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Trudy Inst. Mat. i Mekh. UrO RAN, 2018, Volume 24, Number 1, Pages 131–142 (Mi timm1502)  

This article is cited in 2 scientific papers (total in 2 papers)

On a class of optimal control problems for functional differential systems

V. P. Maksimov

Perm State National Research University

Abstract: A linear functional differential control system of general form with aftereffect is considered. An optimal control problem with linear constraints on the state and control variables is studied. The control is realized by a linear operator of general form. The cases of distributed and lumped delay in the control loop, as well as the case of impulsive control, are covered. The Cauchy matrix is used to reduce the problem under consideration to a problem formulated only in terms of control variables with the use of some auxiliary variables linked with the defining relations for the Cauchy matrix of the system. In the case when the control is chosen from a finitedimensional subspace of the control space, a problem effectively solvable by standard software tools is written explicitly. An example of an applied optimal control problem that arises in economic dynamics is presented. A class of hybrid systems (systems with continuous and discrete times) reducible to the system under consideration is described.

Keywords: linear systems, control, optimization.

DOI: https://doi.org/10.21538/0134-4889-2018-24-1-131-142

Full text: PDF file (225 kB)
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Bibliographic databases:

UDC: 517.929
MSC: 34H05, 34K10, 34K34, 34K35
Received: 28.08.2017

Citation: V. P. Maksimov, “On a class of optimal control problems for functional differential systems”, Trudy Inst. Mat. i Mekh. UrO RAN, 24, no. 1, 2018, 131–142

Citation in format AMSBIB
\Bibitem{Mak18}
\by V.~P.~Maksimov
\paper On a class of optimal control problems for functional differential systems
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2018
\vol 24
\issue 1
\pages 131--142
\mathnet{http://mi.mathnet.ru/timm1502}
\crossref{https://doi.org/10.21538/0134-4889-2018-24-1-131-142}
\elib{http://elibrary.ru/item.asp?id=32604050}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Maksimov V.P., “On the l-Attainability Sets of Continuous Discrete Functional Differential Systems”, IFAC PAPERSONLINE, 51:32 (2018), 310–313  crossref  isi  scopus
    2. V. P. Maksimov, “The structure of the Cauchy operator to a linear continuous-discrete functional differential system with aftereffect and some properties of its components”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 29:1 (2019), 40–51  mathnet  crossref  elib
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