Learning the Uncertainty Sets of Linear Control Systems via Set Membership: A Non-asymptotic Analysis

Yingying Li, Jing Yu, Lauren Conger, Taylan Kargin, Adam Wierman
Proceedings of the 41st International Conference on Machine Learning, PMLR 235:29234-29265, 2024.

Abstract

This paper studies uncertainty set estimation for unknown linear systems. Uncertainty sets are crucial for the quality of robust control since they directly influence the conservativeness of the control design. Departing from the confidence region analysis of least squares estimation, this paper focuses on set membership estimation (SME). Though good numerical performances have attracted applications of SME in the control literature, the non-asymptotic convergence rate of SME for linear systems remains an open question. This paper provides the first convergence rate bounds for SME and discusses variations of SME under relaxed assumptions. We also provide numerical results demonstrating SME’s practical promise.

Cite this Paper

BibTeX
@InProceedings{pmlr-v235-li24ci, title = {Learning the Uncertainty Sets of Linear Control Systems via Set Membership: A Non-asymptotic Analysis}, author = {Li, Yingying and Yu, Jing and Conger, Lauren and Kargin, Taylan and Wierman, Adam}, booktitle = {Proceedings of the 41st International Conference on Machine Learning}, pages = {29234--29265}, year = {2024}, editor = {Salakhutdinov, Ruslan and Kolter, Zico and Heller, Katherine and Weller, Adrian and Oliver, Nuria and Scarlett, Jonathan and Berkenkamp, Felix}, volume = {235}, series = {Proceedings of Machine Learning Research}, month = {21--27 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v235/main/assets/li24ci/li24ci.pdf}, url = {https://proceedings.mlr.press/v235/li24ci.html}, abstract = {This paper studies uncertainty set estimation for unknown linear systems. Uncertainty sets are crucial for the quality of robust control since they directly influence the conservativeness of the control design. Departing from the confidence region analysis of least squares estimation, this paper focuses on set membership estimation (SME). Though good numerical performances have attracted applications of SME in the control literature, the non-asymptotic convergence rate of SME for linear systems remains an open question. This paper provides the first convergence rate bounds for SME and discusses variations of SME under relaxed assumptions. We also provide numerical results demonstrating SME’s practical promise.} }
Endnote
%0 Conference Paper %T Learning the Uncertainty Sets of Linear Control Systems via Set Membership: A Non-asymptotic Analysis %A Yingying Li %A Jing Yu %A Lauren Conger %A Taylan Kargin %A Adam Wierman %B Proceedings of the 41st International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2024 %E Ruslan Salakhutdinov %E Zico Kolter %E Katherine Heller %E Adrian Weller %E Nuria Oliver %E Jonathan Scarlett %E Felix Berkenkamp %F pmlr-v235-li24ci %I PMLR %P 29234--29265 %U https://proceedings.mlr.press/v235/li24ci.html %V 235 %X This paper studies uncertainty set estimation for unknown linear systems. Uncertainty sets are crucial for the quality of robust control since they directly influence the conservativeness of the control design. Departing from the confidence region analysis of least squares estimation, this paper focuses on set membership estimation (SME). Though good numerical performances have attracted applications of SME in the control literature, the non-asymptotic convergence rate of SME for linear systems remains an open question. This paper provides the first convergence rate bounds for SME and discusses variations of SME under relaxed assumptions. We also provide numerical results demonstrating SME’s practical promise.
APA
Li, Y., Yu, J., Conger, L., Kargin, T. & Wierman, A.. (2024). Learning the Uncertainty Sets of Linear Control Systems via Set Membership: A Non-asymptotic Analysis. Proceedings of the 41st International Conference on Machine Learning, in Proceedings of Machine Learning Research 235:29234-29265 Available from https://proceedings.mlr.press/v235/li24ci.html.

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