Robust Least-Squares Optimization for Data-Driven Predictive Control: A Geometric Approach

• URL: http://arxiv.org/abs/2511.09242v1
• Date: Thu, 13 Nov 2025 01:42:24 GMT
• Title: Robust Least-Squares Optimization for Data-Driven Predictive Control: A Geometric Approach
• Authors: Shreyas Bharadwaj, Bamdev Mishra, Cyrus Mostajeran, Alberto Padoan, Jeremy Coulson, Ravi N. Banavar,
• Abstract summary: The uncertainty in this geometric relation is modeled as a ball on the Grassmannian manifold.<n>The inner admits a closed-form solution, enabling an efficient algorithm with a transparent geometric interpretation.
• Score: 5.2456503500395275
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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