Machine Learning for Modeling the Singular Multi-Pantograph Equations

In this study, a new approach to basis of intelligent systems and machine learning algorithms is introduced for solving singular multi-pantograph differential equations (SMDEs). For the first time, a type-2 fuzzy logic based approach is formulated to find an approximated solution. The rules of the s...

Full description

Saved in:
Bibliographic Details
Published in:Entropy (Basel, Switzerland) Switzerland), 2020-09, Vol.22 (9), p.1041
Main Authors: Mosavi, Amirhosein, Shokri, Manouchehr, Mansor, Zulkefli, Qasem, Sultan Noman, Band, Shahab S, Mohammadzadeh, Ardashir
Format: Article
Language:English
Subjects:
fuzzy systems
Lyapunov function
singular multi-pantograph differential equations
square root cubature kalman filter
statistical analysis
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:In this study, a new approach to basis of intelligent systems and machine learning algorithms is introduced for solving singular multi-pantograph differential equations (SMDEs). For the first time, a type-2 fuzzy logic based approach is formulated to find an approximated solution. The rules of the suggested type-2 fuzzy logic system (T2-FLS) are optimized by the square root cubature Kalman filter (SCKF) such that the proposed fineness function to be minimized. Furthermore, the stability and boundedness of the estimation error is proved by novel approach on basis of Lyapunov theorem. The accuracy and robustness of the suggested algorithm is verified by several statistical examinations. It is shown that the suggested method results in an accurate solution with rapid convergence and a lower computational cost.
ISSN:1099-4300
1099-4300
DOI:10.3390/e22091041