Standard

Variational Approach to Construction of Piecewise-Constant Approximations of the Solution of Dynamic Reconstruction Problem. / Subbotina, Nina; Krupennikov, Evgenii.
International Conference on Differential Equations, Mathematical Modeling and Computational Algorithms, DEMMCA 2021: Conference Proceeding. ed. / V. Vasilyev. Springer, 2023. p. 227-242 (Springer Proceedings in Mathematics and Statistics; Vol. 423).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Harvard

Subbotina, N & Krupennikov, E 2023, Variational Approach to Construction of Piecewise-Constant Approximations of the Solution of Dynamic Reconstruction Problem. in V Vasilyev (ed.), International Conference on Differential Equations, Mathematical Modeling and Computational Algorithms, DEMMCA 2021: Conference Proceeding. Springer Proceedings in Mathematics and Statistics, vol. 423, Springer, pp. 227-242. https://doi.org/10.1007/978-3-031-28505-9_16

APA

Subbotina, N., & Krupennikov, E. (2023). Variational Approach to Construction of Piecewise-Constant Approximations of the Solution of Dynamic Reconstruction Problem. In V. Vasilyev (Ed.), International Conference on Differential Equations, Mathematical Modeling and Computational Algorithms, DEMMCA 2021: Conference Proceeding (pp. 227-242). (Springer Proceedings in Mathematics and Statistics; Vol. 423). Springer. https://doi.org/10.1007/978-3-031-28505-9_16

Vancouver

Subbotina N, Krupennikov E. Variational Approach to Construction of Piecewise-Constant Approximations of the Solution of Dynamic Reconstruction Problem. In Vasilyev V, editor, International Conference on Differential Equations, Mathematical Modeling and Computational Algorithms, DEMMCA 2021: Conference Proceeding. Springer. 2023. p. 227-242. (Springer Proceedings in Mathematics and Statistics). doi: 10.1007/978-3-031-28505-9_16

Author

Subbotina, Nina ; Krupennikov, Evgenii. / Variational Approach to Construction of Piecewise-Constant Approximations of the Solution of Dynamic Reconstruction Problem. International Conference on Differential Equations, Mathematical Modeling and Computational Algorithms, DEMMCA 2021: Conference Proceeding. editor / V. Vasilyev. Springer, 2023. pp. 227-242 (Springer Proceedings in Mathematics and Statistics).

BibTeX

@inproceedings{4361a3d38d914033be97a7277c679b15,
title = "Variational Approach to Construction of Piecewise-Constant Approximations of the Solution of Dynamic Reconstruction Problem",
abstract = "In the paper, the problem of dynamic reconstruction of controls and trajectories for deterministic control-affine systems is considered. The reconstruction is performed in real time using known discrete inaccurate measurements of the observed trajectory of the system. This trajectory is generated by an unknown measurable control that satisfies known geometric constraints. A well-posed statement of the problem is given. A solution is proposed using the variational approach developed by the authors. This approach uses auxiliary variational problem with regularized integral residual functional. The integrant of the functional is a d.c. function. The suggested algorithm reduces the reconstruction problem to integration of Hamiltonian systems of ordinary differential equations. This paper offers a method for construction of piecewise-constant approximations that satisfy the given geometric control constraints. The approximations converge almost everywhere to the desired control, and the reconstructed trajectories of the dynamical system converge uniformly to the observed trajectory. {\textcopyright} 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.",
author = "Nina Subbotina and Evgenii Krupennikov",
year = "2023",
doi = "10.1007/978-3-031-28505-9_16",
language = "English",
isbn = "978-303128504-2",
series = "Springer Proceedings in Mathematics and Statistics",
publisher = "Springer",
pages = "227--242",
editor = "V. Vasilyev",
booktitle = "International Conference on Differential Equations, Mathematical Modeling and Computational Algorithms, DEMMCA 2021",
address = "Germany",

}

RIS

TY - GEN

T1 - Variational Approach to Construction of Piecewise-Constant Approximations of the Solution of Dynamic Reconstruction Problem

AU - Subbotina, Nina

AU - Krupennikov, Evgenii

PY - 2023

Y1 - 2023

N2 - In the paper, the problem of dynamic reconstruction of controls and trajectories for deterministic control-affine systems is considered. The reconstruction is performed in real time using known discrete inaccurate measurements of the observed trajectory of the system. This trajectory is generated by an unknown measurable control that satisfies known geometric constraints. A well-posed statement of the problem is given. A solution is proposed using the variational approach developed by the authors. This approach uses auxiliary variational problem with regularized integral residual functional. The integrant of the functional is a d.c. function. The suggested algorithm reduces the reconstruction problem to integration of Hamiltonian systems of ordinary differential equations. This paper offers a method for construction of piecewise-constant approximations that satisfy the given geometric control constraints. The approximations converge almost everywhere to the desired control, and the reconstructed trajectories of the dynamical system converge uniformly to the observed trajectory. © 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.

AB - In the paper, the problem of dynamic reconstruction of controls and trajectories for deterministic control-affine systems is considered. The reconstruction is performed in real time using known discrete inaccurate measurements of the observed trajectory of the system. This trajectory is generated by an unknown measurable control that satisfies known geometric constraints. A well-posed statement of the problem is given. A solution is proposed using the variational approach developed by the authors. This approach uses auxiliary variational problem with regularized integral residual functional. The integrant of the functional is a d.c. function. The suggested algorithm reduces the reconstruction problem to integration of Hamiltonian systems of ordinary differential equations. This paper offers a method for construction of piecewise-constant approximations that satisfy the given geometric control constraints. The approximations converge almost everywhere to the desired control, and the reconstructed trajectories of the dynamical system converge uniformly to the observed trajectory. © 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.

UR - http://www.scopus.com/inward/record.url?partnerID=8YFLogxK&scp=85163930486

U2 - 10.1007/978-3-031-28505-9_16

DO - 10.1007/978-3-031-28505-9_16

M3 - Conference contribution

SN - 978-303128504-2

T3 - Springer Proceedings in Mathematics and Statistics

SP - 227

EP - 242

BT - International Conference on Differential Equations, Mathematical Modeling and Computational Algorithms, DEMMCA 2021

A2 - Vasilyev, V.

PB - Springer

ER -

ID: 41593248