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Function projective lag synchronization of chaotic systems with certain parameters via adaptive-impulsive control

  • Xiu-Li Chai
  • Zhi-Hua GanEmail author
Research Article

Abstract

A new method is presented to study the function projective lag synchronization (FPLS) of chaotic systems via adaptiveimpulsive control. To achieve synchronization, suitable nonlinear adaptive-impulsive controllers are designed. Based on the Lyapunov stability theory and the impulsive control technology, some effective sufficient conditions are derived to ensure the drive system and the response system can be rapidly lag synchronized up to the given scaling function matrix. Numerical simulations are presented to verify the effectiveness and the feasibility of the analytical results.

Keywords

Function projective lag synchronization (FPLS) adaptive-impulsive chaotic systems numerical simulation Lyapunov stability theory 

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References

  1. [1]
    L. M. Pecora, T. L. Carroll. Synchronization in chaotic systems. Physical Review Letters, vol. 64, no. 8, pp. 821–824, 1990.MathSciNetCrossRefzbMATHGoogle Scholar
  2. [2]
    H. G. Zhang, D. R. Liu, Z. L. Wang. Controlling Chaos: Suppression, Synchronization and Chaotification. London, UK: Springer, pp. 69–83, 2009.CrossRefzbMATHGoogle Scholar
  3. [3]
    S. Vaidyanathan, S. Sampath. Anti-synchronization of fourwing chaotic systems via sliding mode control. International Journal of Automation and Computing, vol. 9, no. 3, pp. 274–279, 2012.CrossRefGoogle Scholar
  4. [4]
    G. L. Cai, P. Hu, Y. X. Li. Modified function lag projective synchronization of a financial hyperchaotic system. Nonlinear Dynamics, vol. 69, no. 3, pp. 1457–1464, 2012.MathSciNetCrossRefzbMATHGoogle Scholar
  5. [5]
    L. M. Lopes, S. Fernandes, C. Grácio. Complete synchronization and delayed synchronization in couplings. Nonlinear Dynamics, vol. 79, no. 2, pp. 1615–1624, 2015.MathSciNetCrossRefzbMATHGoogle Scholar
  6. [6]
    Q. K. Song, Z. J. Zhao. Cluster, local and complete synchronization in coupled neural networks with mixed delays and nonlinear coupling. Neural Computing and Applications, vol. 24, no. 5, pp. 1101–1113, 2014.CrossRefGoogle Scholar
  7. [7]
    F. A. Breve, L. Zhao, M. G. Quiles, E. E. N. Macau. Chaotic phase synchronization and desynchronization in an oscillator network for object selection. Neural Networks, vol. 22, no. 5–6, pp. 728–737, 2009.CrossRefGoogle Scholar
  8. [8]
    X. Y. Wang, B. Fan. Generalized projective synchronization of a class of hyperchaotic systems based on state observer. Communications in Nonlinear Science and Numerical Simulation, vol. 17, no. 2, pp. 953–963, 2012.MathSciNetCrossRefGoogle Scholar
  9. [9]
    W. L. Guo, M. Z. Mao. Projective lag synchronization and parameter identification of a new hyperchaotic system. International Journal of Automation and Computing, vol. 10, no. 3, pp. 256–259, 2013.CrossRefGoogle Scholar
  10. [10]
    C. Luo, X. Y. Wang. Hybrid modified function projective synchronization of two different dimensional complex nonlinear systems with parameters identification. Journal of the Franklin Institute, vol. 350, no. 9, pp. 2646–2663, 2013.MathSciNetCrossRefzbMATHGoogle Scholar
  11. [11]
    H. Y. Du, Q. S. Zeng, C. H. Wang, M. X. Ling. Function projective synchronization in coupled chaotic systems. Nonlinear Analysis: Real World Applications, vol. 11, no. 2, pp. 705–712, 2010.MathSciNetCrossRefzbMATHGoogle Scholar
  12. [12]
    Y. G. Yu, H. X. Li. Adaptive generalized function projective synchronization of uncertain chaotic systems. Nonlinear Analysis: Real World Applications, vol. 11, no. 4, pp. 2456–2464, 2010.MathSciNetCrossRefzbMATHGoogle Scholar
  13. [13]
    T. H. Lee, J. H. Park, S. C. Lee. Functional projective lag synchronization of chaotic systems with disturbances. Scientific Research and Essays, vol. 5, no. 10, pp. 1189–1193, 2010.Google Scholar
  14. [14]
    H. Y. Du, Q. S. Zeng, N. Lü. A general method for modified function projective lag synchronization in chaotic systems. Physics Letters A, vol. 374, no. 13–14, pp. 1493–1496, 2010.CrossRefzbMATHGoogle Scholar
  15. [15]
    X. J. Wu, H. T. Lu. Generalized function projective (lag, anticipated and complete) synchronization between two different complex networks with nonidentical nodes. Communications in Nonlinear Science and Numerical Simulation, vol. 17, no. 7, pp. 3005–3021, 2012.MathSciNetCrossRefzbMATHGoogle Scholar
  16. [16]
    S. Wang, Y. G. Yu, H. Wang, A. Rahmani. Function projective lag synchronization of fractional-order chaotic systems. Chinese Physics B, vol. 23, no. 4, Article number 040502, 2014.CrossRefGoogle Scholar
  17. [17]
    G. Y. Fu. Robust adaptive modified function projective synchronization of different hyperchaotic systems subject to external disturbance. Communications in Nonlinear Science and Numerical Simulation, vol. 17, no. 6, pp. 2602–2608, 2012.MathSciNetCrossRefzbMATHGoogle Scholar
  18. [18]
    T. B. Wang, W. N. Zhou, S. W. Zhao. Robust synchronization for stochastic delayed complex networks with switching topology and unmodeled dynamics via adaptive control approach. Communications in Nonlinear Science and Numerical Simulation, vol. 18, no. 8, pp. 2097–2106, 2013.MathSciNetCrossRefzbMATHGoogle Scholar
  19. [19]
    C. L. Li, Y. N. Tong. Adaptive control and synchronization of a fractional-order chaotic system. Pramana, vol. 80, no. 4, pp. 583–592, 2013.CrossRefGoogle Scholar
  20. [20]
    X. Y. Wang, X. P. Zhang, C. Ma. Modified projective synchronization of fractional-order chaotic systems via active sliding mode control. Nonlinear Dynamics, vol. 69, no. 1–2, pp. 511–517, 2012.MathSciNetCrossRefzbMATHGoogle Scholar
  21. [21]
    Y. Chun, S. Dadras, S. M. Zhong, Y. Q. Chen. Control of a novel class of fractional-order chaotic systems via adaptive sliding mode control approach. Applied Mathematical Modelling, vol. 37, no. 4, pp. 2469–2483, 2013.MathSciNetCrossRefzbMATHGoogle Scholar
  22. [22]
    H. B. Jiang. Indirect adaptive fuzzy and impulsive control of nonlinear systems. International Journal of Automation and Computing, vol. 7, no. 4, pp. 484–491, 2010.CrossRefGoogle Scholar
  23. [23]
    X. Y. Wang, M. J. Wang. Impulsive synchronization of hyperchaotic Lü system. International Journal of Modern Physics B, vol. 25, no. 27, pp. 3671–3678, 2011.CrossRefzbMATHGoogle Scholar
  24. [24]
    M. Yang, Y. W. Wang, J. W. Xiao, Y. H. Huang. Robust synchronization of singular complex switched networks with parametric uncertainties and unknown coupling topologies via impulsive control. Communications in Nonlinear Science and Numerical Simulation, vol. 17, no. 11, pp. 4404–4416, 2012.MathSciNetCrossRefzbMATHGoogle Scholar
  25. [25]
    C. Ma, X. Y. Wang. Impulsive control and synchronization of a new unified hyperchaotic system with varying control gains and impulsive intervals. Nonlinear Dynamics, vol. 70, no. 1, pp. 551–558, 2012.MathSciNetCrossRefzbMATHGoogle Scholar
  26. [26]
    T. Yang, L. O. Chua. Impulsive stabilization for control and synchronization of chaotic systems: Theory and application of secure communication. IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, vol. 44, no. 10, pp. 976–988, 1997.MathSciNetCrossRefGoogle Scholar
  27. [27]
    J. J. Huang, C. D. Li, W. Zhang, P. C. Wei, Q. Han. Lag synchronization of hyperchaotic systems via intermittent control. Abstract and Applied Analysis, vol. 2012, Article number 236830, 2012.MathSciNetzbMATHGoogle Scholar
  28. [28]
    J. J. Huang, C. D. Li, W. Zhang, P. C. Wei. Projective synchronization of a hyperchaotic system via periodically intermittent control. Chinese Physics B, vol. 21, no. 9, Article number 090508, 2012.CrossRefGoogle Scholar
  29. [29]
    Z. G.Wu, P. Shi, H. Y. Su, J. Chu. Sampled-data fuzzy control of chaotic systems based on a T-S fuzzy model. IEEE Transactions on Fuzzy Systems, vol. 22, no. 1, pp. 153–163, 2014.CrossRefGoogle Scholar
  30. [30]
    V. Vembarasan, P. Balasubramaniam. Chaotic synchronization of Rikitake system based on T-S fuzzy control techniques. Nonlinear Dynamics, vol. 74, no. 1–2, pp. 31–44, 2013.MathSciNetCrossRefzbMATHGoogle Scholar
  31. [31]
    R. E. Precup, M. L. Tomescu. Stable fuzzy logic control of a general class of chaotic systems. Neural Computing and Applications, vol. 26, no. 3, pp. 541–550, 2015.CrossRefGoogle Scholar
  32. [32]
    X. J. Wan, J. T. Sun. Adaptive-impulsive synchronization of chaotic systems. Mathematics and Computers in Simulation, vol. 81, no. 8, pp. 1609–1617, 2010.MathSciNetCrossRefzbMATHGoogle Scholar
  33. [33]
    C. L. Li, Y. N. Tong, H. M. Li, K. L. Su. Adaptive impulsive synchronization of a class of chaotic and hyperchaotic systems. Physica Scripta, vol. 86, no. 5, Article number 055003, 2010.CrossRefzbMATHGoogle Scholar
  34. [34]
    Y. S. Chen, C. C. Chang. Adaptive impulsive synchronization of nonlinear chaotic systems. Nonlinear Dynamics, vol. 70, no. 3, pp. 1795–1803, 2012.MathSciNetCrossRefGoogle Scholar
  35. [35]
    R. C. Wu, D. X. Cao. Function projective synchronization of chaotic systems via nonlinear adaptive-impulsive control. International Journal of Modern Physics C, vol. 22, no. 11, pp. 1281–1291, 2011.CrossRefzbMATHGoogle Scholar
  36. [36]
    D. Li, X. P. Zhang, Y. T. Hu and Y. Y. Yang. Adaptive impulsive synchronization of fractional order chaotic system with uncertain and unknown parameters. Neurocomputing, vol. 167, no. 12, pp. 165–171, 2015.CrossRefGoogle Scholar
  37. [37]
    X. J. Gao, H. P. Hu. Adaptive-impulsive synchronization and parameters estimation of chaotic systems with unknown parameters by using discontinuous drive signals. Applied Mathematical Modelling, vol. 39, no. 14, pp. 3980–3989, 2015.MathSciNetCrossRefGoogle Scholar
  38. [38]
    Q. J. Zhang, J. Luo, L. Wan. Parameter identification and synchronization of uncertain general complex networks via adaptive-impulsive control. Nonlinear Dynamics, vol. 71, no. 1–2, pp. 353–359, 2013.MathSciNetCrossRefzbMATHGoogle Scholar
  39. [39]
    Z. Y. Wu, G. R. Chen, X. C. Fu. Outer synchronization of drive-response dynamical networks via adaptive impulsive pinning control. Journal of the Franklin Institute, vol. 352, no. 10, pp. 4297–4308, 2015.MathSciNetCrossRefGoogle Scholar
  40. [40]
    G. Y. Qi, S. Z. Du, G. Chen, Z. Q. Chen and Z. Z. Yuan. On a four-dimensional chaotic system. Chaos, Solitons & Fractals, vol. 23, no. 5, pp. 1671–1682, 2005.MathSciNetCrossRefzbMATHGoogle Scholar
  41. [41]
    J. H. L’u, G. R. Chen, D. Z. Cheng, S. Celikovsky. Bridge the gap between the Lorenz system and the Chen system. International Journal of Bifurcation and Chaos, vol. 12, no. 12, pp. 2917–2926, 2002.MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Institute of Automation, Chinese Academy of Sciences and Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.Institute of Image Processing and Pattern RecognitionHenan UniversityKaifengChina
  2. 2.Institute of Intelligent Network System, School of SoftwareHenan UniversityKaifengChina

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