论文标题
大规模动态系统的计算有效学习：库普曼理论方法
Computationally Efficient Learning of Large Scale Dynamical Systems: A Koopman Theoretic Approach
论文作者
论文摘要
近年来，朝着动态系统的数据驱动分析，发现和控制方面有很大的推动力。为此，操作者理论方法，即库普曼操作员方法引起了很多兴趣。通常，Koopman操作员是作为解决最小二乘问题的解决方案的，因此，Koopman操作员可以作为封闭形式的解决方案表示，该解决方案涉及计算矩阵的Moore-Penrose。对于高维系统，如果获得的数据集的大小很大，则摩尔 - 柔性逆的计算在计算上变得具有挑战性。在本文中，我们提供了一种用于计算高维系统的Koopman操作员的算法。我们进一步证明了所提出的方法在两个不同系统上的功效，即耦合振荡器网络（具有最高2500个状态空间尺寸）和IEEE 68 BUS系统（具有204个状态空间尺寸和24,000个时间点）。
In recent years there has been a considerable drive towards data-driven analysis, discovery and control of dynamical systems. To this end, operator theoretic methods, namely, Koopman operator methods have gained a lot of interest. In general, the Koopman operator is obtained as a solution to a least-squares problem, and as such, the Koopman operator can be expressed as a closed-form solution that involves the computation of Moore-Penrose inverse of a matrix. For high dimensional systems and also if the size of the obtained data-set is large, the computation of the Moore-Penrose inverse becomes computationally challenging. In this paper, we provide an algorithm for computing the Koopman operator for high dimensional systems in a time-efficient manner. We further demonstrate the efficacy of the proposed approach on two different systems, namely a network of coupled oscillators (with state-space dimension up to 2500) and IEEE 68 bus system (with state-space dimension 204 and up to 24,000 time-points).
