Open AccessRelaxation of the attainability problem for a linear control system of neutral type
Author(s) -
А. Г. Ченцов,
A. N. Sesekin
Publication year - 2021
Publication title -
vestnik udmurtskogo universiteta. matematika, mehanika, kompʹûternye nauki
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.354
H-Index - 8
eISSN - 2076-5959
pISSN - 1994-9197
DOI - 10.35634/vm210106
Subject(s) - impulse (physics) , relaxation (psychology) , mathematics , type (biology) , class (philosophy) , linear system , domain (mathematical analysis) , impulse control , extension (predicate logic) , set (abstract data type) , pure mathematics , mathematical analysis , control theory (sociology) , control (management) , computer science , physics , classical mechanics , psychology , social psychology , ecology , artificial intelligence , psychotherapist , biology , programming language
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.