Differential-integral Euler-Lagrange equations

Document Type : Research Article

Author

• Mohammed Shehata

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.

Keywords

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

Main Subjects

• Optimal Control

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