Application of fuzzy systems on the numerical solution of the elliptic PDE-constrained optimal control problems

Azizi, Masoomeh; Amirfakhrian, Majid; Fariborzi Araghi, Mohammad Ali

doi:10.22034/cmde.2021.39351.1725

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	Application of fuzzy systems on the numerical solution of the elliptic PDE-constrained optimal control problems
Computational Methods for Differential Equations
مقاله 6، دوره 10، شماره 2، تیر 2022، صفحه 351-371 اصل مقاله (1.81 M)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2021.39351.1725
نویسندگان
Masoomeh Azizi¹؛ Majid Amirfakhrian^* ¹^{، 2}؛ Mohammad Ali Fariborzi Araghi¹
¹Department of Mathematics, Central Tehran Branch, Islamic Azad University, Tehran, Iran.
²Department of Computer Sciences, University of Calgary, Calgary, Canada.
چکیده
This paper presents a numerical fuzzy indirect method based on the fuzzy basis functions technique to solve an optimal control problem governed by Poisson’s differential equation. The considered problem may or may not be accompanied by a control box constraint. The first-order necessary optimality conditions have been derived, which may contain a variational inequality in function space. In the presented method, the obtained optimality conditions have been discretized using fuzzy basis functions and a system of equations introduced as the discretized optimality conditions. The derived system mostly contains some nonsmooth equations and conventional system solvers fail to solve them. A fuzzy system-based semi-smooth Newton method has also been introduced to deal with the obtained system. Solving optimality systems by the presented method gets us unknown fuzzy quantities on the state and control fuzzy expansions. Finally, some test problems have been studied to demonstrate the efficiency and accuracy of the presented fuzzy numerical technique.
کلیدواژه‌ها
Optimal control problems؛ Fuzzy system؛ Fuzzy basis functions؛ Universal approximation properties؛ Poisson’s equation؛ Optimality conditions؛ Semi-smooth Newton method

مراجع
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Application of fuzzy systems on the numerical solution of the elliptic PDE-constrained optimal control problems