On Comparison of Dynamics of Dissipative and Finite-Time Systems Using Koopman Operator Methods<ce:cross-ref refid='fn1'> <ce:sup loc='post'>*</ce:sup> </ce:cross-ref> <ce:footnote id='fn1'> <ce:label>*</ce:label> <ce:note-para id='npara0001' view='all'>The funding provided by ARO Grant W911NF-11-1-0511.</ce:note-para> </ce:footnote>

Igor Mezic

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On Comparison of Dynamics of Dissipative and Finite-Time Systems Using Koopman Operator Methods * * The funding provided by ARO Grant W911NF-11-1-0511.

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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Abstract: Comparison of different dynamical systems or a dynamical system with data is one of the core issues in both dynamical systems and control theory. The fruitful approaches are particularly hard to come by for systems and data that show nonlinear behavior and non-Gaussian noise characteristics. We describe a theory that utilizes spectral theory of linear operators (composition, or Koopman) to provide the methodology, that was originally formulated for measure-preserving systems. Here we extend it to capture dissipative and finite-time dynamics. The approach combines a version of ergodic partition theory with Hardy space theory in observable space (rather than in time).

机译：摘要：将不同的动力学系统或动力学系统与数据进行比较是动力学系统和控制理论的核心问题之一。对于表现出非线性行为和非高斯噪声特征的系统和数据，尤其难以获得富有成效的方法。我们描述了一种利用线性算子的频谱理论（组合或Koopman）来提供方法的理论，该方法最初是为度量保留系统制定的。在这里，我们将其扩展为捕获耗散和有限时间的动力学。该方法在可观察空间（而不是时间）中结合了遍历分区理论和Hardy空间理论的版本。

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《IFAC PapersOnLine》 |2016年第18期|共8页
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Igor Mezic;
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中图分类自动化技术、计算机技术;
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1. 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。
2. H ∞ dynamic observer design for linear discrete-time systems * * This work is supported by the Fundamental Research Funds for the Central Universities (under Grant 310822171005 ), in Chang’an University, China. [J] . Nao Gao, Mohamed Darouach, Marouane Alma IFAC PapersOnLine . 2017,第1期

机译：H ∞线性离散时间系统的动态观察者设计 * * 这项工作得到了中国长安大学中央大学基础研究基金（赠款310822171005）的支持。
3. Koopman Mode Decomposition for Periodic/Quasi-periodic Time Dependence * * The funding provided by UTRC is greatly appreciated. [J] . Igor Mezic, Amit Surana IFAC PapersOnLine . 2016,第18期

机译：周期性/准周期性时间相关性的Koopman模式分解 * * UTRC提供的资金非常感谢。
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On Comparison of Dynamics of Dissipative and Finite-Time Systems Using Koopman Operator Methods * * The funding provided by ARO Grant W911NF-11-1-0511.

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