On the question of construction of an attraction set under constraints of asymptotic nature / Chentsov A. G.,Baklanov A. P. // PROCEEDINGS OF THE STEKLOV INSTITUTE OF MATHEMATICS. - 2015. - V. 291, l. 1. - P. S40-S55.

ISSN/EISSN:

0081-5438 / 1531-8605

Type:

Article

Abstract:

We study a variant of the reachability problem with constraints of asymptotic character on the choice of controls. More exactly, we consider a control problem in the class of impulses of given intensity and vanishingly small length. The situation is complicated by the presence of discontinuous dependences, which produce effects of the type of multiplying a discontinuous function by a generalized function. The constructed extensions in the special class of finitely additive measures make it possible to present the required solution, defined as an asymptotic analog of a reachable set, in terms of a continuous image of a compact, which is described with the use of the Stone space corresponding to the natural algebra of sets of the control interval. One of the authors had the honor of communicating with Nikolai Nikolaevich Krasovskii for many years and discussed with him problems that led to the statement considered in the paper. Krasovskii's support of this research direction provided possibilities for its fruitful development. His disciples and colleagues will always cherish the memory of Nikolai Nikolaevich in their hearts.

Author keywords:

filter base; finitely additive measure; attraction set; generalized element; ultrafilter EXTENSIONS; SYSTEM

DOI:

10.1134/S0081543815090035

Web of Science ID:

ISI:000366347200003

Соавторы в МНС:

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Другие поля

Поле	Значение
Month	DEC
Publisher	MAIK NAUKA/INTERPERIODICA/SPRINGER
Address	233 SPRING ST, NEW YORK, NY 10013-1578 USA
Language	English
EISSN	1531-8605
Keywords-Plus	EXTENSIONS; SYSTEM
Research-Areas	Mathematics
Web-of-Science-Categories	Mathematics, Applied; Mathematics
Author-Email	chentsov@imm.uran.ru artem.baklanov@gmail.com
ORCID-Numbers	Baklanov, Artem/0000-0003-1599-3618
Funding-Acknowledgement	Russian Foundation for Basic Research {[}12-01-00537 a, 13-01-90414 ukr\_f\_a, 13-01-00304 a]; Programs for Fundamental Research of Presidium of Russian Academy of Sciences {[}12-P-1-1012, 12-P-1-1019]
Funding-Text	This work was supported by the Russian Foundation for Basic Research (project nos. 12-01-00537 a, 13-01-90414 ukr\_f\_a, and 13-01-00304 a) and by Programs for Fundamental Research of the Presidium of the Russian Academy of Sciences (project nos. 12-P-1-1012 and 12-P-1-1019).
Number-of-Cited-References	30
Usage-Count-Since-2013	2
Journal-ISO	Proc. Steklov Inst. Math.
Doc-Delivery-Number	CY3ZA