title: L. S. Pontryagin maximum principle for some optimal control problems by trajectories pencils
metadata.name: dc.contributor.author
metadata.value: Nikolskii, Mikhail S.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Belyaevskikh, Elena A.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2018-04-05T09:11:50Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2018-04-05T09:11:50Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2018-03
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Nikolskii M. S., Belyaevskikh E. A. L. S. Pontryagin maximum principle for some optimal control problems by trajectories pencils. Vestnik of Saint Petersburg University. Applied Mathematics. Computer Science. Control Processes, 2018, vol. 14, iss. 1, pp. 59–68.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: 10.21638/11701/spbu10.2018.107
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/9327
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: In this paper we consider some optimal problems for pencils of trajectories of nonlinear control
  systems, when integral functional of general type is minimized. For these problems an initial
  state of control system belongs to some compact set with positive Lebesgue measure. Such
  control systems are connected, for example, with study of control pencils of charged particles
  in physics (D. A. Ovsyannikov and other) and in problems of control when initial state of
  control system is known with error. An importance problem in this field is proof of Pontryagin’s
  maximum principle. In the paper we continue research of Ovsyannikov on this problem.We have
  proved the Pontryagin’s maximum principle for the case of integral functional and instantaneous
  geometric restrictions on control for Lebesgue measured control functions (previously piecewise
  continuous control functions were considered in literature). We used classical techniques of
  variations for measured optimal control function with some modifications. We note that our
  form of Pontryagin’s maximum principle is distinguished from some another forms. In the end
  of our paper there is a remark of D. A. Ovsyannikov about the connections of different forms of
  Pontryagn’s principle maximum. As some illustration, we consider a control object with linear
  dynamics. For this case our maximum principle can be written in more simple form than in
  general nonlinear case. Refs 8.
metadata.lang: en_GB
metadata.name: dc.description.sponsorship
metadata.value: При подготовке работы М. С. Никольский пользовался поддержкой программы Президиума
  РАН № 01 «Фундаментальная математика и ее приложения» (грант PRAC-18-01).
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 14; Issue 1
metadata.lang: -
metadata.name: dc.subject
metadata.value: control object
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: pencils of trajectories
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: maximum principle
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: L. S. Pontryagin maximum principle for some optimal control problems by trajectories pencils
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 07-Nikolsky.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/9327/1/07-Nikolsky.pdf
resources.format: Adobe PDF
resources.size: 242,64 kB