Optimal Control of Elliptic Type Polyhedral Inclusions

Elimhan N. Mahmudov; Dilara I. Mastaliyeva

doi:10.1109/PCI60110.2023.10325954

Optimal Control of Elliptic Type Polyhedral Inclusions

Elimhan N. Mahmudov, Dilara I. Mastaliyeva^*

^*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

The article considers an optimal control problem described by partial differential inclusions. At the same time, the problem with a polyhedral discrete inclusion is studied in detail. Using the Farkas theorem, locally adjoint mappings are calculated and necessary and sufficient conditions of optimality for polyhedral elliptic discrete inclusions are proved. After that, with the help of the polyhedral elliptic discretization method for the discrete-approximate problem, necessary and sufficient optimality conditions are formulated in the Euler-Lagrange form of the adjoint polyhedral inclusion. In addition, linear discrete-approximate and continuous optimal control problems of elliptic type are also considered. Using the polyhedral nature of the problem, optimality conditions for a polyhedral differential inclusion (DFI) are proved. An example is given to demonstrate the proposed approach.

Original language	English
Title of host publication	2023 5th International Conference on Problems of Cybernetics and Informatics, PCI 2023
Publisher	Institute of Electrical and Electronics Engineers Inc.
ISBN (Electronic)	9798350319064
DOIs	https://doi.org/10.1109/PCI60110.2023.10325954
Publication status	Published - 2023
Externally published	Yes
Event	5th International Conference on Problems of Cybernetics and Informatics, PCI 2023 - Baku, Azerbaijan Duration: 28 Aug 2023 → 30 Aug 2023

Publication series

Name	2023 5th International Conference on Problems of Cybernetics and Informatics, PCI 2023

Conference

Conference	5th International Conference on Problems of Cybernetics and Informatics, PCI 2023
Country/Territory	Azerbaijan
City	Baku
Period	28/08/23 → 30/08/23

Bibliographical note

Publisher Copyright:
© 2023 IEEE.

Keywords

approximate
elliptic differential inclusions
Euler-Lagrange
necessary and sufficient
polyhedral

Access to Document

10.1109/PCI60110.2023.10325954

Cite this

Mahmudov, E. N., & Mastaliyeva, D. I. (2023). Optimal Control of Elliptic Type Polyhedral Inclusions. In 2023 5th International Conference on Problems of Cybernetics and Informatics, PCI 2023 (2023 5th International Conference on Problems of Cybernetics and Informatics, PCI 2023). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/PCI60110.2023.10325954

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abstract = "The article considers an optimal control problem described by partial differential inclusions. At the same time, the problem with a polyhedral discrete inclusion is studied in detail. Using the Farkas theorem, locally adjoint mappings are calculated and necessary and sufficient conditions of optimality for polyhedral elliptic discrete inclusions are proved. After that, with the help of the polyhedral elliptic discretization method for the discrete-approximate problem, necessary and sufficient optimality conditions are formulated in the Euler-Lagrange form of the adjoint polyhedral inclusion. In addition, linear discrete-approximate and continuous optimal control problems of elliptic type are also considered. Using the polyhedral nature of the problem, optimality conditions for a polyhedral differential inclusion (DFI) are proved. An example is given to demonstrate the proposed approach.",

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author = "Mahmudov, {Elimhan N.} and Mastaliyeva, {Dilara I.}",

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year = "2023",

doi = "10.1109/PCI60110.2023.10325954",

language = "English",

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Mahmudov, EN & Mastaliyeva, DI 2023, Optimal Control of Elliptic Type Polyhedral Inclusions. in 2023 5th International Conference on Problems of Cybernetics and Informatics, PCI 2023. 2023 5th International Conference on Problems of Cybernetics and Informatics, PCI 2023, Institute of Electrical and Electronics Engineers Inc., 5th International Conference on Problems of Cybernetics and Informatics, PCI 2023, Baku, Azerbaijan, 28/08/23. https://doi.org/10.1109/PCI60110.2023.10325954

Optimal Control of Elliptic Type Polyhedral Inclusions. / Mahmudov, Elimhan N.; Mastaliyeva, Dilara I.
2023 5th International Conference on Problems of Cybernetics and Informatics, PCI 2023. Institute of Electrical and Electronics Engineers Inc., 2023. (2023 5th International Conference on Problems of Cybernetics and Informatics, PCI 2023).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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N2 - The article considers an optimal control problem described by partial differential inclusions. At the same time, the problem with a polyhedral discrete inclusion is studied in detail. Using the Farkas theorem, locally adjoint mappings are calculated and necessary and sufficient conditions of optimality for polyhedral elliptic discrete inclusions are proved. After that, with the help of the polyhedral elliptic discretization method for the discrete-approximate problem, necessary and sufficient optimality conditions are formulated in the Euler-Lagrange form of the adjoint polyhedral inclusion. In addition, linear discrete-approximate and continuous optimal control problems of elliptic type are also considered. Using the polyhedral nature of the problem, optimality conditions for a polyhedral differential inclusion (DFI) are proved. An example is given to demonstrate the proposed approach.

AB - The article considers an optimal control problem described by partial differential inclusions. At the same time, the problem with a polyhedral discrete inclusion is studied in detail. Using the Farkas theorem, locally adjoint mappings are calculated and necessary and sufficient conditions of optimality for polyhedral elliptic discrete inclusions are proved. After that, with the help of the polyhedral elliptic discretization method for the discrete-approximate problem, necessary and sufficient optimality conditions are formulated in the Euler-Lagrange form of the adjoint polyhedral inclusion. In addition, linear discrete-approximate and continuous optimal control problems of elliptic type are also considered. Using the polyhedral nature of the problem, optimality conditions for a polyhedral differential inclusion (DFI) are proved. An example is given to demonstrate the proposed approach.

KW - approximate

KW - elliptic differential inclusions

KW - Euler-Lagrange

KW - necessary and sufficient

KW - polyhedral

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Optimal Control of Elliptic Type Polyhedral Inclusions

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