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Asymptotic Attainability: General Questions

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Asymptotic Attainability

Part of the book series: Mathematics and Its Applications ((MAIA,volume 383))

Abstract

In the previous chapters, we considered numerous examples and whole classes of problems dealing with effects arising under the perturbation of the conditions on the choice of controls. Namely, we formed controls with a premeditated but “small” breakdown of a complex of conditions and investigated the realization “as a limit” of the corresponding desirable states for us. However, this “smallness” is often “seeming”. In reality, the influence of controls may be deep. It is displayed “on the level of asymptotics” under the realization of elements which are very far from those attainable under rigid fulfillment of conditions (see Section 1.2). In essence, we have here effects which are typical for ill-posed problems [27, 38]; the sets of the asymptotical attainability play the role of a peculiar regularizations of the initial statements. Beginning with this chapter, we are going to systematically investigate the given occurrences for some class of problems with restrictions of an integral character. However, we shall preliminarily discuss (in the next section) the given question on a profound level. Later, we shall introduce general designations and definitions connected with the problem of the asymptotic attainability.

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Authors and Affiliations

  1. Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Science, Ekatarinburg, Russia

    A. G. Chentsov

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  1. A. G. Chentsov
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© 1997 Springer Science+Business Media Dordrecht

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Chentsov, A.G. (1997). Asymptotic Attainability: General Questions. In: Asymptotic Attainability. Mathematics and Its Applications, vol 383. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-0805-0_3

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  • DOI: https://doi.org/10.1007/978-94-017-0805-0_3

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-4765-6

  • Online ISBN: 978-94-017-0805-0

  • eBook Packages: Springer Book Archive

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