title: Alpha-sets in finite-dimensional Euclidean spaces and their applications in control theory
metadata.name: dc.contributor.author
metadata.value: Ushakov, Vladimir N.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Uspenskii, Aleksander A.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Ershov, Aleksander A.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2018-09-14T11:10:10Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2018-09-14T11:10:10Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2018-09
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Ushakov V. N., Uspenskii A. A., Ershov A. A. Alpha-sets in finite-dimensional Euclidean spaces and their applications in control theory. Vestnik of Saint Petersburg University. Applied Mathematics. Computer Science. Control Processes, 2018, vol. 14, iss. 3, pp. 261–272.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: 10.21638/11702/spbu10.2018.307
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/14829
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: In this paper, a technique for investigating nonconvex sets that occur when describing the
  evolution of wave fronts, in the construction of generalized solutions of boundary value
  problems for equations of Hamilton—Jacobi type, in the formation of resolving structures
  in the problems of dynamic control is developed. An estimate is obtained for the Hausdorff
  distance between such sets and their convex hulls. The estimate is based on the concept
  of a measure of nonconvexity α. It is shown that for small α, nonconvex α-sets are close
  to convex. An example of a solution of the optimal control problem on the basis of α-sets
  is give.
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 3
metadata.lang: -
metadata.name: dc.subject
metadata.value: α-set
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: convex hull
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: Hausdorff distance
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: control
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: performance
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: Hamilton—Jacobi equation
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: Alpha-sets in finite-dimensional Euclidean spaces and their applications in control theory
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 07-Ushakov.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/14829/1/07-Ushakov.pdf
resources.format: Adobe PDF
resources.size: 440,78 kB