We address the problem of identifying a stable linear time-invariant system from a single sample trajectory. The least squares estimate (LSE) is a commonly used algorithm for this purpose. However, LSE may exhibit poor identification errors when the number of samples is small. To mitigate the issue, we introduce the robust LSE, which integrates robust optimization techniques. We demonstrate that our robust LSE is equivalent to regularizing LSE using general Schatten p-norms. Moreover, we provide finite-sample analyses for the robust LSE, which can be directly transferred to the regularized LSE due to their equivalence. We showcase the empirical performance of our method in system identification tasks. Additionally, we combine our robust LSE with several online adaptive linear quadratic control algorithms and demonstrate that our method significantly outperforms existing approaches in regret.
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