A Local Nonlinear Model for the Approximation and Identification of a Class of Systems

Based on Volterra series the work presents a novel local nonlinear model of a certain class of linear-analytic systems. The special form of the expressions for the Laplace-domain Volterra kernels of such systems is exploited to obtain an approximation structure that results in an appealingly simple feed-forward block structure. It comprises a composition of the linearization and the multivariate nonlinear function of the original system. Although based on Volterra series the model does not involve a truncation in the power series expansion nor in the memory depths. Compared to the exponential increase in parameters of classical memory truncated Volterra models, the structure offers an economic parametrization. The model is shown to be linear identifiable in one step if a priori information about the linearized dynamics is provided. We present simulation results for a simple nonlinear circuit showing the validity of the model.