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

TL;DR

This paper establishes the first non-asymptotic convergence rate bounds for set membership estimation in linear systems, enhancing robust control design by improving uncertainty set estimation.

Contribution

It introduces non-asymptotic convergence rate bounds for SME in linear systems and explores variations under relaxed assumptions.

Findings

First non-asymptotic convergence rate bounds for SME

Numerical results demonstrate SME's practical effectiveness

Analysis of SME variations under relaxed assumptions

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.