| Riccati方程的几何求解方法 |
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| 引用本文： | 纳文,曹越琦,张世强,孙华飞. Riccati方程的几何求解方法[J]. 北京理工大学学报, 2020, 40(4): 448-451. DOI: 10.15918/j.tbit1001-0645.2019.028 |
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| 作者姓名： | 纳文 曹越琦 张世强 孙华飞 |
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| 作者单位： | 北京理工大学 数学与统计学院, 北京 100081 |
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| 基金项目： | 北京市科委创新资助项目（Z161100005016043） |
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| 摘 要： | 本文首先介绍线性系统的最优控制概念,引入经典的Riccati方程.之后,在4种不同的黎曼度量下给出正定矩阵流形上的测地距离.最后,利用几何方法求出对应的黎曼梯度,给出了关于测地距离的求解Riccati方程的迭代公式.
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| 关 键 词： | 最优控制 测地距离 Riccati方程 黎曼梯度 |
| 收稿时间： | 2019-01-17 |
The Geometric Approach of Riccati Equations |
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| AUNG Naing Win,CAO Yue-qi,ZHANG Shi-qiang and SUN Hua-fei. The Geometric Approach of Riccati Equations[J]. Journal of Beijing Institute of Technology(Natural Science Edition), 2020, 40(4): 448-451. DOI: 10.15918/j.tbit1001-0645.2019.028 |
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| Authors: | AUNG Naing Win CAO Yue-qi ZHANG Shi-qiang SUN Hua-fei |
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| Affiliation: | School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, China |
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| Abstract: | In this paper, the concept of optimal control for linear system, as well as the classical Riccati equation was introduced first. Then four kinds of Riemannian metrics were presented to obtain the geodesic distances on symmetric positive definite matrix manifold. At last, solving the corresponding Riemannian gradient, the new methods were provided for solving the Riccati equations. |
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| Keywords: | optimal control geodesic distance Riccati equation Riemannian gradient |
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