Properties of Solutions of Nonlinear Systems with Deep Learning and Functional Analysis.
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| Title: | Properties of Solutions of Nonlinear Systems with Deep Learning and Functional Analysis. |
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| Authors: | Zhiyong Xing1 painieb5303@163.com, Li Huang2 xuanyouw21904@163.com, Zhitao Zhao3 zuiyinglaoth30@163.com |
| Source: | IAENG International Journal of Applied Mathematics. Nov2025, Vol. 55 Issue 11, p3549-3555. 7p. |
| Subjects: | Nonlinear systems, Functional analysis, Function spaces, Model validation, Deep learning, Uniqueness (Mathematics), Control theory (Engineering), Hybrid systems |
| Abstract: | Nonlinear switching systems, as a special class of hybrid systems, are widely used in the field of control. The existence and uniqueness of solutions to systems have always been highly concerned. The theory of nonlinear systems originally appeared at the beginning of the calculus theory. Since then, functional analysis has gradually become an important theoretical basis for study of nonlinear systems. Functional analysis originates from the study of various function spaces, in which the convergence of sequences of functions has different types. On the one hand, functional analysis use of the content provided by many other disciplines to extract its own research objects and some research methods, and it has formed many important branches. Based on this, this paper proposes a to solve nonlinear systems. Deep learning is guided by functional analysis to perform a series of solving tasks. Experimental verification is carried out on different nonlinear systems. The experimental results show that the model can accurately and efficiently calculate the solutions of nonlinear systems. Through comparative experiments, it is found that other methods often lose solutions in the process of solving. The model in this can calculate all the solutions. This reflects the accuracy of the method. [ABSTRACT FROM AUTHOR] |
| Copyright of IAENG International Journal of Applied Mathematics is the property of International Association of Engineers (IAENG) and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
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| Items | – Name: Title Label: Title Group: Ti Data: Properties of Solutions of Nonlinear Systems with Deep Learning and Functional Analysis. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Zhiyong+Xing%22">Zhiyong Xing</searchLink><relatesTo>1</relatesTo><i> painieb5303@163.com</i><br /><searchLink fieldCode="AR" term="%22Li+Huang%22">Li Huang</searchLink><relatesTo>2</relatesTo><i> xuanyouw21904@163.com</i><br /><searchLink fieldCode="AR" term="%22Zhitao+Zhao%22">Zhitao Zhao</searchLink><relatesTo>3</relatesTo><i> zuiyinglaoth30@163.com</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22IAENG+International+Journal+of+Applied+Mathematics%22">IAENG International Journal of Applied Mathematics</searchLink>. Nov2025, Vol. 55 Issue 11, p3549-3555. 7p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Nonlinear+systems%22">Nonlinear systems</searchLink><br /><searchLink fieldCode="DE" term="%22Functional+analysis%22">Functional analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Function+spaces%22">Function spaces</searchLink><br /><searchLink fieldCode="DE" term="%22Model+validation%22">Model validation</searchLink><br /><searchLink fieldCode="DE" term="%22Deep+learning%22">Deep learning</searchLink><br /><searchLink fieldCode="DE" term="%22Uniqueness+%28Mathematics%29%22">Uniqueness (Mathematics)</searchLink><br /><searchLink fieldCode="DE" term="%22Control+theory+%28Engineering%29%22">Control theory (Engineering)</searchLink><br /><searchLink fieldCode="DE" term="%22Hybrid+systems%22">Hybrid systems</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: Nonlinear switching systems, as a special class of hybrid systems, are widely used in the field of control. The existence and uniqueness of solutions to systems have always been highly concerned. The theory of nonlinear systems originally appeared at the beginning of the calculus theory. Since then, functional analysis has gradually become an important theoretical basis for study of nonlinear systems. Functional analysis originates from the study of various function spaces, in which the convergence of sequences of functions has different types. On the one hand, functional analysis use of the content provided by many other disciplines to extract its own research objects and some research methods, and it has formed many important branches. Based on this, this paper proposes a to solve nonlinear systems. Deep learning is guided by functional analysis to perform a series of solving tasks. Experimental verification is carried out on different nonlinear systems. The experimental results show that the model can accurately and efficiently calculate the solutions of nonlinear systems. Through comparative experiments, it is found that other methods often lose solutions in the process of solving. The model in this can calculate all the solutions. This reflects the accuracy of the method. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of IAENG International Journal of Applied Mathematics is the property of International Association of Engineers (IAENG) and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 7 StartPage: 3549 Subjects: – SubjectFull: Nonlinear systems Type: general – SubjectFull: Functional analysis Type: general – SubjectFull: Function spaces Type: general – SubjectFull: Model validation Type: general – SubjectFull: Deep learning Type: general – SubjectFull: Uniqueness (Mathematics) Type: general – SubjectFull: Control theory (Engineering) Type: general – SubjectFull: Hybrid systems Type: general Titles: – TitleFull: Properties of Solutions of Nonlinear Systems with Deep Learning and Functional Analysis. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Zhiyong Xing – PersonEntity: Name: NameFull: Li Huang – PersonEntity: Name: NameFull: Zhitao Zhao IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 11 Text: Nov2025 Type: published Y: 2025 Identifiers: – Type: issn-print Value: 19929978 Numbering: – Type: volume Value: 55 – Type: issue Value: 11 Titles: – TitleFull: IAENG International Journal of Applied Mathematics Type: main |
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