A New Objective for Identification of Partially Observed Linear Time-Invariant Dynamical Systems from Input-Output Data

Nicholas Galioto, Alex Arkady Gorodetsky
Proceedings of the 3rd Conference on Learning for Dynamics and Control, PMLR 144:1180-1191, 2021.

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 this Paper

BibTeX
@InProceedings{pmlr-v144-galioto21a, 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}, pages = {1180--1191}, year = {2021}, editor = {Jadbabaie, Ali and Lygeros, John and Pappas, George J. and A. Parrilo, Pablo and Recht, Benjamin and Tomlin, Claire J. and Zeilinger, Melanie N.}, volume = {144}, series = {Proceedings of Machine Learning Research}, month = {07 -- 08 June}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v144/galioto21a/galioto21a.pdf}, url = {https://proceedings.mlr.press/v144/galioto21a.html}, 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.} }
Endnote
%0 Conference Paper %T A New Objective for Identification of Partially Observed Linear Time-Invariant Dynamical Systems from Input-Output Data %A Nicholas Galioto %A Alex Arkady Gorodetsky %B Proceedings of the 3rd Conference on Learning for Dynamics and Control %C Proceedings of Machine Learning Research %D 2021 %E Ali Jadbabaie %E John Lygeros %E George J. Pappas %E Pablo A. Parrilo %E Benjamin Recht %E Claire J. Tomlin %E Melanie N. Zeilinger %F pmlr-v144-galioto21a %I PMLR %P 1180--1191 %U https://proceedings.mlr.press/v144/galioto21a.html %V 144 %X 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.
APA
Galioto, N. & Gorodetsky, A.A.. (2021). 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, in Proceedings of Machine Learning Research 144:1180-1191 Available from https://proceedings.mlr.press/v144/galioto21a.html.

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