Learning the Uncertainty Sets for Control Dynamics via Set Membership: A Non-Asymptotic Analysis

• URL: http://arxiv.org/abs/2309.14648v2
• Date: Mon, 10 Jun 2024 03:05:58 GMT
• Title: Learning the Uncertainty Sets for Control Dynamics via Set Membership: A Non-Asymptotic Analysis
• Authors: Yingying Li, Jing Yu, Lauren Conger, Taylan Kargin, Adam Wierman,
• Abstract summary: This paper focuses on set membership estimation (SME) for unknown linear systems. We provide the first convergence rate bounds for SME and discuss variations of SME under relaxed assumptions. We also provide numerical results demonstrating SME's practical promise.
• Score: 18.110158316883403
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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