao, J.: Finite-time synchronization of coupled neural networks via discontinuous controllers. Cognit. Neurodyn. 5(4), 373–385 (2011)MathSciNetCrossRefGoogle Scholar
  39. 39.
    Sun, J., Shen, Y., Wang, X., Chen, J.: Finite-time combination-combination synchronization of four different chaotic systems with unknown parameters via sliding mode control. Nonlinear Dyn. 76(1), 383–397 (2014)MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  1. 1.College of Electronic and Information EngineeringZhengzhou University of Light IndustryZhengzhouChina
  2. 2.School of AutomationHuazhong University of Science and TechnologyWuhanChina

Personalised recommendations