论文标题
关于从数据稳定线性动力学系统的样品复杂性
On the sample complexity of stabilizing linear dynamical systems from data
论文作者
论文摘要
从数据稳定动力学系统的数据中学习控制器通常遵循首先识别模型，然后基于确定模型构建控制器的两个步骤。但是，学习模型意味着确定系统动力学的通用描述，这些描述可能需要大量数据并提取对稳定的特定任务不必要的信息。这项工作的贡献是表明，如果线性动力学系统具有尺寸（McMillan度）$ n $，那么总是存在$ n $状态，可以从中可以构建稳定的反馈控制器，而与观察到的状态的表示和输入数量无关。通过基于先前的工作，这一发现意味着，与学习动力学模型所需的最少状态数量相比，观察到的状态较少的任何线性动力系统都可以稳定。通过数值实验证明了理论发现，这些实验表明了从学习模型所需的数据较少的数据中稳定圆柱体后面的流动。
Learning controllers from data for stabilizing dynamical systems typically follows a two step process of first identifying a model and then constructing a controller based on the identified model. However, learning models means identifying generic descriptions of the dynamics of systems, which can require large amounts of data and extracting information that are unnecessary for the specific task of stabilization. The contribution of this work is to show that if a linear dynamical system has dimension (McMillan degree) $n$, then there always exist $n$ states from which a stabilizing feedback controller can be constructed, independent of the dimension of the representation of the observed states and the number of inputs. By building on previous work, this finding implies that any linear dynamical system can be stabilized from fewer observed states than the minimal number of states required for learning a model of the dynamics. The theoretical findings are demonstrated with numerical experiments that show the stabilization of the flow behind a cylinder from less data than necessary for learning a model.
