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| Autori principali: | , , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2511.09242 |
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| _version_ | 1866908994680913920 |
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| author | Bharadwaj, Shreyas Mishra, Bamdev Mostajeran, Cyrus Padoan, Alberto Coulson, Jeremy Banavar, Ravi N. |
| author_facet | Bharadwaj, Shreyas Mishra, Bamdev Mostajeran, Cyrus Padoan, Alberto Coulson, Jeremy Banavar, Ravi N. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_09242 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Robust Least-Squares Optimization for Data-Driven Predictive Control: A Geometric Approach Bharadwaj, Shreyas Mishra, Bamdev Mostajeran, Cyrus Padoan, Alberto Coulson, Jeremy Banavar, Ravi N. Optimization and Control Machine Learning 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. |
| title | Robust Least-Squares Optimization for Data-Driven Predictive Control: A Geometric Approach |
| topic | Optimization and Control Machine Learning |
| url | https://arxiv.org/abs/2511.09242 |