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

arXiv: https://arxiv.org/abs/2511.09242 · HTML: https://mlsanity.com/paper/2511.09242/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 36 references that are in the map.
- First posted on arXiv 12 Nov 2025.

## Builds on (most cited first, 15 of 15)

- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [On the Sample Complexity of the Linear Quadratic Regulator](https://mlsanity.com/paper/1710.01688/) (2017)
- [Formulas for Data-driven Control: Stabilization, Optimality and Robustness](https://mlsanity.com/paper/1903.06842/) (2019)
- [Data-Enabled Predictive Control: In the Shallows of the DeePC](https://mlsanity.com/paper/1811.05890/) (2018)
- [Data-Driven Model Predictive Control with Stability and Robustness Guarantees](https://mlsanity.com/paper/1906.04679/) (2019)
- [Simple algorithms for optimization on Riemannian manifolds with constraints](https://mlsanity.com/paper/1901.10000/) (2019)
- [Bridging direct & indirect data-driven control formulations via regularizations and relaxations](https://mlsanity.com/paper/2101.01273/) (2021)
- [Linear tracking MPC for nonlinear systems Part II: The data-driven case](https://mlsanity.com/paper/2105.08567/) (2021)
- [Robust Data-Enabled Predictive Control: Tractable Formulations and Performance Guarantees](https://mlsanity.com/paper/2105.07199/) (2021)
- [Data-driven predictive control in a stochastic setting: a unified framework](https://mlsanity.com/paper/2203.10846/) (2022)
- [Behavioral uncertainty quantification for data-driven control](https://mlsanity.com/paper/2204.02671/) (2022)
- [Bilinear Data-Driven Min-Max MPC: Designing Rational Controllers via Sum-of-squares Optimization](https://mlsanity.com/paper/2504.04870/) (2025)
- [Data-Driven Min-Max MPC for LPV Systems with Unknown Scheduling Signal](https://mlsanity.com/paper/2411.05624/) (2024)
- [Distances between finite-horizon linear behaviors](https://mlsanity.com/paper/2503.22849/) (2025)
- [Geometrically robust least squares through manifold optimization](https://mlsanity.com/paper/2511.03644/) (2025)

## Abstract (arXiv)

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.