Table of Contents
Journal of Nonlinear Dynamics
Volume 2016, Article ID 3512917, 9 pages
http://dx.doi.org/10.1155/2016/3512917
Research Article

Finite-Time Synchronization for Uncertain Master-Slave Chaotic System via Adaptive Super Twisting Algorithm

1Department of Mathematics, Faculty of Science, Kasetsart University, Bangkok 10900, Thailand
2Department of Mathematics, Faculty of Applied Science, King Mongkut’s University North Bangkok, Bangkok 10800, Thailand

Received 23 March 2016; Accepted 2 June 2016

Academic Editor: Marius-F. Danca

Copyright © 2016 P. Siricharuanun and C. Pukdeboon. 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. T. Kapitaniak, Chaotic Oscillations in Mechanical Systems, Manchester University Press, New York, NY, USA, 1991. View at MathSciNet
  2. M. Lakshmanan and K. Murali, Chaos in Nonlinear Oscillators: Controlling and Synchronization, World Scientific, Singapore, 1996.
  3. S. Bowong, “Adaptive synchronization between two different chaotic dynamical systems,” Communications in Nonlinear Science and Numerical Simulation, vol. 12, no. 6, pp. 976–985, 2007. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  4. F. Wang and C. Liu, “Synchronization of unified chaotic system based on passive control,” Physica D, vol. 225, no. 1, pp. 55–60, 2007. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  5. H. Wang, Z. Han, Q. Xie, and W. Zhang, “Finite-time chaos synchronization of unified chaotic system with uncertain parameters,” Communications in Nonlinear Science and Numerical Simulation, vol. 14, no. 5, pp. 2239–2247, 2009. View at Publisher · View at Google Scholar
  6. H. Wang, Z.-Z. Han, Q.-Y. Xie, and W. Zhang, “Sliding mode control for chaotic systems based on LMI,” Communications in Nonlinear Science and Numerical Simulation, vol. 14, no. 4, pp. 1410–1417, 2009. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  7. M. T. Yassen, “Controlling, synchronization and tracking chaotic Liu system using active backstepping design,” Physics Letters, Section A: General, Atomic and Solid State Physics, vol. 360, no. 4-5, pp. 582–587, 2007. View at Publisher · View at Google Scholar · View at Scopus
  8. 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, vol. 70, no. 12, pp. 4393–4401, 2009. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  9. H.-T. Yau and C.-S. Shieh, “Chaos synchronization using fuzzy logic controller,” Nonlinear Analysis: Real World Applications, vol. 9, no. 4, pp. 1800–1810, 2008. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  10. V. I. Utkin, Sliding Modes in Control and Optimization, Communications and Control Engineering Series, Springer, Berlin, Germany, 1992. View at Publisher · View at Google Scholar · View at MathSciNet
  11. C. Edwards, E. Fossas Colet, and L. Fridman, Eds., Advances in Variable Structure and Sliding Mode Control, Springer, Berlin, Germany, 2006. View at Publisher · View at Google Scholar · View at MathSciNet
  12. A. Levant, “Higher-order sliding modes, differentiation and output-feedback control,” International Journal of Control, vol. 76, no. 9-10, pp. 924–941, 2003. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  13. W. Perruquetti and J. P. Barbot, Sliding Mode Control in Engineering, Marcel Dekker, New York, NY, USA, 2002.
  14. A. Damiano, G. L. Gatto, I. Marongiu, and A. Pisano, “Second-order sliding-mode control of dc drives,” IEEE Transactions on Industrial Electronics, vol. 51, no. 2, pp. 364–373, 2004. View at Publisher · View at Google Scholar · View at Scopus
  15. S. P. Bhat and D. S. Bernstein, “Finite-time stability of continuous autonomous systems,” SIAM Journal on Control and Optimization, vol. 38, no. 3, pp. 751–766, 2000. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  16. S. P. Bhat and D. S. Bernstein, “Geometric homogeneity with applications to finite-time stability,” Mathematics of Control, Signals, and Systems, vol. 17, no. 2, pp. 101–127, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  17. A. Levant, A. Pridor, R. Gitizadeh, I. Yaesh, and J. Z. Ben-Asher, “Aircraft pitch control via second-order sliding technique,” Journal of Guidance, Control, and Dynamics, vol. 23, no. 4, pp. 586–594, 2000. View at Publisher · View at Google Scholar · View at Scopus
  18. Y. B. Shtessel, I. A. Shkolnikov, and A. Levant, “Smooth second-order sliding modes: missile guidance application,” Automatica, vol. 43, no. 8, pp. 1470–1476, 2007. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  19. C. Pukdeboon, “Finite-time second-order sliding mode controllers for spacecraft attitude tracking,” Mathematical Problems in Engineering, vol. 2013, Article ID 930269, 12 pages, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  20. S. Yu, X. Yu, B. Shirinzadeh, and Z. Man, “Continuous finite-time control for robotic manipulators with terminal sliding mode,” Automatica, vol. 41, no. 11, pp. 1957–1964, 2005. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  21. J. A. Moreno and M. Osorio, “Strict Lyapunov functions for the super-twisting algorithm,” IEEE Transactions on Automatic Control, vol. 57, no. 4, pp. 1035–1040, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus