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
9/1/2023

No official code found. Best implementation: jy-cds/non-asymptotic-set-membership (3 stars, last commit 2024-06-03).

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.

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Code Implementations(1)

jy-cds/non-asymptotic-set-membershipCommunity100%

Code for reproducing results in the paper "Learning the Uncertainty Sets of Linear Control Systems via Set Membership: A Non-asymptotic Analysis" published at ICML '24.

30MATLAB, PythonJun 3, 20242 years ago

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Cite this paper

@article{li2023learning,
  title  = {Learning the Uncertainty Sets of Linear Control Systems via Set Membership: A Non-asymptotic Analysis},
  author = {Yingying Li and Jing Yu and Lauren Conger and Taylan Kargin and Adam Wierman},
  year   = {2023},
  eprint = {2309.14648},
  archivePrefix = {arXiv},
  url    = {https://arxiv.org/abs/2309.14648},
  journal = {ICML 2023 2023}
}

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