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Optimal production control problem taking into account environmental pollution

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Abstract

We consider a simplified production control model taking into account environmental pollution. We obtain constructive conditions under which each optimal control is Lebesgue equivalent to an optimal bang-bang control.

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References

  1. Kolemaev, V.A., Matematicheskaya ekonomika (Mathematical Economics), Moscow, 2002.

    Google Scholar 

  2. Ashmanov, S.A., Vvedenie v matematicheskuyu ekonomiku (Introduction to Mathematical Economics), Moscow: Nauka, 1984.

    MATH  Google Scholar 

  3. Intriligator, M.D., Mathematical Optimization and Economic Theory, Englewood Cliffs: Prentice-Hall, 1971. Translated under the title Matematicheskie metody optimizatsii i ekonomicheskaya teoriya, Moscow: Airis-Press, 2002.

    Book  MATH  Google Scholar 

  4. Pontryagin, L.S., et al., Matematicheskaya teoriya optimal’nykh protsessov (Mathematical Theory of Optimal Processes), Moscow, 1969.

    Google Scholar 

  5. Lee, E.B. and Markus, L., Foundations of Optimal Control Theory, New York–London–Sydney, 1967. Translated under the title Osnovy teorii optimal’nogo upravleniya, Moscow: Nauka, 1972.

    MATH  Google Scholar 

  6. Fillipov, A.F., On Some Questions in the Theory of Optimal Control: Existence of a Solution of an Optimal Control Problem in the Class of Bounded Measurable Functions, Vestnik Moskov. Univ. Mat. Mekh. Astronom., 1959, no. 2, pp. 25–38.

    Google Scholar 

  7. Gabasov, R. and Kirillova, F.M., Printsip maksimuma v teorii optimal’nogo upravleniya (The Maximum Principle in Optimal Control Theory), Minsk: Nauka i Tekhnika, 1974.

    MATH  Google Scholar 

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Authors and Affiliations

  1. Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia

    M. S. Nikol’skii

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  1. M. S. Nikol’skii
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Correspondence to M. S. Nikol’skii.

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Original Russian Text © M.S. Nikol’skii, 2016, published in Differentsial’nye Uravneniya, 2016, Vol. 52, No. 3, pp. 404–408.

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Nikol’skii, M.S. Optimal production control problem taking into account environmental pollution. Diff Equat 52, 400–404 (2016). https://doi.org/10.1134/S0012266116030137

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  • DOI: https://doi.org/10.1134/S0012266116030137

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