On the series expansion approach to the identification of Hammerstein systems

A polynomial identification algorithm for recovering a nonlinearity in the Hammerstein system is proposed. The estimate employs the Legendre orthogonal system with adaptively selected number of terms. The global consistency along with rates of convergence are established. No assumptions concerning continuity of the nonlinearity or its functional form are made. A data-driven method using the cross-validation technique for selecting the number of terms in the estimate is presented.>