Adaptive Fuzzy Observer without SPR Condition for Uncertain Nonlinear Systems

불확실한 비선형 계통에 대한 SPR 조건이 필요 없는 적응 퍼지 관측기

  • Park, Jang-Hyun (Dept. of Control System Engineering, Mokpo National Univ.) ;
  • Kim, Seong-Hwan (Dept. of Control System Engineering, Mokpo National Univ.)
  • 박장현 (목포대학교 제어계통공학과) ;
  • 김성환 (목포대학교 제어계통공학과)
  • Published : 2003.12.01

Abstract

This paper describes the design of a robust adaptive fuzzy observer for uncertain nonlinear dynamical system. We propose a new method in which no strictly positive real (SPR) condition is needed. No a priori knowledge of an upper bound on the lumped uncertainty is required. The Lyapunov synthesis approach is used to guarantee a semi-global uniform ultimate boundedness property of the state observation error, as well as of all other signals in the closed-loop system. The theoretical results are illustrated through a simulation example of a mass-spring-damper system.

본 논문은 불확실한 비선형 계통에 대해서 강인한 적응 퍼지 관측기를 설계하는 방법을 제시한다. 새로 제시하는 관측기는 관측기 설계시 관측오차의 동특성식이 SPR (strictly positive real)이어야 한다는 조건이 불필요하다. 또한 불확실한 항에 대한 유계상수도 추정하는 알고리듬을 사용하여 강인항의 이득값을 설계자가 미리 결정할 필요가 없게 된다. 설계된 관측기를 포함한 전체 폐루프 계통에 대해서 리아프노브 안정도를 증명하였으며 관측오차를 포함한 계통의 모든 신호들의 반전역적 유계(semi-global uniform ultimate boundedness)임을 증명하였다. 이론적으로 도출된 결과를 mass-spring-damper 계통에 대한 모의실험을 수행하여 제안된 관측기의 효율성과 성능을 보였다.

Keywords

References

  1. IEEE Trans. Neural Network v.3 no.5 Fuzzy basis functions universal approximation, and orthogonal least-squares learning Wang, L.X.;Mendel, J.M.
  2. IEEE Trans. System, Man, and Cybernetics v.25 no.4 Fuzzy logic controllers are universal approximators Castro, J.L.
  3. Neural Networks v.2 Multilayer feedforward networks are universal approximators Hornik, Kurt
  4. Robust and Nonlinear Control v.2 Stable control of nonlinear systems using neural networks Tzirkel-Hancook, E.;Fallside, F.
  5. IEEE Trans. Neural Networks v.7 no.5 Dynamic structure neural networks for stable adaptive control of nonlinear system Fabri, S.;Kadirkamanathan, V.
  6. Int.J.Control v.70 no.3 Stable adaptive tracking of uncertain systems using nonlinearly parameterized on-line approximators Polycarpou, M.U.;Mears, M.J.
  7. IEEE Trans. Systems, Man and Cybernetics-Part B:Cybernetics v.29 no.6 Adaptive neural network control of nonlinear systems by state and output feedback Ge, S.S.;Hang, C.C.;Zhang, T.
  8. IEEE Trans. Fuzzy Systems v.26 no.5 Stable adaptive fuzzy controllers with application to inverted tracking Wang, L.X.
  9. Int.J.Systems science v.27 no.12 Robust model reference adaptive control of nonlinear systems using fuzzy systems Chen, C.S.;Chen, W.L.
  10. Fuzzy Sets and Systems v.133 no.1 Robust adaptive fuzzy controller for nonlinear system with unknown nonlinearities Park, Jang-Hyun;Seo, Sam-Jun;Park, Gwi-Tae
  11. IEEE Trans. Syst. Man Cybern.-Park B:Cybern v.29 no.5 Observer-based adaptive fuzzy-neural control of nonlinear dynamocal systems Leu, Y.G.;Lee, T.T.;Wang, E.Y.
  12. Automatica v.33 no.8 A dynamic recurrent neural-network-based adaptive observer for a class of nonlinear systems Kim, Y.H.;Lewis, F.L.;Abdalla, C.T.
  13. Proceedings of the 1999 IEEE International Symposium on Intelligent control/Intelligent Systems and semiotics Adaptive observer for a class of nonlinear systems using neural networks Choi, Y.J.;Farrell, J.
  14. Nonlinear Systems Khalil, H.K.
  15. Robust Adaptive Control Ioannou, P.A.;Sun, J.
  16. Robust and Nonlinear Control v.13 no.2 Robust Adaptive Fuzzy Controller for Nonaffine Nonlinear Systems with Dynamic Rule Activation Park, J.H.;Park, G.T.