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2004 | 14 | 2 | 201-208

Tytuł artykułu

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

Treść / Zawartość

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

Tom

14

Numer

2

Strony

201-208

Opis fizyczny

Daty

wydano
2004
otrzymano
2004-01-26
poprawiono
2004-05-28

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

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  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • De Boor C., (1978): A Practical Guide to Splines. - New York: Springer.
  • 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.
  • Eubank R.L. (1988): Spline Smoothing and Nonparametric Regression. -New York: Marcel Dekker.
  • Gasser T., Muller H.G. and Mammitzsch V. (1985): Kernels for nonparametric curve estimation. - J. Roy. Statist. Soc., Vol. B47, pp. 238-252.
  • 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.
  • Georgiev A.A. (1984): Kernel estimates of functions and their derivatives with applications. - Statist. Prob. Lett., Vol. 2, pp. 45-50.
  • Hardle W. (1984): Robust regression function estimation. - Multivar.Anal., Vol. 14, pp. 169-180.
  • Hardle W. (1985): On robust kernel estimation of derivatives of regression functions. -Scand. J. Statist., Vol. 12, pp. 233-240.
  • Ibrir S. (1999): Numerical algorithm for filtering and state observation. -Int. J. Appl. Math. Comp. Sci., Vol. 9, No.4, pp. 855-869.
  • Ibrir S. (2000): Methodes numriques pour la commande et l'observation des systèmes non lineaires. - Ph.D. thesis, Laboratoire des Signaux et Systèmes, Univ. Paris-Sud.
  • Ibrir S. (2001): New differentiators for control and observation applications. -Proc. Amer. Contr. Conf., Arlington, pp. 2522-2527.
  • Ibrir S. (2003): Algebraic riccati equation based differentiation trackers. -AIAA J. Guid. Contr. Dynam., Vol. 26, No. 3, pp. 502-505.
  • 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.
  • 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.
  • Luenberger D.G. (1971): An introduction to observers. - IEEE Trans.Automat. Contr., Vol. 16, No.6, pp. 596-602.
  • 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.
  • Muller H.G. (1984): Smooth optimum kernel estimators of densities, regression curves and modes. - Ann. Statist., Vol. 12, pp. 766-774.
  • Rajamani R. (1998): Observers for Lipschitz nonlinear systems. - IEEE Trans. Automat. Contr., Vol. 43, No. 3, pp. 397-400.
  • Reinsch C.H. (1967): Smoothing by spline functions. - Numer.Math., Vol. 10, pp. 177-183.
  • Reinsch C.H. (1971): Smoothing by spline functions ii. - Numer. Math., Vol. 16, No.5, pp. 451-454.
  • 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.
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Typ dokumentu

Bibliografia

Identyfikatory

Identyfikator YADDA

bwmeta1.element.bwnjournal-article-amcv14i2p201bwm
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