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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2021, Volume 315, Pages 34–63
DOI: https://doi.org/10.4213/tm4247 (Mi tm4247) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Refined Euler–Lagrange Inclusion for an Optimal Control Problem with Discontinuous Integrand

S. M. Aseevab

a Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
b Lomonosov Moscow State University
Full-text PDF (361 kB) Citations (2)
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DOI: https://doi.org/10.4213/tm4247
Abstract: We study a free-time optimal control problem for a differential inclusion with mixed-type functional in which the integral term contains the characteristic function of a given open set of “undesirable” states of the system. The statement of this problem can be viewed as a weakening of the statement of the classical optimal control problem with state constraints. Using the approximation method, we obtain first-order necessary optimality conditions in the form of the refined Euler–Lagrange inclusion. We also present sufficient conditions for their nondegeneracy and pointwise nontriviality and give an illustrative example.
Keywords: optimal control, differential inclusion, Pontryagin's maximum principle, refined Euler–Lagrange inclusion, state constraint, discontinuous integrand, risk zone.
Funding agency Grant number
Russian Science Foundation 19-11-00223
This work is supported by the Russian Science Foundation under grant 19-11-00223.
Received: August 30, 2021
Revised: September 26, 2021
Accepted: October 1, 2021
English version:
Proceedings of the Steklov Institute of Mathematics, 2021, Volume 315, Pages 27–55
DOI: https://doi.org/10.1134/S0081543821050047
Bibliographic databases:
Document Type: Article
UDC: 517.977
Language: Russian
Citation: S. M. Aseev, “Refined Euler–Lagrange Inclusion for an Optimal Control Problem with Discontinuous Integrand”, Optimal Control and Differential Games, Collected papers, Trudy Mat. Inst. Steklova, 315, Steklov Math. Inst., Moscow, 2021, 34–63; Proc. Steklov Inst. Math., 315 (2021), 27–55
Citation in format AMSBIB
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\by S.~M.~Aseev
\paper Refined Euler--Lagrange Inclusion for an Optimal Control Problem with Discontinuous Integrand
\inbook Optimal Control and Differential Games
\bookinfo Collected papers
\serial Trudy Mat. Inst. Steklova
\yr 2021
\vol 315
\pages 34--63
\publ Steklov Math. Inst.
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/tm4247}
\crossref{https://doi.org/10.4213/tm4247}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2021
\vol 315
\pages 27--55
\crossref{https://doi.org/10.1134/S0081543821050047}
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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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