On the Initialization of Nonlinear LFR Model Identification with the Best Linear Approximation

Abstract

Balancing the model complexity and the representation capability towards the process to be captured remains one of the main challenges in nonlinear system identification. One possibility to reduce model complexity is to impose structure on the model representation. To this end, this work considers the linear fractional representation framework. In a linear fractional representation the linear dynamics and the system nonlinearities are modeled by two separate blocks that are interconnected with one another. This results in a structured, yet flexible model structure. Estimating such a model directly from input-output data is not a trivial task as the involved optimization is nonlinear in nature. This paper proposes an initialization scheme for the model parameters based on the best linear approximation of the system and shows that this approach results in high quality models on a set of benchmark data sets.