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In this paper the problem of identifying a fuzzy model from noisy data is addressed. The piecewise-affine fuzzy model structure is used as non-linear prototype for a multi–input, single–output unknown system. The consequents of the fuzzy model are identified from noisy data which are collected from experiments on the real system. The identification procedure is formulated within the Frisch scheme, well established for linear systems, which is extended so that it applies to piecewise-affine, constrained models.

The problem of determining linear models from data corrupted by noise has been revisited by several authors in recent years. With reference to the Frisch scheme, this work presents some geometrical aspects regarding the sets of solutions obtained in the identification procedure. An analysis is made on how these sets vary as the amount of noise on the data varies; the existence of particular solutions for data linked by a number of linear relations greater than one, is also shown.

This paper addresses the identification of non-linear dynamic systems. A wide class of these systems can be described using non-linear time-invariant regression models, that can be approximated by means of piecewise affine prototypes with an arbitrary degree of accuracy. This work concerns the identification of piecewise affine model structure through input-output data acquired from a dynamic process. In order to show the effectiveness of the developed technique, the results obtained in the identification of both a simple simulated system and a real dynamic process are reported.

This paper addresses the identification of non-linear systems. A wide class of these systems can be described using non-linear time-invariant regression models, that can be approximated by means of piecewise affine prototypes with an arbitrary degree of accuracy. This work concerns the identification of piecewise affine model parameters through input-output data affected by additive noise. In order to show the effectiveness of the developed technique, the results obtained in the identification of both a simple simulated system and a real dynamic process are reported.

The structural identification of linear muitivariabie systems can be performed on the basis of the predicted percentage of reconstruction errors (PPCRE) associated to a sequence of increasing-complexity models. This paper extends some previous results describing the properties of the PPCRE for canonical models whose parameters are estimated by means of the eigenvector method.

Some classical schemes in algebraic system identification are first recalled and compared. It is shown that, in most cases, the solution is obtained thanks to additional assumptions which are not deducible from the available data. The identification problem for linear dynamic systems is then solved on the basis of the Frisch scheme, in order to obtain the whole set of models compatible with noisy input-output sequences. The main result here proposed concerns the unicity of the solution when the data are affected by additive white noise.

This paper presents an identification method for errors-in-variables systems with input-output measurements affected by white and mutually correlated noises. The procedure, based on a frequency-domain approach, allows to uniquely determine both the characteristics of the noises affecting the data and the transfer function of the process under investigation. A numerical example is reported in order to illustrate the suggested technique and to verify its numerical implementation.

A nonlinear dynamic process can be described as a composition of several local affine models selected according to the process operating conditions. Such a compound system requires the identification of the local models from data. This work addresses a method for the identification and the optimal selection of the local affine models from a sequence of noisy measurements acquired from the process. The developed technique is applied to the identification of a simulated model.