Standard

Weak* Approximations to the Solution of a Dynamic Reconstruction Problem. / Subbotina, N. N.; Krupennikov, E. A.
In: Proceedings of the Steklov Institute of Mathematics, Vol. 317, No. S1, 01.08.2022, p. S142-S152.

Research output: Contribution to journal › Article › peer-review

Harvard

Subbotina, NN & Krupennikov, EA 2022, 'Weak* Approximations to the Solution of a Dynamic Reconstruction Problem', Proceedings of the Steklov Institute of Mathematics, vol. 317, no. S1, pp. S142-S152. https://doi.org/10.1134/S0081543822030130

APA

Subbotina, N. N., & Krupennikov, E. A. (2022). Weak* Approximations to the Solution of a Dynamic Reconstruction Problem. Proceedings of the Steklov Institute of Mathematics, 317(S1), S142-S152. https://doi.org/10.1134/S0081543822030130

Vancouver

Subbotina NN, Krupennikov EA. Weak* Approximations to the Solution of a Dynamic Reconstruction Problem. Proceedings of the Steklov Institute of Mathematics. 2022 Aug 1;317(S1):S142-S152. doi: 10.1134/S0081543822030130

Author

Subbotina, N. N. ; Krupennikov, E. A. / Weak* Approximations to the Solution of a Dynamic Reconstruction Problem. In: Proceedings of the Steklov Institute of Mathematics. 2022 ; Vol. 317, No. S1. pp. S142-S152.

BibTeX

@article{f8d4c6a81cf34ea5935a8f1b1357471f,
title = "Weak* Approximations to the Solution of a Dynamic Reconstruction Problem",
abstract = "We consider the problem of the dynamic reconstruction of an observed state trajectory x∗(⋅) of an affine deterministic dynamic system and a control that has generated this trajectory. The reconstruction is based on current information about inaccurate discrete measurements of x∗(⋅) . A correct statement of the problem on the construction of approximations ul(⋅) to the normal control u∗(⋅) generating x∗(⋅) is refined. The solution of this problem obtained using the variational approach proposed by the authors is discussed. Conditions on the input data and matching conditions for the approximation parameters (parameters of the accuracy and frequency of measurements of the trajectory and an auxiliary regularizing parameter) are given. Under these conditions, the reconstructed trajectories xl(⋅) of the dynamical system converge uniformly to the observed trajectory x∗(⋅) in the space C of continuous functions as l→∞ . It is proved that the proposed controls ul(⋅) converge weakly* to u∗(⋅) in the space L1 of integrable functions.",
keywords = "convex–concave discrepancy, dynamic reconstruction problems, Hamiltonian systems, problems of calculus of variations",
author = "Subbotina, {N. N.} and Krupennikov, {E. A.}",
note = "This work was supported by the Russian Foundation for Basic Research (project no. 20-01-00362). ",
year = "2022",
month = aug,
day = "1",
doi = "10.1134/S0081543822030130",
language = "English",
volume = "317",
pages = "S142--S152",
journal = "Proceedings of the Steklov Institute of Mathematics",
issn = "0081-5438",
publisher = "Pleiades Publishing",
number = "S1",

}

RIS

TY - JOUR

T1 - Weak* Approximations to the Solution of a Dynamic Reconstruction Problem

AU - Subbotina, N. N.

AU - Krupennikov, E. A.

N1 - This work was supported by the Russian Foundation for Basic Research (project no. 20-01-00362).

PY - 2022/8/1

Y1 - 2022/8/1

N2 - We consider the problem of the dynamic reconstruction of an observed state trajectory x∗(⋅) of an affine deterministic dynamic system and a control that has generated this trajectory. The reconstruction is based on current information about inaccurate discrete measurements of x∗(⋅) . A correct statement of the problem on the construction of approximations ul(⋅) to the normal control u∗(⋅) generating x∗(⋅) is refined. The solution of this problem obtained using the variational approach proposed by the authors is discussed. Conditions on the input data and matching conditions for the approximation parameters (parameters of the accuracy and frequency of measurements of the trajectory and an auxiliary regularizing parameter) are given. Under these conditions, the reconstructed trajectories xl(⋅) of the dynamical system converge uniformly to the observed trajectory x∗(⋅) in the space C of continuous functions as l→∞ . It is proved that the proposed controls ul(⋅) converge weakly* to u∗(⋅) in the space L1 of integrable functions.

AB - We consider the problem of the dynamic reconstruction of an observed state trajectory x∗(⋅) of an affine deterministic dynamic system and a control that has generated this trajectory. The reconstruction is based on current information about inaccurate discrete measurements of x∗(⋅) . A correct statement of the problem on the construction of approximations ul(⋅) to the normal control u∗(⋅) generating x∗(⋅) is refined. The solution of this problem obtained using the variational approach proposed by the authors is discussed. Conditions on the input data and matching conditions for the approximation parameters (parameters of the accuracy and frequency of measurements of the trajectory and an auxiliary regularizing parameter) are given. Under these conditions, the reconstructed trajectories xl(⋅) of the dynamical system converge uniformly to the observed trajectory x∗(⋅) in the space C of continuous functions as l→∞ . It is proved that the proposed controls ul(⋅) converge weakly* to u∗(⋅) in the space L1 of integrable functions.

KW - convex–concave discrepancy

KW - dynamic reconstruction problems

KW - Hamiltonian systems

KW - problems of calculus of variations

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UR - https://elibrary.ru/item.asp?id=51707258

U2 - 10.1134/S0081543822030130

DO - 10.1134/S0081543822030130

M3 - Article

VL - 317

SP - S142-S152

JO - Proceedings of the Steklov Institute of Mathematics

JF - Proceedings of the Steklov Institute of Mathematics

SN - 0081-5438

IS - S1

ER -

ID: 32805380