{"paper":{"title":"Convergence Analysis of Gradient Flow for Overparameterized LQR Formulations","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":["cs.SY","math.DS"],"primary_cat":"eess.SY","authors_text":"Arthur Castello B. de Oliveira, Eduardo D. Sontag, Milad Siami","submitted_at":"2024-08-28T00:30:37Z","abstract_excerpt":"Motivated by the growing use of artificial intelligence (AI) tools in control design, this paper analyses the intersection between results from gradient methods for the model-free linear quadratic regulator (LQR), and linear feedforward neural networks (LFFNNs), More specifically, it looks into the case where one wants to find a LFFNN feedback that minimizes a LQR cost. This paper starts by analyzing the structure of the gradient expression for the parameters of each layer, which implies a key conservation law of the system. This conservation law is then leveraged to generalize existing result"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2408.15456","kind":"arxiv","version":3},"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/2408.15456/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"}