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LMI based fuzzy observer design for Takagi-Sugeno models containing vestigial nonlinear terms

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The paper deals with the problem of full order fuzzy observer design for the class of continuous-time nonlinear systems, represented by Takagi-Sugeno models containing vestigial nonlinear terms. On the basis of the Lyapunov stability criterion and the incremental quadratic inequalities, two design conditions for this kind of system model are outlined in the terms of linear matrix inequalities. A numerical example is given to illustrate the procedure and to validate the performances of the proposed approach.
Rocznik
Strony
39--52
Opis fizyczny
Bibliogr. 22 poz., wzory
Twórcy
autor
  • Technical University of Košice, Faculty of Electrical Engineering and Informatics, Department of Cybernetics and Artificial Intelligence, Letná 9, 042 00 Košice, Slovakia, dusan.krokavec@tuke.sk
autor
  • Technical University of Košice, Faculty of Electrical Engineering and Informatics, Department of Cybernetics and Artificial Intelligence, Letná 9, 042 00 Košice, Slovakia, anna.filasova@tuke.sk
Bibliografia
  • [1] M. Abbaszadeh and H. J. Marquez: Robust H∞ observer design for a class of nonlinear uncertain systems via convex optimization. Proc. of the American Control Conference, New York City, NY, USA, (2007), 1699-1704.
  • [2] A. B. Acikmese and M. Corless: Observers for systems with nonlinearities satisfying an incremental quadratic inequality. Proc. of the American Control Conference, Portland, OR, USA, (2005), 3622-3629.
  • [3] A. B. Acikmese and M. Corless: Observers for systems with nonlinearities satisfying incremental quadratic constraints. Automatica, 47(7), (2011), 1339-1348.
  • [4] M. Arcak and P. Kokotovic: Nonlinear observers. A circle criterion design and robustness analysis. Automatica, 37(12), (2001), 1923-1930.
  • [5] J. Dong, Y. Wang and G. Yang: Control synthesis of continuous-time T-S fuzzy systems with local nonlinear models. IEEE Trans. on Systems, Man, and Cybernetics, Part B: Cybernetics, 39(5), (2009), 1245-1258.
  • [6] J. Dong, Y. Wang and G. Yang: H∞ and mixed H2/H∞ control of discrete-time T-S fuzzy systems with local nonlinear models. Fuzzy Sets and Systems, 164(1), (2011), 1-24.
  • [7] X. Fan, N. Zhang and S. Teng: Trajectory planning and tracking of ball and plate system using hierarchical fuzzy control scheme. Fuzzy Sets and Systems, 144(2), (2004), 297-312.
  • [8] A. Filasová and D. Krokavec: State estimate based control design using the unified algebraic approach. Archives of Control Sciences, 20(1), (2010), 5-18.
  • [9] A. Filasová and D. Krokavec: Observer state feedback control of discretetime systems with state equality constraints. Archives of Control Sciences, 20(3), (2010), 253-266.
  • [10] A. Filasová and D. Krokavec: Partially decentralized design principle in large-scale system control. Recent Advances in Robust Control. Novel Approaches and Design Methods, A. Mueller (Ed.), InTech, Rijeca, Croatia, 2011, 361-388.
  • [11] Z. Gao, X. Shi, and S. X. Ding: Fuzzy state/disturbance observer design for T-S fuzzy systems with application to sensor fault estimation. IEEE Trans. on Systems, Man, and Cybernetics, Part B: Cybernetics, 38(3), (2008), 875-880.
  • [12] W. M. Haddad and V. Chellaboina: Nonlinear Dynamical Systems and Control.A Lyapunov-Based Approach. Princeton Univ. Press, Princeton, NJ, USA, 2008.
  • [13] A. L. Juloski, W. P. M. H. Heemels and S. Weiland: Observer design for a class of piecewise linear systems. Int. J. Robust Nonlinear Control, 17(15), (2007), 1387-1404.
  • [14] D. Krokavec and A. Filasová: Optimal fuzzy control for a class of nonlinear systems. Math. Problems in Engineering, 2012(1), 2012, 29p.
  • [15] D. Krokavec and A. Filasová: Fuzzy observers for Takagi-Sugeno models with local nonlinear terms. Proc. of the 2nd International Conference on Circuits, Systems, Communications, Computers and Applications CSCCA ’13, Dubrovnik, Croatia, (2013), 183-187.
  • [16] C. Lin, Q. G. Wang and T. H. Lee: Improvement on observer-based H∞ control for T-S fuzzy systems. Automatica, 41(9), (2005), 1651-1656.
  • [17] X. Liu and Q. Zhang: New approaches to H∞ controller design based on fuzzy observers for T-S fuzzy systems via LMI. Automatica, 39(9), (2003), 1571-1582.
  • [18] D. Peaucelle, D. Henrion, Y. Labit and K. Taitz: User’s Guide for SeDuMi Interface 1.04, LAAS-CNRS, Toulouse, 2002.
  • [19] A. Soukkou, S. Leulmi and H. Khellaf: Intelligent nonlinear optimal controller of a biotechnological process. Archives of Control Sciences, 19(2), (2009), 217-240.
  • [20] T. Takagi and M. Sugeno: Fuzzy identification of systems and its applications to modeling and control. IEEE Trans. on Systems, Man, and Cybernetics, 15(1), (1985), 116-132.
  • [21] K. Tanaka and H. O. Wang: Fuzzy Control Systems Design and Analysis. A Linear Matrix Inequality Approach, John Wiley & Sons, New York, NY, USA, 2001.
  • [22] F. E. Thau: Observing the state of nonlinear dynamical systems. Int. J. Control, 17(3), (1973), 471-479.
Uwagi
The work presented in this paper was supported by VEGA, the Grant Agency of the Ministry of Education and the Academy of Science of Slovak Republic, under Grant No. 1/0348/14. This support is very gratefully acknowledged.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-647ffe28-2870-4354-8954-8abcc2a8a3a9
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