信息几何与控制理论
Information Geometry and Control Theory
DOI: 10.12677/DSC.2016.54015, PDF,    国家自然科学基金支持
作者: 韩希武, 孙华飞：北京理工大学数学与统计学院，北京 ；张真宁：北京工业大学数理学院，北京
关键词: 信息几何；矩阵信息几何；Fisher信息矩阵；Lie群；Information Geometry； Matrix Information Geometry； Fisher Information Matrix； Lie Group
摘要: 本文首先简要介绍信息几何的基本内容，包含随机的情形和非随机的情形。通过引入Fisher信息矩阵、对偶联络的引入，来处理随机的统计流形；通过利用一般线性群的李子群以及子流形的理论，建立矩阵信息几何理论。然后介绍信息几何在控制理论中的应用，包含随机的情形和非随机的情形。
Abstract: In this paper, we first introduce briefly the fundamental contents of information geometry. By in-troducing the Fisher information matrix and the dual connections, we can deal with the statistical manifold. At the same time, by using the theory of Lie groups and submanifolds of the general linear group, the theory of matrix information geometry is constructed. Then we introduce the ap-plications of information geometry to control theory, including the random case and the non- random case.
文章引用：韩希武, 孙华飞, 张真宁. 信息几何与控制理论[J]. 动力系统与控制, 2016, 5(4): 135-142. https://dx.doi.org/10.12677/DSC.2016.54015

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