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State- and Output-feedback Adaptive Controller for Pure-feedback Nonlinear Systems using Self-structuring Fuzzy System

완전 궤환 비선형 계통에 대한 자기 구조화 퍼지 시스템을 이용한 상태변수 및 출력 궤환 적응 제어기

  • 박장현 (목포대 공대 제어로봇공학과) ;
  • 김성환 (목포대 공대 제어로봇공학과) ;
  • 장영학 (목포대 공대 제어로봇공학과) ;
  • 유영재 (목포대 공대 제어로봇공학과)
  • Received : 2012.02.10
  • Accepted : 2012.08.09
  • Published : 2012.09.01

Abstract

Globally stabilizing adaptive fuzzy state- and output-feedback controllers for the fully nonaffine pure-feedback nonlinear system are proposed in this paper. By reformulating the original pure-feedback system to a standard normal form with respect to newly defined state variables, the proposed controllers require no backstepping design procedures. Avoiding backstepping makes the controller structure and stability analysis to be considerably simplified. For the global stabilty of the clossed-loop system, the self-structuring fuzzy system whose memebership functions and fuzzy rules are automatically generated and tuned is adopted. The proposed controllers employ only one fuzzy logic system to approximate unknown nonlinear function, which highlights the simplicity of the proposed adaptive fuzzy controller. Moreover, the output-feedback controller of the considered system proposed in this paper have not been dealt with in any literature yet.

Keywords

References

  1. M. Kristic, I. Kanellakopoulos, and P. Kokotovic, Nonlinear and Adaptive Control Design. A Wiley-Interscience publication, 1995.
  2. P. A. Ioannou and J. Sun, Robust Adaptive Control. Englewood Cliffs, NJ:Prentice-Hall, 1996.
  3. S. Behatsh, "Robust output tracking for nonlinear systems," Int. J. Control, vol. 51, no. 6, pp. 1381-1407, 1990. https://doi.org/10.1080/00207179008934141
  4. L.-X. Wang, "Stable adaptive fuzzy control of nonlinear systems," IEEE Trans. Fuzzy Systems, vol. 1, no. 2, pp. 146-155, 1993. https://doi.org/10.1109/91.227383
  5. L.-X. Wang, "Stable adaptive fuzzy controllers with application to inverted tracking," IEEE Trans. Fuzzy Systems, vol. 26, no. 5, pp. 677-691, 1996.
  6. J. T. Spooner, K. M. Passino, "Stalbe adaptive control using fuzzy systems and neural networks," IEEE Trans. Fuzzy Systems, vol. 4, no. 3, pp. 339-359, 1996. https://doi.org/10.1109/91.531775
  7. 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
  8. 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 & Systems, vol. 151, no. 1, pp. 21-42, Apr., 2005. https://doi.org/10.1016/j.fss.2004.07.007
  9. J.-H. Park, S.-H. Huh, S.-H. Kim, G.-T. Park, "Direct Adaptive Controller for Nonaffine Nonlinear Systems Using Self-Structuring Neural Networks," IEEE Trans. Neural Networks, vol. 16, no. 2, pp. 414-422, 2005. https://doi.org/10.1109/TNN.2004.841786
  10. J.-H. Park, 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
  11. 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 & Systems, vol. 153, no. 3, pp. 429-445, Aug., 2005. https://doi.org/10.1016/j.fss.2005.01.003
  12. 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
  13. I. Kanellakopoulos, P. V. Kokotovic, and A. S. Morse, "Systematic design of adaptive controllers for feedback linearizable systems," IEEE Trans. Autom. Control, vol. 36, no. 11, pp. 1241-1253, 1991. https://doi.org/10.1109/9.100933
  14. M. U. Polycarpou and M. J. Mears, "Stable adaptive tracking of uncertain systems using nonlinearly parameterized on-line approximators," Int. J. Control, vol. 70, no. 3, pp. 363-384, 1998. https://doi.org/10.1080/002071798222280
  15. W.-Y. Wang, M.-L. Chan, T.-T. Lee and C.-H. Liu, "Adaptive fuzzy control for strict-feedback canonical nonlinear systems with $H^\infty$ tracking performance," IEEE Trans. System, Man, and Cybernetics-Part B:Cybernetaics, vol. 30, no. 6, pp. 878-885, 2000. https://doi.org/10.1109/3477.891149
  16. Y. Li, S. Qiang, X. Zhuang, O. Kaynak, "Robust and adaptive backstepping control for nonlinear systems using RBF neural networks," IEEE Trans. Neural Networks, vol. 15, no. 3, pp. 693-701, 2004. https://doi.org/10.1109/TNN.2004.826215
  17. S. S. Ge, C. Wang, "Direct adaptive NN control of a class of nonlinear systems," IEEE Trans. Neural Networks, vol. 13, no. 1, pp. 214-221, 2002. https://doi.org/10.1109/72.977306
  18. J. Q. Gong, B. Yao, "Neural network adaptive robust control of nonlinear systems in semi-strict feedback form," Automatica, vol. 37, pp. 1149-1160, 2001. https://doi.org/10.1016/S0005-1098(01)00069-3
  19. Y. Yang, G. Geng, J. Ren, "A combined backstepping and small-gain approach to robust adaptive fuzzy control for strict-feedback nonlinear systems," IEEE Trans. System, Man, and Cybernetics-Part A, vol. 34, no. 3, pp. 406-420, 2004. https://doi.org/10.1109/TSMCA.2004.824870
  20. Y. Yang, C. Zhou, "Adaptive fuzzy $H^\infty$ stabilization for strict-feedback canonical nonlinear systems via backstepping and small-gain approach," IEEE Trans. Fuzzy Systems, vol. 13, no. 1, pp. 104-114, 2005. https://doi.org/10.1109/TFUZZ.2004.839663
  21. S. S. Ge, C. Wang, "Adaptive NN control of uncertain nonlinear pure-feedback systems," Automatica, vol. 38, pp. 671-682, 2002. https://doi.org/10.1016/S0005-1098(01)00254-0
  22. D. Wang, J. Huang, "Adaptive neural network control for a class of uncertain nonlinear systems in pure-feedback form," Automatica, vol. 38, pp. 1365-1372, 2002. https://doi.org/10.1016/S0005-1098(02)00034-1
  23. C. Wang, D. J. Hill, and S. S. Ge, G. Chem "An ISS-modular approach for adaptive neural control of pure-feedback systems," Automatica, vol. 42, pp. 723-732, 2006. https://doi.org/10.1016/j.automatica.2006.01.004
  24. T. P. Zhang, S. S. Ge, "Adaptive dynamic surface control of nonlinear systems with unknown dead zone in pure feddback form," Autimatica, vol. 44, pp. 1895-1903, 2008. https://doi.org/10.1016/j.automatica.2007.11.025
  25. B. Ren, S. S. Ge, C.-Y. Su, T. H. Lee, "Adaptive Neural Control for a Class of Uncertain Nonlinear Systems in Pure-Feedback Form with Hysteresis Input," IEEE Trans. Sys. man, and Cybern.-part B:Cybern, vol , no , pp, 2008.
  26. 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 Trans. Neural Networks, vol. 21, no. 11, pp. 1804-1816, 2010. https://doi.org/10.1109/TNN.2010.2073719
  27. A.-M. Zou, Z.-G. Hou, M. Tan, "Adaptive Control of a Class of Nonlinear Pure-Feedback Systems Using Fuzzy Backstepping Approach," IEEE Trans. Fuzzy Systems, vol. 16, no. 4, pp. 886-897, 2008. https://doi.org/10.1109/TFUZZ.2008.917301
  28. T.-P, Zhang, H. Wen, Q. Zhu, "Adaptive Fuzzy Control of Nonlinear Systems in Pure Feedback Form Based on Input-to-State Stability," IEEE Trans. Fuzzy Systems, vol. 18, no. 1, pp. 80-93, 2010. https://doi.org/10.1109/TFUZZ.2009.2036906
  29. J.-H. Park, S.-H. Kim, and Y.-H. Chang, "Adaptive Neural Control of Nonlinear Pure-feedback Systems," Journal of IKEEE, vol. 14, no. 3, pp. 10-17, 2010.
  30. J.-H. Park, S.-H. Kim, C.-J. Moon, "Adaptive Control for Strict-Feedback Nonlinear Systems Without Backstepping," IEEE Trans. Neural Networks, vol. 20, no. 7, pp. 1204-1209, 2009. https://doi.org/10.1109/TNN.2009.2020982
  31. S. Behatsh, "Robust output tracking for nonlinear systems," Int. J. Control, vol. 51, no. 6, pp. 1381-1407, 1990. https://doi.org/10.1080/00207179008934141
  32. J.-J. E. Slotine, W. Li, Applied Nonlinear Control. Prentice Hall, 1991.

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