A framework for fitting quadratic-bilinear systems with applications to models of electrical circuits

Abstract

We propose a method for fitting quadratic-bilinear models from data. Although the dynamics characterizing the original model consist of general analytic nonlinearities, we rely on lifting techniques for equivalently embedding the original model into the quadratic-bilinear structure. Here, data are given by generalized transfer function values that can be sampled from the time-domain steady-state response. This method is an extension of methods that perform bilinear, or quadratic inference, separately. It is based on first identifying the underline minimal linear model with the interpolatory method known as the Loewner framework, and then on inferring the best supplementing nonlinear (quadratic and bilinear) operators, by solving an optimization problem. The proposed data-driven method finds applications in engineering serving the scopes of robust simulation, design, and control. Model examples of electrical circuits with nonlinear components (diodes) were used to test the method's performance.