Differential-integral Euler–Lagrange equations

Document Type : Research Article

Author

• Mohammedd Shehata

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

10.22067/ijnao.2024.86104.1367

Abstract

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.

Keywords

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

Main Subjects

• Optimal Control

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