This article is cited in 2 papers

Deterministic Systems

Certain problems of asymptotic analysis and extensions. I

A. G. Chentsov

Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences

Abstract: Asymptotic attainability interpreted as the approximate realization of desirable states under weak slackening of constraints is studied. Constructs ensuring the realization of asymptotically attainable states in terms of standard constraints on the choice of generalized elements and interpreted as finitely additive measures on a suitable measurable space are designed. Special attention is paid to “Boolean-valued” realizations of generalized problems (extensions) in the class of (0,1)-measures or ultrafilters of measurable spaces and are interpreted as direct extension constructs (in the sense of transitions from exact solutions to approximate solutions).

Presented by the member of Editorial Board: B. M. Miller

Received: 15.12.2002

 English version: Automation and Remote Control, 2005, 66:12, 1983–1999

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