Результаты исследований: Вклад в журнал › Статья › Рецензирование
Результаты исследований: Вклад в журнал › Статья › Рецензирование
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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
UR - https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcAuth=tsmetrics&SrcApp=tsm_test&DestApp=WOS_CPL&DestLinkType=FullRecord&KeyUT=000883773100013
UR - http://www.scopus.com/inward/record.url?scp=85143800493&partnerID=8YFLogxK
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