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Discrete generalized-Sylvester matrix equation solved by RNN with a novel direct discretization numerical method

Yang Shi Orcid Logo, Chenling Ding, Shuai Li Orcid Logo, Bin Li, Xiaobing Sun

Numerical Algorithms

Swansea University Author: Shuai Li Orcid Logo

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DOI (Published version): 10.1007/s11075-022-01449-x

Abstract

In the fields of artificial intelligence and control engineering, generalized-Sylvester matrix equation is considered as an important mathematic problem, and its solving process is usually viewed as a challenge that deserves particular attention. In this paper, a creative discrete-form recurrent neu...

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Published in: Numerical Algorithms
ISSN: 1017-1398 1572-9265
Published: Springer Science and Business Media LLC 2022
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URI: https://cronfa.swan.ac.uk/Record/cronfa62198
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spelling v2 62198 2022-12-22 Discrete generalized-Sylvester matrix equation solved by RNN with a novel direct discretization numerical method 42ff9eed09bcd109fbbe484a0f99a8a8 0000-0001-8316-5289 Shuai Li Shuai Li true false 2022-12-22 MECH In the fields of artificial intelligence and control engineering, generalized-Sylvester matrix equation is considered as an important mathematic problem, and its solving process is usually viewed as a challenge that deserves particular attention. In this paper, a creative discrete-form recurrent neural network (RNN) model is developed, analyzed and investigated for solving discrete-form time-variant generalized-Sylvester matrix equation (DF-TV-GSME), which is derived by a direct discretization numerical method. Specifically, first of all, DF-TV-GSME, which includes the well-known Lyapunov matrix equation and Sylvester matrix equation, is presented as the target problem of this research. Secondly, for solving such problem, different from the traditional discrete-form RNN design philosophy, second-order Taylor expansion is applied to derive the discrete-form RNN model. This creative process avoids involving the continuous time-variant environment and continuous-form model. Then, theoretical properties analyses are presented, which present the convergence and precision of the discrete-form RNN model. Abundant numerical experiments are further carried out with different perspectives of DF-TV-GSME, which further confirm the excellent properties of discrete-form RNN model. Journal Article Numerical Algorithms Springer Science and Business Media LLC 1017-1398 1572-9265 Generalized-Sylvester matrix equation; Recurrent neural network (RNN); Direct discretization method; Second-order Taylor expansion; Intelligent control; Residual error 12 12 2022 2022-12-12 10.1007/s11075-022-01449-x http://dx.doi.org/10.1007/s11075-022-01449-x COLLEGE NANME Mechanical Engineering COLLEGE CODE MECH Swansea University This work was supported in part by the National Natural Science Foundation of China (with numbers 61906164 and 61972335), in part by the Natural Science Foundation of Jiangsu Province of China (with number BK20190875), in part by the Six Talent Peaks Project in Jiangsu Province (with number RJFW-053), in part by Jiangsu “333” Project, in part by Qinglan project of Yangzhou University, in part by the Cross-Disciplinary Project of the Animal Science Special Discipline of Yangzhou University, in part by the Yangzhou University Interdisciplinary Research Foundation for Animal Husbandry Discipline of Targeted Support (with number yzuxk202015), in part by the Yangzhou City-Yangzhou University Science and Technology Cooperation Fund Project (with number YZ2021157), in part by the Yangzhou University Top-level Talents Support Program (2021, 2019) by the Postgraduate Research & Practice Innovation Program of Jiangsu Province (with numbers KYCX21_3234 and SJCX22_1709). 2023-06-01T12:17:27.5648568 2022-12-22T09:11:37.3938932 Faculty of Science and Engineering School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Mechanical Engineering Yang Shi 0000-0003-3014-7858 1 Chenling Ding 2 Shuai Li 0000-0001-8316-5289 3 Bin Li 4 Xiaobing Sun 5
title Discrete generalized-Sylvester matrix equation solved by RNN with a novel direct discretization numerical method
spellingShingle Discrete generalized-Sylvester matrix equation solved by RNN with a novel direct discretization numerical method
Shuai Li
title_short Discrete generalized-Sylvester matrix equation solved by RNN with a novel direct discretization numerical method
title_full Discrete generalized-Sylvester matrix equation solved by RNN with a novel direct discretization numerical method
title_fullStr Discrete generalized-Sylvester matrix equation solved by RNN with a novel direct discretization numerical method
title_full_unstemmed Discrete generalized-Sylvester matrix equation solved by RNN with a novel direct discretization numerical method
title_sort Discrete generalized-Sylvester matrix equation solved by RNN with a novel direct discretization numerical method
author_id_str_mv 42ff9eed09bcd109fbbe484a0f99a8a8
author_id_fullname_str_mv 42ff9eed09bcd109fbbe484a0f99a8a8_***_Shuai Li
author Shuai Li
author2 Yang Shi
Chenling Ding
Shuai Li
Bin Li
Xiaobing Sun
format Journal article
container_title Numerical Algorithms
publishDate 2022
institution Swansea University
issn 1017-1398
1572-9265
doi_str_mv 10.1007/s11075-022-01449-x
publisher Springer Science and Business Media LLC
college_str Faculty of Science and Engineering
hierarchytype
hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Mechanical Engineering{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Mechanical Engineering
url http://dx.doi.org/10.1007/s11075-022-01449-x
document_store_str 0
active_str 0
description In the fields of artificial intelligence and control engineering, generalized-Sylvester matrix equation is considered as an important mathematic problem, and its solving process is usually viewed as a challenge that deserves particular attention. In this paper, a creative discrete-form recurrent neural network (RNN) model is developed, analyzed and investigated for solving discrete-form time-variant generalized-Sylvester matrix equation (DF-TV-GSME), which is derived by a direct discretization numerical method. Specifically, first of all, DF-TV-GSME, which includes the well-known Lyapunov matrix equation and Sylvester matrix equation, is presented as the target problem of this research. Secondly, for solving such problem, different from the traditional discrete-form RNN design philosophy, second-order Taylor expansion is applied to derive the discrete-form RNN model. This creative process avoids involving the continuous time-variant environment and continuous-form model. Then, theoretical properties analyses are presented, which present the convergence and precision of the discrete-form RNN model. Abundant numerical experiments are further carried out with different perspectives of DF-TV-GSME, which further confirm the excellent properties of discrete-form RNN model.
published_date 2022-12-12T12:17:26Z
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score 11.012678

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