title: Synthesis of optimal boundary control of parabolic systems with delay and distributed parameters on the graph
metadata.name: dc.contributor.author
metadata.value: Provotorov, Vyacheslav V.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Provotorova, Elena N.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2017-07-19T11:28:46Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2017-07-19T11:28:46Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2017-06
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Provotorov V. V., Provotorova E. N. Synthesis of optimal boundary control of parabolic systems with delay and distributed parameters on the graph. Vestnik of Saint Petersburg University. Applied Mathematics. Computer Science. Control Processes, 2017, vol. 13, iss. 2, pp. 209– 224.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: 10.21638/11701/spbu10.2017.207
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/6973
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: The problem of optimal boundary control of evolutionary systems with constant delay and
  distributed parameters on the graph. System status is determined by a weak solution of the
  boundary value problem for a parabolic equation in the space of Sobolev type whose elements
  are functions satisfying the conditions in a certain way matching all the internal nodes of the graph. The control action on the system and monitoring its state is made in the boundary nodes
  of the graph on the entire time interval. The dual status of the system is defined as a weak
  solution of the boundary value problem with delay and distributed parameters on the graph
  with the final condition. The conditions of weak unique solvability of the original and the dual
  challenges of weak continuous dependence of solutions on initial data. We present necessary
  and sufficient conditions for the existence of optimal control using the dual system state solved
  the problem of optimal control synthesis for the case of absence of restrictions on the control
  action and an analogue-known finite-dimensional case the Kalman results. The method used
  is applicable to many optimization problems of differential systems whose state is determined
  by weak solutions of evolution equations on networks. These results are fundamental in the
  study of problems of boundary control the dynamics of laminar flows of multiphase media.
  All techniques and methods can be used for the numerical solution of optimal control problem
  under consideration. Refs 20.
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. Applied Mathematics. Computer Science. Control Processes;Volume 13; Issue 2
metadata.lang: -
metadata.name: dc.subject
metadata.value: information networks
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: differential equations
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: probability
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: spreading rumors
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: Synthesis of optimal boundary control of parabolic systems with delay and distributed parameters on the graph
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 07-Provotorov.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/6973/1/07-Provotorov.pdf
resources.format: Adobe PDF
resources.size: 304,63 kB