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Zh. Vychisl. Mat. Mat. Fiz., 2011, Volume 51, Number 5, Pages 814–833 (Mi zvmmf9334)  

This article is cited in 10 scientific papers (total in 10 papers)

Functional gradient evaluation in the optimal control of a complex dynamical system

A. V. Albu, A. F. Albu, V. I. Zubov

Dorodnicyn Computing Center, Russian Academy of Sciences, ul. Vavilova 40, Moscow, 119333 Russia

Abstract: The gradient of the cost functional in a discrete optimal control problem for metal solidification in metal casting is exactly calculated. In contrast to previous studies, the object under analysis has a complex geometric shape. The mathematical model for describing the solidification process is based on a three-dimensional two-phase initial–boundary value problem of the Stefan type. Formulas for exact gradient evaluation are derived using the fast automatic differentiation technique.

Key words: heat equation, metal solidification, Stefan problem, optimal control problem, fast automatic differentiation, adjoint optimal control problem.

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English version:
Computational Mathematics and Mathematical Physics, 2011, 51:5, 762–780

Bibliographic databases:

UDC: 519.626
Received: 17.11.2010

Citation: A. V. Albu, A. F. Albu, V. I. Zubov, “Functional gradient evaluation in the optimal control of a complex dynamical system”, Zh. Vychisl. Mat. Mat. Fiz., 51:5 (2011), 814–833; Comput. Math. Math. Phys., 51:5 (2011), 762–780

Citation in format AMSBIB
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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. Albu A. Zubov V., “On the controlling of liquid metal solidification in foundry practice”, Operations Research Proceedings 2011, Operations Research Proceedings, ed. Klatte D. Luthi H. Schmedders K., Springer-Verlag, Berlin, 2012, 3–8  crossref  mathscinet  isi
    2. A. V. Albu, A. F. Albu, V. I. Zubov, “Control of substance solidification in a complex-geometry mold”, Comput. Math. Math. Phys., 52:12 (2012), 1612–1623  mathnet  crossref  mathscinet  zmath  isi  elib  elib
    3. Chernov A.V., “O priblizhennom reshenii zadach optimalnogo upravleniya so svobodnym vremenem”, Vestn. Nizhegorodskogo universiteta im. M.I. Lobachevskogo, 2012, no. 6-1, 107–114  elib
    4. A. F. Albu, V. I. Zubov, “On the influence of setup parameters on the control of solidification in metal casting”, Comput. Math. Math. Phys., 53:2 (2013), 170–179  mathnet  crossref  crossref  zmath  adsnasa  isi  elib  elib
    5. A. F. Albu, V. I. Zubov, “Investigation of the optimal control problem for metal solidification in a new formulation”, Comput. Math. Math. Phys., 54:5 (2014), 756–766  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    6. A. F. Albu, V. I. Zubov, “Investigation of the optimal control of metal solidification for a complex-geometry object in a new formulation”, Comput. Math. Math. Phys., 54:12 (2014), 1804–1816  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    7. Albu A.F., “Control of the Phase Boundary Evolution in Solidification”, Dokl. Math., 92:2 (2015), 627–629  crossref  mathscinet  zmath  isi  elib  scopus
    8. A. F. Albu, “Control of phase boundary evolution in metal solidification for new thermodynamic parameters of the metal”, Comput. Math. Math. Phys., 56:5 (2016), 756–763  mathnet  crossref  crossref  isi  elib
    9. Yu. G. Evtushenko, V. I. Zubov, “Generalized fast automatic differentiation technique”, Comput. Math. Math. Phys., 56:11 (2016), 1819–1833  mathnet  crossref  crossref  isi  elib
    10. Albu A. Zubov V., “An Approach to Solving Control Problems of Heat Processes With Phase Transitions”, 2017 International Conference on Control, Artificial Intelligence, Robotics & Optimization (Iccairo), IEEE, 2017, 147–153  crossref  isi  scopus
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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