Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia
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Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia, 2020, Volume 493, Pages 99–103
DOI: https://doi.org/10.31857/S2686954320040104 (Mi danma103) 		 
This article is cited in 1 scientific paper (total in 1 paper)

CONTROL PROCESSES

Contact geometry in optimal control of thermodynamic processes for gases

A. G. Kushnerab, V. V. Lychaginc, M. Roopac

a Lomonosov Moscow State University, Moscow, Russian Federation
b Moscow Pedagogical University, Moscow, Russian Federation, Moscow, Russian Federation
c V. A. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences, Moscow, Russian Federation
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DOI: https://doi.org/10.31857/S2686954320040104
Abstract: We solve an optimal control problem for thermodynamic processes in an ideal gas. The thermodynamic state is given by a Legendrian manifold in a contact space. Pontryagin’s maximum principle is used to find an optimal trajectory (thermodynamic process) on this manifold that maximizes the work of the gas. In the case of ideal gases, it is shown that the corresponding Hamiltonian system is completely integrable and its quadrature-based solution is given.
Keywords: contact geometry, thermodynamics, optimal control, Hamiltonian systems, integrability.
Funding agency Grant number
Russian Foundation for Basic Research 18–29–10013
Foundation for the Advancement of Theoretical Physics and Mathematics BASIS 19-7-1-13-3
Kushner acknowledges the partial support from the Russian Foundation for Basic Research (project no. 18-29-10013), while Lychagin and Roop acknowledge the partial support from the Foundation for the Advancement of Theoretical Physics and Mathematics “BASIS” (project no. 19-7-1-13-3).
Presented: S. N. Vassilyev
Received: 27.03.2020
Revised: 14.04.2020
Accepted: 06.06.2020
English version:
Doklady Mathematics, 2020, Volume 102, Issue 1, Pages 346–349
DOI: https://doi.org/10.1134/S1064562420040109
Bibliographic databases:
Document Type: Article
UDC: 517.977
Language: Russian
Citation: A. G. Kushner, V. V. Lychagin, M. Roop, “Contact geometry in optimal control of thermodynamic processes for gases”, Dokl. RAN. Math. Inf. Proc. Upr., 493 (2020), 99–103; Dokl. Math., 102:1 (2020), 346–349
Citation in format AMSBIB
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\by A.~G.~Kushner, V.~V.~Lychagin, M.~Roop
\paper Contact geometry in optimal control of thermodynamic processes for gases
\jour Dokl. RAN. Math. Inf. Proc. Upr.
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\vol 493
\pages 99--103
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\crossref{https://doi.org/10.31857/S2686954320040104}
\zmath{https://zbmath.org/?q=an:7424625}
\elib{https://elibrary.ru/item.asp?id=43795355}
\transl
\jour Dokl. Math.
\yr 2020
\vol 102
\issue 1
\pages 346--349
\crossref{https://doi.org/10.1134/S1064562420040109}
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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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