Title: Data-driven Meets Geometric Control: Zero Dynamics, Subspace Stabilization, and Malicious Attacks Show Chinese title

Title: 数据驱动与几何控制的结合：零动态、子空间稳定性和恶意攻击

Abstract: 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. Show Chinese abstract

Abstract: 通过不变子空间研究线性动态系统的结构特性是几何方法对系统理论的关键贡献之一。 通常，为了计算感兴趣的不变子空间，需要动态模型。 在本文中，我们通过为几何控制的一些基础工具找到数据驱动的公式来克服这一限制。 特别是，对于一个未知的线性系统，我们展示了如何直接从实验数据中找到受控和条件不变子空间。 我们使用这些公式和方法来（i）找到一个反馈增益，使系统状态限制在期望的子空间内，（ii）计算未知系统的不变零点，以及（iii）设计不可检测的攻击。