On controllability of driftless control systems on symmetric spaces

IF 0.9 Q2 MATHEMATICS Arabian Journal of Mathematics Pub Date : 2024-08-30 DOI:10.1007/s40065-024-00469-w

Archana Tiwari, Rudra Narayan Padhan, Kishor Chandra Pati

引用次数: 0

Abstract

Symmetric spaces arise in wide variety of problems in Mathematics and Physics. They are mostly studied in Representation theory, Harmonic analysis and Differential geometry. As many physical systems have symmetric spaces as their configuration spaces, the study of controllability on symmetric space is quite interesting. In this paper, a driftless control system of type \({\dot{x}}= \sum _{i=1}^m u_if_i(x)\) is considered on a symmetric space. For this we have established global controllability condition which is illustrated by few examples of exponential submanifolds of SE(3) and random matrix ensembles.

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论对称空间上无漂移控制系统的可控性

对称空间出现在数学和物理学的各种问题中。对称空间主要用于研究表示理论、谐波分析和微分几何。由于许多物理系统都以对称空间作为其配置空间，因此对称空间的可控性研究相当有趣。本文考虑了对称空间上的无漂移控制系统（{\dot{x}}= \sum _{i=1}^m u_if_i(x)）。为此，我们建立了全局可控性条件，并通过几个 SE(3) 指数子曲面和随机矩阵集合的例子加以说明。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Arabian Journal of Mathematics MATHEMATICS-

CiteScore

2.20

自引率

8.30%

发文量

审稿时长

13 weeks

期刊介绍： The Arabian Journal of Mathematics is a quarterly, peer-reviewed open access journal published under the SpringerOpen brand, covering all mainstream branches of pure and applied mathematics. Owned by King Fahd University of Petroleum and Minerals, AJM publishes carefully refereed research papers in all main-stream branches of pure and applied mathematics. Survey papers may be submitted for publication by invitation only.To be published in AJM, a paper should be a significant contribution to the mathematics literature, well-written, and of interest to a wide audience. All manuscripts will undergo a strict refereeing process; acceptance for publication is based on two positive reviews from experts in the field.Submission of a manuscript acknowledges that the manuscript is original and is not, in whole or in part, published or submitted for publication elsewhere. A copyright agreement is required before the publication of the paper.Manuscripts must be written in English. It is the author''s responsibility to make sure her/his manuscript is written in clear, unambiguous and grammatically correct language.