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Conditional Cost Function and Necessary Optimality Conditions for Infinite Horizon Optimal Control Problems

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Abstract

An infinite horizon optimal control problem with general endpoint constraints is reduced to a family of standard problems on finite time intervals containing the conditional cost of the phase vector as a terminal term. A new version of the Pontryagin maximum principle containing an explicit characterization of the adjoint variable is obtained for the problem with a general asymptotic endpoint constraint. In the case of the problem with a free final state, this approach leads to a normal form version of the maximum principle formulated completely in the terms of the conditional cost function.

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Funding

This work was supported by the Russian Science Foundation, project no. 19-11-00223.

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Authors and Affiliations

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

    S. M. Aseev

  2. Lomonosov Moscow State University, Moscow, Russia

    S. M. Aseev

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  1. S. M. Aseev
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Correspondence to S. M. Aseev.

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Translated by I. Ruzanova

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Aseev, S.M. Conditional Cost Function and Necessary Optimality Conditions for Infinite Horizon Optimal Control Problems. Dokl. Math. 108, 425–430 (2023). https://doi.org/10.1134/S1064562423600586

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  • DOI: https://doi.org/10.1134/S1064562423600586

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