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
Received January 20, 2024
Revised February 11, 2025
Accepted February 11, 2025
Published online March 20, 2025
Alexander Georgievich Chentsov, Dr. Phys.-Math. Sci, RAS Corresponding Member, Prof., Krasovskii Institute of Mathematics and Mechanics of the Ural Branch of the Russian Academy of Sciences, Yekaterinburg, 620108 Russia; Ural Federal University, Yekaterinburg, 620000 Russia, e-mail: chentsov@imm.uran.ru
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Cite this article as: A.G. Ghentsov. Attraction sets in abstract reachability problems. Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2025, vol. 31, no. 2, pp. 294–315
