Optimization of bolza problem for third-order polyhedral delay-differential inclusions with state constraints

Sevilay Demir Sǎglam; Elimhan N. Mahmudov

doi:10.1063/5.0042177

Optimization of bolza problem for third-order polyhedral delay-differential inclusions with state constraints

Sevilay Demir Sǎglam^*, Elimhan N. Mahmudov

^*Corresponding author for this work

Department of Mathematics Engineering

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

1 Citation (Scopus)

Abstract

The present paper studies a Bolza problem of optimal control theory with third-order polyhedral delay-differential inclusions and state constraints. We aim to establish well verifiable sufficient conditions of optimality for the polyhedral thirdorder delay-differential inclusions. Discrete-approximate inclusions are investigated using the method of discretization to ensure the transition to a continuous problem. The idea for obtaining sufficient conditions of the problem is based on passing the formal limit on the optimality conditions of the discrete-approximation problem. Thus, the sufficient conditions are formulated by using polyhedral Euler-Lagrange inclusions and the distinctive "transversality" conditions.

Original language	English
Title of host publication	4th International Conference of Mathematical Sciences, ICMS 2020
Editors	Huseyin Cakalli, Ljubisa D. R. Kocinac, Allaberen Ashyralyev, Robin Harte, Mehmet Dik, Ibrahim Canak, Hacer Sengul Kandemir, Mujgan Tez, Ozay Gurtug, Ekrem Savas, Kadri Ulas Akay, Sahin Uyaver, Charyyar Ashyralyyev, Sefa Anil Sezer, Arap Duran Turkoglu, Oruc Raif Onvural, Hakan Sahin, Filiz Cagatay Ucgun
Publisher	American Institute of Physics Inc.
ISBN (Electronic)	9780735440784
DOIs	https://doi.org/10.1063/5.0042177
Publication status	Published - 2 Mar 2021
Event	4th International Conference of Mathematical Sciences, ICMS 2020 - Istanbul, Turkey Duration: 17 Jun 2020 → 21 Jun 2020

Publication series

Name	AIP Conference Proceedings
Volume	2334
ISSN (Print)	0094-243X
ISSN (Electronic)	1551-7616

Conference

Conference	4th International Conference of Mathematical Sciences, ICMS 2020
Country/Territory	Turkey
City	Istanbul
Period	17/06/20 → 21/06/20

Bibliographical note

Publisher Copyright:
© 2021 American Institute of Physics Inc.. All rights reserved.

Keywords

Delay-differential inclusion
Polyhedral
Transversality

Access to Document

10.1063/5.0042177

Cite this

Sǎglam, S. D., & Mahmudov, E. N. (2021). Optimization of bolza problem for third-order polyhedral delay-differential inclusions with state constraints. In H. Cakalli, L. D. R. Kocinac, A. Ashyralyev, R. Harte, M. Dik, I. Canak, H. S. Kandemir, M. Tez, O. Gurtug, E. Savas, K. U. Akay, S. Uyaver, C. Ashyralyyev, S. A. Sezer, A. D. Turkoglu, O. R. Onvural, H. Sahin, & F. C. Ucgun (Eds.), 4th International Conference of Mathematical Sciences, ICMS 2020 Article 030008 (AIP Conference Proceedings; Vol. 2334). American Institute of Physics Inc.. https://doi.org/10.1063/5.0042177

Sǎglam, Sevilay Demir ; Mahmudov, Elimhan N. / Optimization of bolza problem for third-order polyhedral delay-differential inclusions with state constraints. 4th International Conference of Mathematical Sciences, ICMS 2020. editor / Huseyin Cakalli ; Ljubisa D. R. Kocinac ; Allaberen Ashyralyev ; Robin Harte ; Mehmet Dik ; Ibrahim Canak ; Hacer Sengul Kandemir ; Mujgan Tez ; Ozay Gurtug ; Ekrem Savas ; Kadri Ulas Akay ; Sahin Uyaver ; Charyyar Ashyralyyev ; Sefa Anil Sezer ; Arap Duran Turkoglu ; Oruc Raif Onvural ; Hakan Sahin ; Filiz Cagatay Ucgun. American Institute of Physics Inc., 2021. (AIP Conference Proceedings).

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abstract = "The present paper studies a Bolza problem of optimal control theory with third-order polyhedral delay-differential inclusions and state constraints. We aim to establish well verifiable sufficient conditions of optimality for the polyhedral thirdorder delay-differential inclusions. Discrete-approximate inclusions are investigated using the method of discretization to ensure the transition to a continuous problem. The idea for obtaining sufficient conditions of the problem is based on passing the formal limit on the optimality conditions of the discrete-approximation problem. Thus, the sufficient conditions are formulated by using polyhedral Euler-Lagrange inclusions and the distinctive {"}transversality{"} conditions.",

keywords = "Delay-differential inclusion, Polyhedral, Transversality",

author = "Sǎglam, {Sevilay Demir} and Mahmudov, {Elimhan N.}",

note = "Publisher Copyright: {\textcopyright} 2021 American Institute of Physics Inc.. All rights reserved.; 4th International Conference of Mathematical Sciences, ICMS 2020 ; Conference date: 17-06-2020 Through 21-06-2020",

year = "2021",

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doi = "10.1063/5.0042177",

language = "English",

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editor = "Huseyin Cakalli and Kocinac, {Ljubisa D. R.} and Allaberen Ashyralyev and Robin Harte and Mehmet Dik and Ibrahim Canak and Kandemir, {Hacer Sengul} and Mujgan Tez and Ozay Gurtug and Ekrem Savas and Akay, {Kadri Ulas} and Sahin Uyaver and Charyyar Ashyralyyev and Sezer, {Sefa Anil} and Turkoglu, {Arap Duran} and Onvural, {Oruc Raif} and Hakan Sahin and Ucgun, {Filiz Cagatay}",

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Sǎglam, SD & Mahmudov, EN 2021, Optimization of bolza problem for third-order polyhedral delay-differential inclusions with state constraints. in H Cakalli, LDR Kocinac, A Ashyralyev, R Harte, M Dik, I Canak, HS Kandemir, M Tez, O Gurtug, E Savas, KU Akay, S Uyaver, C Ashyralyyev, SA Sezer, AD Turkoglu, OR Onvural, H Sahin & FC Ucgun (eds), 4th International Conference of Mathematical Sciences, ICMS 2020., 030008, AIP Conference Proceedings, vol. 2334, American Institute of Physics Inc., 4th International Conference of Mathematical Sciences, ICMS 2020, Istanbul, Turkey, 17/06/20. https://doi.org/10.1063/5.0042177

Optimization of bolza problem for third-order polyhedral delay-differential inclusions with state constraints. / Sǎglam, Sevilay Demir; Mahmudov, Elimhan N.
4th International Conference of Mathematical Sciences, ICMS 2020. ed. / Huseyin Cakalli; Ljubisa D. R. Kocinac; Allaberen Ashyralyev; Robin Harte; Mehmet Dik; Ibrahim Canak; Hacer Sengul Kandemir; Mujgan Tez; Ozay Gurtug; Ekrem Savas; Kadri Ulas Akay; Sahin Uyaver; Charyyar Ashyralyyev; Sefa Anil Sezer; Arap Duran Turkoglu; Oruc Raif Onvural; Hakan Sahin; Filiz Cagatay Ucgun. American Institute of Physics Inc., 2021. 030008 (AIP Conference Proceedings; Vol. 2334).

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

TY - GEN

T1 - Optimization of bolza problem for third-order polyhedral delay-differential inclusions with state constraints

AU - Sǎglam, Sevilay Demir

AU - Mahmudov, Elimhan N.

PY - 2021/3/2

Y1 - 2021/3/2

N2 - The present paper studies a Bolza problem of optimal control theory with third-order polyhedral delay-differential inclusions and state constraints. We aim to establish well verifiable sufficient conditions of optimality for the polyhedral thirdorder delay-differential inclusions. Discrete-approximate inclusions are investigated using the method of discretization to ensure the transition to a continuous problem. The idea for obtaining sufficient conditions of the problem is based on passing the formal limit on the optimality conditions of the discrete-approximation problem. Thus, the sufficient conditions are formulated by using polyhedral Euler-Lagrange inclusions and the distinctive "transversality" conditions.

AB - The present paper studies a Bolza problem of optimal control theory with third-order polyhedral delay-differential inclusions and state constraints. We aim to establish well verifiable sufficient conditions of optimality for the polyhedral thirdorder delay-differential inclusions. Discrete-approximate inclusions are investigated using the method of discretization to ensure the transition to a continuous problem. The idea for obtaining sufficient conditions of the problem is based on passing the formal limit on the optimality conditions of the discrete-approximation problem. Thus, the sufficient conditions are formulated by using polyhedral Euler-Lagrange inclusions and the distinctive "transversality" conditions.

KW - Delay-differential inclusion

KW - Polyhedral

KW - Transversality

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U2 - 10.1063/5.0042177

DO - 10.1063/5.0042177

M3 - Conference contribution

AN - SCOPUS:85102258804

T3 - AIP Conference Proceedings

BT - 4th International Conference of Mathematical Sciences, ICMS 2020

A2 - Cakalli, Huseyin

A2 - Kocinac, Ljubisa D. R.

A2 - Ashyralyev, Allaberen

A2 - Harte, Robin

A2 - Dik, Mehmet

A2 - Canak, Ibrahim

A2 - Kandemir, Hacer Sengul

A2 - Tez, Mujgan

A2 - Gurtug, Ozay

A2 - Savas, Ekrem

A2 - Akay, Kadri Ulas

A2 - Uyaver, Sahin

A2 - Ashyralyyev, Charyyar

A2 - Sezer, Sefa Anil

A2 - Turkoglu, Arap Duran

A2 - Onvural, Oruc Raif

A2 - Sahin, Hakan

A2 - Ucgun, Filiz Cagatay

PB - American Institute of Physics Inc.

T2 - 4th International Conference of Mathematical Sciences, ICMS 2020

Y2 - 17 June 2020 through 21 June 2020

ER -

Sǎglam SD, Mahmudov EN. Optimization of bolza problem for third-order polyhedral delay-differential inclusions with state constraints. In Cakalli H, Kocinac LDR, Ashyralyev A, Harte R, Dik M, Canak I, Kandemir HS, Tez M, Gurtug O, Savas E, Akay KU, Uyaver S, Ashyralyyev C, Sezer SA, Turkoglu AD, Onvural OR, Sahin H, Ucgun FC, editors, 4th International Conference of Mathematical Sciences, ICMS 2020. American Institute of Physics Inc. 2021. 030008. (AIP Conference Proceedings). doi: 10.1063/5.0042177

Optimization of bolza problem for third-order polyhedral delay-differential inclusions with state constraints

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