Table of Contents Author Guidelines Submit a Manuscript
Mathematical Problems in Engineering
Volume 2016 (2016), Article ID 4085929, 11 pages
http://dx.doi.org/10.1155/2016/4085929
Research Article

Adaptive Neural Control of Nonaffine Nonlinear Systems without Differential Condition for Nonaffine Function

The College of Aeronautics and Astronautics Engineering, Air Force Engineering University, Xi’an 710038, China

Received 10 December 2015; Revised 4 May 2016; Accepted 16 May 2016

Academic Editor: Haranath Kar

Copyright © 2016 Chaojiao Sun 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. J. Wang and J. Hu, “Robust adaptive neural control for a class of uncertain non-linear time-delay systems with unknown dead-zone non-linearity,” IET Control Theory & Applications, vol. 5, no. 15, pp. 1782–1795, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  2. W. Chen and L. Jiao, “Adaptive tracking for periodically time-varying and nonlinearly parameterized systems using multilayer neural networks,” IEEE Transactions on Neural Networks, vol. 21, no. 2, pp. 348–351, 2010. View at Publisher · View at Google Scholar · View at Scopus
  3. C.-F. Hsu, C.-M. Lin, and T.-T. Lee, “Wavelet adaptive backstepping control for a class of nonlinear systems,” IEEE Transactions on Neural Networks, vol. 17, no. 5, pp. 1175–1183, 2006. View at Publisher · View at Google Scholar · View at Scopus
  4. 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, Part B: Cybernetics, vol. 40, no. 3, pp. 915–927, 2010. View at Publisher · View at Google Scholar · View at Scopus
  5. Z. Liu, X. Dong, J. Xue, and L. Zhang, “Adaptive tracking control for nonlinear systems with a class of input nonlinearities,” Asian Journal of Control, vol. 18, no. 2, pp. 771–778, 2016. View at Publisher · View at Google Scholar
  6. Y. Wen and X. Ren, “Neural networks-based adaptive control for nonlinear time-varying delays systems with unknown control direction,” IEEE Transactions on Neural Networks, vol. 22, no. 10, pp. 1599–1612, 2011. View at Publisher · View at Google Scholar · View at Scopus
  7. S.-C. Tong, Y.-M. Li, G. Feng, and T.-S. Li, “Observer-based adaptive fuzzy backstepping dynamic surface control for a class of MIMO nonlinear systems,” IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics, vol. 41, no. 4, pp. 1124–1135, 2011. View at Publisher · View at Google Scholar · View at Scopus
  8. H. Lee, “Robust adaptive fuzzy control by backstepping for a class of MIMO nonlinear systems,” IEEE Transactions on Fuzzy Systems, vol. 19, no. 2, pp. 265–275, 2011. View at Publisher · View at Google Scholar · View at Scopus
  9. S. Jagannathan and P. He, “Neural-network-based state feedback control of a nonlinear discrete-time system in nonstrict feedback form,” IEEE Transactions on Neural Networks, vol. 19, no. 12, pp. 2073–2087, 2008. View at Publisher · View at Google Scholar · View at Scopus
  10. Q. Zhou, P. Shi, J. Lu, and S. Xu, “Adaptive output-feedback fuzzy tracking control for a class of nonlinear systems,” IEEE Transactions on Fuzzy Systems, vol. 19, no. 5, pp. 972–982, 2011. View at Publisher · View at Google Scholar · View at Scopus
  11. T.-P. Zhang, H. Wen, and Q. Zhu, “Adaptive fuzzy control of nonlinear systems in pure feedback form based on input-to-state stability,” IEEE Transactions on Fuzzy Systems, vol. 18, no. 1, pp. 80–93, 2010. View at Publisher · View at Google Scholar · View at Scopus
  12. M. Chen, S. S. Ge, and B. V. E. How, “Robust adaptive neural network control for a class of uncertain MIMO nonlinear systems with input nonlinearities,” IEEE Transactions on Neural Networks, vol. 21, no. 5, pp. 796–812, 2010. View at Publisher · View at Google Scholar · View at Scopus
  13. T. Zhang, S. S. Ge, and C. C. Hang, “Adaptive neural network control for strict-feedback nonlinear systems using backstepping design,” Automatica, vol. 36, no. 12, pp. 1835–1846, 2000. View at Google Scholar · View at MathSciNet
  14. 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. View at Google Scholar
  15. B. Chen, X. Liu, K. Liu, and C. Lin, “Fuzzy-approximation-based adaptive control of strict-feedback nonlinear systems with time delays,” IEEE Transactions on Fuzzy Systems, vol. 18, no. 5, pp. 883–892, 2010. View at Publisher · View at Google Scholar · View at Scopus
  16. 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, Part B: Cybernetics, vol. 40, no. 3, pp. 915–927, 2010. View at Publisher · View at Google Scholar · View at Scopus
  17. M. Krstic, I. Kanellakopoulos, and P. Kokotovic, Nonlinear and Adaptive Control Design, Wiley, New York, NY, USA, 1995.
  18. X. Dong, G. Chen, and L. Chen, “Adaptive control of the uncertain duffing oscillator,” International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, vol. 7, no. 7, pp. 1651–1658, 1997. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  19. L. R. Hunt and G. Meyer, “Stable inversion for nonlinear systems,” Automatica, vol. 33, no. 8, pp. 1549–1554, 1997. View at Publisher · View at Google Scholar · View at MathSciNet
  20. 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 Publisher · View at Google Scholar · View at Scopus
  21. 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 MathSciNet · View at Scopus
  22. J.-H. Park, S.-H. Huh, S.-H. Kim, S.-J. Seo, and G.-T. Park, “Direct adaptive controller for nonaffine nonlinear systems using self-structuring neural networks,” IEEE Transactions on Neural Networks, vol. 16, no. 2, pp. 414–422, 2005. View at Publisher · View at Google Scholar · View at Scopus
  23. J.-H. Park, G.-T. Park, S.-H. Kim, and C.-J. Moon, “Direct adaptive self-structuring fuzzy controller for nonaffine nonlinear system,” Fuzzy Sets and Systems, vol. 153, no. 3, pp. 429–445, 2005. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  24. Y.-G. Leu, W.-Y. Wang, and T.-T. Lee, “Observer-based direct adaptive fuzzy-neural control for nonaffine nonlinear systems,” IEEE Transactions on Neural Networks, vol. 16, no. 4, pp. 853–861, 2005. View at Publisher · View at Google Scholar · View at Scopus
  25. S. S. Ge, C. C. Hang, and T. Zhang, “Adaptive neural network control of nonlinear systems by state and output feedback,” IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics, vol. 29, no. 6, pp. 818–828, 1999. View at Publisher · View at Google Scholar · View at Scopus
  26. M. Chen and S. S. Ge, “Direct adaptive neural control for a class of uncertain nonaffine nonlinear systems based on disturbance observer,” IEEE Transactions on Cybernetics, vol. 43, no. 4, pp. 1213–1225, 2013. View at Publisher · View at Google Scholar · View at Scopus
  27. S.-L. Dai, C. Wang, and M. Wang, “Dynamic learning from adaptive neural network control of a class of nonaffine nonlinear systems,” IEEE Transactions on Neural Networks and Learning Systems, vol. 25, no. 1, pp. 111–123, 2014. View at Publisher · View at Google Scholar · View at Scopus
  28. W. J. Dong, Y. Y. Zhao, Y. M. Chen, and J. A. Farrell, “Tracking control for nonaffine systems: a self-organizing approximation approach,” IEEE Transactions on Neural Networks and Learning Systems, vol. 23, no. 2, pp. 223–235, 2012. View at Publisher · View at Google Scholar · View at Scopus
  29. S. C. Tong and Y. M. Li, “Adaptive fuzzy output feedback backstepping control of pure-feedback nonlinear systems via dynamic surface control technique,” International Journal of Adaptive Control and Signal Processing, vol. 27, no. 7, pp. 541–561, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  30. 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, vol. 22, no. 5, pp. 1341–1347, 2014. View at Publisher · View at Google Scholar · View at Scopus
  31. W. D. Zhou, C. Y. Liao, L. Zheng, and M. M. Liu, “Adaptive fuzzy control for a class of chaotic systems with nonaffine inputs,” Nonlinear Dynamics, vol. 79, no. 4, pp. 2609–2621, 2014. View at Google Scholar
  32. Y.-S. Huang, D.-Q. Zhou, and X. X. Chen, “Decentralized direct adaptive output feedback fuzzy H tracking design of large-scale nonaffine nonlinear systems,” Nonlinear Dynamics, vol. 58, no. 1, pp. 153–167, 2009. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  33. J. Xiang, Y. Li, and W. Wei, “Stabilisation of a class of non-affine systems via modelling error compensation,” IET Control Theory & Applications, vol. 2, no. 2, pp. 108–116, 2008. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  34. J.-H. Park and S.-H. Kim, “Direct adaptive output-feedback fuzzy controller for a nonaffine nonlinear system,” IET Control Theory & Applications, vol. 151, no. 1, pp. 65–72, 2004. View at Publisher · View at Google Scholar · View at Scopus
  35. A. Boulkroune, M. M'Saad, and M. Farza, “Fuzzy approximation-based indirect adaptive controller for multi-input multi-output non-affine systems with unknown control direction,” IET Control Theory & Applications, vol. 6, no. 17, pp. 2619–2629, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  36. J.-H. Park and G.-T. Park, “Robust adaptive fuzzy controller for non-affine nonlinear systems with dynamic rule activation,” International Journal of Robust and Nonlinear Control, vol. 13, no. 2, pp. 117–139, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  37. A. Boulkroune, M. Tadjine, M. M'Saad, and M. Farza, “Adaptive fuzzy controller for non-affine systems with zero dynamics,” International Journal of Systems Science, vol. 40, no. 4, pp. 367–382, 2009. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  38. S. Labiod and T. M. Guerra, “Adaptive fuzzy control of a class of SISO nonaffine nonlinear systems,” Fuzzy Sets and Systems, vol. 158, no. 10, pp. 1126–1137, 2007. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  39. A. Boulkroune, M. Tadjine, M. M'Saad, and M. Farza, “Adaptive control based on SPO for nonaffine nonlinear systems and its application to CSTR system,” Mediterranean Journal of Measurement and Control, vol. 3, no. 2, pp. 93–103, 2007. View at Google Scholar · View at Scopus
  40. T. Zhang, “Adaptive control of first-order nonlinear systems with input non-affine nonlinearities,” in Proceedings of the 45th IEEE Conference on Decision and Control, pp. 3436–3441, IEEE, San Diego, Calif, USA, 2006. View at Publisher · View at Google Scholar
  41. T. P. 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
  42. J. Zhou, C. Zhang, and C. Wen, “Robust adaptive output control of uncertain nonlinear plants with unknown backlash nonlinearity,” IEEE Transactions on Automatic Control, vol. 52, no. 3, pp. 503–509, 2007. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  43. X.-S. Wang, C.-Y. Su, and H. Hong, “Robust adaptive control of a class of nonlinear systems with unknown dead-zone,” Automatica, vol. 40, no. 3, pp. 407–413, 2004. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  44. M. L. Corradini and G. Orlando, “Robust stabilization of nonlinear uncertain plants with backlash or dead zone in the actuator,” IEEE Transactions on Control Systems Technology, vol. 10, no. 1, pp. 158–166, 2002. View at Publisher · View at Google Scholar · View at Scopus
  45. Z. C. Liu, X. M. Dong, J. P. Xue, and Y. Chen, “Adaptive neural control for a class of time-delay systems in the presence of backlash or dead-zone non-linearity,” IET Control Theory & Applications, vol. 8, no. 11, pp. 1009–1022, 2014. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  46. D. Swaroop, J. K. Hedrick, P. P. Yip, and J. J. 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
  47. 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
  48. T. Zhang, S. S. Ge, and C. C. Hang, “Stable adaptive control for a class of nonlinear systems using a modified Lyapunov function,” IEEE Transactions on Automatic Control, vol. 45, no. 1, pp. 129–132, 2000. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  49. R. M. Sanner and J.-J. E. Slotine, “Gaussian networks for direct adaptive control,” IEEE Transactions on Neural Networks, vol. 3, no. 6, pp. 837–863, 1992. View at Publisher · View at Google Scholar · View at Scopus