Continuous time nonlinear systems identification in real generalized Fock space

The paper presents a unified procedure for construction of Real Generalized Fock Space (RGFS) oriented for continuous time nonlinear systems identification whose inputs belong to a separable Hilbert space. The basic characteristic of this approach is the construction of a tensor space generated by an n-linear natural embedding map. This natural embedding map can be defined according to the practical problem of identification. The inner product of the built tensor space is dependent on the scalar product of the input variables Hilbert space. The properties of the defined tensor product space are transferred to some linear space, in particular the Hilbert-Schmidt space of n-degree polynomials. The nonlinear identification problem can be formulated as a minimum norm problem. Finally, the formula for the nonlinear functionals identification is obtained, solved by dual approximation in Hilbert spaces. Some numerical examples are presented.