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Mathematical Problems in Engineering
Volume 2015, Article ID 723425, 11 pages
http://dx.doi.org/10.1155/2015/723425
Research Article

Adaptive NN State-Feedback Control for Stochastic High-Order Nonlinear Systems with Time-Varying Control Direction and Delays

School of Electrical Engineering & Automation, Jiangsu Normal University, Xuzhou 221116, China

Received 11 March 2015; Accepted 14 May 2015

Academic Editor: Asier Ibeas

Copyright © 2015 Huifang Min and Na Duan. 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. M. Krstić and H. Deng, Stabilization of Uncertain Nonlinear Systems, Springer, New York, NY, USA, 1998.
  2. 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 Scopus
  3. X. R. Mao, Stochastic Differential Equations and Their Applications, Horwood Publishing, Chichester, UK, 2007.
  4. H. E. Psillakis and A. T. Alexandridis, “NN-based adaptive tracking control of uncertain nonlinear systems disturbed by unknown covariance noise,” IEEE Transactions on Neural Networks, vol. 18, no. 6, pp. 1830–1835, 2007. View at Publisher · View at Google Scholar · View at Scopus
  5. W. S. Chen, L. C. Jiao, and Z. B. Du, “Output-feedback adaptive dynamic surface control of stochastic non-linear systems using neural network,” IET Control Theory & Applications, vol. 4, no. 12, pp. 3012–3021, 2010. View at Publisher · View at Google Scholar · View at Scopus
  6. W. S. Chen, “Output-feedback adaptive stochastic nonlinear stabilization using neural networks,” Journal of Systems Engineering and Electronics, vol. 21, no. 1, pp. 81–87, 2010. View at Publisher · View at Google Scholar · View at Scopus
  7. T. Wang, S. C. Tong, and Y. M. Li, “Adaptive neural network output feedback control of stochastic nonlinear systems with dynamical uncertainties,” Neural Computing and Applications, vol. 23, no. 5, pp. 1481–1494, 2013. View at Publisher · View at Google Scholar · View at Scopus
  8. H.-Q. Wang, B. Chen, and C. Lin, “Adaptive neural tracking control for a class of stochastic nonlinear systems,” International Journal of Robust and Nonlinear Control, vol. 24, no. 7, pp. 1262–1280, 2014. View at Publisher · View at Google Scholar · View at Scopus
  9. H. Q. Wang, B. Chen, and C. Lin, “Adaptive neural control for strict-feedback stochastic nonlinear systems with time-delay,” Neurocomputing, vol. 77, no. 1, pp. 267–274, 2012. View at Publisher · View at Google Scholar · View at Scopus
  10. H. T. Gao, T. P. Zhang, and X. N. Xia, “Adaptive neural control of stochastic nonlinear systems with unmodeled dynamics and time-varying state delays,” Journal of the Franklin Institute, vol. 351, no. 6, pp. 3182–3199, 2014. View at Publisher · View at Google Scholar · View at Scopus
  11. Z. X. Yu, S. G. Li, and H. B. Du, “Adaptive neural output feedback control for stochastic nonlinear time-delay systems with unknown control directions,” Neural Computing and Applications, vol. 25, no. 7-8, pp. 1979–1992, 2014. View at Publisher · View at Google Scholar · View at Scopus
  12. Z. X. Yu and S. G. Li, “Neural-network-based output-feedback adaptive dynamic surface control for a class of stochastic nonlinear time-delay systems with unknown control directions,” Neurocomputing, vol. 129, pp. 540–547, 2014. View at Publisher · View at Google Scholar · View at Scopus
  13. Q. Zhou, P. Shi, Y. S. Xu, and Y. H. Li, “Observer-based adaptive neural network control for nonlinear stochastic systems with time delay,” IEEE Transactions on Neural Networks and Learning Systems, vol. 24, no. 1, pp. 71–80, 2013. View at Publisher · View at Google Scholar · View at Scopus
  14. Z. X. Yu and H. B. Du, “Adaptive neural control for uncertain stochastic nonlinear strict-feedback systems with time-varying delays: a Razumikhin functional method,” Neurocomputing, vol. 74, no. 12-13, pp. 2072–2082, 2011. View at Publisher · View at Google Scholar · View at Scopus
  15. Z. X. Yu, Z. H. Jin, and H. B. Du, “Adaptive neural control for a class of non-affine stochastic non-linear systems with time-varying delay: a Razumikhin-Nussbaum method,” IET Control Theory & Applications, vol. 6, no. 1, pp. 14–23, 2012. View at Publisher · View at Google Scholar · View at Scopus
  16. Z.-X. Yu and Z.-S. Yu, “Adaptive neural dynamic surface control for nonlinear pure-feedback systems with multiple time-varying delays: a Lyapunov-Razumikhin method,” Asian Journal of Control, vol. 15, no. 4, pp. 1124–1138, 2013. View at Publisher · View at Google Scholar · View at Scopus
  17. G. Z. Cui, T. C. Jiao, Y. L. Wei, G. Song, and Y. Chu, “Adaptive neural control of stochastic nonlinear systems with multiple time-varying delays and input saturation,” Neural Computing and Applications, vol. 25, no. 3-4, pp. 779–791, 2014. View at Publisher · View at Google Scholar · View at Scopus
  18. 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 Scopus
  19. W. Q. Li, Y. W. Jing, and S. Y. Zhang, “State feedback control of a class of high-order stochastic nonlinear systems,” International Journal of Robust and Nonlinear Control, vol. 22, no. 14, pp. 1583–1601, 2012. View at Publisher · View at Google Scholar · View at Scopus
  20. J.-Y. Zhai and H.-B. Du, “Global output feedback stabilisation for a class of upper triangular stochastic nonlinear systems,” International Journal of Control, vol. 87, no. 10, pp. 2106–2117, 2014. View at Publisher · View at Google Scholar · View at Scopus
  21. J.-Y. Zhai, “Decentralised output-feedback control for a class of stochastic non-linear systems using homogeneous domination approach,” IET Control Theory & Applications, vol. 7, no. 8, pp. 1098–1109, 2013. View at Publisher · View at Google Scholar · View at Scopus
  22. W. Q. Li, X.-J. Xie, and S. Y. Zhang, “Output-feedback stabilization of stochastic high-order nonlinear systems under weaker conditions,” SIAM Journal on Control and Optimization, vol. 49, no. 3, pp. 1262–1282, 2011. View at Publisher · View at Google Scholar · View at Scopus
  23. C.-R. Zhao and X.-J. Xie, “Output feedback stabilization using small-gain method and reduced-order observer for stochastic nonlinear systems,” IEEE Transactions on Automatic Control, vol. 58, no. 2, pp. 523–529, 2013. View at Publisher · View at Google Scholar · View at Scopus
  24. 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 · View at Scopus
  25. J.-Y. Zhai, “Finite-time output feedback stabilization for stochastic high-order nonlinear systems,” Circuits, Systems, and Signal Processing, vol. 33, no. 12, pp. 3809–3837, 2014. View at Publisher · View at Google Scholar · View at Scopus
  26. X.-J. Xie and N. Duan, “Output tracking of high-order stochastic nonlinear systems with application to benchmark mechanical system,” IEEE Transactions on Automatic Control, vol. 55, no. 5, pp. 1197–1202, 2010. View at Publisher · View at Google Scholar · View at Scopus
  27. X.-J. Xie, N. Duan, and C.-R. Zhao, “A combined homogeneous domination and sign function approach to output-feedback stabilization of stochastic high-order nonlinear systems,” IEEE Transactions on Automatic Control, vol. 59, no. 5, pp. 1303–1309, 2014. View at Publisher · View at Google Scholar · View at Scopus
  28. L. Liu and X.-J. Xie, “Output-feedback stabilization for stochastic high-order nonlinear systems with time-varying delay,” Automatica, vol. 47, no. 12, pp. 2772–2779, 2011. View at Publisher · View at Google Scholar · View at Scopus
  29. X.-J. Xie and L. Liu, “Further results on output feedback stabilization for stochastic high-order nonlinear systems with time-varying delay,” Automatica, vol. 48, no. 10, pp. 2577–2586, 2012. View at Publisher · View at Google Scholar · View at Scopus
  30. X.-J. Xie and L. Liu, “A homogeneous domination approach to state feedback of stochastic high-order nonlinear systems with time-varying delay,” IEEE Transactions on Automatic Control, vol. 58, no. 2, pp. 494–499, 2013. View at Publisher · View at Google Scholar · View at Scopus
  31. C. J. Qian, “A homogeneous domination approach for global output feedback stabilization of a class of nonlinear systems,” in Proceedings of the American Control Conference, pp. 4708–4715, June 2005. View at Scopus
  32. X. J. Xie, C. R. Zhao, and N. Duan, “Further results on state feedback stabilization of stochastic high-order nonlinear systems,” Science China Information Sciences, vol. 57, no. 7, pp. 1–14, 2014. View at Publisher · View at Google Scholar · View at Scopus
  33. F. Z. Gao, Z. Yuan, and F. S. Yuan, “State-feedback stabilization for stochastic high-order nonlinear systems with time-varying delays,” Abstract and Applied Analysis, vol. 2014, Article ID 673869, 11 pages, 2014. View at Publisher · View at Google Scholar · View at Scopus
  34. W. T. Zha, J. Y. Zhai, and S. M. Fei, “Output feedback control for a class of stochastic high-order nonlinear systems with time-varying delays,” International Journal of Robust and Nonlinear Control, vol. 24, no. 16, pp. 2243–2260, 2013. View at Publisher · View at Google Scholar · View at Scopus
  35. R. D. Nussbaum, “Some remarks on a conjecture in parameter adaptive control,” Systems and Control Letters, vol. 3, no. 5, pp. 243–246, 1983. View at Publisher · View at Google Scholar · View at Scopus
  36. Y.-C. Wang, H.-G. Zhang, and Y.-Z. Wang, “Fuzzy adaptive control of stochastic nonlinear systems with unknown virtual control gain function,” Acta Automatica Sinica, vol. 32, no. 2, pp. 170–178, 2006. View at Google Scholar · View at Scopus
  37. T. S. Li, Z. F. Li, D. Wang, and C. L. P. Chen, “Output-feedback adaptive neural control for stochastic nonlinear time varying delay systems with unknown control directions,” IEEE Transactions on Neural Networks and Learning Systems, vol. 26, no. 6, pp. 1188–1201, 2014. View at Publisher · View at Google Scholar
  38. T. Wang, S. C. Tong, and Y. M. Li, “Robust adaptive fuzzy output feedback control for stochastic nonlinear systems with unknown control direction,” Neurocomputing, vol. 106, pp. 31–41, 2013. View at Publisher · View at Google Scholar · View at Scopus