Abstract
Presently, a modelling and identification of nonlinear systems is proposed. This study is developed based on spectral approach. The proposed nonlinear system is nonparametric and can be described by Hammerstein models. These systems consist of nonlinear element followed by a linear block. This latter (the linear subsystem) is not necessarily parametric and the nonlinear function can be nonparametric smooth nonlinearity. This identification problem of Hammerstein models is studied in the presence of possibly infinite-order linear dynamics. The determination of linear and nonlinear block can be done using a unique stage.
Highlights
The Hammerstein model is a series connection of a nonlinear function and a linear dynamical element (Fig. 1)
It is interesting to emphasize that, all the internal signals (x(t), w(t), and ξ(t)) are not accessible to measurement. In view of these difficulties, it is not surprising that few parameter determination methods are available that deal with nonparametric Hammerstein models
The paper is organized as follows: The identification problem is formally described in Section 2; relevant mathematical tools are described in Section 3; Section 4 is devoted to the determination of nonlinear element as well as the estimation of system nonlinearity
Summary
The Hammerstein model is a series connection of a nonlinear function and a linear dynamical element (Fig. 1). Parameters determination of black-box nonlinear system is a very wide research area [1]-[4] These models can describe several industrial systems, e.g. It is interesting to emphasize that, all the internal signals (x(t), w(t), and ξ(t)) are not accessible to measurement In view of these difficulties, it is not surprising that few parameter determination methods are available that deal with nonparametric Hammerstein models. Unlike most of previous work, the parameter determination problem is developed with in the continuous-time context. The determination of linear block as well as the system nonlinearity is done at the same time (in one stage), unlike most of previous papers [1]-[4]. In most previous works devoted to Hammerstein system identification, the nonlinear element is supposed to be smooth continuous function. The paper is organized as follows: The identification problem is formally described in Section 2; relevant mathematical tools are described in Section 3; Section 4 is devoted to the determination of nonlinear element as well as the estimation of system nonlinearity
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