title: Optimal control of a differential-difference parabolic system with distributed parameters on the graph
metadata.name: dc.contributor.author
metadata.value: Zhabko, Alexey P.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Provotorov, Vyacheslav V.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Shindyapin, Andrey I.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2022-01-18T12:08:57Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2022-01-18T12:08:57Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2021-12
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Zhabko A. P., Provotorov V. V., Shindyapin A. I. Optimal control of a differential-difference parabolic system with distributed parameters on the graph. Vestnik of Saint Petersburg University. Applied Mathematics. Computer Science. Control Processes, 2021, vol. 17, iss. 4, рр. 433-448.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: https://doi.org/10.21638/11701/spbu10.2021.411
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/34173
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: In the paper be considered the problem of optimal control of the differential-difference
  equation with distributed parameters on the graph in the class of summable functions.
  Particular attention is given to the connection of the differential-differential system with
  the evolutionary differential system and the search conditions in which the properties of the
  differential system are preserved. This connection establishes a universal method of semi-
  digitization by temporal variable for differential system, providing an effective tool in finding
  conditions of uniqueness solvability and continuity on the initial data for the differential-
  differential system. A priori estimates of the norms of a weak solution of differential-
  differential system give an opportunity to establish not only the solvability of this system
  but also the existence of a weak solution of the evolutionary differential system. For the
  differential-difference system analysis of the optimal control problem is presented, containing
  natural in that cases a additional study of the problem with a time lag. This essentially
  uses the conjugate state of the system and the conjugate system for a differential-difference
  system — defining ratios that determine optimal control or the set optimal controls. The work
  shows courses to transfer the results in case of analysis of optimal control problems in the
  class of functions with bearer in network-like domains. The transition from an evolutionary
  differential system to a differential-difference system was a natural step in the study of applied
  problems of the theory of the transfer of solid mediums. The obtained results underlie the
  analysis of optimal control problems for differential systems with distributed parameters
  on a graph, which have interesting analogies with multiphase problems of multidimensional
  hydrodynamics.
metadata.lang: en_GB
metadata.name: dc.language.iso
metadata.value: en
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. Applied Mathematics. Computer Science. Control Processes;Volume 17; Issue 4
metadata.lang: -
metadata.name: dc.subject
metadata.value: differential-difference system
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: conjugate system
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: oriented graph
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: optimal control
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: delay
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: Optimal control of a differential-difference parabolic system with distributed parameters on the graph
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 433-448.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/34173/1/433-448.pdf
resources.format: Adobe PDF
resources.size: 438,5 kB