State vector estimation of high dimensional systems based on functional spline operators

An estimation procedure 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 is 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. Motivation is given by the need for order reduction and input-output analysis of Carleman bilinearization. An illustration of the technique is made to a forced version of Duffing's equation and merits and eventual extension of the procedure are also highlighted.<>