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A Numerical Method for Finding the Optimal Solution of a Differential Inclusion. / Fominyh, A. V.

In: Vestnik St. Petersburg University: Mathematics, Vol. 51, No. 4, 10.2018, p. 397-406.

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

Harvard

Fominyh, AV 2018, 'A Numerical Method for Finding the Optimal Solution of a Differential Inclusion', Vestnik St. Petersburg University: Mathematics, vol. 51, no. 4, pp. 397-406. https://doi.org/10.3103/S1063454118040076

APA

Fominyh, A. V. (2018). A Numerical Method for Finding the Optimal Solution of a Differential Inclusion. Vestnik St. Petersburg University: Mathematics, 51(4), 397-406. https://doi.org/10.3103/S1063454118040076

Vancouver

Fominyh AV. A Numerical Method for Finding the Optimal Solution of a Differential Inclusion. Vestnik St. Petersburg University: Mathematics. 2018 Oct;51(4):397-406. https://doi.org/10.3103/S1063454118040076

Author

Fominyh, A. V. / A Numerical Method for Finding the Optimal Solution of a Differential Inclusion. In: Vestnik St. Petersburg University: Mathematics. 2018 ; Vol. 51, No. 4. pp. 397-406.

BibTeX

@article{dcd36dc6747c49d699544223f32c12e1,
title = "A Numerical Method for Finding the Optimal Solution of a Differential Inclusion",
abstract = "In the paper, we study a differential inclusion with a given continuous convex multivalued mapping. For a prescribed finite time interval, it is required to construct a solution to the differential inclusion, which satisfies the prescribed initial and final conditions and minimizes the integral functional. By means of support functions, the original problem is reduced to minimizing some functional in the space of partially continuous functions. When the support function of the multivalued mapping is continuously differentiable with respect to the phase variables, this functional is Gateaux differentiable. In the study, the Gateaux gradient is determined and the necessary conditions for the minimum of the functional are obtained. Based on these conditions, the method of steepest descent is applied to the original problem. The numerical examples illustrate the implementation of the constructed algorithm.",
keywords = "differential inclusion, steepest descent method, support function",
author = "Fominyh, {A. V.}",
year = "2018",
month = oct,
doi = "10.3103/S1063454118040076",
language = "Английский",
volume = "51",
pages = "397--406",
journal = "Vestnik St. Petersburg University: Mathematics",
issn = "1063-4541",
publisher = "Pleiades Publishing",
number = "4",

}

RIS

TY - JOUR

T1 - A Numerical Method for Finding the Optimal Solution of a Differential Inclusion

AU - Fominyh, A. V.

PY - 2018/10

Y1 - 2018/10

N2 - In the paper, we study a differential inclusion with a given continuous convex multivalued mapping. For a prescribed finite time interval, it is required to construct a solution to the differential inclusion, which satisfies the prescribed initial and final conditions and minimizes the integral functional. By means of support functions, the original problem is reduced to minimizing some functional in the space of partially continuous functions. When the support function of the multivalued mapping is continuously differentiable with respect to the phase variables, this functional is Gateaux differentiable. In the study, the Gateaux gradient is determined and the necessary conditions for the minimum of the functional are obtained. Based on these conditions, the method of steepest descent is applied to the original problem. The numerical examples illustrate the implementation of the constructed algorithm.

AB - In the paper, we study a differential inclusion with a given continuous convex multivalued mapping. For a prescribed finite time interval, it is required to construct a solution to the differential inclusion, which satisfies the prescribed initial and final conditions and minimizes the integral functional. By means of support functions, the original problem is reduced to minimizing some functional in the space of partially continuous functions. When the support function of the multivalued mapping is continuously differentiable with respect to the phase variables, this functional is Gateaux differentiable. In the study, the Gateaux gradient is determined and the necessary conditions for the minimum of the functional are obtained. Based on these conditions, the method of steepest descent is applied to the original problem. The numerical examples illustrate the implementation of the constructed algorithm.

KW - differential inclusion

KW - steepest descent method

KW - support function

UR - http://www.scopus.com/inward/record.url?scp=85061188349&partnerID=8YFLogxK

U2 - 10.3103/S1063454118040076

DO - 10.3103/S1063454118040076

M3 - статья

AN - SCOPUS:85061188349

VL - 51

SP - 397

EP - 406

JO - Vestnik St. Petersburg University: Mathematics

JF - Vestnik St. Petersburg University: Mathematics

SN - 1063-4541

IS - 4

ER -

ID: 39628699