Averaging method in optimal control problems for integro-differential equations

被引：0

作者：

Lakhva, Roksolana ^{[1
]}

Uteshova, Roza ^{[2
]}

Stanzhytskyi, Oleksandr ^{[1
]}

Mogylova, Viktoria ^{[3
]}

机构：

[1] Taras Shevchenko Natl Univ Kyiv, 64-13 Volodymyrska St, UA-01601 Kiev, Ukraine

[2] Inst Math & Math Modeling, 125 Pushkin St, Alma Ata 050010, Kazakhstan

[3] Natl Tech Univ Ukraine, Igor Sikorsky Kyiv Polytech Inst, 37 Peremohy Ave, UA-03056 Kiev, Ukraine

来源：

OPEN MATHEMATICS | 2025年 / 23卷 / 01期

关键词：

optimal control; weak convergence; averaging; oscillation; quality criterion; weakly compact; MODEL;

D O I：

10.1515/math-2025-0167

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The averaging method is applied to the study of optimal control problems for systems of integro-differential equations with rapidly oscillating coefficients and a small parameter. The original problem is associated with an averaged optimal control problem, formulated for a system of ordinary differential equations, which significantly simplifies the analysis. It is proven that as the small parameter tends to zero, the quality criterion, optimal control, and optimal trajectory of the original problem converge to those of the averaged problem.

引用

页数：19

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