Adaptive Neural Control for Strict-feedback Nonlinear Systems without Backstepping

순궤환 비선형계통의 백스테핑 없는 적응 신경망 제어기

  • 박장현 (목포대학교 전기제어신소재공학부) ;
  • 김성환 (목포대학교 전기제어신소재공학부) ;
  • 박영환 (충주대학교 정보제어공학과)
  • Published : 2008.05.01

Abstract

A new adaptive neuro-control algorithm for a SISO strict-feedback nonlinear system is proposed. All the previous adaptive neural control algorithms for strict-feedback nonlinear systems are based on the backstepping scheme, which makes the control law and stability analysis very complicated. The main contribution of the proposed method is that it demonstrates that the state-feedback control of the strict-feedback system can be viewed as the output-feedback control problem of the system in the normal form. As a result, the proposed control algorithm is considerably simpler than the previous ones based on backstepping. Depending heavily on the universal approximation property of the neural network (NN), only one NN is employed to approximate the lumped uncertain system nonlinearity. The Lyapunov stability of the NN weights and filtered tracking error is guaranteed in the semi-global sense.

Keywords

References

  1. M. Kristic, I. Kanellakopoulos, and P. Kokotovic, Nonlinear and Adaptive Control Design. A Wiley-Interscience publication, 1995
  2. 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
  3. J.-H. Park, S.-H Huh, S.-H. Kim, S.-J. Seo, 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
  4. S. S. Ge and C. C. Hang and T. Zhang, "Adaptive Neural network control of nonlinear systems by state and output feedback," IEEE Trans. Systems, Man and Cybernetics-Part B:Cybernetics, vol. 29, no. 6, pp. 818-828, 1999 https://doi.org/10.1109/3477.809035
  5. M. U. Polycarpou and M. J. Mears, "Stable adaptive tracking of uncertain systems using nonliearly parameterized on-line approximators," Int. J. Control, vol. 70, no. 3, pp. 363-384, 1998 https://doi.org/10.1080/002071798222280
  6. Y. Li, S. Qiang, X. Zhuang, O. Kaynak, "Robust and adptive backstepping control for nonlinaer 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
  7. 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
  8. 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
  9. 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
  10. 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
  11. D. M. Dawson, J. J. Carroll, and M. Schneider, "Integrator backstepping control of a brush dc motor turning a rogotic load," IEEE Trans. System, Man, and Cybernetics - Part B:Cybernetaics, vol. 2, pp. 233-244, 1994
  12. 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
  13. S. N. Huang, K. K. Tan, and T. H. Lee, "Futher results on adaptive control for a class of nonlinear systems using neural networks," IEEE Trans. Neural Networks, vol. 14, no. 3, pp. 719-722, 2003 https://doi.org/10.1109/TNN.2003.811712
  14. P. A. Ioannou and J. Sun, Robust Adaptive Control. Englewood Cliffs, NJ:Prentice-Hall, 1996