Koopman Operator Methods for Global Phase Space Exploration of Equivariant Dynamical Systems <ce:cross-ref refid='fn1'> <ce:sup loc='post'>?</ce:sup> </ce:cross-ref>

Subhrajit Sinha; Sai Pushpak Nandanoori; Enoch Yeung

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Koopman Operator Methods for Global Phase Space Exploration of Equivariant Dynamical Systems ?

机译：Koopman操作员对于等分症动态系统的全局阶段空间探索的方法

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In this paper, we develop the Koopman operator theory for dynamical systems with symmetry. In particular, we investigate how the Koopman operator and eigenfunctions behave under the action of the symmetry group of the underlying dynamical system. Further, exploring the underlying symmetry, we propose an algorithm to construct a global Koopman operator from local Koopman operators. In particular, we show, by exploiting the symmetry, data from all the invariant sets are not required for constructing the global Koopman operator; that is, local knowledge of the system is enough to infer the global dynamics.

机译：在本文中，我们开发了具有对称性的动态系统的Koopman操作员理论。特别是，我们调查Koopman运营商和特征功能如何在潜在的动态系统的对称组的作用下行为。此外，探索潜在的对称性，我们提出了一种从本地Koopman运算符构建全球Koopman运算符的算法。特别是，我们通过利用对称性来显示来自所有不变集的数据，不需要构建全球Koopman运算符;也就是说，系统的本地知识足以推断出全球动态。

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《IFAC PapersOnLine》 |2020年第2期|共6页
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Subhrajit Sinha; Sai Pushpak Nandanoori; Enoch Yeung;
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Dynamic systemsOperatorsLearning algorithmsEquivariant systemsKoopman operatorsData-driven analysis;

机译：动态系统流放器算法Sequivariant SystemsKoopman operatorsData驱动分析;

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2. On Comparison of Dynamics of Dissipative and Finite-Time Systems Using Koopman Operator Methods * * The funding provided by ARO Grant W911NF-11-1-0511. [J] . Igor Mezic IFAC PapersOnLine . 2016,第18期

机译：使用Koopman算子方法比较耗散系统和有限时间系统的动力学 * * ARO Grant W911NF-11提供的资金-1-0511。
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6. Koopman Invariant Subspaces and Finite Linear Representations of Nonlinear Dynamical Systems for Control [O] . Steven L. Brunton, Bingni W. Brunton, Joshua L. Proctor, -1

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7. Koopman Operator Methods for Global Phase Space Exploration of Equivariant Dynamical Systems [O] . Subhrajit Sinha, Sai Pushpak Nandanoori, Enoch Yeung 2020

机译：Koopman运算符的全局相位空间探索等级动力系统

Koopman Operator Methods for Global Phase Space Exploration of Equivariant Dynamical Systems ?

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