title: Construction of reachability and controllability sets in a special linear control problem
metadata.name: dc.contributor.author
metadata.value: Popkov, Alexander S.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2021-10-06T10:52:58Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2021-10-06T10:52:58Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2021-09
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Popkov A.S. Construction of reachability and controllability sets in a special linear control problem. Vestnik of Saint Petersburg University. Applied Mathematics. Computer Science. Control Processes, 2021, vol. 17, iss. 3, pp. 294-308.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: https://doi.org/10.21638/11701/spbu10.2021.307
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/33253
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: The article considers the problem of constructing reachability and controllability sets for
  a control problem. The motion of an object is described by a linear system of ordinary
  differential equations, and control is selected from the class of piecewise-constant functions.
  Straight boundaries are also set on the controls. The article provides definitions of reacha-
  bility and controllability sets. It is shown that the problems of constructing these sets are
  equivalent and can be reduced to the problem of linear mapping of a multidimensional cube.
  The properties of these sets are also given. In addition, the existing approaches to solving
  the problem are analyzed. Since they are all too computationally complex, the question of
  creating a more efficient algorithm arises. The work proposes an algorithm for constructing the required sets as a system of linear inequalities. A proof of the theorem showing the correctness of the algorithm is provided. The complexity of the presented approach is estimated.
metadata.lang: en_GB
metadata.name: dc.description.sponsorship
metadata.value: This work was supported by the Russian Foundation for Basic Research (project N 19-31-90033).
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 17; Issue 3
metadata.lang: -
metadata.name: dc.subject
metadata.value: control
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: optimal control
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: piecewise-constant control
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: reachability set
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: controllability set
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: linear mapping
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: Fourier — Motzkin elimination
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: Construction of reachability and controllability sets in a special linear control problem
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 294-308.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/33253/1/294-308.pdf
resources.format: Adobe PDF
resources.size: 407,11 kB