A New Objective for Identification of Partially Observed Linear Time-Invariant Dynamical Systems from Input-Output Data
Abstract
In this work we consider the identification of partially observed dynamical systems from a single trajectory of arbitrary input-output data. We propose a new optimization objective, derived as a MAP estimator of a certain posterior, that explicitly accounts for model, measurement, and parameter uncertainty. This algorithm identifies a linear time invariant model on a hidden latent space of pre-specified dimension. In contrast to Markov-parameter based least squares approaches, our algorithm can be applied to systems with arbitrary forcing and initial conditions, and we empirically show several magnitude improvement in prediction quality compared to state-of-the-art approaches on both linear and nonlinear systems. Furthermore, we theoretically demonstrate how these existing approaches can be derived from simplifying assumptions on our system that neglect the possibility of model errors.
Cite
Text
Galioto and Gorodetsky. "A New Objective for Identification of Partially Observed Linear Time-Invariant Dynamical Systems from Input-Output Data." Proceedings of the 3rd Conference on Learning for Dynamics and Control, 2021.Markdown
[Galioto and Gorodetsky. "A New Objective for Identification of Partially Observed Linear Time-Invariant Dynamical Systems from Input-Output Data." Proceedings of the 3rd Conference on Learning for Dynamics and Control, 2021.](https://mlanthology.org/l4dc/2021/galioto2021l4dc-new/)BibTeX
@inproceedings{galioto2021l4dc-new,
title = {{A New Objective for Identification of Partially Observed Linear Time-Invariant Dynamical Systems from Input-Output Data}},
author = {Galioto, Nicholas and Gorodetsky, Alex Arkady},
booktitle = {Proceedings of the 3rd Conference on Learning for Dynamics and Control},
year = {2021},
pages = {1180-1191},
volume = {144},
url = {https://mlanthology.org/l4dc/2021/galioto2021l4dc-new/}
}