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Mathematical Problems in Engineering
Volume 2015, Article ID 529862, 13 pages
http://dx.doi.org/10.1155/2015/529862
Research Article

Adaptive Neural Output Feedback Control of Stochastic Nonlinear Systems with Unmodeled Dynamics

Department of Automation, College of Information Engineering, Yangzhou University, Yangzhou 225127, China

Received 9 April 2014; Revised 17 June 2014; Accepted 4 July 2014

Academic Editor: Ming Gao

Copyright © 2015 Xiaonan Xia and Tianping Zhang. 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. I. Kanellakopoulos, P. V. Kokotovic, and A. S. Morse, “Systematic design of adaptive controllers for feedback linearizable systems,” IEEE Transactions on Automatic Control, vol. 36, no. 11, pp. 1241–1253, 1991. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  2. D. Swaroop, J. K. Hedrick, P. P. Yip, and J. C. Gerdes, “Dynamic surface control for a class of nonlinear systems,” IEEE Transactions on Automatic Control, vol. 45, no. 10, pp. 1893–1899, 2000. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  3. Z. Jiang and L. Praly, “Design of robust adaptive controllers for nonlinear systems with dynamic uncertainties,” Automatica, vol. 34, no. 7, pp. 825–840, 1998. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  4. Z. P. Jiang and D. J. Hill, “A robust adaptive backstepping scheme for nonlinear systems with unmodeled dynamics,” IEEE Transactions on Automatic Control, vol. 44, no. 9, pp. 1705–1711, 1999. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  5. D. Wang and J. Huang, “Neural network-based adaptive dynamic surface control for a class of uncertain nonlinear systems in strict-feedback form,” IEEE Transactions on Neural Networks, vol. 16, no. 1, pp. 195–202, 2005. View at Publisher · View at Google Scholar · View at Scopus
  6. T. S. Li, D. Wang, G. Feng, and S. C. Tong, “A DSC approach to robust adaptive nn tracking control for strict-feedback nonlinear systems,” IEEE Transactions on Systems, Man, and Cybernetics B: Cybernetics, vol. 40, no. 3, pp. 915–927, 2010. View at Publisher · View at Google Scholar · View at Scopus
  7. T. P. Zhang and S. S. Ge, “Adaptive dynamic surface control of nonlinear systems with unknown dead zone in pure feedback form,” Automatica, vol. 44, no. 7, pp. 1895–1903, 2008. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  8. T. P. Zhang, Q. Zhu, and Y. Q. Yang, “Adaptive neural control of non-affine pure-feedback non-linear systems with input nonlinearity and perturbed uncertainties,” International Journal of Systems Science, vol. 43, no. 4, pp. 691–706, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  9. T. Zhang, X. Shi, Q. Zhu, and Y. Yang, “Adaptive neural tracking control of pure-feedback nonlinear systems with unknown gain signs and unmodeled dynamics,” Neurocomputing, vol. 121, pp. 290–297, 2013. View at Publisher · View at Google Scholar · View at Scopus
  10. X. Y. Zhang and Y. Lin, “Adaptive tracking control for a class of pure-feedback non-linear systems including actuator hysteresis and dynamic uncertainties,” IET Control Theory and Applications, vol. 5, no. 16, pp. 1868–1880, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  11. T. Zhang and S. S. Ge, “Adaptive neural network tracking control of MIMO nonlinear systems with unknown dead zones and control directions,” IEEE Transactions on Neural Networks, vol. 20, no. 3, pp. 483–497, 2009. View at Publisher · View at Google Scholar · View at Scopus
  12. S. J. Yoo and J. B. Park, “Neural-network-based decentralized adaptive control for a class of large-scale nonlinear systems with unknown time-varying delays,” IEEE Transactions on Systems, Man, and Cybernetics B: Cybernetics, vol. 39, no. 5, pp. 1316–1323, 2009. View at Publisher · View at Google Scholar · View at Scopus
  13. S. J. Yoo, “Decentralised adaptive control of a class of interconnected non-linear systems with unknown time delays and dead-zone inputs,” IET Control Theory & Applications, vol. 4, no. 11, pp. 2639–2650, 2010. View at Publisher · View at Google Scholar · View at MathSciNet
  14. M. Krstic, I. Kanellakopoulos, and P. V. Kokotocic, Nonlinear and Adaptive Control Design, Wiley-Interscience, New York, NY, USA, 1995.
  15. Y. J. Liu and W. Wang, “Adaptive output feedback control of uncertain nonlinear systems based on dynamic surface control technique,” International Journal of Robust and Nonlinear Control, vol. 22, no. 9, pp. 945–958, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  16. S. Tong, C. Liu, and Y. Li, “Adaptive fuzzy backstepping output feedback control for strict feedback nonlinear systems with unknown sign of high-frequency gain,” Neurocomputing, vol. 77, no. 1, pp. 58–70, 2012. View at Publisher · View at Google Scholar · View at Scopus
  17. Y. M. Li, S. C. Tong, Y. J. Liu, and T. S. Li, “Adaptive fuzz y robust otput feedback control of nonlinear systems with unknown dead-zones based on a small-gain approach,” IEEE Transactions on Fuzzy Systems, vol. 22, no. 1, pp. 164–176, 2014. View at Google Scholar
  18. C. Wang and Y. Lin, “Decentralised adaptive dynamic surface control for a class of interconnected non-linear systems,” IET Control Theory & Applications, vol. 6, no. 9, pp. 1172–1181, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  19. H. Deng and M. Krstić, “Stochastic nonlinear stabilization—I: a backstepping design,” Systems and Control Letters, vol. 32, no. 3, pp. 143–150, 1997. View at Publisher · View at Google Scholar · View at Scopus
  20. 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 MathSciNet · View at Scopus
  21. 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 MathSciNet · View at Scopus
  22. H. Fan and W. Xie, “Adaptive state feedback control for a class of stochastic nonlinear systems with unknown backlash-like hysteresis,” in Proceedings of the 2nd IEEE Conference on Industrial Electronics and Applications (ICIEA '07), pp. 2797–2801, May 2007. View at Publisher · View at Google Scholar · View at Scopus
  23. H. Fan, L. Han, C. Wen, and L. Xu, “Decentralized adaptive output-feedback controller design for stochastic nonlinear interconnected systems,” Automatica, vol. 48, no. 11, pp. 2866–2873, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  24. T. Wang, S. Tong, and Y. Li, “Robust adaptive fuzzy control for a class of stochastic nonlinear systems with dynamical uncertainties,” Journal of the Franklin Institute, vol. 349, no. 10, pp. 3121–3141, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  25. 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
  26. 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 MathSciNet · View at Scopus
  27. X. Yu and X. Xie, “Output feedback regulation of stochastic nonlinear systems with stochastic iISS inverse dynamics,” IEEE Transactions on Automatic Control, vol. 55, no. 2, pp. 304–320, 2010. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  28. S. Liu and J. Zhang, “Output-feedback control of a class of stochastic nonlinear systems with linearly bounded unmeasurable states,” International Journal of Robust and Nonlinear Control, vol. 18, no. 6, pp. 665–687, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  29. W. Li, Y. Jing, and S. Zhang, “Output-feedback stabilization for stochastic nonlinear systems whose linearizations are not stabilizable,” Automatica, vol. 46, no. 4, pp. 752–760, 2010. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  30. X. Yu, X. J. Xie, and N. Duan, “Small-gain control method for stochastic nonlinear systems with stochastic iISS inverse dynamics,” Automatica, vol. 46, no. 11, pp. 1790–1798, 2010. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  31. C. Zhao and X. 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. 523–528, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  32. T. P. Zhang and X. N. Xia, “Adaptive output feedback tracking control of stochastic nonlinear systems with dynamic uncertainties,” International Journal of Robust and Nonlinear Control, 2014. View at Publisher · View at Google Scholar
  33. 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
  34. R. Z. Khasminskii, Stochastic Stability of Differential Equations, Kluwer Academic, Norwell, Mass, USA, 1980. View at MathSciNet