This article is cited in 1 paper

Attraction sets in abstract reachability problems

A. G. Chentsov<sup>ab

a</sup> N.N. Krasovskii Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg
^b Ural Federal University named after the First President of Russia B. N. Yeltsin, Ekaterinburg

Abstract: The abstract reachability problems in topological space with constraints of asymptotic nature (CAN) are considered; given CAN can arise (in particular) through the consistent weakening of one or more standard constraints. The above-mentioned CAN are generated by a nonempty family of sets in the initial space of usual solutions (controls). As a result of the action of CAN, we can (in the above-mentioned cases) consider attraction set being the limit with respect to “usual” reachable sets (RS); in control problems, a given RS may correspond to reachability domains under one or more concrete constraints on the control choice.

Keywords: attainability problem, attraction set, filter.

UDC: 517.977

MSC: 05A05, 97N70, 97N80

Received: 20.01.2025
Revised: 11.02.2025
Accepted: 11.02.2025

DOI: 10.21538/0134-4889-2025-31-2-fon-02

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