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2013 | 23 | 4 | 711-723
Tytuł artykułu

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

Treść / Zawartość
Warianty tytułu
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 modeling 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
Tom
23
Numer
4
Strony
711-723
Opis fizyczny
Daty
wydano
2013
otrzymano
2012-11-23
poprawiono
2013-04-16
poprawiono
2013-08-18
Twórcy
autor
  • Department of Electrical Engineering, Iran University of Science and Technology, Narmak, Farjam St., Tehran 16846, Iran
  • Department of Electrical Engineering, Iran University of Science and Technology, Narmak, Farjam St., Tehran 16846, Iran
Bibliografia
  • 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.
  • Açikmese, A.B. and Corless, M. (2011). Observers for systems with nonlinearities satisfying incremental quadratic constraints, Automatica 47(7): 1339-1348.
  • 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.
  • 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.
  • 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.
  • 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.
  • Dong, J., Wang, Y. and Yang, G.H. (2011). $H_∞$ and mixed H₂/$H_∞$ control of discrete-time T-S fuzzy systems with local nonlinear models,, Fuzzy Sets and Systems 164(1): 1-24.
  • 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.
  • 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.
  • Guerra, T.M. and Bernal, M. (2012). Strategies to exploit non-quadratic local stability analysis, International Journal of Fuzzy Systems 14(3): 372-379.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • Sala, A. (2009). On the conservativeness of fuzzy and fuzzy-polynomial control of nonlinear systems, Annual Reviews in Control 33(1): 48-58.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • Yoneyama, J. (2009). $H_∞$ filtering for fuzzy systems with immeasurable premise variables: An uncertain system approach, Fuzzy Sets and Systems 160(12): 1738-1748.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-amcv23z4p711bwm
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