将动态模式分解扩展到来自多个输出的数据
Extending dynamic mode decomposition to data from multiple outputs
摘要：
基于Koopman算子理论的系统辨识近年来得到了广泛的应用。证明了系统的Koopman算子的谱性质与系统的不变集、稳定性、周期性等性质有关。这些光谱对象的估计已成为广泛访问与近年来开发的众多算法。我们展示了如何一个这样的算法-扩展的动态模式分解-可以用于从一个系统的多个输出的数据。这些输出是状态的函数，在文献中称为可观量，可以是已知的输出，如状态本身，也可以是未知的输出，如来自生物系统中使用的传感器的数据。为此，我们近似所需的观测量和迭代的时间使用正则化最小二乘问题，具有分析解的启发式规定的预期估计的最小值。
英文摘要：
System identification based on Koopman operator theory has grown in popularity recently. Spectral properties of the Koopman operator of a system were proven to relate to properties like invariant sets, stability, periodicity, etc. of the underlying system. Estimation of these spectral objects has become widely accessible with the numerous algorithms developed in recent years. We show how one such algorithm -- extended dynamic mode decomposition -- can be used on data from multiple outputs of a system. These outputs that are functions of state are called observables in the literature and could be known outputs like the state itself or unknown outputs like data from sensors used in systems of biological interest. To this end, we approximate the desired observables and their iterates in time using minimizers of regularized least-squares problems which have analytic solutions with heuristic provisions for expected estimates.
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