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THE EXTENSION OF ABSTRACT ATTAINABILITY PROBLEMS

Annotation

The problem of attainability in topological space under constraints of asymptotic character is investigated; the above-mentioned constraints can be defined initially or can arise under the weakening of «standard» conditions (boundary and intermediate conditions, phase constraints in control problems and inequalities in mathematical programming). For investigation of above-mentioned problems, extension construction including the generalized elements structure and continuous extension of goal operator is used. This construction admits idea analogies with constructions of J. Warga.

Keywords

compactificator; attraction set; topology

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UDC

517.972.8

Pages

1517-1521

References

1. Varga Dzh. Optimal'noe upravlenie differentsial'nymi i funktsional'nymi uravneniyami. M.: Nauka, 1977. 624 s. 2. Chentsov A.G. Fil'try i ul'trafil'try v konstruktsiyakh mnozhestv prityazheniya // Vestn. Udmurtsk. un-ta. Matem. Mekh. Komp'yut. nauki. 2011. № 1. S. 113–142. 3. Engel'king R. Obshchaya topologiya. M.: Mir, 1986. 751 s. 4. Chentsov A.G. Yarusnye otobrazheniya i preobrazovaniya na osnove ul'trafil'trov // Tr. In-ta matematiki i mekhaniki UrO RAN. 2012. T. 18. № 4. S. 298–314. 5. Chentsov A.G. Mnozhestva prityazheniya v abstraktnykh zadachakh o dostizhimosti: ekvivalentnye predstavleniya i osnovnye svoystva // Izv. vuzov. Matem. 2013. № 11. S. 33–50. 6. Aleksandrov P.S. Vvedenie v teoriyu mnozhestv i obshchuyu topologiyu. M.: Editorial URSS, 2004. 368 s. 7. Kelli Dzh.L. Obshchaya topologiya. M.: Nauka, 1968. 384 s. 8. Chentsov A.G., Morina S.I. Extensions and relaxations. Dordrecht; Boston; London: Kluwer Acad. Publ., 2002. 408 p.

Received

2015-05-21

Section of issue

Scientific articles

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