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In this paper, we propose a technique to reduce the complexity of an existing (initial) model via the Laguerre filters. We present an analytical method for the parameter identification of the Fourier coefficients of the Laguerre model. This technique is based on the bilinear discrete transformation and in which the Fourier coefficients are expressed in recurrent form in terms of the Laguerre pole. This latter is estimated by an iterative technique, based on the Newton algorithm. This identification technique is after extended to the case of the ARX-Laguerre model and the MISO-ARX-Laguerre model and its performances are illustrated by numerical simulations. [ABSTRACT FROM AUTHOR]

In this article, the Meixner-like model is used to represent the linear discrete-time system in comparison with the Laguerre model. Furthermore, we propose from input/output measurements a new recursive representation of the Meixner-like model. However, a significant approximation of this model is subject to an optimal choice of Meixner-like parameters: pole, order of generalization and Fourier coefficients. The present research yields a series of computational experiments, through a simulation example of a linear parameter varying (LPV) system. This study tests this approach, verifies the theoretical results and points out the positive outcomes of using the Meixner-like model in comparison with the Laguerre model. [ABSTRACT FROM AUTHOR]

The ARX-Laguerre model is a very important reduced complexity representation of linear system. However a significant reduction of this model is subject to an optimal choice of both Laguerre poles. Therefore we propose in this paper two new methods to estimate, from input/output measurements, the optimal values of Laguerre poles of the ARX-Laguerre model. The first method is based on the Newton-Raphson's iterative technique where we prove that the gradient and the Hessian can be expressed analytically. The second method is based on Genetic Algorithms. Both proposed algorithms are tested on a numerical example and on a heating benchmark. [ABSTRACT FROM AUTHOR]

In this article, an optimal linear MIMO system approximation by using discrete-time MIMO autoregressive with exogenous input (ARX) model is proposed. Each polynomial function of the MIMO ARX model associated with the inputs and with the outputs is expanded on independent Laguerre orthonormal basis. The resulting model is entitled MIMO ARX-Laguerre model. The optimal approximation of which is ensured once the poles characterizing each Laguerre orthonormal basis are set to their optimal values. In this paper, a new method to estimate, from input/output measurements, the optimal Laguerre poles of the MIMO ARX-Laguerre model is proposed. The method consists in applying the Newton-Raphson's iterative technique in which the gradient and the Hessian are expressed analytically. The proposed algorithm is tested on a numerical example and on a benchmark system. Simulation results show the effectiveness of the proposed optimal modeling method. Copyright © 2015 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper proposes a new representation of discrete bilinear model by developing its coefficients associated to the input, to the output and to the crossed product on three independent Laguerre orthonormal bases. Compared to classical bilinear model, the resulting model entitled bilinear-Laguerre model ensures a significant parameter number reduction as well as simple recursive representation. However, this reduction is still subject to an optimal choice of the Laguerre poles defining the three Laguerre bases. Therefore, we propose an analytical solution to optimise the Laguerre poles which depend on Fourier coefficients defining the bilinear-Laguerre model, and that are identified using the regularised square error. The identification procedures of the Laguerre poles and Fourier coefficients are combined and carried out on a sliding window to provide an online identification algorithm of the bilinear-Laguerre model. The bilinear-Laguerre model as well as the proposed algorithm are illustrated and tested on a numerical simulation and validated on the continuous stirred tank reactor system. [ABSTRACT FROM PUBLISHER]

This article proposes a new representation of the ARX models on independent and orthonormal Laguerre bases by filtering the process input and output using Laguerre orthonormal functions. The resulting model, entitled ARX–Laguerre model, ensures the parameter number reduction with a recursive and easy representation. However, this reduction is still subject to an optimal choice of the Laguerre poles defining both Laguerre bases. Therefore, we propose an analytical solution to optimise the Laguerre poles which depend on Fourier coefficients defining the ARX–Laguerre model, and that are identified using the regularised square error. The identification procedures of the Laguerre poles and Fourier coefficients are combined and carried out on a sliding window to provide an online identification algorithm of the ARX–Laguerre model. The proposed algorithm is tested on numerical simulation and validated on a benchmark system manufactured by Feedback known as Process Trainer PT326. [ABSTRACT FROM PUBLISHER]

Abstract: In this paper, we propose a new reduced complexity model by expanding a discrete-time ARX model on Laguerre orthonormal bases. To ensure an efficient complexity reduction, the coefficients associated to the input and the output of the ARX model are expanded on independent Laguerre bases, to develop a new black-box linear ARX-Laguerre model with filters on model input and output. The parametric complexity reduction with respect to the classical ARX model is proved theoretically. The structure and parameter identification of the ARX-Laguerre model is achieved by a new proposed approach which consists in solving an optimization problem built from the ARX model without using system input/output observations. The performances of the resulting ARX-Laguerre model and the proposed identification approach are illustrated by numerical simulations and validated on benchmark manufactured by Feedback known as Process Trainer PT326. A possible extension of the proposed model to a multivariable process is formulated. [Copyright &y& Elsevier]