Open AccessStabilizability And Solvability Of Fuzzy Differential Equations Using Backstepping Method
Author(s) -
Muna S. Abbas,
Fadhel S. Fadhel
Publication year - 2021
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1963/1/012171
Subject(s) - mathematics , backstepping , fuzzy logic , nonlinear system , ordinary differential equation , stability (learning theory) , differential equation , mathematical optimization , control theory (sociology) , computer science , mathematical analysis , control (management) , adaptive control , artificial intelligence , physics , quantum mechanics , machine learning
Solution and stability of systems of fuzzy ordinary differential equations are of great important and may be sometimes difficult to carry out in the theory of fuzzy differential equations. Therefore, need for efficient approaches and techniques seem to be necessary for solving and stabilizing such type of problems. In this paper the backstepping method will be modified and used for analyzing systems of fuzzy ordinary differential equations. Such type of problems that might be encountered in studying the mathematical problems resulting from modeling complex physical or engineering real life phenomena’s. The topic of this paper is considered as a part of the control theory of fuzzy differential equations, in which the adaptive backstepping method based on constructing Lyapunove function in quadratic form will be combined with the so called the α -level sets in fuzzy set theory. The reliability of the proposed approach is presented by solving three examples, linear and nonlinear, in which the orginal system may be unstable.