| Summary: | In this work, we deal with the problem of approximating and equivalently formulating generic nonlinear systems by means of specific classes thereof. Bilinear and quadratic-bilinear systems accomplish precisely this goal. Hence, by means of exact and inexact lifting transformations, we are able to reformulate the original nonlinear dynamics into a different, more simplified format. Additionally, we study the problem of complexity/model reduction of large-scale lifted models of nonlinear systems from data. The method under consideration is the Loewner framework, an established data-driven approach that requires samples of input–output mappings. The latter are known as generalized transfer functions, which are appropriately defined for both bilinear and quadratic-bilinear systems. We show connections between these mappings as well as between the matrices of reduced-order models. Finally, we illustrate the theoretical discussion with two numerical examples.
|
|---|