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Russia Yekaterinburg
Year
2021
Volume
31
Issue
1
Pages
70-88
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Section Mathematics
Title Relaxation of the attainability problem for a linear control system of neutral type
Author(-s) Chentsov A.G.ab, Sesekin A.N.ab
Affiliations Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciencesa, Ural Federal Universityb
Abstract The problem of control of a linear system of neutral type with impulse constraints is developed. In addition, a given system of intermediate conditions is assumed. A setting is investigated in which a vanishingly small relaxation of the mentioned restrictions is allowed. In this regard, the attainability domain (AD) at a fixed time of the end of the process is replaced by a natural asymptotic analog, the attraction set (AS). To construct the latter, we use the construction of an extension in the class of finitely additive (f.-a.) measures used as generalized controls. It is shown that the AS coincides with the AD of the system in the class of generalized controls – f.-a. measures. The structure of the mentioned AS is investigated.
Keywords linear systems with time delay of neutral type, attraction sets, finitely additive measures
UDC 517.977
MSC 34A37, 34K06
DOI 10.35634/vm210106
Received 11 January 2021
Language Russian
Citation Chentsov A.G., Sesekin A.N. Relaxation of the attainability problem for a linear control system of neutral type, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2021, vol. 31, issue 1, pp. 70-88.
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