Interval system identification for MIMO ARX models of minimal order

Set-membership errors-in-variables identification of MIMO linear systems

“…However, this approach may lead to overestimation of the degree of the denominators of some transfer functions G ij . On the contrary, by exploiting the approach described in Zaiser et al (2014a), the actual order of each single transfer function can be estimated.…”

“…Zaiser and co-workers focus on the problem of computing parameter bounds for MIMO state-space model (Zaiser et al (2014b)) and for MIMO ARX models (Zaiser et al (2014a)), by assuming that both the input and the output sequences are corrupted by additive noise (errorsin-variables) bounded in the ℓ ∞ norm, a problem only apparently close to the one considered in this work. In fact, the work in Zaiser et al (2014a) mainly focuses on the problem of estimating the order of the multivariable system to be identified; once the order has been estimated, standard interval analysis tools available in the literature are used to estimate the parameters. However, as usually done in the interval analysis-based algorithms, the correlation among different occurrences of the same uncertainty variable in the regressor are neglected, since each uncertainty variable is replaced by an independent interval.…”

“…In this work, a different framework is considered, since the noise affecting the input and the output sequences is assumed to be bounded, while it is not required, in general, to be a random variable. Only few works can be found in the literature addressing the identification of MIMO systems in the presence of bounded noise (Wang et al (2013); Pouliquen et al (2011); Zaiser et al (2014a)); all these works exploit interval analysis-based algorithms, where the (possible) correlation among different occurrences of the same uncertainty variable in the regressor are neglected; the approach presented in this paper overcomes this limitation. The proposed algorithm is the first attempt to extend the convex-relaxation based approach to set-membership identification, previously proposed by the authors for different classes of linear and nonlinear SISO systems, to the case of MIMO linear systems.…”