A data-driven nonlinear frequency response approach based on the Loewner framework: preliminary analysis. Issue 1 (2023) - Gosea, Ion Victor; Živković, Luka A.; Karachalios, Dimitrios S.; Vidaković-Koch, Tanja; Antoulas, Athanasios C.
Abstract: We propose a hybrid method based on the combination of computed-aided nonlinear frequency response analysis with the Loewner framework, for the characterization of nonlinear dynamical processes with application in electrochemistry. The method is data-driven, i.e., requiring only samples of the first two generalized transfer functions of the underlying system, given as values of the sampled nonlinear frequency response. Then, the established system fitting and complexity reduction approach (in the frequency domain), known as the Loewner framework, is used to extract the system's invariant quantities. In this analysis, we have used a nonlinear electrical circuit model as a test case, for which the new method provides good results.