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A numerical method for solving boundary optimal control problem modeled by heat transfer equation, in the presence of a scale invariance property | ||
| Journal of Mathematical Modeling | ||
| مقاله 20، دوره 13، شماره 1، خرداد 2025 اصل مقاله (224.48 K) | ||
| نوع مقاله: Research Article | ||
| شناسه دیجیتال (DOI): 10.22124/jmm.2024.27197.2403 | ||
| نویسندگان | ||
| Benalia Karim* 1؛ Beddek Karim2؛ Oukacha Brahim3 | ||
| 1Department of Mathematical Sciences, Faculty of Hydrocarbons and Chemistry, University of Boumerdes, Boumerdes, Algeria | ||
| 2Laboratory of Applied Automation (LAA), Department of Automation, Faculty of Hydrocarbons and Chemistry, University of Boumerdes, Algeria | ||
| 3Laboratory of Operational Research and Mathematical decision, University of Tizi-Ouzou, Hasnaoua II 15000, Algeria | ||
| چکیده | ||
| In this paper, we present a computational approach for solving a boundary optimal control problem modeled by heat transfer equation with two-point boundary conditions, in the presence of a scale invariance property under dilation. First, we establish a scale-invariant solution. Indeed, the dependence of this solution towards a scale invariance factor naturally leads to an optimal control problem. Second, we propose a numerical approach to solve this problem. The idea consists in transforming the problem into an optimal control problem modeled by a system of ordinary differential equations invariant under dilation using the finite difference approximation. Therefor, the minimum principle of Pontryagin is applied to derive the necessary optimality conditions that are solved by the vartiational iteration method to get an approximate scale-invariant solutions for the optimal control law. Finally, to show the efficiency of this approach, a numerical example is illustrated and comparison with another method is performed. | ||
| کلیدواژه‌ها | ||
| Optimal control؛ heat-transfer equation؛ scale invariance؛ iteration variational method؛ minimum principe of Pontryagin | ||
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آمار تعداد مشاهده مقاله: 210 تعداد دریافت فایل اصل مقاله: 169 |
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