Speaker
Description
We consider the task of data-driven identification of dynamical systems, specifically for systems whose behavior at large frequencies is nonproper, as encoded by a higher relative degree.
In this work, we review existing approaches to interpolate transfer function data most of which rely on a-priori knowledge of the relative degree or on high-frequency data with the term "high" remaining rather unspecifed. Then, we present our newly developed surrogate modeling strategies [1] that allow for state-of-the-art rational approximation algorithms (e.g., AAA and vector fitting) to better handle data coming from such systems with non-trivial relative degrees.
The approach rests on two pillars. Firstly, the possible surrogate model's relative degree is achieved through constraints on barycentric coefficients, rather than through ad-hoc modifications of the rational expressions. Secondly, we combine the model synthesis with an index-identification routine that allows one to estimate the relative degree of a system from low-frequency data.
Once the relative degree is identified, we can build a surrogate model that, in addition to matching the data well (at low frequencies), has enhanced extrapolation capabilities (at high frequencies). We showcase the effectiveness and robustness of the method through a suite of numerical tests.
References
[1] D. Pradovera, V. Gosea, J. Heiland. Barycentric rational approximation for learning the index of a dynamical system from limited data, 2024. https://arxiv.org/abs/2410.02000
