Properties of Solutions of Nonlinear Systems with Deep Learning and Functional Analysis.

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Bibliographic Details
Title:	Properties of Solutions of Nonlinear Systems with Deep Learning and Functional Analysis.
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]
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Database:	Engineering Source

Description
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]
ISSN:	19929978