Differential-integral Euler-Lagrange equations

Iranian Journal of Numerical Analysis and Optimization

مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 26 اسفند 1402

نوع مقاله: Research Article

شناسه دیجیتال (DOI): 10.22067/ijnao.2024.86104.1367

نویسنده

Mohammed Shehata^*

Department of Basic Science, Bilbeis Higher Institute For Engineering, Sharqia, Egypt

چکیده

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

کلیدواژه‌ها

Calculus of variations؛ Euler-Lagrange equation؛ optimal control problems؛ differential-integral equation؛ RLC electrical circuit