Identification of nonlinear systems by the new representation ARX-Laguerre decoupled multimodel

This paper proposes a new alternative in the multimodel approach by expanding each ARX sub-model on independent orthonormal Laguerre bases by filtering the process input and output using Laguerre orthonormal functions. The resulting multimodel, entitled ARX-Laguerre decoupled multimodel, ensures the parameter number reduction with a recursive and easy representation. However, such reduction is still constrained by an optimal choice of Laguerre pole characterizing each basis. To do so, we develop a pole optimization algorithm which constitutes an extension of that proposed by Tanguy et al. [17]. The ARX-Laguerre decoupled multimodel as well as the proposed pole optimization algorithm are illustrated and validated on a numerical simulation.

[1]  Leon O. Chua,et al.  Fading memory and the problem of approximating nonlinear operators with volterra series , 1985 .

[2]  Dimitar Filev.  Fuzzy modeling of complex systems , 1991, Int. J. Approx. Reason..

[3]  T. Johansen,et al.  Constructing NARMAX models using ARMAX models , 1993 .

[4]  G. Dumont,et al.  An optimum time scale for discrete Laguerre network , 1993, IEEE Trans. Autom. Control..

[5]  Tor Arne Johansen,et al.  Identification of non-linear system structure and parameters using regime decomposition , 1995, Autom..

[6]  D. Sbarbaro,et al.  Multiple local Laguerre models for modelling nonlinear dynamic systems of the Wiener class , 1997 .

[7]  Roderick Murray-Smith,et al.  Multiple Model Approaches to Modelling and Control , 1997 .

[8]  R. Malti.  Représentation de systèmes discrets sur la base des filtres orthogonaux : application à la modélisation de systèmes dynamiques multi-variables , 1999 .

[9]  José A. Romagnoli,et al.  Application of Wiener model predictive control (WMPC) to a pH neutralization experiment , 1999, IEEE Trans. Control. Syst. Technol..

[10]  Komi Gasso.  Identification des systèmes dynamiques non-linéaires : approche multi-modèle , 2000 .

[11]  Noël Tanguy,et al.  Online optimization of the time scale in adaptive Laguerre-based filters , 2000, IEEE Trans. Signal Process..

[12]  Sachin C. Patwardhan,et al.  MODELING AND PREDICTIVE CONTROL OF MIMO NONLINEAR SYSTEMS USING WIENER-LAGUERRE MODELS , 2004 .

[13]  Ricardo J. G. B. Campello,et al.  Optimal expansions of discrete-time Volterra models using Laguerre functions , 2003, Autom..

[14]  Gérard Favier,et al.  Laguerre-Volterra Filters Optimization Based on Laguerre Spectra , 2005, 2005 13th European Signal Processing Conference.

[15]  Rodolfo Orjuela.  Contribution à l'estimation d'état et au diagnostic des systèmes représentés par des multimodèles , 2008 .

[16]  Yongsheng Gao,et al.  Non-linear system identification of gear crack failure based on second order Volterra kernel , 2010, Int. J. Model. Identif. Control..

[17]  Mark Beale,et al.  Neural Network Toolbox™ User's Guide , 2015 .