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Zh. Vychisl. Mat. Mat. Fiz., 2012, Volume 52, Number 4, Pages 628–652 (Mi zvmmf9683)  

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

Asymptotic solution of singularly perturbed linear-quadratic optimal control problems with discontinuous coefficients

G. A. Kurinaa, Nguyên Thị Hoàib

a Voronezh State Academy of Forestry Engineering, Timiriazeva st., 8, Voronezh, 394087 Russia
b Petro Vietnam University, 173 Trung Kinh, Yen Hoa, Cau Giay, Ha Noi, Vietnam

Abstract: An asymptotic solution of a singularly perturbed linear-quadratic optimal control problem with discontinuous coefficients is constructed by directly substituting an boundary-layer asymptotic expansion of the solution into the condition of the problem and considering a series of problems for finding the asymptotic terms. The error in the approximate solution is estimated. It is shown that the values of the minimized functional do not increase when the next approximations of the optimal control are used.

Key words: Keywords: linear-quadratic optimal control problem, singular perturbations, discontinuous coefficients, asymptotic expansion.

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English version:
Computational Mathematics and Mathematical Physics, 2012, 52:4, 524–547

Bibliographic databases:

UDC: 519.626
Received: 24.01.2011

Citation: G. A. Kurina, Nguyên Th{\d i} Hoài, “Asymptotic solution of singularly perturbed linear-quadratic optimal control problems with discontinuous coefficients”, Zh. Vychisl. Mat. Mat. Fiz., 52:4 (2012), 628–652; Comput. Math. Math. Phys., 52:4 (2012), 524–547

Citation in format AMSBIB
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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. G. Kurina, Nguyen Thi Hoai, “Asymptotic solution of a linear-quadratic problem with discontinuous coefficients and cheap control”, Appl. Math. Comput., 232 (2014), 347–364  crossref  mathscinet  zmath  isi  elib  scopus
    2. I. V. Grebennikova, A. G. Kremlev, “Approksimatsiya upravleniya singulyarno vozmuschennoi sistemoi s zapazdyvaniem pri integralnykh kvadratichnykh ogranicheniyakh”, Izv. Sarat. un-ta. Nov. ser. Ser. Matematika. Mekhanika. Informatika, 17:4 (2017), 368–380  mathnet  crossref  elib
    3. Nguyen Thi Hoai, “Asymptotic solution of a singularly perturbed linear-quadratic problem in critical case with cheap control”, J. Optim. Theory Appl., 175:2 (2017), 324–340  crossref  mathscinet  zmath  isi  scopus
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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