title: Procedure for regularization of bilinear optimal control problems based on a finite-dimensional model
metadata.name: dc.contributor.author
metadata.value: Arguchintsev, Alexander V.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Srochko, Vladimir A.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2022-06-23T15:31:03Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2022-06-23T15:31:03Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2022-03
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Arguchintsev A. V., Srochko V. A. Procedure for regularization of bilinear optimal control problems based on a finite-dimensional model. Vestnik of Saint Petersburg University. Applied Mathematics. Computer Science. Control Processes, 2022, vol. 18, iss. 1, pp. 179–187.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: https://doi.org/10.21638/11701/spbu10.2022.115
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/36942
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: An optimization problem of a linear system of ordinary differential equations on a set of
  piecewise continuous scalar controls with two-sided restrictions is considered. The cost functional
  contains the bilinear part (control, state) and a control square with a parameter,
  which plays the role of a regularization term. An approximate solution of the optimal control
  problem is carried out on a subset of piecewise constant controls with a non-uniform grid
  of possible switching points. As a result of the proposed parametrization, reduction to the
  finite-dimensional problem of quadratic programming was carried out with the parameter in
  the objective function and the simplest restrictions. In the case of a strictly convex objective
  function, the finite-dimensional problem can be solved in a finite number of iterations by the
  method of special points. For strictly concave objective functions, the corresponding problem
  is solved by simple or specialized brute force methods. In an arbitrary case, parameter
  conditions and switching points are found at which the objective function becomes convex
  or concave. At the same time, the corresponding problems of mathematical programming
  allow a global solution in a finite number of iterations. Thus, the proposed approach allows
  to approximate the original non-convex variation problem with a finite-dimensional model
  that allows to find a global solution in a finite number of iterations.
metadata.lang: en_GB
metadata.name: dc.description.sponsorship
metadata.value: This project was supported by the Vladimir Potanin Foundation (grant GSAD-0022/21).
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 18; Issue 1
metadata.lang: -
metadata.name: dc.subject
metadata.value: linear phase system
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: bilinear-quadratic functional
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: finite-dimensional model
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: finite iterative methods
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: global solution
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: Procedure for regularization of bilinear optimal control problems based on a finite-dimensional model
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 179-187.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/36942/1/179-187.pdf
resources.format: Adobe PDF
resources.size: 334,83 kB