On excitation of control-affine systems and its use for data-driven Koopman approximants
Philipp Schmitz, Lea Bold, Friedrich M. Philipp, Mario Rosenfelder, Peter Eberhard, Henrik Ebel, Karl Worthmann
Koopman操作员和扩展动态模式分解(EDMD)作为其近似数据驱动的技术,作为复杂动态系统建模,分析和控制的关键工具,引起了相当大的关注。 然而,对控制亲和系统扩展,导致双线性代理模型,容易产生苛刻的数据要求,使其适用性错综复杂。 在本文中,我们提出了一个控制亲和映射数据拟合框架,以增加相关系统识别问题的鲁棒性边缘,从而提供更可靠的双线性EDMD方案。 特别是,根据子空间角度的输入选择准则被推导出,以确保对最小奇异值的预期阈值。 此外,我们得出了必要和足够的最优条件,以最大化最小单值。 此外,我们展示了使用双线性EDMD对非全息机器人控制的拟议方法的有用性。
The Koopman operator and extended dynamic mode decomposition (EDMD) as a data-driven technique for its approximation have attracted considerable attention as a key tool for modeling, analysis, and control of complex dynamical systems. However, extensions towards control-affine systems resulting in bilinear surrogate models are prone to demanding data requirements rendering their applicability intricate. In this paper, we propose a framework for data-fitting of control-affine mappings to increase...