Asymptotics of a Solution to an Optimal Control Problem with a Terminal Convex Performance Index and a Perturbation of the Initial Data

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Asymptotics of a Solution to an Optimal Control Problem with a Terminal Convex Performance Index and a Perturbation of the Initial Data. / Danilin, A.; Kovrizhnykh, O.
в: Proceedings of the Steklov Institute of Mathematics, Том 323, № S1, 01.12.2023, стр. S85-S97.

Результаты исследований: Вклад в журнал › Статья › Рецензирование

BibTeX

@article{6092693c738344b9b6366b811d16beb6,

title = "Asymptotics of a Solution to an Optimal Control Problem with a Terminal Convex Performance Index and a Perturbation of the Initial Data",

abstract = "In this paper, we investigate a problem of optimal control over a finite time interval for a linear systemwith constant coefficients and a small parameter in the initial data in the class of piecewise continuous controlswith smooth geometric constraints. We consider a terminal convex performance index. We substantiate the limit relationsas the small parameter tends to zero for the optimal value of the performance index and for the vector generatingthe optimal control in the problem. We show that the asymptotics of the solution can be of complicated nature. Inparticular, it may have no expansion in the Poincar{\'e} sense in any asymptotic sequence of rational functions of thesmall parameter or its logarithms",

author = "A. Danilin and O. Kovrizhnykh",

note = "This work was supported by ongoing institutional funding. No additional grants to carry out or direct this particular research were obtained.",

year = "2023",

month = dec,

day = "1",

doi = "10.1134/S008154382306007X",

language = "English",

volume = "323",

pages = "S85--S97",

journal = "Proceedings of the Steklov Institute of Mathematics",

issn = "0081-5438",

publisher = "Pleiades Publishing",

number = "S1",

}

RIS

TY - JOUR

T1 - Asymptotics of a Solution to an Optimal Control Problem with a Terminal Convex Performance Index and a Perturbation of the Initial Data

AU - Danilin, A.

AU - Kovrizhnykh, O.

N1 - This work was supported by ongoing institutional funding. No additional grants to carry out or direct this particular research were obtained.

PY - 2023/12/1

Y1 - 2023/12/1

N2 - In this paper, we investigate a problem of optimal control over a finite time interval for a linear systemwith constant coefficients and a small parameter in the initial data in the class of piecewise continuous controlswith smooth geometric constraints. We consider a terminal convex performance index. We substantiate the limit relationsas the small parameter tends to zero for the optimal value of the performance index and for the vector generatingthe optimal control in the problem. We show that the asymptotics of the solution can be of complicated nature. Inparticular, it may have no expansion in the Poincaré sense in any asymptotic sequence of rational functions of thesmall parameter or its logarithms

AB - In this paper, we investigate a problem of optimal control over a finite time interval for a linear systemwith constant coefficients and a small parameter in the initial data in the class of piecewise continuous controlswith smooth geometric constraints. We consider a terminal convex performance index. We substantiate the limit relationsas the small parameter tends to zero for the optimal value of the performance index and for the vector generatingthe optimal control in the problem. We show that the asymptotics of the solution can be of complicated nature. Inparticular, it may have no expansion in the Poincaré sense in any asymptotic sequence of rational functions of thesmall parameter or its logarithms

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UR - https://elibrary.ru/item.asp?id=65567087

U2 - 10.1134/S008154382306007X

DO - 10.1134/S008154382306007X

M3 - Article

VL - 323

SP - S85-S97

JO - Proceedings of the Steklov Institute of Mathematics

JF - Proceedings of the Steklov Institute of Mathematics

SN - 0081-5438

IS - S1

ER -

ID: 53754579