16 Mars – Thesis defense - Abir Mayoufi

09 h Institut Supérieur des Sciences Appliquées et Technologies (Tunisie)

Identification of MISO fractional systems : Application to terrestrial climate modelling.

This thesis concerns the  experiment design and the identification of non-fractional multi-input-single-output systems (MISO) from a transfer function representation. Concerning the  experiment design, a study has been carried out  to adapt the excitation signal to the studied system in order to estimate its parameters, one or two parameters of a second kind transfer function, with the best possible accuracy. Concerning the identification of MISO systems, two methods have been mainly developed. One is based on the optimal instrumental variable, which initially allows to estimate only the coefficients, and which has been extended for the estimation of the derivation orders, by integrating the instrumental variable with a nonlinear programming technique. The other method is based on the minimization of the output error which offers the advantage of estimating the coefficients and the derivation orders simultaneously, namely the MISO-oosrivcf and the MISO-oe. A notion of S-commensurability (structured commensurability) has been introduced to limit the number of parameters to be estimated of a multi-input-single-output (MISO) system, thus improving the convergence of identification methods. When the derivation orders are unknown, three variants have been proposed: either a global S-commensurable order is estimated for the whole fractional multi-input-single-output (MISO) system, or local S-commensurable orders are estimated for each subsystem, or all derivation orders are estimated without the S-commensurability constraint. An initialization procedure is proposed, consisting in estimating first a global S-commensurable model, then the local S-commensurable orders, and finally all the derivation orders. Finally, an application to the identification of the Earth's climate system is proposed to predict future temperature evolutions at the end of the thesis.

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