Necessary first and second order optimality conditions for a fractional order differential equation with state delay
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866911767277338624 |
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| author | Gasimov, Jasarat J. Mahmudov, Nazim I. |
| author_facet | Gasimov, Jasarat J. Mahmudov, Nazim I. |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2401_13813 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Necessary first and second order optimality conditions for a fractional order differential equation with state delay Gasimov, Jasarat J. Mahmudov, Nazim I. Optimization and Control 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. |
| title | Necessary first and second order optimality conditions for a fractional order differential equation with state delay |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2401.13813 |