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2016 | 26 | 3 | 543-553
Tytuł artykułu

Recursive set membership estimation for output-error fractional models with unknown-but-bounded errors

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
This paper presents a new formulation for set-membership parameter estimation of fractional systems. In such a context, the error between the measured data and the output model is supposed to be unknown but bounded with a priori known bounds. The bounded error is specified over measurement noise, rather than over an equation error, which is mainly motivated by experimental considerations. The proposed approach is based on the optimal bounding ellipsoid algorithm for linear output-error fractional models. A numerical example is presented to show effectiveness and discuss results.
Rocznik
Tom
26
Numer
3
Strony
543-553
Opis fizyczny
Daty
wydano
2016
otrzymano
2015-07-15
poprawiono
2015-12-08
zaakceptowano
2016-03-07
Twórcy
  • Research Laboratory of Modeling, Analysis and Control of Systems, National Engineering School of Gabes (ENIG), University of Gabes, Omar Ibn el Khattab St., 6029 Gabes, Tunisia
Bibliografia
  • Amairi, M. (2015). Recursive set-membership parameter estimation using fractional model, Circuits, Systems, and Signal Processing 34(12): 3757-3788.
  • Amairi, M., Aoun, M., Najar, S. and Abdelkrim, M.N. (2012). Guaranteed frequency-domain identification of fractional order systems: Application to a real system, International Journal of Modelling, Identification and Control 17(1): 32-42.
  • Amairi, M., Najar, S., Aoun, M. and Abdelkrim, M. (2010). Guaranteed output-error identification of fractional order model, 2nd IEEE International Conference on Advanced Computer Control (ICACC), Shenyang, China, pp. 246-250.
  • Busłowicz, M. and Ruszewski, A. (2015). Robust stability check of fractional discrete-time linear systems with interval uncertainties, in K.J. Latawiec et al. (Eds.), Advances in Modelling and Control of Non-Integer-Order Systems, Springer, Berlin/Heidelberg, pp. 199-208.
  • Clement, T. and Gentil, S. (1988). Reformulation of parameter identification with unknown-but-bounded errors, Mathematics and Computers in Simulation 30(3): 257-270.
  • Ferreres, G. and M'Saad, M. (1997). Estimation of output error models in the presence of unknown but bounded disturbances, International Journal of Adaptive Control and Signal Processing 11(2): 115-140.
  • Fogel, E. and Huang, Y. (1982). On the value of information in system identification-bounded noise case, Automatica 18(2): 229-238.
  • Machado, J.T., Kiryakova, V. and Mainardi, F. (2011). Recent history of fractional calculus, Communications in Nonlinear Science and Numerical Simulation 16(3): 1140-1153.
  • Malti, R., Ra¨ıssi, T., Thomassin, M. and Khemane, F. (2010). Set membership parameter estimation of fractional models based on bounded frequency domain data, Communications in Nonlinear Science and Numerical Simulation 15(4): 927-938.
  • Matignon, D. (1996). Stability results for fractional differential equations with applications to control processing, Computational Engineering in Systems Applications, Lille, France, Vol. 2, pp. 963-968.
  • Milanese, M., Norton, J., Piet-Lahanier, H. and Walter, E. (1996). Bounding Approaches to System Identification, Plenum Press, London.
  • Narang, A., Shah, S. and Chen, T. (2011). Continuous-time model identification of fractional-order models with time delays, Control Theory & Applications 5(7): 900-912.
  • Ostalczyk, P. (2012). Equivalent descriptions of a discrete-time fractional-order linear system and its stability domains, International Journal of Applied Mathematics and Computer Science 22(3): 533-538, DOI: 10.2478/v10006-012-0040-7.
  • Polyak, B.T., Nazin, S.A., Durieu, C. and Walter, E. (2004). Ellipsoidal parameter or state estimation under model uncertainty, Automatica 40(7): 1171-1179.
  • Raissi, T., Ramdani, N. and Candau, Y. (2004). Set membership state and parameter estimation for systems described by nonlinear differential equations, Automatica 40(10): 1771-1777.
  • Samko, S., Kilbas, A. and Marichev, O. (1993). Fractional Integrals and Derivatives: Theory and Applications. Gordon and Breach, New York, NY.
  • Victor, S., Malti, R., Garnier, H., Oustaloup, A. (2013). Parameter and differentiation order estimation in fractional models, Automatica 49(4): 926-935.
  • Yakoub, Z., Chetoui, M., Amairi, M. and Aoun, M. (2015). A bias correction method for fractional closed-loop system identification, Journal of Process Control 33: 25-36.
Typ dokumentu
Bibliografia
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bwmeta1.element.bwnjournal-article-amcv26i3p543bwm
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