Geodesic
Constraints of asymptotic nature and attainability problems
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 29 (2019) no. 4, pp. 569-582

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In control problems, construction and investigation of attainability domains and their analogs are very important. This paper addresses attainability problems in topological spaces. Constraints of asymptotic nature defined in the form of nonempty families of sets are used. The solution of the corresponding attainability problem is defined as an attraction set. Points of this attraction set (attraction elements) are realized in the class of approximate solutions which are nonsequential analogs of the Warga approximate solutions. Some possibilities of applying compactifiers are discussed. Questions of the realization of attraction sets up to a given neighborhood are considered. Some topological properties of attraction sets are investigated. An example with an empty attraction set is considered.
Keywords: attraction set, extension, topological space, compactness. 
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     author = {A. G. Chentsov and E. G. Pytkeev},
     title = {Constraints of asymptotic nature and attainability problems},
     journal = {Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹ\^uternye nauki},
     pages = {569--582},
     publisher = {mathdoc},
     volume = {29},
     number = {4},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/VUU_2019_29_4_a7/}
}
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A. G. Chentsov; E. G. Pytkeev. Constraints of asymptotic nature and attainability problems. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 29 (2019) no. 4, pp. 569-582. http://geodesic.mathdoc.fr/item/VUU_2019_29_4_a7/