Zainab John1,2This email address is being protected from spambots. You need JavaScript enabled to view it., Teh Yuan Ying1, Fadhel Subhi Fadhel3, and Ali F. Jameel4
1School of Quantitative Sciences, College of Art and Sciences, Universiti Utara Malaysia (UUM), Malaysia
2Department of Mathematics, College of Science, Mustansiriyah University, Baghdad, Iraq
3Department of Mathematics and Computer Applications, College of Science, Al-Nahrain University, Jadriya, Baghdad, Iraq
4Faculty of Education and Arts, Sohar University, Sultanate of Oman
Received: October 1, 2024 Accepted: November 25, 2024 Publication Date: March 7, 2025
Copyright The Author(s). This is an open access article distributed under the terms of the Creative Commons Attribution License (CC BY 4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are cited.
In this work, asetoflawshasbeenproposedasagroupoffeedbackcontrolstabilizingaboundarylawforalinear fuzzy reaction-advection-diffusion equation. Stabilization is achieved by designing coordinate transformations that form recursive relationships; by using the fuzzy finite difference method, we can convert coordinates into other coordinates. This design process is unlimited to any specific kinds of boundary actuation and can handle systems with an arbitrarily finite number of eigenvalues for the unstable open-loop system. We noticed that there is another problem when converting coordinates, which is that the equation includes lower and upper functions, so we wrote the equations in the form of matrices and then converted them into ordinary differential equations. The problem of feedback, which becomes increasingly unbounded as the grid gets infinitely fine, is solved by carefully selecting the target system to which the original system is transformed. Then we stabilize the closed loop system and the regularity of control and solutions to the fuzzy reaction-advection-diffusion equation.
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