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Mathematical Problems in Engineering
Volume 2013, Article ID 407436, 9 pages
http://dx.doi.org/10.1155/2013/407436
Research Article

Robust Adaptive Sliding Mode Control for Generalized Function Projective Synchronization of Different Chaotic Systems with Unknown Parameters

1Centre for High Performance Computing, Northwestern Polytechnical University, Xi’an 710072, China
2Department of Applied Mathematics, Northwestern Polytechnical University, Xi’an 710072, China

Received 26 April 2013; Revised 16 July 2013; Accepted 16 July 2013

Academic Editor: Ningsu Luo

Copyright © 2013 Xiuchun Li et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. L. M. Pecora and T. L. Carroll, “Synchronization in chaotic systems,” Physical Review Letters, vol. 64, no. 8, pp. 821–824, 1990. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. F. Wang and C. Liu, “A new criterion for chaos and hyperchaos synchronization using linear feedback control,” Physics Letters A, vol. 360, no. 2, pp. 274–278, 2006. View at Publisher · View at Google Scholar · View at Scopus
  3. X. Wu, G. Chen, and J. Cai, “Chaos synchronization of the master-slave generalized Lorenz systems via linear state error feedback control,” Physica D, vol. 229, no. 1, pp. 52–80, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. H.-H. Chen, G.-J. Sheu, Y.-L. Lin, and C.-S. Chen, “Chaos synchronization between two different chaotic systems via nonlinear feedback control,” Nonlinear Analysis. Theory, Methods & Applications A, vol. 70, no. 12, pp. 4393–4401, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. D. B. Huang, “Simple adaptive-feedback controller for identical chaos synchronization,” Physical Review E, vol. 71, Article ID 037203, 2005. View at Google Scholar
  6. Z.-M. Ge and C.-H. Yang, “Pragmatical generalized synchronization of chaotic systems with uncertain parameters by adaptive control,” Physica D, vol. 231, no. 2, pp. 87–94, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. D. Zhang and J. Xu, “Projective synchronization of different chaotic time-delayed neural networks based on integral sliding mode controller,” Applied Mathematics and Computation, vol. 217, no. 1, pp. 164–174, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. N. Cai, Y. Jing, and S. Zhang, “Modified projective synchronization of chaotic systems with disturbances via active sliding mode control,” Communications in Nonlinear Science and Numerical Simulation, vol. 15, no. 6, pp. 1613–1620, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. Y. Wang, X. Xu, L. Dai, and B. Hou, “Synchronization of a class of partially unknown chaotic systems with integral observer,” in Proceedings of the 36th Annual Conference of the IEEE Industrial Electronics Society (IECON '10), pp. 231–235, November 2010. View at Publisher · View at Google Scholar · View at Scopus
  10. R. Mainieri and J. Rehacek, “Projective synchronization in three-dimensional chaotic systems,” Physical Review Letters, vol. 82, no. 15, pp. 3042–3045, 1999. View at Google Scholar · View at Scopus
  11. Y. Chen, H. An, and Z. Li, “The function cascade synchronization approach with uncertain parameters or not for hyperchaotic systems,” Applied Mathematics and Computation, vol. 197, no. 1, pp. 96–110, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. X.-Y. Wang and 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. View at Publisher · View at Google Scholar · View at MathSciNet
  13. Z. Li and X. Zhao, “Generalized function projective synchronization of two different hyperchaotic systems with unknown parameters,” Nonlinear Analysis. Real World Applications, vol. 12, no. 5, pp. 2607–2615, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. C.-C. Yang and C.-J. Ou, “Adaptive terminal sliding mode control subject to input nonlinearity for synchronization of chaotic gyros,” Communications in Nonlinear Science and Numerical Simulation, vol. 18, no. 3, pp. 682–691, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  15. W. Xiang and F. Chen, “Robust synchronization of a class of chaotic systems with disturbance estimation,” Communications in Nonlinear Science and Numerical Simulation, vol. 16, no. 8, pp. 2970–2977, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  16. M. P. Aghababa and M. E. Akbari, “A chattering-free robust adaptive sliding mode controller for synchronization of two different chaotic systems with unknown uncertainties and external disturbances,” Applied Mathematics and Computation, vol. 218, no. 9, pp. 5757–5768, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  17. X. C. Li, W. Xu, and Y. Z. Xiao, “Adaptive slide mode control for a class of chaotic systems with perturbations,” Acta Physica Sinica. Wuli Xuebao, vol. 57, no. 8, pp. 4721–4728, 2008. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  18. C.-C. Yang, “Robust synchronization and anti-synchronization of identical Φ6 oscillators via adaptive sliding mode control,” Journal of Sound and Vibration, vol. 331, no. 3, pp. 501–509, 2012. View at Publisher · View at Google Scholar · View at Scopus