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

Shreyas Bharadwaj, Bamdev Mishra, Cyrus Mostajeran, Alberto Padoan, Jeremy Coulson, Ravi N. Banavar
Proceedings of The 8th Annual Learning for Dynamics and Control Conference, PMLR 331:511-531, 2026.

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v331-bharadwaj26a, title = {Robust Least-Squares Optimization for Data-Driven Predictive Control: A Geometric Approach}, author = {Bharadwaj, Shreyas and Mishra, Bamdev and Mostajeran, Cyrus and Padoan, Alberto and Coulson, Jeremy and Banavar, Ravi N.}, booktitle = {Proceedings of The 8th Annual Learning for Dynamics and Control Conference}, pages = {511--531}, year = {2026}, editor = {Sukhatme, Gaurav and Lindemann, Lars and Tu, Stephen and Wierman, Adam and Atanasov, Nikolay}, volume = {331}, series = {Proceedings of Machine Learning Research}, month = {17--19 Jun}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v331/main/assets/bharadwaj26a/bharadwaj26a.pdf}, url = {https://proceedings.mlr.press/v331/bharadwaj26a.html}, 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.} }
Endnote
%0 Conference Paper %T Robust Least-Squares Optimization for Data-Driven Predictive Control: A Geometric Approach %A Shreyas Bharadwaj %A Bamdev Mishra %A Cyrus Mostajeran %A Alberto Padoan %A Jeremy Coulson %A Ravi N. Banavar %B Proceedings of The 8th Annual Learning for Dynamics and Control Conference %C Proceedings of Machine Learning Research %D 2026 %E Gaurav Sukhatme %E Lars Lindemann %E Stephen Tu %E Adam Wierman %E Nikolay Atanasov %F pmlr-v331-bharadwaj26a %I PMLR %P 511--531 %U https://proceedings.mlr.press/v331/bharadwaj26a.html %V 331 %X 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.
APA
Bharadwaj, S., Mishra, B., Mostajeran, C., Padoan, A., Coulson, J. & Banavar, R.N.. (2026). Robust Least-Squares Optimization for Data-Driven Predictive Control: A Geometric Approach. Proceedings of The 8th Annual Learning for Dynamics and Control Conference, in Proceedings of Machine Learning Research 331:511-531 Available from https://proceedings.mlr.press/v331/bharadwaj26a.html.

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