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Asymptotic Expansion of the Solution of a Singularly Perturbed Optimal Control Problem with Elliptical Control Constraints

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Abstract

The main distinction of the present paper from our previous publications is that the integral part of the performance functional has a more general form and the control is subjected to elliptical rather than spherical constraints. We prove that, in the case of finitely many control type switching points, one can construct the asymptotics of the initial costate vector \( l_\varepsilon \) determining the form of the optimal control. The asymptotics is shown to be of power-law character.

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ACKNOWLEDGMENTS

The authors express their gratitude to the referee for a number of valuable comments, which allowed the authors to improve the exposition when preparing the paper for publication.

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Authors and Affiliations

  1. Krasovskii Institute of Mathematics and Mechanics, Ural Branch, Russian Academy of Sciences, Yekaterinburg, 620108, Russia

    A. R. Danilin & A. A. Shaburov

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  1. A. R. Danilin
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  2. A. A. Shaburov
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Correspondence to A. R. Danilin or A. A. Shaburov.

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Translated by V. Potapchouck

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Danilin, A.R., Shaburov, A.A. Asymptotic Expansion of the Solution of a Singularly Perturbed Optimal Control Problem with Elliptical Control Constraints. Autom Remote Control 83, 1–16 (2022). https://doi.org/10.1134/S0005117922010015

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  • DOI: https://doi.org/10.1134/S0005117922010015

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