Title: Order reduction of MIMO ARX systems using Laguerre bases

Authors: Ameni El Anes; Saber Maraoui; Kais Bouzrara

Addresses: Laboratory of Automatic, Signal and Image Processing, National School of Engineers of Monastir, University of Monastir, 5019, Tunisia ' Laboratory of Automatic, Signal and Image Processing, Higher Institute of Informatics and Multimedia of Gabes, University of Gabes, 6033, Tunisia ' Laboratory of Automatic, Signal and Image Processing, National School of Engineers of Monastir, University of Monastir, 5019, Tunisia

Abstract: In this article, we explore the use of the Laguerre functions for the estimation of multivariable autoregressive with exogenous (ARX) input model. Each polynomial function of the MIMO ARX model associated to the inputs and to the outputs is expanded on independent Laguerre orthonormal bases. The resulting model is entitled MIMO ARX-Laguerre model. The optimal approximation of which is ensured once the poles characterising each Laguerre orthonormal basis are set to their optimal values. In this paper, a minimal recursive representation realisations for MIMO discrete-time linear systems are derived using Laguerre functions. Further we propose, from input/output measurements, an iterative optimisation algorithm for the free parameters (Laguerre poles). Simulation results show the effectiveness of the proposed optimal modelling method.

Keywords: parameter reduction; MIMO coupled systems; Laguerre functions; pole optimisation; order reduction; ARX input models; polynomial functions; discrete-time linear systems; simulation; modelling.

DOI: 10.1504/IJESMS.2016.079429

International Journal of Engineering Systems Modelling and Simulation, 2016 Vol.8 No.4, pp.307 - 315

Received: 21 Aug 2015
Accepted: 26 Jan 2016

Published online: 17 Sep 2016 *

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