Nonlinear system identification: Interpreting Volterra kernels using tensors

To capture the nonlinear effects of the real world, today the focus of system identification is shifting from linear to nonlinear dynamical models. Every nonlinear dynamic system with fading memory can be approximated arbitrarily well by its Volterra kernel description, which is a generalization of the Taylor series for systems with memory. However, the Volterra series provides a non-parametric representation, lacking physical and intuitive interpretation. To take advantage of the Volterra representation while aiming for an interpretable block-oriented model, we imposed the desired structure using tensor techniques (see figure below).