International Journal of Control, Automation, and Systems

Institute of Control, Robotics and Systems (제어로봇시스템학회)
권호 표지

Adaptive Fuzzy Controller for the Nonlinear System with Unknown Sign of the Input Gain

  • Park Jang-Hyun (School of Electrical, Control, and Advanced Material Engineering, Mokpo National University) ;
  • Kim Seong-Hwan (School of Electrical, Control, and Advanced Material Engineering, Mokpo National University) ;
  • Moon Chae-Joo (School of Electrical, Control, and Advanced Material Engineering, Mokpo National University)
  • Published : 2006.04.01
Download PDF
⟨ Previous Next ⟩

Abstract

We propose and analyze a robust adaptive fuzzy controller for nonlinear systems without a priori knowledge of the sign of the input gain function. No assumptions are made about the type of nonlinearities of the system, except that such nonlinearities are smooth. The uncertain nonlinearities are captured by the fuzzy systems that have been proven to be universal approximators. The proposed control scheme completely overcomes the singularity problem that occurs in the indirect adaptive feedback linearizing control. Projection in the estimated parameters and switching in the control input are both not required. The stability of the closed-loop system is guaranteed in the Lyapunov viewpoint.

Keywords

References

  1. L.-X. Wang and J. M. Mendel, 'Fuzzy basis functions universal approximation, and orthogonal least-squares learning,' IEEE Trans. on Neural Network, vol. 3, no. 5, pp. 807-814, 1992 https://doi.org/10.1109/72.159070
  2. J. L. Castro, 'Fuzzy logic controllers are universal approximators,' IEEE Trans. on System, Man, and Cybernetics, vol. 25, no. 4, pp. 629-635, 1995 https://doi.org/10.1109/21.370193
  3. K. Hornic and M. Stinchombe, 'Multilayer feedforward neural networks are universal approximators,' Neural Networks, vol. 2, pp. 359-366, 1989 https://doi.org/10.1016/0893-6080(89)90020-8
  4. N. E. Cotter, 'The stone-weierstrass theorem and its application to neural networks,' IEEE Trans. on Neural Networks, vol. 1, no. 4, pp. 290-295, 1990 https://doi.org/10.1109/72.80265
  5. L.-X. Wang, 'Stable adaptive fuzzy controllers with application to inverted tracking,' IEEE Trans. on Fuzzy Systems, vol. 26, no. 5, pp. 677-691, 1996
  6. C.-S. Chen and W.-L. Chen, 'Robust model reference adaptive control of nonlinear systems using fuzzy systems,' Int. J. Systems Science, vol. 27, no. 12, pp. 1435-1442, 1996 https://doi.org/10.1080/00207729608929349
  7. A. Yesildirek and F. L. Lewis, 'Feedback linearization using neural network,' Automatica, vol. 31, no. 11, pp. 1659-1664, 1995 https://doi.org/10.1016/0005-1098(95)00078-B
  8. E. B. Kosmatopoulos, 'Universal stabilizing using control lyapunov functions, adaptive derivative feedback, and neural network approximators,' IEEE Trans. on Systems, Man, and Cybernetics:Part B - Cybernatics, vol. 28, no. 3, pp. 472-477, 1998 https://doi.org/10.1109/3477.678656
  9. J.-H. Park, S.-J. Seo and G.-T. Park, 'Adaptive fuzzy observer with minimal dynamic order for uncertain nonlinear systems,' IEE Proceedings - Control Theory and Applications, vol. 150, no. 2, pp. 189-197, 2003 https://doi.org/10.1049/ip-cta:20030148
  10. J.-H. Park and G.-T. Park, 'Robust adaptive fuzzy controller for nonlinear system using estimation of bounds for approximation errors,' Fuzzy Sets & Systems, vol. 133, no. 1, pp. 19-36, 2003 https://doi.org/10.1016/S0165-0114(02)00137-9
  11. J.-H. Park and G.-T. Park, 'Robust adaptive fuzzy controller for nonaffine nonlinear systems with dynamic rule activation,' Int. J. Robust and Nonliner Control, vol. 13, no. 2, pp. 117-139, 2003 https://doi.org/10.1002/rnc.717
  12. J.-H. Park and S.-H. Kim, 'Direct adaptive output-feedback fuzzy controller for nonaffine nonlinear system,' IEE Proceedings - Control Theory and Applications, vol. 151, no. 1, pp. 65- 72, 2004 https://doi.org/10.1049/ip-cta:20040011
  13. J.-H. Park, G.-T. Park, S.-H. Kim and C.-J. Moon, 'Output-feedback control of uncertain nonlinear systems using a self-structuring adaptive fuzzy observer,' Fuzzy Sets and Systems, vol. 151, no. 1, pp. 21-42, 2005 https://doi.org/10.1016/j.fss.2004.07.007
  14. J.-H. Park, S.-H Huh, S.-H. Kim, and G.-T. Park, 'Direct adaptive controller for nonaffine nonlinear systems using self-structuring neural networks,' IEEE Trans. on Neural Networks, vol. 15, no. 2, pp. 414-422, 2005
  15. J.-H. Park, G.-T. Park, S.-H. Kim, and C.-J. Moon, 'Direct adaptive self-structuring fuzzy controller for nonaffine nonlinear systems,' Fuzzy Sets and Systems, vol. 153, no. 3, pp. 429-445, 2005 https://doi.org/10.1016/j.fss.2005.01.003
  16. R. D. Nussbaum, 'Some remarks on a conjecture in parameter adaptive control,' Systems & Control Letters, vol. 3, pp. 201-210, 1983
  17. X. D. Ye and J. P. Jiang, 'Adaptive nonlinear design without a priori knowledge on control directions,' IEEE Trans. on Automatic Control, vol. 43, pp. 1617-1621, 1998 https://doi.org/10.1109/9.728882
  18. X. D. Ye and Z. Ding, 'Robust tracking control of uncertain nonlinear systems with unknown control directions,' Systems & Control Letters, vol. 42, pp. 1-10, 2001 https://doi.org/10.1016/S0167-6911(00)00069-4
  19. Z. Ding, 'Global adaptive output feedback stabilization of nonlinear systems of any relative degree with unknown high frequency gain,' IEEE Trans. on Automatic Control, vol. 43, pp. 1442-1446, 1998 https://doi.org/10.1109/9.720504
  20. R. Lozano, J. Collado, and S. Mondie, 'Model reference adaptive control without a priori knowledge of the high frequency gain,' IEEE Trans. on Automatic Control, vol. 35, pp. 71-78, 1990 https://doi.org/10.1109/9.45147
  21. B. Brogliato and R. Lozano, 'Adaptive control of first-order nonlinear systems with reduced knowledge of the plant parameters,' IEEE Trans. on Automatic Control, vol. 39, pp. 1764-1768, 1994 https://doi.org/10.1109/9.310070
  22. J.-H. Park and G.-T. Park, 'Robust adaptive fuzzy controller for nonlinear systems with unknown nonlinearities,' J. Intelligent & Fuzzy Systems, vol. 10, pp. 87-98, 2001
  23. S. S. Ge, C. C. Hang, and T. Zhang, 'Adaptive neural network control of nonlinear systems by state and output feedback,' IEEE Trans. on Systems, Man and Cybernetics-Part B: Cybernetics, vol. 29, no. 6, pp. 818-828, 1999
  24. Y.-C. Chang, 'Adaptive fuzzy-based tracking control for nonlinear siso systems via vss and $H_{\infty}$ approaches,' IEEE Trans. on Fuzzy Systems, vol. 9, no. 2, pp. 278-292, 2001 https://doi.org/10.1109/91.919249