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Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]:
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Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 2011, Issue 2(23), Pages 24–33 (Mi vsgtu951)  

This article is cited in 3 scientific papers (total in 3 papers)

Differential Equations

On the numerical solution convergence of optimal control problems for Leontief type system

G. A. Sviridyuka, A. V. Kellerb

a Dept. of Mathematical Physics Equations, South Ural State University, Chelyabinsk
b Dept. of General Educational Subjects, South Ural State University, Chelyabinsk

Abstract: This article contains proving the convergence of numerical solving of optimal control problem for degenerate linear systems of ordinary differential equations with constant coefficients. Considering different appendixes of such systems, they belong to Leontief type system, as in the first time such systems were investigated as a dynamic Leontief input-output model with noninvertible operator on derivative. By using the initial condition of Showalter–Sidorov we gain an ability to extend the range of practical applicability for this model. The article includes existence and uniqueness theorem of numerical solution of investigated problem, his kind, and results of numerical experiment for dynamic input-output model, which was offered by W. Leontief.

Keywords: Showalter–Sidorov problem, optimal control, numerical solution, convergence

DOI: https://doi.org/10.14498/vsgtu951

Full text: PDF file (252 kB) (published under the terms of the Creative Commons Attribution 4.0 International License)
References: PDF file   HTML file

Bibliographic databases:

UDC: 517.977.5
MSC: Primary 49J27; Secondary 93C25, 34A30
Original article submitted 26/II/2011
revision submitted – 05/V/2011

Citation: G. A. Sviridyuk, A. V. Keller, “On the numerical solution convergence of optimal control problems for Leontief type system”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 2(23) (2011), 24–33

Citation in format AMSBIB
\Bibitem{SviKel11}
\by G.~A.~Sviridyuk, A.~V.~Keller
\paper On the numerical solution convergence of optimal control problems for Leontief type system
\jour Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]
\yr 2011
\vol 2(23)
\pages 24--33
\mathnet{http://mi.mathnet.ru/vsgtu951}
\crossref{https://doi.org/10.14498/vsgtu951}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Y. Xu, Z. Ouyang, C. Xiao, “Optimal Control of Pseudoparabolic Equations with Pointwise Obstacle Type Constraints”, 2013 25th Chinese Control and Decision Conference (Ccdc), Chinese Control and Decision Conference, IEEE, 2013, 505–509  isi  scopus
    2. A. L. Shestakov, G. A. Sviridyuk, M. D. Butakova, “The mathematical modelling of the production of construction mixtures with prescribed properties”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 8:1 (2015), 100–110  mathnet  crossref  elib
    3. N. A. Manakova, G. A. Sviridyuk, “Neklassicheskie uravneniya matematicheskoi fiziki. Fazovye prostranstva polulineinykh uravnenii sobolevskogo tipa”, Vestn. Yuzhno-Ur. un-ta. Ser. Matem. Mekh. Fiz., 8:3 (2016), 31–51  mathnet  crossref  elib
  • Вестник Самарского государственного технического университета. Серия: Физико-математические науки
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