Identification of Linear Parameter-Varying Systems Using Nonlinear Programming

Abstract

This paper deals with the identification of a linear parameter-varying (LPV) system whose parameter dependence can be written as a linear-fractional transformation (LFT). We formulate an output-error identification problem and present a parameter estimation scheme in which a prediction error-based cost function is minimized using nonlinear programming; its gradients and (approximate) Hessians can be computed using LPV filters and inner products, and identifiable model sets (i.e., local canonical forms) are obtained efficiently using a natural geometrical approach. Some computational issues and experiences are discussed, and a simple numerical example is provided for illustration.