Learning the Uncertainty Sets for Control Dynamics via Set Membership: A Non-Asymptotic Analysis
This work addresses a gap in control theory by analyzing SME's convergence for linear systems, which is incremental as it builds on existing numerical applications but provides theoretical foundations.
The paper tackles the problem of estimating uncertainty sets for unknown linear systems, which affects the conservativeness of robust control designs, by providing the first non-asymptotic convergence rate bounds for set membership estimation (SME) and demonstrating its practical promise through numerical results.
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.