关联控制系统的动态模态分解
Dynamic mode decomposition for interconnected control systems
摘要：
动态模式分解（DMD）是一种数据驱动的技术，用于捕获复杂系统的动态特性。DMD已经连接到Koopman算子的谱分析，并且基本上从数据获得的Koopman算子的估计中提取动态的时空模式。Proctor、Brunton和Kutz最近的工作扩展了DMD和Koopman理论，以适应具有控制输入的系统：具有控制的动态模式分解（DMDc）和具有输入和控制的Koopman（KIC）。在本文中，我们介绍了一种技术，称为网络动态模式分解与控制，或网络DMDC，它扩展的DMDC互连，或网络，控制系统。此外，我们提供了一个适应Koopman理论的网络作为执行此算法的上下文。网络DMDC方法仔细分析了仅在网络结构中连接的系统中的组件之间的动态关系。通过专注于这些直接的动态连接，并削减计算之间的关系不连接的组件，这个过程允许在计算强度和精度的改进。
英文摘要：
Dynamic mode decomposition (DMD) is a data-driven technique used for capturing the dynamics of complex systems. DMD has been connected to spectral analysis of the Koopman operator, and essentially extracts spatial-temporal modes of the dynamics from an estimate of the Koopman operator obtained from data. Recent work of Proctor, Brunton, and Kutz has extended DMD and Koopman theory to accommodate systems with control inputs: dynamic mode decomposition with control (DMDc) and Koopman with inputs and control (KIC). In this paper, we introduce a technique, called Network dynamic mode decomposition with control, or Network DMDc, which extends the DMDc to interconnected, or networked, control systems. Additionally, we provide an adaptation of Koopman theory for networks as a context in which to perform this algorithm. The Network DMDc method carefully analyzes the dynamical relationships only between components in systems which are connected in the network structure. By focusing on these direct dynamical connections and cutting out computation for relationships between unconnected components, this process allows for improvements in computational intensity and accuracy.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
