Geodesic
Relaxation of the attainability problem for a linear control system of neutral type
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 31 (2021) no. 1, pp. 70-88

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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. 
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     title = {Relaxation of the attainability problem for a linear control system of neutral type},
     journal = {Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹ\^uternye nauki},
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A. G. Chentsov; A. N. Sesekin. Relaxation of the attainability problem for a linear control system of neutral type. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 31 (2021) no. 1, pp. 70-88. http://geodesic.mathdoc.fr/item/VUU_2021_31_1_a5/