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arXiv · 2401.13813

Necessary first and second order optimality conditions for a fractional order differential equation with state delay

Jasarat J. Gasimov·Nazim I. Mahmudov
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Abstract

In this research paper, we examine an optimal control problem involving a dynamical system governed by a nonlinear Caputo fractional time-delay state equation. The primary objective of this study is to obtain the necessary conditions for optimality, both the first and second order, for the Caputo fractional time-delay optimal control problem. We derive the first-order necessary condition for optimality for the given fractional time-delay optimal control problem. Moreover, we focus on a case where the Pontryagin maximum principle degenerates, meaning that it is satisfied in a tivial manner. Consequently, we proceed to derive the second order optimality conditions specific to the problem under investigation. At the end illustrative examples are provided.

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Jasarat J. Gasimov, Nazim I. Mahmudov. 2024-01-24. Necessary first and second order optimality conditions for a fractional order differential equation with state delay. https://arxiv.org/abs/2401.13813

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