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On a Class of Control Problems with Mixed Constraints

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Abstract

An optimal control problem with a nonregular mixed constraint linear in the control variable is studied. Necessary optimality conditions are proposed in the form of Pontryagin’s maximum principle for such a class of problems. The corresponding examples are considered.

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Notes

  1. Here \(\mathrm {Lim\thinspace sup} \) means the set of all limit points, or the so-called upper limit in the sense of Kuratowski (see [3]).

  2. Here \(\ell \) means the Lebesgue measure on the line.

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Funding

This work was supported by the Russian Science Foundation, project no. 20-11-20131.

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Authors and Affiliations

  1. Trapeznikov Institute of Control Sciences, Russian Academy of Sciences, Moscow, 117997, Russia

    A. V. Arutyunov

  2. Federal Research Center “Computer Science and Control,” Russian Academy of Sciences, Moscow, 119333, Russia

    D. Yu. Karamzin

Authors
  1. A. V. Arutyunov
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  2. D. Yu. Karamzin
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Correspondence to A. V. Arutyunov or D. Yu. Karamzin.

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Translated by V. Potapchouck

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Arutyunov, A.V., Karamzin, D.Y. On a Class of Control Problems with Mixed Constraints. Diff Equat 59, 529–539 (2023). https://doi.org/10.1134/S0012266123040092

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