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Mathematical Problems in Engineering
Volume 2014, Article ID 693268, 7 pages
http://dx.doi.org/10.1155/2014/693268
Research Article

Synchronizing Spatiotemporal Chaos via a Composite Disturbance Observer-Based Sliding Mode Control

School of Automation, Southeast University, 2 Sipailou, Nanjing 210096, China

Received 20 May 2014; Accepted 27 October 2014; Published 20 November 2014

Academic Editor: Dan Wang

Copyright © 2014 Congyan Chen and Shi Qiu. 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 MathSciNet · View at Scopus
  2. E.-W. Bai, K. E. Lonngren, and J. C. Sprott, “On the synchronization of a class of electronic circuits that exhibit chaos,” Chaos, Solitons & Fractals, vol. 13, no. 7, pp. 1515–1521, 2002. View at Publisher · View at Google Scholar · View at Scopus
  3. C.-N. Wang, J. Ma, Y. Liu, and L. Huang, “Chaos control, spiral wave formation, and the emergence of spatiotemporal chaos in networked Chua circuits,” Nonlinear Dynamics, vol. 67, no. 1, pp. 139–146, 2012. View at Publisher · View at Google Scholar · View at Scopus
  4. L. Kocarev and U. Parlitz, “Synchronizing spatiotemporal chaos in coupled nonlinear oscillators,” Physical Review Letters, vol. 77, no. 11, pp. 2206–2209, 1996. View at Publisher · View at Google Scholar · View at Scopus
  5. S. Codreanu, “Synchronization of spatiotemporal nonlinear dynamical systems by an active control,” Chaos, Solitons & Fractals, vol. 15, no. 3, pp. 507–510, 2003. View at Publisher · View at Google Scholar · View at Scopus
  6. S. F. Brandt, B. K. Dellen, and R. Wessel, “Synchronization from disordered driving forces in arrays of coupled oscillators,” Physical Review Letters, vol. 96, no. 3, 2006. View at Publisher · View at Google Scholar · View at Scopus
  7. A. M. dos Santos, R. L. Viana, S. R. Lopes, S. E. D. S. Pinto, and A. M. Batista, “Chaos synchronization in a lattice of piecewise linear maps with regular and random couplings,” Physica A: Statistical Mechanics and Its Applications, vol. 367, pp. 145–157, 2006. View at Publisher · View at Google Scholar · View at Scopus
  8. L. Lü, Y. Li, and A. Sun, “Parameter identification and chaos synchronization for uncertain coupled map lattices,” Nonlinear Dynamics, vol. 73, no. 4, pp. 2111–2117, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  9. M. D. Shrimali, S. Poria, and S. Sinha, “Under what kind of parametric fluctuations is spatiotemporal regularity the most robust?” Pramana—Journal of Physics, vol. 74, no. 6, pp. 895–906, 2010. View at Publisher · View at Google Scholar · View at Scopus
  10. Y. Li, X. Liao, C. Li, T. Huang, and D. Yang, “Impulsive synchronization and parameter mismatch of the three-variable autocatalator model,” Physics Letters A, vol. 366, no. 1-2, pp. 52–60, 2007. View at Publisher · View at Google Scholar · View at Scopus
  11. E. M. Shahverdiev, R. A. Nuriev, R. H. Hashimov, and K. A. Shore, “Parameter mismatches, variable delay times and synchronization in time-delayed systems,” Chaos, Solitons and Fractals, vol. 25, no. 2, pp. 325–331, 2005. View at Publisher · View at Google Scholar · View at Scopus
  12. S. Dadras, H. R. Momeni, and V. J. Majd, “Sliding mode control for uncertain new chaotic dynamical system,” Chaos, Solitons and Fractals, vol. 41, no. 4, pp. 1857–1862, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  13. J.-J. Yan, Y.-S. Yang, T.-Y. Chiang, and C.-Y. Chen, “Robust synchronization of unified chaotic systems via sliding mode control,” Chaos, Solitons and Fractals, vol. 34, no. 3, pp. 947–954, 2007. View at Publisher · View at Google Scholar · View at Scopus
  14. K. Ohnishi, “A new servo method in mechatronics,” Transactions of Japanese Society of Electrical Engineers, vol. 107, pp. 83–86, 1987. View at Google Scholar
  15. S. Li, J. Yang, W. Chen, and X. Chen, Disturbance Observer-Based Control: Methods and Applications, CRC Press, 2014.
  16. W.-H. Chen, “Disturbance observer based control for nonlinear systems,” IEEE/ASME Transactions on Mechatronics, vol. 9, no. 4, pp. 706–710, 2004. View at Publisher · View at Google Scholar · View at Scopus
  17. L. Guo and W.-H. Chen, “Disturbance attenuation and rejection for systems with nonlinearity via DOBC approach,” International Journal of Robust and Nonlinear Control, vol. 15, no. 3, pp. 109–125, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  18. S. Li, M. Zhou, and X. Yu, “Design and implementation of terminal sliding mode control method for PMSM speed regulation system,” IEEE Transactions on Industrial Informatics, vol. 9, no. 4, pp. 1879–1891, 2013. View at Publisher · View at Google Scholar · View at Scopus
  19. S. Li, J. Yang, W.-H. Chen, and X. Chen, “Generalized extended state observer based control for systems with mismatched uncertainties,” IEEE Transactions on Industrial Electronics, vol. 59, no. 12, pp. 4792–4802, 2012. View at Publisher · View at Google Scholar · View at Scopus
  20. J. Yang, S. Li, J. Su, and X. Yu, “Continuous nonsingular terminal sliding mode control for systems with mismatched disturbances,” Automatica, vol. 49, no. 7, pp. 2287–2291, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  21. J. Yang, J. Su, S. Li, and X. Yu, “High-order mismatched disturbance compensation for motion control systems via a continuous dynamic sliding-mode approach,” IEEE Transactions on Industrial Informatics, vol. 10, no. 1, pp. 604–614, 2014. View at Publisher · View at Google Scholar · View at Scopus