The optimal control problem for systems of integro-differential equations with finite and infinite horizon

被引：1

作者：

Lakhva, Roksolana ^{[1
]}

Khaletska, Zoia ^{[2
]}

Mogylova, Viktoriia ^{[3
]}

机构：

[1] Taras Shevchenko Natl Univ Kyiv, Fac Mech & Math, Kyiv, Ukraine

[2] Volodymyr Vinnichenko Cent Ukrainian State Univ, Fac Math Nat Sci & Technol, Kropyvnytskyi, Ukraine

[3] Igor Sikorsky Kyiv Polytech Inst, Fac Phys & Math, Kyiv, Ukraine

来源：

GEORGIAN MATHEMATICAL JOURNAL | 2025年 / 32卷 / 03期

关键词：

Optimal control; finite interval; infinite interval; convexity; weak convergence; integro-differential system;

D O I：

10.1515/gmj-2024-2065

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we study the optimal control problem for integro-differential equations on the semi-axis, which are non-linear with respect to the phase variables and linear with respect to the control. We obtained the sufficient conditions for existence of optimal control in terms of the right-hand side and the quality criterion. Also, we studied the relation between the solutions of the problems on infinite and finite intervals when the length of the interval goes to infinity.

引用

页码：465 / 476

页数：12

共 18 条

[1] Reliable algorithms for solving integro-differential equations with applications [J].

Alawneh, Ameen ;

Al-Khaled, Kamel ;

Al-Towaiq, Mohammed .

INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, 2010, 87 (07) :1538-1554

[2] Stability analysis of delay integro-differential equations of HIV-1 infection model [J].

Ali, Nigar ;

Zaman, Gul ;

Jung, Il Hyo .

GEORGIAN MATHEMATICAL JOURNAL, 2020, 27 (03) :331-340

[3] On solvability of boundary value problem for a nonlinear Fredholm integro-differential equation [J].

Assanova, A. T. ;

Zhumatov, S. S. ;

Mynbayeva, S. T. ;

Karakenova, S. G. .

BULLETIN OF THE KARAGANDA UNIVERSITY-MATHEMATICS, 2022, 105 (01) :25-34

[4]

Bochuk O. A., 2013, NELNN KOLIV, V16, P460

[5]

Boichuk O. A., 2014, J MATH SCI NY, V203, P306, DOI DOI 10.1007/s10958-014-2135-1

[6] A METHOD OF SOLVING A NONLINEAR BOUNDARY VALUE PROBLEM FOR THE FREDHOLM INTEGRO-DIFFERENTIAL EQUATION [J].

Dzhumabaev, Dulat S. ;

Mynbayeva, Sandugash .

JOURNAL OF INTEGRAL EQUATIONS AND APPLICATIONS, 2021, 33 (01) :53-75

[7] Averaged semi-discrete scheme of sum-approximation for one nonlinear multi-dimensional integro-differential parabolic equation [J].

Jangveladze, Temur ;

Kiguradze, Zurab .

GEORGIAN MATHEMATICAL JOURNAL, 2020, 27 (03) :367-373

[8]

Kean JM, 2001, J APPL ECOL, V38, P162, DOI 10.1046/j.1365-2664.2001.00579.x

[9] OPTIMAL CONTROL PROBLEMS FOR SOME CLASSES OF FUNCTIONAL-DIFFERENTIAL EQUATIONS ON THE SEMI-AXIS [J].

Kichmarenko, O. ;

Stanzhytskyi, O. .

MISKOLC MATHEMATICAL NOTES, 2019, 20 (02) :1021-1037

[10]

Kichmarenko O., 2018, NONLINEAR DYN SYST T, V18, P196

← 1 2 →