A Unified Approach of Nonlinear Systems Indentification in Generalized Fock Spaces

C. Marin, D. Selisteanu, D. Sendrescu, V. Finca, and R. Zglimbea (Romania)


Identification, Volterra series, Fock space, Reproducing Kernel Hilbert Spaces


In this paper the problem of base selection for nonlinear system identification based on weighted Fock spaces is presented. The Fock spaces consist of power series or infinite Volterra functional series, equipped with an appropriate weighted inner product. They are reproducing kernel Hilbert spaces (RKHS) whose kernels strongly depend on the weights choice, related on the particular problem under consideration. In identification literature, weights are usually geometrical series so the kernels are exponentials. The nonlinear identification problem is transformed in a dual approximation problem whose solution is the orthogonal projection on the subspace generated by the kernel representers of the Fock space elements. In such way the representers are interpreted as bases for the approximate solution. In the paper, the Fock spaces weights are expressed as a linear combination of some known strings. So the representers, that mean the base functions, are weighted sum of known functions which incorporate easily the prior information regarding the identification problem. In this approach, the parameters and the representing base functions are determined simultaneously. Furthermore, the best solution is obtained without any truncation of the power or Volterra infinite series. This development is illustrated by means of application to nonlinear continuous time dynamic system identification.

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