Department of Basic Science, Bilbeis Higher Institute For Engineering, Sharqia, Egypt
10.22067/ijnao.2024.86104.1367
Abstract
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.
Shehata, M. (2024). Differential-integral Euler-Lagrange equations. Iranian Journal of Numerical Analysis and Optimization, (), -. doi: 10.22067/ijnao.2024.86104.1367
MLA
Mohammed Shehata. "Differential-integral Euler-Lagrange equations". Iranian Journal of Numerical Analysis and Optimization, , , 2024, -. doi: 10.22067/ijnao.2024.86104.1367
HARVARD
Shehata, M. (2024). 'Differential-integral Euler-Lagrange equations', Iranian Journal of Numerical Analysis and Optimization, (), pp. -. doi: 10.22067/ijnao.2024.86104.1367
VANCOUVER
Shehata, M. Differential-integral Euler-Lagrange equations. Iranian Journal of Numerical Analysis and Optimization, 2024; (): -. doi: 10.22067/ijnao.2024.86104.1367
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