New consistent methods for order and coefficient estimation of continuous-time errors-in-variables fractional models

The errors-in-variables identification problem concerns dynamic systems in which input and output signals are contaminated by an additive noise. Several estimation methods have been proposed for identifying dynamic errors-in-variables rational models. This paper presents new consistent methods for order and coefficient estimation of continuous-time systems by errors-in-variables fractional models. First, differentiation orders are assumed to be known and only differential equation coefficients are estimated. Two estimators based on Higher-Order Statistics (third-order cumulants) are developed: the fractional third-order based least squares algorithm (ftocls) and the fractional third-order based iterative least squares algorithm (ftocils). Then, they are extended, using a nonlinear optimization algorithm, to estimate both the differential equation coefficients and the commensurate order. The performances of the proposed algorithms are illustrated with a numerical example.

[1]  Patrick Lanusse,et al.  CRONE Control-System Design Toolbox for the Control Engineering Community , 2013 .

[2]  Torsten Söderström,et al.  A generalized instrumental variable estimation method for errors-in-variables identification problems , 2011, Autom..

[3]  Mohamed Naceur Abdelkrim,et al.  Guaranteed frequency-domain identification of fractional order systems: application to a real system , 2012, Int. J. Model. Identif. Control..

[4]  Xavier Moreau,et al.  Robust estimation of fractional models in the frequency domain using set membership methods , 2012, Signal Process..

[5]  T. Poinot,et al.  Identification of Fractional Systems Using an Output-Error Technique , 2004 .

[6]  M Amairi,et al.  Guaranteed output-error identičation of fractional order model , 2010, 2010 2nd International Conference on Advanced Computer Control.

[7]  Xavier Moreau,et al.  Stability and resonance conditions of elementary fractional transfer functions , 2011, Autom..

[8]  Kaushik Mahata,et al.  An improved bias-compensation approach for errors-in-variables model identification , 2007, Autom..

[9]  D. Brillinger.  Time series - data analysis and theory , 1981, Classics in applied mathematics.

[10]  J. Lacoume,et al.  Statistiques d'ordre supérieur pour le traitement du signal , 1997 .

[11]  R. Malti,et al.  Subspace method for continuous-time fractional system identification , 2009 .

[12]  Alain Oustaloup,et al.  Analytical computation of the H2-norm of fractional commensurate transfer functions , 2011, Autom..

[13]  Marion Gilson,et al.  Survey of Analytical IV Estimates for Errors-In-Variables Model Identification , 2011 .

[14]  Peter Young,et al.  Parameter estimation for continuous-time models - A survey , 1979, Autom..

[15]  Olivier Cois,et al.  Systèmes linéaires non entiers et identification par modèle non entier : application en thermique , 2002 .

[16]  Thierry Poinot,et al.  Fractional modelling and identification of thermal systems , 2011, Signal Process..

[17]  K. B. Oldham,et al.  The Fractional Calculus: Theory and Applications of Differentiation and Integration to Arbitrary Order , 1974 .

[18]  Hugues Garnier,et al.  Third-order cumulants based methods for continuous-time errors-in-variables model identification , 2008, Autom..

[19]  Jerry M. Mendel,et al.  Tutorial on higher-order statistics (spectra) in signal processing and system theory: theoretical results and some applications , 1991, Proc. IEEE.

[20]  Patrick Lanusse,et al.  CRONE control system design toolbox for the control engineering community: tutorial and case study , 2013, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[21]  Alain Oustaloup,et al.  Fractional system identification for lead acid battery state of charge estimation , 2006, Signal Process..

[22]  Stéphane Thil,et al.  Contributions à l’identification de modèles avec des erreurs en les variables , 2007 .

[23]  Umberto Soverini,et al.  Maximum likelihood identification of noisy input-output models , 2007, Autom..

[24]  Hugues Garnier,et al.  Continuous-time model identification from noisy input/output measurements using fourth-order cumulants , 2007, 2007 46th IEEE Conference on Decision and Control.

[25]  Hugues Garnier,et al.  Parameter and differentiation order estimation in fractional models , 2013, Autom..

[26]  Lennart Ljung,et al.  System Identification: Theory for the User , 1987 .

[27]  Hugues Garnier,et al.  Identification of continuous-time errors-in-variables models , 2006, Autom..

[28]  T. Raïssi,et al.  Set membership parameter estimation of fractional models based on bounded frequency domain data , 2010 .

[29]  Jitendra Tugnait.  Stochastic system identification with noisy input using cumulant statistics , 1992 .

[30]  David R. Brillinger,et al.  Time Series , 2018, Randomization, Bootstrap and Monte Carlo Methods in Biology.

[31]  R. Malti,et al.  Differentiation similarities in fractional pseudo-state space representations and the subspace-based methods , 2012 .

[32]  Mohamed Naceur Abdelkrim,et al.  EIV methods for system identification with fractional models , 2012 .

[33]  M. N. Abdelkrim,et al.  Third-order cumulants based method for continuous-time Errors-In-Variables system identification by fractional models , 2011, Eighth International Multi-Conference on Systems, Signals & Devices.

[34]  Alain Oustaloup,et al.  Object-oriented CRONE toolbox for fractional differential signal processing , 2012, Signal Image Video Process..