用几何方法提升数据驱动预测控制的鲁棒性
Robust Least-Squares Optimization for Data-Driven Predictive Control: A Geometric Approach
- 将最小二乘理解为近似子空间包含，通过流形建模不确定性
- 在小不确定性下实现更强鲁棒性与良好可扩展性
- 适合研究数据驱动控制鲁棒性的学者和工程师
本文研究一种几何鲁棒的最小二乘问题，扩展了经典的范数型鲁棒方法。不直接最小化固定或扰动数据的残差误差，而是将最小二乘解释为强制测量数据空间与真实数据空间近似包含于同一子空间。该几何关系的不确定性被建模为格拉斯曼流形上的度量球，形成欧氏空间与流形变量的极小极大优化问题。内部最大化可解析求解，从而得到高效算法并具有清晰的几何解释。应用于数据启用的有限时域线性二次跟踪预测控制中，该方法优于现有鲁棒最小二乘形式，在小不确定性下实现更强鲁棒性和良好缩放性能。
原文摘要 · Abstract (English)
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.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。