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Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 246579, 13 pages
http://dx.doi.org/10.1155/2012/246579
Research Article

Adaptive State-Feedback Stabilization for High-Order Stochastic Nonlinear Systems Driven by Noise of Unknown Covariance

1School of Electrical Engineering and Automation, Xuzhou Normal University, Xuzhou 221116, China
2Institute of Automation, Qufu Normal University, Qufu 273165, China

Received 20 July 2011; Accepted 10 September 2011

Academic Editor: Weihai Zhang

Copyright © 2012 Cong-Ran Zhao 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. Z. G. Pan and T. Başar, “Backstepping controller design for nonlinear stochastic systems under a risk-sensitive cost criterion,” SIAM Journal on Control and Optimization, vol. 37, no. 3, pp. 957–995, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  2. Z. G. Pan, K. Ezal, A. J. Krener, and P. V. Kokotović, “Backstepping design with local optimality matching,” IEEE Transactions on Automatic Control, vol. 46, no. 7, pp. 1014–1027, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  3. Y. G. Liu, Z. G. Pan, and S. Shi, “Output feedback control design for strict-feedback stochastic nonlinear systems under a risk-sensitive cost,” IEEE Transactions on Automatic Control, vol. 48, no. 3, pp. 509–513, 2003. View at Publisher · View at Google Scholar
  4. Y.-G. Liu and J.-F. Zhang, “Reduced-order observer-based control design for nonlinear stochastic systems,” Systems & Control Letters, vol. 52, no. 2, pp. 123–135, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  5. Y.-G. Liu and J.-F. Zhang, “Practical output-feedback risk-sensitive control for stochastic nonlinear systems with stable zero-dynamics,” SIAM Journal on Control and Optimization, vol. 45, no. 3, pp. 885–926, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  6. H. Deng and M. Krstić, “Output-feedback stochastic nonlinear stabilization,” IEEE Transactions on Automatic Control, vol. 44, no. 2, pp. 328–333, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  7. H. Deng, M. Krstić, and R. J. Williams, “Stabilization of stochastic nonlinear systems driven by noise of unknown covariance,” IEEE Transactions on Automatic Control, vol. 46, no. 8, pp. 1237–1253, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  8. Z.-J. Wu, X.-J. Xie, and S.-Y. Zhang, “Adaptive backstepping controller design using stochastic small-gain theorem,” Automatica, vol. 43, no. 4, pp. 608–620, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  9. S.-J. Liu, J.-F. Zhang, and Z.-P. Jiang, “Decentralized adaptive output-feedback stabilization for large-scale stochastic nonlinear systems,” Automatica, vol. 43, no. 2, pp. 238–251, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  10. Z.-J. Wu, X.-J. Xie, and S.-Y. Zhang, “Stochastic adaptive backstepping controller design by introducing dynamic signal and changing supply function,” International Journal of Control, vol. 79, no. 12, pp. 1635–1646, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  11. W. Lin, 2010, http://nonlinear.cwru.edu/~linwei/.
  12. C. J. Qian, Global synthesis of nonlinear systems with uncontrollable linearization, Ph.D. dissertation, 2001.
  13. M. Krstić and H. Deng, Stabilization of Uncertain Nonlinear Systems, Springer, New York, NY, USA, 1998.
  14. H. Deng, M. Krstić, and R. J. Williams, “Stabilization of stochastic nonlinear systems driven by noise of unknown covariance,” IEEE Transactions on Automatic Control, vol. 46, no. 8, pp. 1237–1253, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  15. X. R. Ma, Stochastic Differential Equations and Their Applications, Horwood, Chichester, UK, 2007.
  16. X.-J. Xie and J. Tian, “State-feedback stabilization for high-order stochastic nonlinear systems with stochastic inverse dynamics,” International Journal of Robust and Nonlinear Control, vol. 17, no. 14, pp. 1343–1362, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  17. J. Tian and X.-J. Xie, “Adaptive state-feedback stabilization for high-order stochastic non-linear systems with uncertain control coefficients,” International Journal of Control, vol. 80, no. 9, pp. 1503–1516, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  18. J. Tian and X. J. Xie, “Adaptive state-feedback stabilization for more general high-order stochastic nonlinear systems,” Acta Automatica Sinica, vol. 34, no. 9, pp. 1188–1191, 2008. View at Publisher · View at Google Scholar
  19. X.-J. Xie and J. Tian, “Adaptive state-feedback stabilization of high-order stochastic systems with nonlinear parameterization,” Automatica, vol. 45, no. 1, pp. 126–133, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  20. L. Liu and X. J. Xie, “State-feedback stabilization for stochastic high-order nonlinear systems with SISS inverse dynamics,” Asian Journal of Control, vol. 14, no. 4, pp. 1–11, 2012. View at Publisher · View at Google Scholar
  21. X.-J. Xie, N. Duan, and X. Yu, “State-feedback control of high-order stochastic nonlinear systems with SiISS inverse dynamics,” IEEE Transactions on Automatic Control, vol. 56, no. 8, pp. 1921–1926, 2011. View at Publisher · View at Google Scholar
  22. X.-J. Xie and W.-Q. Li, “Output-feedback control of a class of high-order stochastic nonlinear systems,” International Journal of Control, vol. 82, no. 9, pp. 1692–1705, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  23. L. Liu, N. Duan, and X.-J. Xie, “Output-feedback stabilization for stochastic high-order nonlinear systems with a ratio of odd integers power,” Acta Automatica Sinica, vol. 36, no. 6, pp. 858–864, 2010. View at Publisher · View at Google Scholar
  24. W.-Q. Li and X.-J. Xie, “Inverse optimal stabilization for stochastic nonlinear systems whose linearizations are not stabilizable,” Automatica, vol. 45, no. 2, pp. 498–503, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  25. H. K. Khalil, Nonlinear Systems, Prentice-Hall, Upper Saddle River, NJ, USA, 3rd edition, 2002.