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Tytuł artykułu

Robust observer design for Sugeno systems with incremental quadratic nonlinearity in the consequent

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Języki publikacji
EN
Abstrakty
EN
This paper is concerned with observer design for nonlinear systems that are modeled by T–S fuzzy systems containing parametric and nonparametric uncertainties. Unlike most Sugeno models, the proposed method contains nonlinear functions in the consequent part of the fuzzy IF-THEN rules. This will allow modeling a wider class of systems with smaller modelling errors. The consequent part of each rule contains a linear part plus a nonlinear term, which has an incremental quadratic constraint. This constraint relaxes the conservativeness introduced by other regular constraints for nonlinearities such as the Lipschitz conditions. To further reduce the conservativeness, a nonlinear injection term is added to the observer dynamics. Simulation examples show the effectiveness of the proposed method compared with the existing techniques reported in well-established journals.
Rocznik
Strony
711--723
Opis fizyczny
Bibliogr. 27 poz., rys., wykr.
Twórcy
autor
  • Department of Electrical Engineering, Iran University of Science and Technology, Narmak, Farjam St., Tehran 16846, Iran
autor
  • Department of Electrical Engineering, Iran University of Science and Technology, Narmak, Farjam St., Tehran 16846, Iran
Bibliografia
  • [1] Abdelmalek, I., Golea, N. and Hadjili, M.L. (2007). A new fuzzy Lyapunov approach to non-quadratic stabilization of Takagi–Sugeno fuzzy models, International Journal of Applied Mathematics and Computer Science 17(1): 39–51, DOI: 10.2478/v10006-007-0005-4.
  • [2] Açikmese, A.B. and Corless, M. (2011). Observers for systems with nonlinearities satisfying incremental quadratic constraints, Automatica 47(7): 1339–1348.
  • [3] Asemani, M.H. and Majd, V.J. (2013). A robust observer-based controller design for uncertain T–S fuzzy systems with unknown premise variables via LMI, Fuzzy Sets and Systems 212: 21–40.
  • [4] Bernal, M. and Hušek, P. (2005). Non-quadratic performance design for Takagi–Sugeno fuzzy systems, International Journal of Applied Mathematics and Computer Science 15(3): 383–391.
  • [5] Boyd, S., Ghaoui, L.E., Feron, E. and Balakrishnan, V. (1994). Linear Matrix Inequalities in System and Control Theory, SIAM Studies in Applied Mathematics, Philadelphia, PA.
  • [6] Chadli, M. and Guerra, T.M. (2012). LMI solution for robust static output feedback control of discrete Takagi–Sugeno fuzzy models, IEEE Transactions on Fuzzy Systems 20(6): 1160–1165.
  • [7] Dong, J., Wang, Y. and Yang, G.H. (2011). H-infinity and mixed H2/H-infinity control of discrete-time T–S fuzzy systems with local nonlinear models,, Fuzzy Sets and Systems 164(1): 1–24.
  • [8] Dong, J., Wang, Y. and Yang, G.H. (2010). Output feedback fuzzy controller design with local nonlinear feedback laws for discrete-time nonlinear systems, IEEE Transactions on Systems, Man and Cybernetics, B: Cybernetics 40(6): 1447–1459.
  • [9] Faria, F.A., Silva, G.N. and Oliveira, V.A. (2012). Reducing the conservatism of LMI-based stabilisation conditions for T–S fuzzy systems using fuzzy Lyapunov functions, International Journal of Systems Science 44(10): 1956–1969, DOI: 10.1080/00207721.2012.670307.
  • [10] Guerra, T.M. and Bernal, M. (2012). Strategies to exploit non-quadratic local stability analysis, International Journal of Fuzzy Systems 14(3): 372–379.
  • [11] Guerra, T.M., Bernal, M., Guelton, K. and Labiod, S. (2012). Non-quadratic local stabilization for continuous-time Takagi–Sugeno models, Fuzzy Sets and Systems 201(16): 40–54.
  • [12] Guerra, T.M., Kruszewski, A. and Lauber, J. (2009). Discrete Tagaki–Sugeno models for control: Where are we?, Annual Reviews in Control 33(1): 37–47.
  • [13] Ichalal, D., Marx, B., Ragot, J. and Maquin, D. (2012). New fault tolerant control strategies for nonlinear Takagi–Sugeno systems, International Journal of Applied Mathematics and Computer Science 22(1): 197–210, DOI: 10.2478/v10006-012-0015-8.
  • [14] Karagiannis, D., Jiang, Z., Ortega, R. and Astolfi, A. (2005). Output-feedback stabilization of a class of uncertain non-minimum phase nonlinear systems, Automatica 41(9): 1609–1615.
  • [15] Löfberg, J. (2004). Yalmip: A toolbox for modeling and optimization in MATLAB, IEEE International Symposium on Computer Aided Control Systems Design, Taipei, Taiwan, pp. 284–289.
  • [16] Lee, C. (2004). Stabilization of nonlinear non-minimum phase system: Adaptive parallel approach using recurrent fuzzy neural network, IEEE Transactions on Systems, Man and Cybernetics, Part B 34(2): 1075–1088.
  • [17] Manai, Y. and Benrejeb, M. (2011). New condition of stabilization for continuous Takagi–Sugeno fuzzy system based on fuzzy Lyapunov function, International Journal of Control and Automation 4(3): 61–64.
  • [18] Mozelli, L.A., Palhares, R.M. and Avellar, G.S.C. (2009). A systematic approach to improve multiple Lyapunov function stability and stabilization conditions for fuzzy systems, Information Sciences 179(8): 1149–1162.
  • [19] Rajesh, R. and Kaimal, M.R. (2007). T–S fuzzy model with nonlinear consequence and PDC controller for a class of nonlinear control systems, Applied Soft Computing 7(3): 772–782.
  • [20] Rhee, B.J. and Won, S. (2006). A new fuzzy Lyapunov function approach for a Takagi–Sugeno fuzzy control system design, Fuzzy Sets and Systems 157(9): 1211–1228.
  • [21] Sala, A. (2009). On the conservativeness of fuzzy and fuzzy-polynomial control of nonlinear systems, Annual Reviews in Control 33(1): 48–58.
  • [22] Sala, A. and Arino, C. (2009). Polynomial fuzzy models for nonlinear control, a Taylor series approach, IEEE Transactions on Fuzzy Systems 17(6): 1284–1295.
  • [23] Tanaka, K. and Wang, H.O. (2001). Fuzzy Control Systems Design and Analysis: A Linear Matrix Inequality Approach, John Wiley and Sons, Inc., New York, NY.
  • [24] Tseng, C.S., Chen, B.S. and Li, Y.F. (2009). Robust fuzzy observer-based fuzzy control design for nonlinear systems with persistent bounded disturbances: A novel decoupled approach, Fuzzy Sets and Systems 160(19): 2824–2843.
  • [25] Tuan, H.D., Apkarian, P., Narikiyo, T. and Yamamoto, Y. (2001). Parameterized linear matrix inequality techniques in fuzzy control system design, IEEE Transactions on Fuzzy Systems 9(2): 324–332.
  • [26] Xu, D., Jiang, B. and Shi, P. (2012). Nonlinear actuator fault estimation observer: An inverse system approach via a T–S fuzzy model, International Journal of Applied Mathematics and Computer Science 22(1): 183–196, DOI: 10.2478/v10006-012-0014-9.
  • [27] Yoneyama, J. (2009). H-infinity filtering for fuzzy systems with immeasurable premise variables: An uncertain system approach, Fuzzy Sets and Systems 160(12): 1738–1748.
Typ dokumentu
Bibliografia
Identyfikator YADDA
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