Title: Convergence analysis of the alternating RELS algorithm for the identification of the reduced complexity Volterra model

Authors: Imen Laamiri; Anis Khouaja; Hassani Messaoud

Addresses: Laboratory of Automatic, Signal and Image Processing (LARATSI), National Engineering School of Monastir (ENIM), Monastir University, Avenue Ibn Al Jazzar, Monastir, 5019, Tunisia ' Electrical Engineering Department, High Institute of Applied Science and Technology (ISSAT), Sousse University, Avenue Ibn Khaldoun, Sousse 4003, Tunisia ' Laboratory of Automatic, Signal and Image Processing (LARATSI), National Engineering School of Monastir (ENIM), Monastir University, Avenue Ibn Al Jazzar, Monastir, 5019, Tunisia

Abstract: In this paper, we provide a sufficient convergence condition of the alternating recursive extended least squares (RELS) algorithm proposed for the identification of the reduced complexity Volterra model describing stochastic nonlinear systems. The reduced Volterra model used is the third order PARAFC-Volterra model provided using the parallel factor (PARAFAC) tensor decomposition of the Volterra kernels of order higher than two of the classical Volterra model. The recursive stochastic algorithm alternating recursive extended least squares (ARELS) consists of the execution in an alternating way of the classical RELS algorithm developed to identify the linear stochastic input-output models. The ARELS convergence was proved using the ordinary differential equation (ODE) method. It is noted that the ARELS algorithm convergence cannot be ensured when the disturbance acting on the system to be identified has specific features. The ARELS algorithm is tested using Monte Carlo simulation under the determined sufficient convergence condition. To raise the supremacy of the ARELS algorithm compared to the classical ARLS algorithm, we compare their performance on a nonlinear satellite channel and a benchmark system continuous stirred tank reactor (CSTR). Moreover, the efficiency of the proposed identification approach is proven on an experimental coupled tanks system (CTS).

Keywords: convergence analysis; ordinary differential equations; ODEs; parallel factor; PARAFAC; recursive extended least squares; RELS; stochastic systems; Volterra model; complexity reduction; model identification; nonlinear systems; Monte Carlo simulation; satellite channels; continuous stirred tank reactors; CSTR; coupled tank system.

DOI: 10.1504/IJMIC.2015.072983

International Journal of Modelling, Identification and Control, 2015 Vol.24 No.4, pp.300 - 318

Received: 08 Apr 2014
Accepted: 27 Mar 2015
Published online: 11 Nov 2015 *

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