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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 462468, 10 pages
http://dx.doi.org/10.1155/2014/462468
Research Article

Direct Adaptive Tracking Control for a Class of Pure-Feedback Stochastic Nonlinear Systems Based on Fuzzy-Approximation

1School of Mathematics and Physics, Bohai University, Jinzhou, Liaoning 121000, China
2Faculty of Engineering, Lakehead University, Orillia, Thunder Bay, ON, Canada P7B 5E1
3Faculty of Electronic and Information Engineering, Liaoning University of Science and Technology, Anshan, Liaoning 114051, China
4College of Information Science and Technology, Bohai University, Jinzhou, Liaoning 121000, China
5Department of Engineering, Faculty of Engineering and Science, University of Agder, 4898 Grimstad, Norway

Received 14 November 2013; Accepted 6 January 2014; Published 13 February 2014

Academic Editor: Xiaojie Su

Copyright © 2014 Huanqing Wang 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. K. S. Narendra and A. M. Annaswamy, Stable Adaptive Systems, Prentice-Hall, Englewood Cliffs, NJ, USA, 1989.
  2. H. Y. Li, J. Y. Yu, C. Hilton, and H. H. Liu, “Adaptive sliding mode control for nonlinear active suspension vehicle systems using T-S fuzzy Approach,” IEEE Transactions on Industrial Electronics, vol. 60, no. 8, pp. 3328–3338, 2013.
  3. H. Y. Li, J. Y. Yu, C. Hilton, and H. H. Liu, “Adaptive sliding mode control for nonlinear active suspension vehicle systems using T-S fuzzy approach,” IEEE Transactions on Industrial Electronics, vol. 60, no. 8, pp. 3328–3338, 2013.
  4. M. Krstic, I. Kanellakopoulos, and P. V. Kokotovic, Nonlinear and Adaptive Control Design, Wiley, New York, NY, USA, 1995.
  5. M. Liu, X. Cao, and P. Shi, “Fault estimation and tolerant control for fuzzy stochastic systems,” IEEE Transactions on Fuzzy Systems, vol. 21, no. 2, pp. 221–2229, 2013.
  6. M. Liu, X. Cao, and P. Shi, “Fuzzy-model-based fault tolerant design for nonlinear stochastic systems against simultaneous sensor and actuator faults,” IEEE Transactions on Fuzzy Systems, vol. 21, no. 5, pp. 789–799, 2013.
  7. S. Yin, S. Ding, and H. Luo, “Real-time implementation of fault tolerant control system with performance optimization,” IEEE Transactions on Industrial Electronics, vol. 61, no. 5, pp. 2402–2411, 2013. View at Publisher · View at Google Scholar
  8. S. Yin, S. Ding, A. Haghani, H. Hao, and P. Zhang, “A comparison study of basic data-driven fault diagnosis and process monitoring methods on the benchmark Tennessee Eastman process,” Journal of Process Control, vol. 22, no. 9, pp. 1567–1581, 2012.
  9. H. Li, H. Liu, H. Gao, and P. Shi, “Reliable fuzzy control for active suspension systems with actuator delay and fault,” IEEE Transactions on Fuzzy Systems, vol. 20, no. 2, pp. 342–357, 2012. View at Publisher · View at Google Scholar · View at Scopus
  10. H. Y. Li, X. J. Jing, H. K. Lam, and P. Shi, “Fuzzy Sampled-data control for uncertain vehicle suspension systems,” IEEE Transactions on Cybernetics, 2013. View at Publisher · View at Google Scholar
  11. H. Y. Li, X. J. Jing, and H. R. Karimi, “Output-feedback based h-infinity control for active suspension systems with control delay,” IEEE Transactions on Industrial Electronics, vol. 61, no. 1, pp. 436–446, 2014.
  12. M. Chen, S. S. Ge, B. V. E. How, and Y. S. Choo, “Robust adaptive position mooring control for marine vessels,” IEEE Transactions on Control Systems Technology, vol. 21, no. 2, pp. 395–409, 2013.
  13. S. Bououden, M. Chadli, F. Allouani, and S. Filali, “A new approach for fuzzy predictive adaptive controller design using particle swarm optimization algorithm,” International Journal of Innovative Computing, Information and Control, vol. 9, no. 9, pp. 3741–3758, 2013.
  14. S. Sefriti, J. Boumhidi, M. Benyakhlef, and I. Boumhidi, “Adaptive decentralized sliding mode neural network control of a class of nonlinear interconnected systems,” International Journal of Innovative Computing, Information and Control, vol. 9, no. 7, pp. 2941–2947, 2013.
  15. C. M. Lin, C. F. Hsu, and R. G. Yeh, “Adaptive fuzzy sliding-mode control system design for brushless DC motors,” International Journal of Innovative Computing, Information and Control, vol. 9, no. 3, pp. 1259–1270, 2013.
  16. T. Shaocheng, C. Bin, and W. Yongfu, “Fuzzy adaptive output feedback control for MIMO nonlinear systems,” Fuzzy Sets and Systems, vol. 156, no. 2, pp. 285–299, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  17. B. Chen, X. Liu, K. Liu, and C. Lin, “Direct adaptive fuzzy control of nonlinear strict-feedback systems,” Automatica, vol. 45, no. 6, pp. 1530–1535, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  18. B. Chen, X.-P. Liu, S.-C. Tong, and C. Lin, “Observer-based stabilization of T-S fuzzy systems with input delay,” IEEE Transactions on Fuzzy Systems, vol. 16, no. 3, pp. 652–663, 2008. View at Publisher · View at Google Scholar · View at Scopus
  19. X. D. Zhao, L. X. Zhang, P. Shi, and H. R. Karimi, “Novel stability criteria for T-S fuzzy systems,” IEEE Transactions on Fuzzy Systems, vol. 21, no. 6, pp. 1–11, 2013.
  20. X. J. Su, P. Shi, L. Wu, and Y. Song, “A novel approach to filter design for T-S fuzzy discretetime systems with time-varying delay,” IEEE Transactions on Fuzzy Systems, vol. 20, no. 6, pp. 1114–1129, 2012.
  21. X. J. Su, P. Shi, L. Wu, and Y. -D. Song, “A novel control design on discrete-time Takagi- Sugeno fuzzy systems with time-varying delays,” IEEE Trans on Fuzzy Systems, vol. 20, no. 6, pp. 655–671, 2013.
  22. X. J. Su, P. Shi, L. Wu, and S. K. Nguang, “Induced 2 filtering of fuzzy stochastic systems with time-varying delays,” IEEE Transactions on Cybernetics, vol. 43, no. 4, pp. 1251–1264, 2013.
  23. H. Deng and M. Krstić, “Stochastic nonlinear stabilization. I. A backstepping design,” Systems & Control Letters, vol. 32, no. 3, pp. 143–150, 1997. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  24. 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 · View at MathSciNet
  25. 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 · View at MathSciNet
  26. 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 Zentralblatt MATH · View at MathSciNet
  27. 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 · View at Zentralblatt MATH · View at MathSciNet
  28. Z. Wu, M. Cui, P. Shi, and H. R. Karimi, “Stability of stochastic nonlinear systems with state-dependent switching,” IEEE Transactions on Automatic Control, vol. 58, no. 8, pp. 1904–1918, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  29. H. R. Karimi, “Robust delay-dependent H control of uncertain time-delay systems with mixed neutral, discrete, and distributed time-delays and Markovian switching parameters,” IEEE Transactions on Circuits and Systems. I, vol. 58, no. 8, pp. 1910–1923, 2011. View at Publisher · View at Google Scholar · View at MathSciNet
  30. S. Huang, Z. Xiang, and H. R. Karimi, “Robust l2-gain control for 2D nonlinear stochastic systems with time-varying delays and actuator saturation,” Journal of the Franklin Institute, vol. 350, no. 7, pp. 1865–1885, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  31. H. E. Psillakis and A. T. Alexandridis, “Adaptive neural tracking for a class of SISO uncertain and stochastic nonlinear systems,” in Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference (CDC-ECC '05), pp. 7822–7827, Seville, Spain, December 2005. View at Publisher · View at Google Scholar · View at Scopus
  32. Q. Zhou, P. Shi, H. H. Liu, and S. Y. Xu, “Neural-network-based decentralized adaptive output-feedback control for large-scale stochastic nonlinear systems,” IEEE Transactions on Systems, Man, and Cybernetics B, vol. 42, no. 6, pp. 1608–1619, 2012.
  33. Y. Li, S. C. Tong, and Y. M. Li, “Observer-based adaptive fuzzy backstepping control for strict-feedback stochastic nonlinear systems with time delays,” International Journal of Innovative Computing, Information and Control, vol. 8, pp. 8103–8114, 2012.
  34. S. C. Tong, T. Wang, Y. M. Li, and B. Chen, “A combined backstepping and stochastic small- gain approach to robust adaptive fuzzy output feedback control,” IEEE Transactions on Fuzzy Systems, vol. 21, no. 2, pp. 314–327, 2013.
  35. H. Q. Wang, B. Chen, and C. Lin, “Adaptive neural tracking control for a class of stochastic nonlinear systems with unknown dead-zone,” International Journal of Innovative Computing, Information and Control, vol. 9, no. 8, pp. 3257–3270, 2013.
  36. A. Ferrara and L. Giacomini, “Control of a class of mechanical systems with uncertainties via a constructive adaptive/second order VSC approach,” Journal of Dynamic Systems, Measurement and Control, vol. 122, no. 1, pp. 33–39, 2000. View at Scopus
  37. S. S. Ge and C. Wang, “Adaptive NN control of uncertain nonlinear pure-feedback systems,” Automatica, vol. 38, no. 4, pp. 671–682, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  38. D. Wang and J. Huang, “Adaptive neural network control for a class of uncertain nonlinear systems in pure-feedback form,” Automatica, vol. 38, no. 8, pp. 1365–1372, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  39. C. Wang, D. J. Hill, S. S. Ge, and G. Chen, “An ISS-modular approach for adaptive neural control of pure-feedback systems,” Automatica, vol. 42, no. 5, pp. 723–731, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  40. 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 Zentralblatt MATH · View at MathSciNet
  41. M. Wang, S. S. Ge, and K.-S. Hong, “Approximation-based adaptive tracking control of pure-feedback nonlinear systems with multiple unknown time-varying delays,” IEEE Transactions on Neural Networks, vol. 21, no. 11, pp. 1804–1816, 2010. View at Publisher · View at Google Scholar · View at Scopus
  42. H. Q. Wang, B. Chen, X. P. Liu, K. F. Liu, and C. Lin, “Robust adaptive fuzzy tracking control for pure-feedback stochastic nonlinear systems with input constraints,” IEEE Transaction on Cybernetics, vol. 43, no. 6, pp. 2093–2104, 2013.
  43. J. J. Yu, K. J. Zhang, and S. M. Fei, “Direct fuzzy tracking control of a class of nonaffine stochastic nonlinear systems with unknown dead-zone input,” in Proceedings of the 17th IFAC World Congress, pp. 12236–12241, International Federation of Automatic Control (IFAC), Seoul, Korea, 2008.
  44. Z. Yu, Z. Jin, and H. 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 MathSciNet
  45. Y. M. Li and S. C. Tong, “Adaptive fuzzy output-feedback control of pure-feedback uncertain nonlinear systems with unknown dead-zone,” IEEE Transactions on Fuzzy Systems, 2013. View at Publisher · View at Google Scholar
  46. S. C. Tong, Y. Li, Y. M. Li, and Y. J. Liu, “Observer-based adaptive fuzzy backstepping control for a class of stochastic nonlinear strict-feedback systems,” IEEE Transactions on Systems, Man, and Cybernetics B, vol. 41, no. 6, pp. 1693–1704, 2011.
  47. L. X. Wang and J. M. Mendel, “Fuzzy basis functions, universal approximation, and orthogonal least squares learning,” IEEE Transactions on Neural Networks, vol. 3, no. 5, pp. 807–814, 1992.
  48. T. M. Apostol, Mathematical Analysis, Addison-Wesley, Reading, Mass, USA, 1963.