On an asymptotic analysis problem related to the construction of an attainability domain / Chentsov A. G.,Baklanov A. P. // PROCEEDINGS OF THE STEKLOV INSTITUTE OF MATHEMATICS. - 2015. - V. 291, l. 1. - P. 279-298.

ISSN/EISSN:

0081-5438 / 1531-8605

Type:

Article

Abstract:

Problems of constructing and analyzing the properties of attainability domains play an important role in control theory and its applications. In particular, this applies to control under impulse constraints that reflect the energetics of a process. The situation is complicated by the possible instability of the process under variation (in particular, under relaxation) of constraints related to boundary and intermediate conditions. Stability of the problem is also missing, in general, under relaxation of state constraints. In these cases, it is natural to focus on the asymptotic variant of the statement; this is especially expedient when one has to deal with initially asymptotic requirements. In all these cases, it seems expedient to use analogs of J. Warga's approximate solutions. At the same time, to seek necessary approximate (and, in fact, asymptotic) solutions, it is natural to use generalized modes. For problems with impulse constraints and discontinuity in the coefficients of control actions, such modes lead to phenomena described by products of discontinuous functions and generalized functions even in the class of linear systems. In a large series of his studies, to overcome the arising difficulties, one of the authors used constructions of extension in the class of finitely additive measures. The present paper follows this approach and is ideologically relevant to the engineering problem of controlling the thrust of an engine under conditions of a given program of variation of its orientation; it is postulated that energy resources are completely consumed in a natural (for a number of impulse control problems) mode of short-duration impulses: the set of time instants at which the instantaneous control is different from zero can be embedded in an interval of vanishingly small length. Within these short periods of time, the engine should consume all energy resources while obeying some other constraints (making the sense of moment constraints) to a high degree of accuracy. In addition, one should take into account the possible discontinuity of the functions defining the coefficients of control actions. As a natural analog of the attainability domain, we use an attraction set, whose construction, together with the subsequent study of its main properties, constitutes the goal of the present study.

Author keywords:

DIFFERENTIAL GAME; ULTRAFILTERS; CONSTRAINTS; EXTENSIONS; EVASION

DOI:

10.1134/S0081543815080222

Web of Science ID:

ISI:000369344400022

Соавторы в МНС:

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Другие поля

Поле	Значение
Month	NOV
Publisher	MAIK NAUKA/INTERPERIODICA/SPRINGER
Address	233 SPRING ST, NEW YORK, NY 10013-1578 USA
Language	English
EISSN	1531-8605
Keywords-Plus	DIFFERENTIAL GAME; ULTRAFILTERS; CONSTRAINTS; EXTENSIONS; EVASION
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 {[}12-01-00537a, 13-01-90414-Ukr\_f\_a, 13-01-00304a]; Presidium of the 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. 12-01-00537a, 13-01-90414-Ukr\_f\_a, and 13-01-00304a) and by the Presidium of the Russian Academy of Sciences within programs for basic research (project nos. 12-P-1-1012 and 12-P-1-1019).
Number-of-Cited-References	40
Usage-Count-Since-2013	1
Journal-ISO	Proc. Steklov Inst. Math.
Doc-Delivery-Number	DC6QJ