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An observer design for Takagi-Sugeno fuzzy bilinear control systems

Tre艣膰 / Zawarto艣膰
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Warianty tytu艂u
J臋zyki publikacji
EN
Abstrakty
EN
In this paper, the observer design problem for a T-S fuzzy bilinear control system is investigated. First, an observer of Kalman type is designed to estimate the system states for the linear case. Then, some new sufficient conditions are derived to show the exponential convergence of the solutions of the error equation for fuzzy bilinear systems. Furthermore, we consider some uncertainties of the system that are bounded and satisfy a certain condition where an observer is designed. Moreover, an application to Van de Vusse system is given.
Rocznik
Strony
631--649
Opis fizyczny
Bibliogr. 32 poz., rys., wzory
Tw贸rcy
  • University of Artois, Bethune, France
  • University of Sfax, IPEIS Sfax, Tunisia
  • University of Sfax, Faculty of Sciences of Sfax, Tunisia
  • University of Sfax, Faculty of Sciences of Sfax, Tunisia
Bibliografia
  • [1] N.A. Baleghi and M.H. Shafiei: An observer-based controller design for nonlinear discrete-time switched systems with time-delay and affine parametric uncertainty. Archives of Control Sciences, 30(3), (2020), 501-521. DOI: 10.24425/acs.2020.134674.
  • [2] P. Bergsten, R. Palm and D. Driankov: Observers for Takagi-Sugeno fuzzy systems. IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics), 32(1), (2002), 114-121. DOI: 10.1109/3477.979966.
  • [3] F. Delmotte, T.M. Guerra and M. Ksontini: Continuous Takagi-Sugeno鈥檚 models: reduction of the number of LMI conditions in various fuzzy control design techniques. IEEE Transactions on Fuzzy Systems, 15(3), (2007), 426-438. DOI: 10.1109/TFUZZ.2006.889829.
  • [4] M. Dlala and M.A. Hammami: Uniform exponential practical stability of impulsive perturbed systems. Journal of Dynamical and Control Systems, 13(3), (2007), 373-386. DOI: 10.1007/s10883-007-9020-x.
  • [5] J. Duda: Lyapunov matrices approach to the parametric optimization of a system with two delay sand a PD-controller. Archives of Control Sciences, 28(4), (2018), 585-600. DOI: 10.24425/acs.2018.125484.
  • [6] J.P. Gauthier and I. Kupka: A separation principle for bilinear systems with dissipative drift. IEEE Transactions on Automatic Control, 37(12), (1992), 1970-1974. DOI: 10.1109/9.182484.
  • [7] P. Gauthier, H. Hammouri and S. Othman: Simple observer for nonlinear systems, applications to bioreactocrs. IEEE Transactions on Automatic Control, 37(6) (1992) 875-880. DOI: 10.1109/9.256352.
  • [8] B. Ghanmi, N. Hadj Taieb and M.A. Hammami: Growth conditions for exponential stability of time-varying perturbed systems. International Journal of Control, 86(6), (2013), 1086-1097. DOI: 10.1080/00207179.2013.774464.
  • [9] 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.
  • [10] M.A. Hammami: Stabilization of a class of nonlinear systems using an observer design. Proceedings of the 32nd IEEE CDC, (1993), 1954-1959.
  • [11] M.A. Hammami: Global convergence of a control system by means of an observer, Journal of Optimization Theory and Applications, 108(2), (2001) 377-388.
  • [12] M.A. Hammami: Global stabilization of a certain class of nonlinear dynamical systems using state detection, Applied mathematics letters, 14(8), (2001) 913-919.
  • [13] M.A. Hammami: Global observers for homogeneous vector fields, Nonlinear Analysis: Modelling and control, 10(3), (2005) 197-210.
  • [14] H.K. Khalil: Nonlinear Systems, Mac-Millan, 2nd edition, 1996.
  • [15] A. Jmal, O. Naifar, A. Ben Makhlouf, N. Derbel and M.A. Hammami: Robust sensor fault estimation for fractional-order systems with monotone nonlinearities, Nonlinear Dynamics, 90(4), (2017) 2673-2685. DOI: 10.1109/CDC.1993.325537.
  • [16] A. Jmal, O. Naifar, A. Ben Makhlouf, N. Derbel and M.A. Hammami: On observer design for nonlinear Caputo fractional-order systems. Asian Journal of Control, 20(4), (2018) 1533-1540. DOI: 10.1002/asjc.1645.
  • [17] A. Larrache, M. Lhous, S.B. Rhila, M. Rachik and A. Tridane: An output sensitivity problem for a class of linear distributed systems with uncertain initial state. Archives of Control Sciences, 30(1), (2020), 139-155. DOI: 10.24425/acs.2020.132589.
  • [18] D.H. Lee, J.B. Park and Y.H. Joo: A fuzzy Lyapunov function approach to estimating the domain of attraction for continuous-time Takagi-Sugeno fuzzy systems. Information Sciences, 185(1), (2012) 230-248. DOI: 10.1016/j.ins.2011.06.008.
  • [19] N. Hadj Taieb, M.A. Hammami and F. Delmotte: A separation principle for Takagi-Sugeno control fuzzy systems. Archives of Control Sciences, 29(2), (2019), 227-245. DOI: 10.24425/acs.2019.129379.
  • [20] 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. DOI: 10.1515/acsc-2017-0028.
  • [21] J. Huang: Nonlinear Output Regulation: Theory and Application. Philadelphia, USA, SIAM, 2004.
  • [22] M. Ksantini, M.A. Hammami and F. Delmotte: On the global exponential stabilization of Takagi-Sugeno fuzzy uncertain systems. International Journal of Innovative Computing, Information and Control, 11(1), (2015), 281-284. DOI: 10.24507/ijicic.11.01.281.
  • [23] Y. Menasria, H. Bouras and N. Debbache: An interval observer design for uncertain nonlinear systems based on the T-S fuzzy model. Archives of Control Sciences, 27(3), (2017), 397-407. DOI: 10.1515/acsc-2017-0025.
  • [24] O. Naifar, A.B. Makhlouf, M.A. Hammami and A. Ouali: State feedback control law for a class of nonlinear time-varying system under unknown time-varying delay. Nonlinear Dynamics, 82(1), (2015) 349-355. DOI: 10.1007/s11071-015-2162-6.
  • [25] H. Perez, B. Ogunnaike and S. Devasia: Output tracking between operating points for nonlinear process: Van de Vusse example. IEEE Transactions on Control Systems Technology, 10(4) (2002), 611-617. DOI: 10.1109/TCST.2002.1014680.
  • [26] K. Tanaka and M. Sugeno: Stability analysis and design of fuzzy control systems. Fuzzy Sets and Systems, 45(2), (1992), 135-156. DOI: 10.1016/0165-0114(92)90113-I.
  • [27] T. Takagi and M. Sugeno: Fuzzy identification of systems and its applications to modeling and control. IEEE Transactions on Systems, Man, and Cybernetics, 15(1), (1985), 116-132. DOI: 10.1109/TSMC.1985.6313399.
  • [28] T.V. Dang, W-J. Wang, Ch-H. Huang, Ch-H. Sun and L. 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 (2011), 173-183. DOI: 10.3233/IFS-2011-0474.
  • [29] N. Vafamand, M.H. Asemani and A. Khayatiyan: A robust 饾惪1 controller design for continuous-time TS systems with persistent bounded disturbance and actuator saturation. Engineering Applications of Artificial Intelligence, 56 (2016) 212-221. DOI: 10.1016/j.engappai.2016.09.002.
  • [30] W-B. Xie, H. Li, Z-H. Wang and J. Zhang: Observer-based controller design for a T-S fuzzy system with unknown premise variables. International Journal of Control, Automation and Systems, 17 (2019), 907-915. DOI: 10.1007/s12555-018-0245-0.
  • [31] J. Yang, S. Li and X. Yu: Sliding-mode control for systems with mismatched uncertainties via a disturbance observer. Industrial Electronics, IEEE Transactions, 60(1), (2013), 160-169. DOI: 10.1109/TIE.2012.2183841.
  • [32] F. You, S. Cheng, K. Tian and X. Zhang: Robust fault estimation based on learning observer for Takagi-Sugeno fuzzy systems with interval time-varying delay. International Journal of Adaptive Control and Signal Processing, 34(1), (2020), 92-109. DOI: 10.1002/acs.3070.
Typ dokumentu
Bibliografia
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