Table of Contents Author Guidelines Submit a Manuscript
Complexity
Volume 2017, Article ID 6743184, 15 pages
https://doi.org/10.1155/2017/6743184
Research Article

Synchronization and Antisynchronization of -Coupled Complex Permanent Magnet Synchronous Motor Systems with Ring Connection

College of Control Science and Engineering, Shandong University, Jinan 250061, China

Correspondence should be addressed to Shutang Liu; nc.ude.uds@uilts

Received 7 July 2016; Revised 18 September 2016; Accepted 20 September 2016; Published 26 January 2017

Academic Editor: Roberto Natella

Copyright © 2017 Cuimei Jiang and Shutang Liu. 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. A. C. Fowler, J. D. Gibbon, and M. J. McGuinness, “The complex Lorenz equations,” Physica D, vol. 4, no. 2, pp. 139–163, 1982. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  2. E. Roldán, G. J. de Valcárcel, R. Vilaseca, and P. Mandel, “Single-mode-laser phase dynamics,” Physical Review A, vol. 48, no. 1, pp. 591–598, 1993. View at Publisher · View at Google Scholar
  3. C.-Z. Ning and H. Haken, “Detuned lasers and the complex Lorenz equations: Subcritical and supercritical Hopf bifurcations,” Physical Review A, vol. 41, no. 7, pp. 3826–3837, 1990. View at Publisher · View at Google Scholar · View at Scopus
  4. V. Y. Toronov and V. L. Derbov, “Boundedness of attractors in the complex Lorenz model,” Physical Review E, vol. 55, no. 3, pp. 3689–3692, 1997. View at Publisher · View at Google Scholar · View at MathSciNet
  5. 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
  6. P. Liu, H. J. Song, and X. Li, “Observe-based projective synchronization of chaotic complex modified van der pol-duffing oscillator with application to secure communication,” Journal of Computational and Nonlinear Dynamics, vol. 10, no. 5, Article ID 051015, 2015. View at Publisher · View at Google Scholar
  7. S. T. Liu and F. F. Zhang, “Complex function projective synchronization of complex chaotic system and its applications in secure communication,” Nonlinear Dynamics, vol. 76, no. 2, pp. 1087–1097, 2014. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  8. L. Wang, B. Yang, and A. Abraham, “Distilling middle-age cement hydration kinetics from observed data using phased hybrid evolution,” Soft Computing, vol. 20, pp. 3637–3656, 2016. View at Publisher · View at Google Scholar · View at Scopus
  9. L. Wang, B. Yang, Y. Chen, X. Q. Zhang, and J. Orchard, “Improving neural-network classifiers using nearest neighbor partitioning,” IEEE Transactions on Neural Networks and Learning Systems, 2016. View at Publisher · View at Google Scholar
  10. G. M. Mahmoud and E. E. Mahmoud, “Complete synchronization of chaotic complex nonlinear systems with uncertain parameters,” Nonlinear Dynamics, vol. 62, no. 4, pp. 875–882, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  11. S. Liu and P. Liu, “Adaptive anti-synchronization of chaotic complex nonlinear systems with unknown parameters,” Nonlinear Analysis: Real World Applications, vol. 12, no. 6, pp. 3046–3055, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  12. P. Liu and S. T. Liu, “Anti-synchronization between different chaotic complex systems,” Physica Scripta, vol. 83, no. 6, Article ID 065006, 2011. View at Publisher · View at Google Scholar · View at Scopus
  13. G. M. Mahmoud and E. E. Mahmoud, “Synchronization and control of hyperchaotic complex Lorenz system,” Mathematics and Computers in Simulation, vol. 80, no. 12, pp. 2286–2296, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  14. G. M. Mahmoud and E. E. Mahmoud, “Lag synchronization of hyperchaotic complex nonlinear systems,” Nonlinear Dynamics, vol. 67, no. 2, pp. 1613–1622, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  15. E. E. Mahmoud, “Complex complete synchronization of two nonidentical hyperchaotic complex nonlinear systems,” Mathematical Methods in the Applied Sciences, vol. 37, no. 3, pp. 321–328, 2014. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  16. Z. Y. Wu, J. Q. Duan, and X. C. Fu, “Complex projective synchronization in coupled chaotic complex dynamical systems,” Nonlinear Dynamics, vol. 69, no. 3, pp. 771–779, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  17. F. Zhang and S. Liu, “Full state hybrid projective synchronization and parameters identification for uncertain chaotic (hyperchaotic) complex systems,” Journal of Computational and Nonlinear Dynamics, vol. 9, no. 2, Article ID 021009, 2014. View at Publisher · View at Google Scholar · View at Scopus
  18. G. M. Mahmoud and E. E. Mahmoud, “Complex modified projective synchronization of two chaotic complex nonlinear systems,” Nonlinear Dynamics, vol. 73, no. 4, pp. 2231–2240, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  19. X. B. Zhou, M. R. Jiang, and Y. Q. Huang, “Combination synchronization of three identical or different nonlinear complex hyperchaotic systems,” Entropy, vol. 15, no. 9, pp. 3746–3761, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  20. X. Zhou, L. Xiong, and X. Cai, “Combination-combination synchronization of four nonlinear complex chaotic systems,” Abstract and Applied Analysis, vol. 2014, Article ID 953265, 14 pages, 2014. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  21. J. Sun, G. Cui, Y. Wang, and Y. Shen, “Combination complex synchronization of three chaotic complex systems,” Nonlinear Dynamics, vol. 79, no. 2, pp. 953–965, 2015. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  22. C. M. Jiang and S. T. Liu, “Generalized combination complex synchronization of new hyperchaotic complex Lü-like systems,” Advances in Difference Equations, vol. 2015, article 214, 2015. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  23. S. B. Wang, X. Y. Wang, X. Y. Wang, and Y. F. Zhou, “Adaptive generalized combination complex synchronization of uncertain real and complex nonlinear systems,” AIP Advances, vol. 6, no. 4, Article ID 045011, 2016. View at Publisher · View at Google Scholar
  24. I. M. Kyprianidis and I. N. Stouboulos, “Chaotic synchronization of three coupled oscillators with ring connection,” Chaos, Solitons & Fractals, vol. 17, no. 2-3, pp. 327–336, 2003. View at Publisher · View at Google Scholar · View at Scopus
  25. Y. G. Yu and S. C. Zhang, “Global synchronization of three coupled chaotic systems with ring connection,” Chaos, Solitons and Fractals, vol. 24, no. 5, pp. 1233–1242, 2005. View at Publisher · View at Google Scholar · View at Scopus
  26. J.-A. Lu, X.-P. Han, Y.-T. Li, and M.-H. Yu, “Adaptive coupled synchronization among multi-Lorenz systems family,” Chaos, Solitons and Fractals, vol. 31, no. 4, pp. 866–878, 2007. View at Publisher · View at Google Scholar · View at Scopus
  27. X. Y. Chen, J. L. Qiu, Q. Song, and A. C. Zhang, “Synchronization of N coupled chaotic systems with ring connection based on special antisymmetric structure,” Abstract and Applied Analysis, vol. 2013, Article ID 680604, 7 pages, 2013. View at Publisher · View at Google Scholar
  28. X. Y. Chen, C. Y. Wang, and J. L. Qiu, “Synchronization and anti-synchronization of N different coupled chaotic systems with ring connection,” International Journal of Modern Physics C, vol. 25, no. 5, Article ID 1440011, 2014. View at Publisher · View at Google Scholar · View at Scopus
  29. X. Chen, J. Qiu, J. Cao, and H. He, “Hybrid synchronization behavior in an array of coupled chaotic systems with ring connection,” Neurocomputing, vol. 173, pp. 1299–1309, 2016. View at Publisher · View at Google Scholar
  30. X.-Y. Wang and J.-M. Song, “Synchronization of the fractional order hyperchaos Lorenz systems with activation feedback control,” Communications in Nonlinear Science and Numerical Simulation, vol. 14, no. 8, pp. 3351–3357, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  31. X. Y. Wang and Y. J. He, “Projective synchronization of fractional order chaotic system based on linear separation,” Physics Letters A, vol. 372, no. 4, pp. 435–441, 2008. View at Publisher · View at Google Scholar · View at Scopus
  32. D. Lin and X. Y. Wang, “Observer-based decentralized fuzzy neural sliding mode control for interconnected unknown chaotic systems via network structure adaptation,” Fuzzy Sets and Systems, vol. 161, no. 15, pp. 2066–2080, 2010. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  33. N. Cai, Y. Jing, and S. Zhang, “Generalized projective synchronization of different chaotic systems based on antisymmetric structure,” Chaos, Solitons and Fractals, vol. 42, no. 2, pp. 1190–1196, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  34. M. Karabacak and H. I. Eskikurt, “Speed and current regulation of a permanent magnet synchronous motor via nonlinear and adaptive backstepping control,” Mathematical and Computer Modelling, vol. 53, no. 9-10, pp. 2015–2030, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  35. M. Zribi, A. Oteafy, and N. Smaoui, “Controlling chaos in the permanent magnet synchronous motor,” Chaos, Solitons and Fractals, vol. 41, no. 3, pp. 1266–1276, 2009. View at Publisher · View at Google Scholar · View at Scopus
  36. Q. Wei and X.-Y. Wang, “Chaos controlling of permanent magnet synchronous motor base on dither signal,” Journal of Vibration and Control, vol. 19, no. 16, pp. 2541–2550, 2013. View at Publisher · View at Google Scholar · View at Scopus
  37. Q. Wei, X.-Y. Wang, and X.-P. Hu, “Optimal control for permanent magnet synchronous motor,” Journal of Vibration and Control, vol. 20, no. 8, pp. 1176–1184, 2014. View at Publisher · View at Google Scholar · View at Scopus
  38. Q. Wei, X.-Y. Wang, and X.-P. Hu, “Inverse optimal control for permanent magnet synchronous motor,” Journal of Vibration and Control, vol. 21, no. 4, pp. 801–807, 2015. View at Publisher · View at Google Scholar · View at Scopus
  39. X.-Y. Wang and H. Zhang, “Backstepping-based lag synchronization of a complex permanent magnet synchronous motor system,” Chinese Physics B, vol. 22, no. 4, Article ID 048902, 2013. View at Publisher · View at Google Scholar · View at Scopus
  40. F. C. Zhang, C. L. Mu, X. Y. Wang, I. Ahmed, and Y. L. Shu, “Solution bounds of a new complex PMSM system,” Nonlinear Dynamics, vol. 74, no. 4, pp. 1041–1051, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  41. G. Tao, “A simple alternative to the Barbalat lemma,” IEEE Transactions on Automatic Control, vol. 42, no. 5, 698 pages, 1997. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  42. B. Liu, Y. M. Zhou, M. Jiang, and Z. K. Zhang, “Synchronizing chaotic systems using control based on tridiagonal structure,” Chaos, Solitons and Fractals, vol. 39, no. 5, pp. 2274–2281, 2009. View at Publisher · View at Google Scholar · View at Scopus
  43. B. Liu and Z. K. Zhang, “Stability of nonlinear systems with tridiagonal structure and its applications,” Acta Automatica Sinica, vol. 33, no. 4, pp. 442–445, 2007. View at Google Scholar · View at MathSciNet