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Model. Anal. Inform. Sist., 2010, Volume 17, Number 1, Pages 93–116 (Mi mais18)  

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

On a zero order approximation of an asymptotic solution for a singularly perturbed linear-quadratic control problem with discontinuous coefficients

G. A. Kurina, Nguyên Thi Hoài

Voronezh State Academy of Forestry Engineering

Abstract: The paper deals with a formalism of constructing a zero order approximation of an asymptotic solution for a singularly perturbed linear-quadratic optimal control problem with discontinuous coefficients. This formalism is based on immediate substituting a postulated asymptotic expansion of boundary layer type for the solution into the problem condition and on defining four optimal control problems for finding asymptotics terms. The unique solvability of the problems, the solutions of which form the zero order approximation for the asymptotic solution, is proven. An illustrative example is given.

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

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UDC: 517.977.5 + 517.928.2
Received: 05.03.2010

Citation: G. A. Kurina, Nguyên Thi Hoài, “On a zero order approximation of an asymptotic solution for a singularly perturbed linear-quadratic control problem with discontinuous coefficients”, Model. Anal. Inform. Sist., 17:1 (2010), 93–116

Citation in format AMSBIB
\Bibitem{KurNgu10}
\by G.~A.~Kurina, Nguy\^en~Thi~Ho\`ai
\paper On a zero order approximation of an asymptotic solution for a singularly perturbed linear-quadratic control problem with discontinuous coefficients
\jour Model. Anal. Inform. Sist.
\yr 2010
\vol 17
\issue 1
\pages 93--116
\mathnet{http://mi.mathnet.ru/mais18}


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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. A. Kurina, Nguyên Th{\d i} Hoài, “Asymptotic solution of singularly perturbed linear-quadratic optimal control problems with discontinuous coefficients”, Comput. Math. Math. Phys., 52:4 (2012), 524–547  mathnet  crossref  mathscinet  adsnasa  isi  elib  elib
    2. Kurina G., “Linear-Quadratic Optimal Control Problems with Switch Points and a Small Parameter”, Control and Optimization with Differential-Algebraic Constraints, Advances in Design and Control, no. 23, eds. Biegler L., Campbell S., Mehrmann V., SIAM, 2012, 165–188  mathscinet  zmath  isi
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