2024-06-11-lawrence24a.md

title	abstract	layout	series	publisher	issn	id	month	tex_title	firstpage	lastpage	page	order	cycles	bibtex_author	author	date	address	container-title	volume	genre	issued	pdf	extras
Deep Hankel matrices with random elements	Willems’ fundamental lemma enables a trajectory-based characterization of linear systems through data-based Hankel matrices. However, in the presence of measurement noise, we ask: Is this noisy Hankel-based model expressive enough to re-identify itself? In other words, we study the output prediction accuracy from recursively applying the same persistently exciting input sequence to the model. We find an asymptotic connection to this self-consistency question in terms of the amount of data. More importantly, we also connect this question to the depth (number of rows) of the Hankel model, showing the simple act of reconfiguring a finite dataset significantly improves accuracy. We apply these insights to find a parsimonious depth for LQR problems over the trajectory space.	inproceedings	Proceedings of Machine Learning Research	PMLR	2640-3498	lawrence24a	0	Deep {H}ankel matrices with random elements	1579	1591	1579-1591	1579	false	Lawrence, Nathan and Loewen, Philip and Wang, Shuyuan and Forbes, Michael and Gopaluni, Bhushan	given family Nathan Lawrence given family Philip Loewen given family Shuyuan Wang given family Michael Forbes given family Bhushan Gopaluni	2024-06-11		Proceedings of the 6th Annual Learning for Dynamics & Control Conference	242	inproceedings	date-parts 2024 6 11	https://proceedings.mlr.press/v242/lawrence24a/lawrence24a.pdf