On the nonlinear system identification of a class of bilinear dynamical models

A nonlinear system identification technique based on the functional spline interpolation for dealing with high-dimensional bilinear dynamical models is described. At first, the nonlinear dynamics of a given system are transformed through Carleman bilinearization into a bilinear form. Decoupled bilinear models are then constructed, with input-output mappings expressible in closed form and with dimension determined by the number of training signals used in a prior learning stage. The motivation is given by the need for order reduction and input-output analysis of Carleman bilinearization. For illustration purposes, the technique is then applied to a forced version of Duffing´s equation