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MATHEMATICS
Relaxation of the attainability problem for a linear control system of neutral type
A. G. Chentsovab, A. N. Sesekinab a Ural Federal University, ul. Mira, 19, Yekaterinburg, 620002, Russia
b N. N. Krasovskii Institute of Mathematics and Mechanics, Ural
Branch of the Russian Academy of Sciences, ul. S. Kovalevskoi, 16, Yekaterinburg, 620108, Russia
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.
Received: 11.01.2021
Citation:
A. G. Chentsov, A. N. Sesekin, “Relaxation of the attainability problem for a linear control system of neutral type”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 31:1 (2021), 70–88
Linking options:
https://www.mathnet.ru/eng/vuu756 https://www.mathnet.ru/eng/vuu/v31/i1/p70
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Abstract page: | 308 | Full-text PDF : | 156 | References: | 39 |
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