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Asymptotics of a Solution to an Optimal Control Problem with a Terminal Convex Performance Index and a Perturbation of the Initial Data

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Abstract

In this paper, we investigate a problem of optimal control over a finite time interval for a linear system with constant coefficients and a small parameter in the initial data in the class of piecewise continuous controls with smooth geometric constraints. We consider a terminal convex performance index. We substantiate the limit relations as the small parameter tends to zero for the optimal value of the performance index and for the vector generating the optimal control in the problem. We show that the asymptotics of the solution can be of complicated nature. In particular, it may have no expansion in the Poincaré sense in any asymptotic sequence of rational functions of the small parameter or its logarithms.

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Funding

This work was supported by ongoing institutional funding. No additional grants to carry out or direct this particular research were obtained.

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Authors and Affiliations

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

    A. R. Danilin & O. O. Kovrizhnykh

  2. Ural Federal University, 620000, Yekaterinburg, Russia

    O. O. Kovrizhnykh

Authors
  1. A. R. Danilin
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  2. O. O. Kovrizhnykh
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Corresponding authors

Correspondence to A. R. Danilin or O. O. Kovrizhnykh.

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Translated from Trudy Instituta Matematiki i Mekhaniki UrO RAN, Vol. 29, No. 2, pp. 41 - 53, 2023 https://doi.org/10.21538/0134-4889-2023-29-2-41-53.

Translated by I. Tselishcheva

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Danilin, A.R., Kovrizhnykh, O.O. Asymptotics of a Solution to an Optimal Control Problem with a Terminal Convex Performance Index and a Perturbation of the Initial Data. Proc. Steklov Inst. Math. 323 (Suppl 1), S85–S97 (2023). https://doi.org/10.1134/S008154382306007X

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  • DOI: https://doi.org/10.1134/S008154382306007X

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