数据驱动满足几何控制：零动态，子空间稳定和恶意攻击
Data-driven Meets Geometric Control: Zero Dynamics, Subspace Stabilization, and Malicious Attacks
摘要：
通过不变子空间研究线性动力系统的结构性质是几何方法对系统理论的重要贡献之一。一般来说，为了计算感兴趣的不变子空间，需要动力学模型。在本文中，我们克服了这一限制，找到数据驱动的公式的一些基本工具的几何控制。特别是，对于一个未知的线性系统，我们展示了如何控制和条件不变的子空间可以直接从实验数据中找到。我们使用我们的公式和方法来（i）找到一个反馈增益，将系统状态限制在所需的子空间内，（ii）计算未知系统的不变零点，以及（iii）设计仍然无法检测的攻击。
英文摘要：
Studying structural properties of linear dynamical systems through invariant subspaces is one of the key contributions of the geometric approach to system theory. In general, a model of the dynamics is required in order to compute the invariant subspaces of interest. In this paper we overcome this limitation by finding data-driven formulas for some of the foundational tools of geometric control. In particular, for an unknown linear system, we show how controlled and conditioned invariant subspaces can be found directly from experimental data. We use our formulas and approach to (i) find a feedback gain that confines the system state within a desired subspace, (ii) compute the invariant zeros of the unknown system, and (iii) design attacks that remain undetectable.
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