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- W4289479005 abstract "The problem of estimating the $mathcal{H}_infty$-norm of an LTI system from noisy input/output measurements has attracted recent attention as an alternative to parameter identification for bounding unmodeled dynamics in robust control. In this paper, we study lower bounds for $mathcal{H}_infty$-norm estimation under a query model where at each iteration the algorithm chooses a bounded input signal and receives the response of the chosen signal corrupted by white noise. We prove that when the underlying system is an FIR filter, $mathcal{H}_infty$-norm estimation is no more efficient than model identification for passive sampling. For active sampling, we show that norm estimation is at most a factor of $log{r}$ more sample efficient than model identification, where $r$ is the length of the filter. We complement our theoretical results with experiments which demonstrate that a simple non-adaptive estimator of the norm is competitive with state-of-the-art adaptive norm estimation algorithms." @default.
- W4289479005 created "2022-08-02" @default.
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- W4289479005 date "2018-09-28" @default.
- W4289479005 modified "2023-09-28" @default.
- W4289479005 title "Minimax Lower Bounds for $mathcal{H}_infty$-Norm Estimation" @default.
- W4289479005 doi "https://doi.org/10.48550/arxiv.1809.10855" @default.
- W4289479005 hasPublicationYear "2018" @default.
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