Non-parametric identification of dynamic non-linear systems by a Hermite Series Approach

Non-linear dynamic block-oriented systems of Hammerstein and Wiener type are identified. The Hammerstein system consists of a memoryless non-linearity followed by a dynamic, linear system, while the Wiener system is a cascade of a linear dynamic system followed by a memoryless non-linearity. The class of non-linearities considered here is large and non-parametric. Identification algorithms based on input‐output observations are proposed for both systems and their convergence and rates are investigated. The performance of identification algorithms is studied in simulation studies.