{"ID":2842792,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2511.09242","arxiv_id":"2511.09242","title":"Robust Least-Squares Optimization for Data-Driven Predictive Control: A Geometric Approach","abstract":"The paper studies a geometrically robust least-squares problem that extends classical and norm-based robust formulations. Rather than minimizing residual error for fixed or perturbed data, we interpret least-squares as enforcing approximate subspace inclusion between measured and true data spaces. The uncertainty in this geometric relation is modeled as a metric ball on the Grassmannian manifold, leading to a min-max problem over Euclidean and manifold variables. The inner maximization admits a closed-form solution, enabling an efficient algorithm with a transparent geometric interpretation. Applied to robust finite-horizon linear-quadratic tracking in data-enabled predictive control, the method improves upon existing robust least-squares formulations, achieving stronger robustness and favorable scaling under small uncertainty.","short_abstract":"The paper studies a geometrically robust least-squares problem that extends classical and norm-based robust formulations. Rather than minimizing residual error for fixed or perturbed data, we interpret least-squares as enforcing approximate subspace inclusion between measured and true data spaces. The uncertainty in th...","url_abs":"https://arxiv.org/abs/2511.09242","url_pdf":"https://arxiv.org/pdf/2511.09242v2","authors":"[\"Shreyas Bharadwaj\",\"Bamdev Mishra\",\"Cyrus Mostajeran\",\"Alberto Padoan\",\"Jeremy Coulson\",\"Ravi N. Banavar\"]","published":"2025-11-12T12:02:14Z","proceeding":"math.OC","tasks":"[\"math.OC\",\"cs.LG\"]","methods":"[]","has_code":false}