PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
Tytuł artykułu

A numerical procedure for filtering and efficient high-order signal differentiation

Autorzy
Treść / Zawartość
Identyfikatory
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this paper, we propose a numerical algorithm for filtering and robust signal differentiation. The numerical procedure is based on the solution of a simplified linear optimization problem. A compromise between smoothing and fidelity with respect to the measurable data is achieved by the computation of an optimal regularization parameter that minimizes the Generalized Cross Validation criterion (GCV). Simulation results are given to highlight the effectiveness of the proposed procedure.
Rocznik
Strony
201--208
Opis fizyczny
Bibliogr. 30 poz., rys., wykr.
Twórcy
autor
  • Department of Automated Production, École de Technologie Supérieure, 1100, rue Notre Dame Ouest, Montreal, Québec, H3C 1K3 Canada
autor
  • Laboratoire des Signaux et Systèmes, CNRS, Supélec, 3 rue Juliot-Curie, 91190 Gif-sur-Yvette, France
Bibliografia
  • [1] Anderson R.S. and Bloomfield P. (1974): A time series approach to numerical differentiation. — Technom., Vol. 16, No. 1, pp. 69–75.
  • [2] Barmish B.R. and Leitmann G. (1982): On ultimate boundness control of uncertain systems in the absence of matching assumptions.—IEEE Trans. Automat. Contr., Vol. AC-27, No. 1, pp. 153–158.
  • [3] Chen Y. H. (1990): State estimation for non-linear uncertain systems: A design based on properties related to the uncertainty bound.—Int. J. Contr., Vol. 52, No. 5, pp. 1131–1146.
  • [4] Chen Y. H. and Leitmann G. (1987): Robustness of uncertain systems in the absence of matching assumptions. — Int. J. Contr., Vol. 45, No. 5, pp. 1527–1542.
  • [5] Ciccarella G., Mora M.D. and Germani A. (1993): A Luenberger-like observer for nonlinear systems. — Int. J. Contr., Vol. 57, No. 3, pp. 537–556.
  • [6] Craven P. and Wahba G. (1979): Smoothing noisy data with spline functions: Estimation the correct degree of smoothing by the method of generalized cross-validation. — Numer. Math., Vol. 31, No.4, pp. 377–403.
  • [7] Dawson D.M., Qu Z. and Caroll J.C. (1992): On the state observation and output feedback problems for nonlinear uncertain dynamic systems. — Syst. Contr. Lett., Vol. 18, No.3, pp. 217–222.
  • [8] De Boor C., (1978): A Practical Guide to Splines.—New York: Springer.
  • [9] Diop S., Grizzle J.W., Morral P.E. and Stefanoupoulou A.G. (1993): Interpolation and numerical differentiation for observer design. — Proc. Amer. Contr. Conf., Evanston, IL, pp. 1329–1333.
  • [10] Eubank R.L. (1988): Spline Smoothing and Nonparametric Regression. — New York: Marcel Dekker.
  • [11] Gasser T., Müller H.G. and Mammitzsch V. (1985): Kernels for nonparametric curve estimation. — J. Roy. Statist. Soc., Vol. B47, pp. 238–252.
  • [12] Gauthier J.P., Hammouri H. and Othman S. (1992): A simple observer for nonlinear systems: Application to bioreactors. — IEEE Trans. Automat. Contr., Vol. 37, No. 6, pp. 875–880.
  • [13] Georgiev A.A. (1984): Kernel estimates of functions and their derivatives with applications.—Statist. Prob. Lett., Vol. 2, pp. 45–50.
  • [14] Härdle W. (1984): Robust regression function estimation. — Multivar. Anal., Vol. 14, pp. 169–180.
  • [15] Härdle W. (1985): On robust kernel estimation of derivatives of regression functions.—Scand. J. Statist., Vol. 12, pp. 233–240.
  • [16] Ibrir S. (1999): Numerical algorithm for filtering and state observation. — Int. J. Appl. Math. Comp. Sci., Vol. 9, No.4, pp. 855–869.
  • [17] Ibrir S. (2000): Méthodes numriques pour la commande et l’observation des systèmes non linéaires. — Ph.D. thesis, Laboratoire des Signaux et Systèmes, Univ. Paris-Sud.
  • [18] Ibrir S. (2001): New differentiators for control and observation applications. — Proc. Amer. Contr. Conf., Arlington, pp. 2522–2527.
  • [19] Ibrir S. (2003): Algebraic riccati equation based differentiation trackers. — AIAA J. Guid. Contr. Dynam., Vol. 26, No. 3, pp. 502–505.
  • [20] Kalman R.E. (1960): A new approach to linear filtering and prediction problems. — Trans. ASME J. Basic Eng., Vol. 82, No. D, pp. 35–45.
  • [21] Leitmann G. (1981): On the efficacy of nonlinear control in uncertain linear systems. — J. Dynam. Syst. Meas. Contr., Vol. 102, No.2, pp. 95–102.
  • [22] Luenberger D.G. (1971): An introduction to observers.—IEEE Trans. Automat. Contr., Vol. 16, No.6, pp. 596–602.
  • [23] Misawa E.A. and Hedrick J.K. (1989): Nonlinear observers. A state of the art survey. — J. Dyn. Syst. Meas. Contr., Vol.111, No.3, pp. 344–351.
  • [24] Müller H.G. (1984): Smooth optimum kernel estimators of densities, regression curves and modes.—Ann. Statist., Vol. 12, pp. 766–774.
  • [25] Rajamani R. (1998): Observers for Lipschitz nonlinear systems. — IEEE Trans. Automat. Contr., Vol. 43, No. 3, pp. 397–400.
  • [26] Reinsch C.H. (1967): Smoothing by spline functions.—Numer. Math., Vol. 10, pp. 177–183.
  • [27] Reinsch C.H. (1971): Smoothing by spline functions ii. — Numer. Math., Vol. 16, No.5, pp. 451–454.
  • [28] Slotine J.J.E., Hedrick J.K. and Misawa E.A. (1987): On sliding observers for nonlinear systems.—J. Dynam. Syst. Meas. Contr., Vol. 109, No.3, pp. 245–252.
  • [29] Tornambè A. (1992): High-gain observers for nonlinear systems.— Int. J. Syst. Sci., Vol. 23, No.9, pp. 1475–1489.
  • [30] Xia X.-H. and Gao W.-B. (1989): Nonlinear observer design by observer error linearization.—SIAM J. Contr. Optim., Vol. 27, No. 1, pp. 199–216.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BPZ1-0007-0021
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.