{"paper":{"title":"Noise Sensitivity of the Semidefinite Programs for Direct Data-Driven LQR","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.SY","eess.SY"],"primary_cat":"math.OC","authors_text":"Laurent Bako, Necmiye Ozay, Xiong Zeng","submitted_at":"2024-12-27T15:59:42Z","abstract_excerpt":"In this paper, we study the noise sensitivity of the semidefinite program (SDP) proposed for direct data-driven infinite-horizon linear quadratic regulator (LQR) problem for discrete-time linear time-invariant systems. While this SDP is shown to find the true LQR controller in the noise-free setting, we show that it leads to a trivial solution with zero gain matrices when data is corrupted by noise, even when the noise is arbitrarily small. We then study a variant of the SDP that includes a robustness promoting regularization term and prove that regularization does not fully eliminate the sens"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.19705","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2412.19705/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}