A robust method for optimal control problems governed by system of Fredholm integral equations in mechanics

Iranian Journal of Numerical Analysis and Optimization

مقاله 26، دوره 13، شماره 2 - شماره پیاپی 25، شهریور 2023، صفحه 243-261   

نوع مقاله: Research Article

شناسه دیجیتال (DOI): 10.22067/ijnao.2022.78543.1178

نویسنده

A. Ebrahimzadeh^*

Department of Educational Mathematics, Farhangian university, Tehran, Iran.

چکیده

This essay considers an optimal control problem (OCP) governed by a system of Fredholm integral equations (FIE). In this paper, collocation approach with utilizing Lagrange polynomials is introduced to transform the OCP into a nonlinear programming problem (NLP). An efficient op-timization method in Mathematica software is utilized to solve NLP. The convergence analysis is discussed, which show the theoretical structure behind the propounded technique under some assumptions. In this es-say, computational outcomes are given to demonstrate the adaptability, forthrightness, and relationship of the calculations manufactured. A prac-tical real-world problem involving hanging chain in classical mechanic is also dissolved utilizing the approach proposed.

کلیدواژه‌ها

Collocation method؛ Lagrange polynomials؛ Optimal control؛ System of Fredholm integral equation؛ Convergence analysis

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