Non-linear system modelling based on NARX model expansion on Laguerre orthonormal bases
- Author(s): Imen Benabdelwahed 1 ; Abdelkader Mbarek 1 ; Kais Bouzrara 1 ; Tarek Garna 1
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View affiliations
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Affiliations:
1:
Research Laboratory of Automatic, Signal and Image Processing, National School of Engineers of Monastir , University of Monastir , Avenue Avicenne, Monastir 5019 , Tunisia
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Affiliations:
1:
Research Laboratory of Automatic, Signal and Image Processing, National School of Engineers of Monastir , University of Monastir , Avenue Avicenne, Monastir 5019 , Tunisia
- Source:
Volume 12, Issue 2,
April
2018,
p.
228 – 241
DOI: 10.1049/iet-spr.2017.0187 , Print ISSN 1751-9675, Online ISSN 1751-9683
This study proposes a new representation of discrete Non-linear AutoRegressive with eXogenous inputs (NARX) model by developing its coefficients associated to the input, the output, the crossed product, the exogenous product and the autoregressive product on five independent Laguerre orthonormal bases. The resulting model, entitled NARX-Laguerre, ensures a significant parameter number reduction with respect to the NARX model. However, this reduction is still subject to an optimal choice of the Laguerre poles defining the five Laguerre bases. Therefore, the authors propose to use the genetic algorithm to optimise the NARX-Laguerre poles, based on the minimisation of the normalised mean square error. The performances of the resulting NARX-Laguerre model and the proposed optimisation algorithm are validated by numerical simulations and tested on the benchmark Continuous Stirred Tank Reactor.
Inspec keywords: genetic algorithms; mean square error methods; minimisation; autoregressive processes; discrete time systems; poles and zeros; nonlinear systems
Other keywords: discrete nonlinear autoregressive with exogenous inputs model; normalised mean square error minimisation; crossed product; NARX model expansion; Laguerre orthonormal bases; benchmark continuous stirred tank reactor; numerical simulations; genetic algorithm; exogenous product; NARX-Laguerre poles; parameter number reduction; autoregressive product; nonlinear system modelling; nonlinear discrete time system; optimisation algorithm
Subjects: Control system analysis and synthesis methods; Optimisation techniques; Interpolation and function approximation (numerical analysis); Nonlinear control systems; Discrete control systems
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