A reproducing kernel Hilbert space (RKHS) approach to the optimal modeling, identification, and design of nonlinear adaptive systems

A general approach is presented for modeling, identification, and design of nonlinear adaptive systems and filters in a setting of a reproducing kernel Hilbert space (RKHS) F(E/sup N/) of Volterra series on the N-dimensional Euclidean space E/sup N/. The space F(E/sup N/) was introduced by De Figueiredo and Dwyer (1980) to solve nonlinear estimation problems by orthogonal projection methods. In the present case, the nonlinear adaptive system model is captured in two stages. In the first stage, which is nonparametric, the model structure is obtained as a best approximation in F(EN). In the second stage, which is parametric, the model parameters, which are coefficients of a linear combination of known nonlinear functions of the data, are obtained by linear mean square estimation. Developments and results of Eltoft and de Figueiredo on models based on dynamical functional artificial neural networks (D-FANNs) are briefly mentioned.