An adaptive approximation method for Hammerstein systems identification

This paper aims to describe a new identification method for Hammerstein systems relying on the framework of basis functions approximation in order to obtain an adequate model for the nonlinear static component. The specific coefficients of the basis functions approximation and also the parameters of the linear dynamic component are estimated using a nonlinear least squares method based on a modified version of Gauss-Newton algorithm. An algorithm is introduced based on wavelet multiresolution analysis that returns a low complexity approximation of the nonlinear component built on a grid hierarchy using adaptive bases. Such bases provides a powerful means to detect local singularities and often lead to quite simple refinement strategies. Finally, we present some numerical results for our method that show its efficiency.