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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2010, Volume 271, Pages 259–277 (Mi tm3229)  
This article is cited in 5 scientific papers (total in 5 papers)

Classical characteristics of the Bellman equation in constructions of grid optimal synthesis

N. N. Subbotina, T. B. Tokmantsev

Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Yekaterinburg, Russia
Full-text PDF (296 kB) Citations (5)
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Abstract: We consider optimal control problems with fixed final time and terminal–integral cost functional, and address the question of constructing a grid optimal synthesis (a universal feedback) on the basis of classical characteristics of the Bellman equation. To construct an optimal synthesis, we propose a numerical algorithm that relies on the necessary optimality conditions (the Pontryagin maximum principle) and sufficient conditions in the Hamiltonian form. We obtain estimates for the efficiency of the numerical method. The method is illustrated by an example of the numerical solution of a nonlinear optimal control problem.
Received in June 2010
English version:
Proceedings of the Steklov Institute of Mathematics, 2010, Volume 271, Pages 246–264
DOI: https://doi.org/10.1134/S0081543810040188
Bibliographic databases:
Document Type: Article
UDC: 517.977
Language: Russian
Citation: N. N. Subbotina, T. B. Tokmantsev, “Classical characteristics of the Bellman equation in constructions of grid optimal synthesis”, Differential equations and topology. II, Collected papers. In commemoration of the centenary of the birth of Academician Lev Semenovich Pontryagin, Trudy Mat. Inst. Steklova, 271, MAIK Nauka/Interperiodica, Moscow, 2010, 259–277; Proc. Steklov Inst. Math., 271 (2010), 246–264
Citation in format AMSBIB
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\paper Classical characteristics of the Bellman equation in constructions of grid optimal synthesis
\inbook Differential equations and topology.~II
\bookinfo Collected papers. In commemoration of the centenary of the birth of Academician Lev Semenovich Pontryagin
\serial Trudy Mat. Inst. Steklova
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\vol 271
\pages 259--277
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
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  • https://www.mathnet.ru/eng/tm3229
  • https://www.mathnet.ru/eng/tm/v271/p259
    • This publication is cited in the following 5 articles:
    1. N. N. Subbotina, T. B. Tokmantsev, E. A. Krupennikov, “On the solution of inverse problems of dynamics of linearly controlled systems by the negative discrepancy method”, Proc. Steklov Inst. Math., 291 (2015), 253–262  mathnet  crossref  crossref  isi  elib
    2. N. N. Subbotina, T. B. Tokmantsev, “A study of the stability of solutions to inverse problems of dynamics of control systems under perturbations of initial data”, Proc. Steklov Inst. Math. (Suppl.), 291, suppl. 1 (2015), 173–189  mathnet  crossref  mathscinet  isi  elib
    3. I. E. Egorov, “Obobschenie metoda kharakteristik Koshi dlya postroeniya gladkikh reshenii uravneniya Gamiltona-Yakobi-Bellmana v zadachakh optimalnogo upravleniya s osobymi rezhimami”, Vestnik Moskovskogo universiteta. Seriya 15: Vychislitelnaya matematika i kibernetika, 2014, no. 3, 30–39  elib
    4. I. Ye. Yegorov, “Generalization of Cauchy's characteristics method to construct smooth solutions to Hamilton-Jacobi-Bellman equations in optimal control problems with singular regimes”, MoscowUniv.Comput.Math.Cybern., 38:3 (2014), 118  crossref
    5. Tokmantsev T.B., “Differentsialnye vklyucheniya v konstruktsiyakh setochnogo optimalnogo sinteza”, Vestnik Tambovskogo universiteta. Seriya: Estestvennye i tekhnicheskie nauki, 16:4 (2011), 1194–1196  elib
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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