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A separation principle for Takagi-Sugeno control fuzzy systems

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
An important application of state estimation is feedback control: an estimate of the state (typically the mean estimate) is used as input to a state-feedback controller. This scheme is known as observer based control, and it is a common way of designing an output-feedback controller (i. e. a controller that does not have access to perfect state measurements). In this paper, under the fact that both the estimator dynamics and the state feedback dynamics are stable we propose a separation principle for Takagi-Sugeno fuzzy control systems with Lipschitz nonlinearities. The considered nonlinearities are Lipschitz or meets an integrability condition which have no influence on the LMI to prove the stability of the associated closed-loop system. Furthermore, we give an example to ullistrate the applicability of the main result.
Rocznik
Strony
227--245
Opis fizyczny
Bibliogr. 24 poz., wzory
Twórcy
  • University of Sfax, Faculty of Sciences of Sfax, Tunisia
  • University of Sfax, Faculty of Sciences of Sfax, Tunisia
autor
  • University of Artois, Bethune France
Bibliografia
  • [1] S. Ammar, M. A. Hammami, H. Jerbi, and J. C. Vivalda: Separation principle for a sampled bilinear system. Journal of Dynamical and Control Systems, 16(4) (2010), 471–484.
  • [2] S. G. Cao, N. W. Rees, G. Feng, and C. K. Chak: Design of fuzzy control systems with guaranteed stability. Fuzzy Sets and Systems, 1(1) (1997), 1–10.
  • [3] B. S. Chen, C. S. Tseng, and H. J. Uang: Mixed H2=H1 fuzzy output feed-back control design for nonlinear dynamic systems: An LMI approach. IEEE Trans. Fuzzy Syst., 8(3) (2000), 249–265.
  • [4] F. Delmotte, T. M. Guerra, and M. Ksontini: Continuous Takagi-Sugeno’s models: reduction of the number of LMI conditions in various fuzzy control design techniques. IEEE Trans. Fuzzy Syst., 15(3) (2007), 426–438.
  • [5] N. Hadj Taieb, M. A. Hammami, F. Delmotte, and Ksantini Mohamed: On the global stabilization of Takagi–Sugeno fuzzy cascaded systems. Nonlinear Dynamics, 67(4) (2012), 2847–2856.
  • [6] N. Hadj Taieb, M. A. Hammami, and F. Delmotte: Stabilization of a certain class of fuzzy control systems with uncertainties. Archives of Control Sciences, 27(3) (2017) 453–481.
  • [7] A. Jadbabaie, A. Titli, and M. Jamshidi: Fuzzy observer based control of nonlinear systems. Proceeding of the 36th IEEE Conference on Decision and Control (1997), 3347–3349.
  • [8] S. Kawamoto, K. Tada, A. Ishigame, and T. Taniguchi: An approach to stability analysis of second order fuzzy systems. Proceeding of the 1st IEEE Conference on Fuzzy Systems (1992), 1427–1434.
  • [9] H. Khalil: Nonlinear systems, third ed. Prentice-Hall, Englewood Cliffs, NJ, 2002.
  • [10] H. J. Lee, J. B. Park, and G. Chen: Robust fuzzy control of nonlinear systems with parameter uncertainties. IEEE Trans. Fuzzy Syst., 9(2) (2001), 369–379.
  • [11] Z. Lendek, R. Babuska, and B. De Schutter: Stability of cascaded Takagi-Sugeno fuzzy systems. Proceeding of the 6th IEEE Conference on Fuzzy Systems (2007), 505–510.
  • [12] X. J. Ma and Z. Q. Sun: Analysis and design of fuzzy reduced-dimentional observer and fuzzy functional observer. Fuzzy Sets and Systems, 120(1) (2001), 35–63.
  • [13] X. J. Ma, Z. Q. Sun, and Y. Y. He: Analysis and design of fuzzy controller and fuzzy observer. IEEE Trans. Fuzzy Syst., 6(1) (1998), 41–51.
  • [14] V. F. Montagner, R. C. L. F. Oliveira, and P. L. D. Peres: Convergent LMI relaxations for quadratic stabilizability and H1 control of Takagi-Sugeno Fuzzy Systems. IEEE Trans. Fuzzy Syst., 17(4) (2009), 863–873.
  • [15] J. Park, J. Kim and D. Park: LMI-based design of stabilizing fuzzy controllers for nonlinear systems described by Takagi-Sugeno fuzzy model. Fuzzy Sets and Systems, 122(1) (2003), 73–82.
  • [16] T. Takagi and M. Sugeno: Fuzzy identification of systems and its applications to modeling and control. IEEE Trans. Syst. Man Cyber., 15 (1985) 116–132.
  • [17] K. Tanaka and H. Wang: Fuzzy Control Systems Design and Analysis: a Linear matrix inequality approach. John Wiley and Sons, ISBN 0-471-32324, United States of America, 2001.
  • [18] K. Tanaka and M. Sugeno: Stability analysis and design of fuzzy control systems. Fuzzy Sets and Systems, 45(2) (1992), 135–156.
  • [19] K. Tanaka, T. Ikeda, and H.O. Wang: Robust stabilization of a class of uncertain nonlinear systems via fuzzy control: quadratic stabilizability, H1 control theory and linear matrix inequalities. IEEE Trans. Fuzzy Syst., 4(1) (1996) 1–13.
  • [20] K. Tanaka, T. Ikeda, and H. O. Wang: Fuzzy regulators and fuzzy observers: relaxed stability conditions and LMI-based designs. IEEE Trans. Fuzzy Syst., 6(2) (1998), 250–265.
  • [21] T. Takagi and M. Sugeno: Fuzzy identification of systems and its applications to modeling and control. IEEE Trans. Syst. Man Cyber., 15 (1985) 116–132.
  • [22] S. Tong, T. Wang, and H. X. Li: Fuzzy robust tracking control for uncertain nonlinear systems. Int. J. Approx. Reason, 30 (2002), 73–90.
  • [23] Thai Viet Dang, Wen-June Wang, Cheng-Hao Huang, Chung-Hsun Sun, and Leh Luoh: Observer synthesis for the T-S fuzzy system with uncertainty and output disturbance. Journal of Intelligent and Fuzzy Systems: Applications in Engineering and Technology, 22(4) (2011), 173–183.
  • [24] J. Yoneyama and M. Nishikawa: Output stabilization of Takagi-Sugeno fuzzy systems. Fuzzy Sets and Systems, 111(2) (2000), 253–266.
Uwagi
PL
Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-fa10dd3c-e2af-41db-a0af-14e2e818a19b
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