Information-theoretic formulation of dynamical systems: causality, modeling, and control
Information-theoretic formulation of dynamical systems: causality, modeling, and control
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DOI：
10.1103/physrevresearch.4.023195
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发表时间：
2021-11
期刊：
影响因子：
--
通讯作者：
Adri'an Lozano-Dur'an;G. Arranz
中科院分区：
文献类型：
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作者：
Adri'an Lozano-Dur'an;G. Arranz
混沌高维动力系统的因果关系、建模和控制问题是用信息论的语言表述的。感兴趣的中心量是香农熵，它衡量系统状态中的信息量。在这个框架内，因果关系通过动力系统中感兴趣的变量之间的信息流动来量化。降阶建模是一个与信息守恒有关的问题，其中模型的目标是最大限度地保留原始系统的相关信息量。类似地，通过将串联传感器-执行器设想为减少待控制状态的未知信息的装置，控制理论被投射到信息论的术语中。新的公式被用来解决关于湍流的因果关系、建模和控制的三个问题，湍流是混沌、高维动力系统的主要例子。这些应用包括湍流叶栅中能量传递的因果关系，用于大涡模拟的亚网格尺度模拟，以及用于壁面湍流减阻的流动控制。
The problems of causality, modeling, and control for chaotic, high-dimensional dynamical systems are formulated in the language of information theory. The central quantity of interest is the Shannon entropy, which measures the amount of information in the states of the system. Within this framework, causality is quantified by the information flux among the variables of interest in the dynamical system. Reduced-order modeling is posed as a problem related to the conservation of information in which models aim at preserving the maximum amount of relevant information from the original system. Similarly, control theory is cast in information-theoretic terms by envisioning the tandem sensor-actuator as a device reducing the unknown information of the state to be controlled. The new formulation is used to address three problems about the causality, modeling, and control of turbulence, which stands as a primary example of a chaotic, high-dimensional dynamical system. The applications include the causality of the energy transfer in the turbulent cascade, subgrid-scale modeling for large-eddy simulation, and flow control for drag reduction in wall-bounded turbulence.