Robust Least-Squares Optimization for Data-Driven Predictive Control: A Geometric Approach
It addresses robust control for systems with data uncertainty, offering incremental improvements in specific formulations.
The paper tackles robust least-squares optimization by modeling uncertainty as a metric ball on the Grassmannian manifold, leading to a min-max problem with a closed-form solution. Applied to data-driven predictive control, it improves robustness and scaling compared to existing methods.
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.