title: A method for finding the optimal solution of a differential inclusion
metadata.name: dc.contributor.author
metadata.value: Fominyh, Alexander V.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2018-12-13T14:39:39Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2018-12-13T14:39:39Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2018-12
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Fominyh A.V. A method for finding the optimal solution of a differential inclusion. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2018, vol. 5 (63), issue 4, pp. 645–657.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: 10.21638/11701/spbu01.2018.411
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/15133
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: In the paper, we study a differential inclusion with a given continuous convex multivalued
  mapping. For a given finite time interval, it is required to construct a solution of the
  differential inclusion, that satisfies the given initial and the final conditions and minimizes
  the integral functional. With the help of support functions, the original problem is reduced
  to minimizing some functional in the space of partially continuous functions. In the case of
  continuous differentiability of the support function of a multivalued mapping with respect to
  the phase variables, this functional is Gateaux differentiable. In the paper, Gateaux gradient
  is found, necessary conditions for the minimum of the given functional are obtained. On
  the basis of these conditions, the method of the steepest descent is applied to the original
  problem. Numerical examples illustrate the constructed algorithm realization.
metadata.lang: en_GB
metadata.name: dc.description.sponsorship
metadata.value: Работа выполнена при финансовой поддержке РФФИ (грант №18-31-00014 мол-а).
metadata.lang: en_GB
metadata.name: dc.language.iso
metadata.value: ru
metadata.lang: en_GB
metadata.name: dc.publisher
metadata.value: St Petersburg State University
metadata.lang: en_GB
metadata.name: dc.relation.ispartofseries
metadata.value: Vestnik of St Petersburg University. Mathematics. Mechanics. Astronomy;Volume 5 (63); Issue 4
metadata.lang: -
metadata.name: dc.subject
metadata.value: differential inclusion
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: support function
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: steepest descent method
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: A method for finding the optimal solution of a differential inclusion
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 11-Fominykh.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/15133/1/11-Fominykh.pdf
resources.format: Adobe PDF
resources.size: 614 kB