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Empirical Least-squares Fitting of Parametrized Dynamical Systems by Grimm, Alexander; Beattie, Christopher; Drmač, Zlatko; Gugercin, Serkan is a scholarly article available to read on EtoBox.

What is Empirical Least-squares Fitting of Parametrized Dynamical Systems about?

Given a set of response observations for a parametrized dynamical system, we seek a parametrized dynamical model that will yield uniformly small response error over a range of parameter values yet has low order. Frequently, access to internal system dynamics or equivalently, to realizations of the original system is either not possible or not practical; only response observations over a range of parameter settings might be known. Respecting these typical operational constraints, we propose a two phase approach that first encodes the response data into a high fidelity intermediate model of modest order, followed then by a compression stage that serves to eliminate redundancy in the intermediate model. For the first phase, we extend non-parametric least-squares fitting approaches so as to accommodate parameterized systems. This results in a (discrete) least-squares problem formulated with respect to both frequency and parameter that identifies "local" system response features. The second phase uses an $\mathbf{\mathcal{H}}_2$-optimal model reduction strategy accommodating the specialized parametric structure of the intermediate model obtained in the first phase. The final compressed

Author

Grimm, Alexander; Beattie, Christopher; Drmač, Zlatko; Gugercin, Serkan

Published

2018

Language

EN