Differential-integral Euler–Lagrange equations

Iranian Journal of Numerical Analysis and Optimization

مقاله 2، دوره 14، Issue 3 - شماره پیاپی 30، آذر 2024، صفحه 662-680   

نوع مقاله: Research Article

شناسه دیجیتال (DOI): 10.22067/ijnao.2024.86104.1367

نویسنده

Mohammedd Shehata^*

Department of Basic Science, Bilbeis Higher Institute for Engineering, Sharqia, Egypt.

چکیده

We study the calculus of variations problem in the presence of a system of differential-integral (D-I) equations. In order to identify the necessary optimality conditions for this problem, we derive the so-called D-I Euler–Lagrange equations. We also generalize this problem to other cases, such as the case of higher orders, the problem of optimal control, and we derive the so-called D-I Pontryagin equations. In special cases, these formulations lead to classical Euler–Lagrange equations. To illustrate our results, we provide simple examples and applications such as obtaining the minimum
power for an RLC circuit.

کلیدواژه‌ها

Calculus of variations؛ Euler–Lagrange equation؛ Optimal con-trol problems؛ Differential-integral equation؛ RLC electrical circuit

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