Adaptive Lag Synchronization of Lorenz Chaotic System with Uncertain Parameters

Abstract

The paper discusses lag synchronization of Lorenz chaotic system with three uncertain parameters. Based on adaptive technique, the lag synchronization of Lorenz chaotic system is achieved by designing a novel nonlinear controller. Furthermore, the parameters identification is realized simultaneously. A sufficient condition is given and proved theoreticcally by Lyapunov stability theory and LaSalle’s invariance principle. Finally, the numerical simulations are provided to show the effectiveness and feasibility of the proposed method.

Share and Cite:

Y. Chen, Z. Jia and G. Deng, "Adaptive Lag Synchronization of Lorenz Chaotic System with Uncertain Parameters," Applied Mathematics, Vol. 3 No. 6, 2012, pp. 549-553. doi: 10.4236/am.2012.36083.

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1] L. M. Pecora and T. L. Carroll, “Synchronization in Chaotic Systems,” Physical Review Letters, Vol. 64, No. 8, 1990, pp. 821-824. doi:10.1103/PhysRevLett.64.821
[2] Z. Li and D. Xu, “A Secure Communication Scheme using Projective Chaos Synchronization,” Chaos, Solitons & Fractals, Vol. 22, No. 2, 2004, pp. 477-481. doi:10.1016/j.chaos.2004.02.019
[3] C. Ling, X. Wu and S. Sun, “A General Efficient Method for Chaotic Signal Estimation,” IEEE Transactions on Signal Processing, Vol. 47, No. 5, 1999, pp. 1424-1428. doi:10.1109/78.757236
[4] H. A. Qais and A. A. Aouda, “Image Encryption Based on the General Approach for Multiple Chaotic Systems,” Journal of Signal and Information Processing, Vol. 2, No. 3, 2011, pp. 238-244.
[5] F. Wang and C. Liu, “A New Criterion for Chaos and Hyperchaos Synchronization using Linear Feedback Control,” Physics Letters A, Vol. 360, No. 2, 2006, pp. 274278. doi:10.1016/j.physleta.2006.08.037
[6] Z. Jia, J. A. Lu, and G. M. Deng, “Nonlinear State Feedback and Adaptive Synchronization of Hyperchaotic Lü Systems,” Systems Engineering and Electronics, Vol. 29, No. 4, 2007, pp. 598-600.
[7] M. T. Yassen, “Controlling, Synchronization and Tracking Chaotic Liu System using Active Backstepping Design,” Physics Letters A, Vol. 360, No. 4-5, 2007, pp. 582-587. doi:10.1016/j.physleta.2006.08.067
[8] R. Z. Luo, “Impulsive Control and Synchronization of a New Chaotic System,” Physics Letters A, Vol. 372, No. 5, 2008, pp. 648-653. doi:10.1016/j.physleta.2007.08.010
[9] J. Lu and J. Cao, “Adaptive Complete Synchronization of Two Identical or Different Chaotic (Hyperchaotic) Systems with Fully Unknown Parameters,” Chaos, Vol. 15, No. 4, 2005, p. 043901. doi:10.1063/1.2089207
[10] Z. Jia, “Linear Generalized Synchronization of Chaotic Systems with Uncertain Parameters,” Journal of Systems Engineering and Electronics, Vol. 19, No. 4, 2008, pp. 779-784. doi:10.1016/S1004-4132(08)60153-X
[11] M. C. Ho, Y. C. Hung and C. H. Chou, “Phase and Anti-Phase Synchronization of Two Chaotic Systems by Using Active Control,” Physics Letters A, Vol. 296, No. 1, 2002, pp. 43-48. doi:10.1016/S0375-9601(02)00074-9
[12] Y. Chen, X. Chen and S. Chen, “Lag Synchronization of Structurally Nonequivalent Chaotic Systems with Time Delays,” Nonlinear Analysis, Vol. 66, No. 9, 2007, pp. 1929-1937. doi:10.1016/j.na.2006.02.033
[13] M. Hu and Z. Xu, “Nonlinear Feedback Mismatch Synchronization of Lorenz Chaotic Systems,” Systems Engineering and Electronics, Vol. 29, No. 8, 2007, pp. 13461348.
[14] C. Li and X. Liao, “Lag Synchronization of R?ssler System and Chua Circuit via a Scalar Signal,” Physics Letters A, Vol. 329, No. 4-5, 2004, pp. 301-308. doi:10.1016/j.physleta.2004.06.077
[15] C. Li, X. Liao and K. Wong, “Lag Synchronization of Hyperchaos with Application to Secure Communications,” Chaos, Solitons & Fractals, Vol. 23, No. 1, 2005, pp. 183-193. doi:10.1016/j.chaos.2004.04.025
[16] Q. J. Zhang, J. A. Lu and Z. Jia, “Global Exponential Projective Synchronization and Lag Synchronization of Hyperchaotic Lü System,” Communications in Theoretical Physics, Vol. 51, No. 4, 2009, pp. 679-683.
[17] E. N. Lorenz, “Deterministic Nonperiodic Flow,” Journal of the Atmospheric Sciences, Vol. 20, No. 2, 1963, pp. 130-141. doi:10.1175/1520-0469(1963)020<0130:DNF>2.0.CO;2
[18] J. P. Lasalle, “The Extent of Asymptotic Stability,” Proceedings of the National Academy of Sciences of United States of America, Vol. 46, No. 3, 1960, pp. 363-365. dx:10.1073/pnas.46.3.363.

Copyright © 2024 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.