Advertisement

Unknown Input Observer Design for Takagi-Sugeno Systems with Fuzzy Output Equation

  • Jitao Li
  • Zhenhua WangEmail author
  • Yi Shen
  • Yipeng Liu
Regular Papers Technical Notes and Correspondence
  • 16 Downloads

Abstract

This paper studies unknown input observer design for discrete-time Takagi-Sugeno fuzzy systems. The proposed unknown input observer has a new structure that can be applied to Takagi-Sugeno fuzzy systems with nonlinear output equation. We derive the design conditions of the proposed unknown input observer based on Lyapunov function and convert them into a set of linear matrix inequalities. Numerical simulations of a vehicle lateral dynamics are given to illustrate the effectiveness of the proposed method.

Keywords

Fuzzy output equation Takagi-Sugeno fuzzy systems unknown input observer 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    C. K. Ahn, P. Shi, and M. V. Basin, “Two–dimensional dissipative control and filtering for roesser model,” IEEE Trans. on Automatic Control, vol. 60, no. 7, pp. 1745–1759, 2015.MathSciNetCrossRefzbMATHGoogle Scholar
  2. [2]
    K. Zhang, B. Jiang, and P. Shi, Observer–based Fault Estimation and Accomodation for Dynamic Systems, vol. 436, Springer, 2012.Google Scholar
  3. [3]
    S. Guo, F. Zhu, and L. Xu, “Unknown input observer design for Takagi–Sugeno fuzzy stochastic system,” International Journal of Control, Automation and Systems, vol. 13, no. 4, pp. 1003–1009, 2015.CrossRefGoogle Scholar
  4. [4]
    Y. Li, H. R. Karimi, M. Zhong, S. X. Ding, and S. Liu, “Fault detection for linear discrete time–varying systems with multiplicative noise: the finite–horizon case,” IEEE Trans. on Circuits and Systems I: Regular Papers, vol. 65, no. 10, pp. 3492–3505, Oct. 2018.MathSciNetCrossRefGoogle Scholar
  5. [5]
    X. Li, F. Zhu, and J. Zhang, “State estimation and simultaneous unknown input and measurement noise reconstruction based on adaptive H¥ observer,” International Journal of Control, Automation and Systems, vol. 14, no. 3, pp. 647–654, 2016.CrossRefGoogle Scholar
  6. [6]
    X. Yu, P. Li, and Y. Zhang, “The design of fixed–time observer and finite–time fault–tolerant control for hypersonic gliding vehicles,” IEEE Trans. on Industrial Electronics, vol. 65, no. 5, pp. 4135–4144, 2018.CrossRefGoogle Scholar
  7. [7]
    Y. Hou, F. Zhu, X. Zhao, and S. Guo, “Observer design and unknown input reconstruction for a class of switched descriptor systems,” IEEE Trans. on Systems, Man, and Cybernetics: Systems, vol. 48, no. 8, pp. 1411–1419, Apr. 2017.CrossRefGoogle Scholar
  8. [8]
    W. Zhang, H. Su, F. Zhu, and G. M. Azar, “Unknown input observer design for one–sided Lipschitz nonlinear systems,” Nonlinear Dynamics, vol. 79, no. 2, pp. 1469–1479, 2015.MathSciNetCrossRefzbMATHGoogle Scholar
  9. [9]
    K. Zhang, B. Jiang, and V. Cocquempot, “Fuzzy unknown input observer–based robust fault estimation design for discrete–time fuzzy systems,” Signal Processing, vol. 128, pp. 40–47, 2016.CrossRefGoogle Scholar
  10. [10]
    S. Mondal, G. Chakraborty, and K. Bhattacharyy, “LMI approach to robust unknown input observer design for continuous systems with noise and uncertainties,” International Journal of Control, Automation and Systems, vol. 8, no. 2, pp. 210–219, 2010.CrossRefGoogle Scholar
  11. [11]
    D. Ichalal and S. Mammar, “On unknown input observers for LPV systems,” IEEE Trans. on Industrial Electronics, vol. 62, no. 9, pp. 5870–5880, 2015.CrossRefGoogle Scholar
  12. [12]
    W.–J. Chang, L.–Z. Liu, and C.–C. Ku, “Passive fuzzy controller design via observer feedback for stochastic Takagi–Sugeno fuzzy models with multiplicative noises,” International Journal of Control, Automation and Systems, vol. 9, no. 3, pp. 550–557, 2011.CrossRefGoogle Scholar
  13. [13]
    J. Cheng, J. H. Park, Y. Liu, Z. Liu, and L. Tang, “Finitetime H¥ fuzzy control of nonlinear Markovian jump delayed systems with partly uncertain transition descriptions,” Fuzzy Sets and Systems, vol. 314, pp. 99–115, 2017.MathSciNetCrossRefzbMATHGoogle Scholar
  14. [14]
    D. Zhai, L. An, J. Dong, and Q. Zhang, “Switched adaptive fuzzy tracking control for a class of switched nonlinear systems under arbitrary switching,” IEEE Trans. on Fuzzy Systems, vol. 26, no. 2, pp. 585–597, 2018.CrossRefGoogle Scholar
  15. [15]
    H. D. Choi, C. K. Ahn, P. Shi, L. Wu, and M. T. Lim, “Dynamic output–feedback dissipative control for T–S fuzzy systems with time–varying input delay and output constraints,” IEEE Trans. on Fuzzy Systems, vol. 25, no. 3, pp. 511–526, 2017.CrossRefGoogle Scholar
  16. [16]
    M. Shen and D. Ye, “Improved fuzzy control design for nonlinear markovian–jump systems with incomplete transition descriptions,” Fuzzy Sets and Systems, vol. 217, pp. 80–95, 2013.MathSciNetCrossRefzbMATHGoogle Scholar
  17. [17]
    C.–C. Ku, W.–J. Chang, C.–H. Lin, and Y.–C. Chang, “Imperfect premise matching based fuzzy control with passive constraints for discrete time–delay multiplicative noised stochastic nonlinear systems,” International Journal of Control, Automation and Systems, vol. 11, no. 3, pp. 614–623, 2013.CrossRefGoogle Scholar
  18. [18]
    W. Xie, Y.–L. Wang, J. Zhang, and M.–Y. Fu, “Novel separation principle based H¥ observer–controller design for a class of ts fuzzy systems,” IEEE Trans. on Fuzzy Systems, vol. 26, no. 6, pp. 3206–3221, December 2018.CrossRefGoogle Scholar
  19. [19]
    S.–J. Yeh, W. Chang, and W.–J. Wang, “Unknown input based observer synthesis for uncertain Takagi–Sugeno fuzzy systems,” IET Control Theory and Applications, vol. 9, no. 5, pp. 729–735, 2015.MathSciNetCrossRefGoogle Scholar
  20. [20]
    M. Chadli and H. R. Karimi, “Robust observer design for unknown inputs Takagi–Sugeno models,” IEEE Trans. on Fuzzy Systems, vol. 21, no. 1, pp. 158–164, 2013.CrossRefGoogle Scholar
  21. [21]
    Z. Nagy, E. Páll, and Z. Lendek, “Unknown input observer for a robot arm using T–S fuzzy descriptor models,” Proc. of IEEE Conference on Control Technology and Applications (CCTA), IEEE, pp. 939–944, 2017.Google Scholar
  22. [22]
    V.–P. Vu and W.–J. Wang, “Observer synthesis for uncertain Takagi–Sugeno fuzzy systems with multiple output matrices,” IET Control Theory and Applications, vol. 10, no. 2, pp. 151–161, 2016.MathSciNetCrossRefGoogle Scholar
  23. [23]
    Z. Wang, Y. Shen, X. Zhang, and Q. Wang, “Observer design for discrete–time descriptor systems: An LMI approach,” System & Control Letters, vol. 61, no. 6, pp. 683–687, 2012.MathSciNetCrossRefzbMATHGoogle Scholar
  24. [24]
    C.–H. Fang, Y.–S. Liu, S.–W. Kau, L. Hong, and C.–H. Lee, “A new LMI–based approach to relaxed quadratic stabilization of T–S fuzzy control systems,” IEEE Trans. on Fuzzy Systems, vol. 14, no. 3, pp. 386–397, 2006.CrossRefGoogle Scholar
  25. [25]
    S. Mammar and D. Koenig, “Vehicle handling improvement by active steering,” Vehicle System Dynamics, vol. 38, no. 3, pp. 211–242, 2002.CrossRefGoogle Scholar

Copyright information

© Institute of Control, Robotics and Systems and The Korean Institute of Electrical Engineers and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of AstronauticsHarbin Institute of TechnologyHarbinP. R. China
  2. 2.College of Information EngineeringZhejiang University of TechnologyHangzhouP. R. China

Personalised recommendations