Interior of the Integral of a Set-Valued Mapping and Problems with a Linear Control System-Reference-Cited by-同舟云学术

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

Published:2023-12-15 Issue:8 Volume:59 Page:1098-1109
ISSN:0374-0641
Container-title:Дифференциальные уравнения
language:
Short-container-title:Differencialʹnye uravneniâ

Author:

Balashov M. V¹

Affiliation:

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

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

Publisher

The Russian Academy of Sciences

Reference22 articles.

1. Aumann R. Integrals of set-valued functions // J. of Math. Anal. Appl. 1965. V. 12. № 1. P. 1-12.

2. Ляпунов А.А. О вполне аддитивных вектор-функциях // Изв. АН СССР. Сер. мат. 1940. Т. 4. № 6. С. 465-478.

3. Половинкин Е.С. Многозначный анализ и дифференциальные включения. М., 2014.

4. Lee E.B., Markus L. Foundations of Optimal Control Theory. New York, 1967.

5. Aubin J.-P., Cellina A. Differential Inclusions. Berlin; Heidelberg, 1984.