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Zh. Vychisl. Mat. Mat. Fiz., 2010, Volume 50, Number 8, Pages 1381–1392 (Mi zvmmf4918)  

This article is cited in 6 scientific papers (total in 6 papers)

Steplike contrast structure in an elementary optimal control problem

Ni Min' Kan'a, M. G. Dmitrievb

a East China Normal University, Shanghai, 200062, People's Republic of China
b Russian State Social University, ul. V. Pika 4, Moskow, 129226 Russia

Abstract: For an elementary nonlinear optimal control problem with a scalar differential constraint and with a small parameter multiplying the derivative but without any constraints on the control, the possibility of emerging fast internal phase transitions in the optimal trajectory is shown as based on results concerning contrast structures in the theory of singularly perturbed boundary value problems.

Key words: optimal control, nonlinear functional, singular perturbations, phase transition, asymptotic approximations.

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English version:
Computational Mathematics and Mathematical Physics, 2010, 50:8, 1312–1323

Bibliographic databases:

UDC: 519.626
Received: 30.11.2009

Citation: Ni Min' Kan', M. G. Dmitriev, “Steplike contrast structure in an elementary optimal control problem”, Zh. Vychisl. Mat. Mat. Fiz., 50:8 (2010), 1381–1392; Comput. Math. Math. Phys., 50:8 (2010), 1312–1323

Citation in format AMSBIB
\by Ni Min' Kan', M.~G.~Dmitriev
\paper Steplike contrast structure in an elementary optimal control problem
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2010
\vol 50
\issue 8
\pages 1381--1392
\jour Comput. Math. Math. Phys.
\yr 2010
\vol 50
\issue 8
\pages 1312--1323

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    This publication is cited in the following articles:
    1. Wu L.-m., Ni M.-k., Lu H.-b., “Step-Like Contrast Structure for Class of Nonlinear Singularly Perturbed Optimal Control Problem”, Appl. Math. Mech.-Engl. Ed., 34:7 (2013), 875–888  crossref  mathscinet  zmath  isi  scopus
    2. Ni Ming Kang, Wu Li Meng, “A step-type solution for the affine singularly perturbed problem of optimal control”, Autom. Remote Control, 74:12 (2013), 2007–2019  mathnet  crossref  isi
    3. Kan N.M., Feng W.A., “Step-like contrast structure for a nonlinear system of singularly perturbed differential equations in the critical case”, Differ. Equ., 52:12 (2016), 1575–1584  crossref  mathscinet  zmath  isi  scopus
    4. Wu L., Zhang J., Ni M., Lu H., “Asymptotic solution of singularly perturbed hybrid dynamical systems”, Acta Math. Sci., 36:5 (2016), 1457–1466  crossref  mathscinet  zmath  isi  scopus
    5. Xu H., Jin Y., “the Asymptotic Expansion For a Class of Non-Linear Singularly Perturbed Problems With Optimal Control”, J. Nonlinear Sci. Appl., 9:5 (2016), 2718–2726  crossref  mathscinet  zmath  isi  elib
    6. Wu L., Ni M., Lu H., “Internal Layer Solution of Singularly Perturbed Optimal Control Problem With Integral Boundary Condition”, Qual. Theor. Dyn. Syst., 17:1 (2018), 49–66  crossref  mathscinet  zmath  isi  scopus
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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