On the Sample Complexity of Stabilizing Linear Dynamical Systems from Data
On the Sample Complexity of Stabilizing Linear Dynamical Systems from Data
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DOI：
10.1007/s10208-023-09605-y
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发表时间：
2022-02
影响因子：
3
通讯作者：
Steffen W. R. Werner;B. Peherstorfer
中科院分区：
文献类型：
--
作者：
Steffen W. R. Werner;B. Peherstorfer
从用于稳定动态系统的数据学习控制器通常遵循两步过程：首先识别模型，然后基于所识别的模型构建控制器。然而，学习模型意味着识别系统动态的一般描述，这可能需要大量数据，并提取稳定特定任务所不必要的信息。本文的贡献是证明了如果一个线性动力系统有维数（McMillan度），那么总存在个状态，可以从这些状态构造一个稳定的反馈控制器，而与观测状态表示的维数和输入的个数无关。通过建立在以前的工作，这一发现意味着，任何线性动力系统可以从更少的观察到的状态比学习动态模型所需的最小数量的状态稳定。理论研究结果表明，数值实验表明，从更少的数据比必要的学习模型的气缸后面的流的稳定。
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), then there always existstates 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.