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Interior of the Integral of a Set-Valued Mapping and Problems with a Linear Control System

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Abstract

The dependence of the radius of a ball centered at zero inscribed in the values of the integral of a set-valued mapping on the upper integration limit is studied. For some types of integrals, exact asymptotics of the radius with respect to the upper limit are found when the upper limit tends to zero. Examples of finding this radius are considered. The results obtained are used to derive new sufficient conditions for the uniformly continuous dependence of the minimum time and solution-point in the linear minimum time control problem on the initial data. We also consider applications in some algorithms with a reachability set of a linear control system.

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Funding

This work was supported by the Russian Science Foundation, https://rscf.ru/en/project/22-11-00042/, at Trapeznikov Institute of Control Sciences of the Russian Academy of Sciences.

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Authors and Affiliations

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

    M. V. Balashov

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  1. M. V. Balashov
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Correspondence to M. V. Balashov.

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Translated by V. Potapchouck

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Balashov, M.V. Interior of the Integral of a Set-Valued Mapping and Problems with a Linear Control System. Diff Equat 59, 1105–1116 (2023). https://doi.org/10.1134/S0012266123080098

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  • DOI: https://doi.org/10.1134/S0012266123080098

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