Table of Contents Author Guidelines Submit a Manuscript
Mathematical Problems in Engineering
Volume 2015, Article ID 651950, 9 pages
http://dx.doi.org/10.1155/2015/651950
Research Article

Time-Delay Robust Nonlinear Dynamic Inversion for Chaos Synchronization with Application to Secure Communications

1Agency for Defense Development, Changwon 645-600, Republic of Korea
2Institute of Biomedical Engineering Research, Kyungpook National University, Daegu 702-701, Republic of Korea
3School of Electronics Engineering, Kyungpook National University, Daegu 702-701, Republic of Korea

Received 1 July 2015; Accepted 8 October 2015

Academic Editor: Mohamed Djemai

Copyright © 2015 Eunro Kim 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. G. Chen and X. Dong, From Chaos to Order: Methodologies, Perspectives and Applications, World Scientific, Singapore, 1998. View at MathSciNet
  2. T.-L. Liao and S.-H. Tsai, “Adaptive synchronization of chaotic systems and its application to secure communications,” Chaos, Solitons and Fractals, vol. 11, no. 9, pp. 1387–1396, 2000. View at Publisher · View at Google Scholar · View at Scopus
  3. G. M. Mahmoud, E. E. Mahmoud, and A. A. Arafa, “On projective synchronization of hyperchaotic complex nonlinear systems based on passive theory for secure communications,” Physica Scripta, vol. 87, no. 5, Article ID 055002, 2013. View at Publisher · View at Google Scholar · View at Scopus
  4. S.-H. Yu, C.-H. Hyun, W.-H. Kim, and M. Park, “Secure communication via active backstepping control and synchronization for new hyperchaotic systems,” International Journal of Digital Content Technology and Its Applications, vol. 6, no. 10, pp. 276–286, 2012. View at Publisher · View at Google Scholar · View at Scopus
  5. C.-C. Cheng, Y.-S. Lin, and S.-W. Wu, “Design of adaptive sliding mode tracking controllers for chaotic synchronization and application to secure communications,” Journal of the Franklin Institute, vol. 349, no. 8, pp. 2626–2649, 2012. View at Publisher · View at Google Scholar
  6. V. H. P. Rodrigues and T. R. Oliveira, “Chaos synchronization applied to secure communication via sliding mode control and norm state observers,” in Proceedings of the 13th International Workshop on Variable Structure Systems (VSS '14), pp. 1–6, IEEE, Nantes, France, July 2014. View at Publisher · View at Google Scholar · View at Scopus
  7. P. P. Singh, J. P. Singh, and B. K. Roy, “Synchronization and anti-synchronization of Lu and Bhalekar-Gejji chaotic systems using nonlinear active control,” Chaos, Solitons & Fractals, vol. 69, pp. 31–39, 2014. View at Publisher · View at Google Scholar
  8. A. N. Njah and U. E. Vincent, “Synchronization and anti-synchronization of chaos in an extended Bonhöffer-van der Pol oscillator using active control,” Journal of Sound and Vibration, vol. 319, no. 1-2, pp. 41–49, 2009. View at Publisher · View at Google Scholar · View at Scopus
  9. F. Wang and C. Liu, “Synchronization of unified chaotic system based on passive control,” Physica D: Nonlinear Phenomena, vol. 225, no. 1, pp. 55–60, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  10. T. Sangpet and S. Kuntanapreeda, “Adaptive synchronization of hyperchaotic systems via passivity feedback control with time-varying gains,” Journal of Sound and Vibration, vol. 329, no. 13, pp. 2490–2496, 2010. View at Publisher · View at Google Scholar · View at Scopus
  11. X. Tan, J. Zhang, and Y. Yang, “Synchronizing chaotic systems using backstepping design,” Chaos, Solitons and Fractals, vol. 16, no. 1, pp. 37–45, 2003. View at Publisher · View at Google Scholar · View at Scopus
  12. B. A. Idowu, U. E. Vincent, and A. N. Njah, “Control and synchronization of chaos in nonlinear gyros via backstepping design,” International Journal of Nonlinear Science, vol. 5, no. 1, pp. 11–19, 2008. View at Google Scholar
  13. J.-J. Yan, M.-L. Hung, and T.-L. Liao, “Adaptive sliding mode control for synchronization of chaotic gyros with fully unknown parameters,” Journal of Sound and Vibration, vol. 298, no. 1-2, pp. 298–306, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  14. T.-H. S. Li, M.-Y. Hsiao, J.-Z. Lee, and S.-H. Tsai, “Interval type 2 fuzzy sliding-mode control of a unified chaotic system,” Journal of Physics: Conference Series, vol. 96, no. 1, Article ID 012086, 2008. View at Publisher · View at Google Scholar · View at Scopus
  15. I. Yang and D. Lee, “Synchronization of chaotic gyros based on robust nonlinear dynamic inversion,” Journal of Applied Mathematics, vol. 2013, Article ID 519796, 8 pages, 2013. View at Publisher · View at Google Scholar · View at Scopus
  16. I. Yang, D. Kim, and D. Lee, “A flight control strategy using robust dynamic inversion based on sliding mode control,” in Proceedings of the AIAA Guidance, Navigation, and Control Conference, AIAA 2012-4527, Minneapolis, Minn, USA, August 2012.
  17. I. Yang, D. Lee, and D. S. Han, “Designing a robust nonlinear dynamic inversion controller for spacecraft formation flying,” Mathematical Problems in Engineering, vol. 2014, Article ID 471352, 12 pages, 2014. View at Publisher · View at Google Scholar
  18. H. P. Ren and W. C. Li, “Heteroclinic orbits in Chen circuit with time delay,” Communications in Nonlinear Science and Numerical Simulation, vol. 15, no. 10, pp. 3058–3066, 2010. View at Publisher · View at Google Scholar · View at Scopus
  19. J. Georgie and J. Valasek, “Evaluation of longitudinal desired dynamics for dynamic-inversion controlled generic reentry vehicles,” Journal of Guidance, Control, and Dynamics, vol. 26, no. 5, pp. 811–819, 2003. View at Publisher · View at Google Scholar · View at Scopus