Alpha sets and their hulls: analytical relationships in the plane case-Reference-Cited by-同舟云学术

Alpha sets and their hulls: analytical relationships in the plane case

Published:2024 Issue:146 Volume: Page:204-217
ISSN:2686-9667
Container-title:Russian Universities Reports. Mathematics
language:ru
Short-container-title:

Author:

Uspenskii Alexander A.¹^ORCID,Lebedev Pavel D.¹^ORCID

Affiliation:

1. N.N. Krasovskii Institute of Mathematics and Mechanics of the Ural Branch of the Russian Academy of Sciences

Abstract

The class of closed sets of two-dimensional Euclidean space that are not Chebyshev sets in common case is considered. Sets are studied from the standpoint of two well-known definitions that generalize the classical definition of a convex set. Within the framework of these definitions, analytical relationships are established between the parameters characterizing non-convex sets. A formula for calculating the function that determines the degree of nonconvexity of a closed set, and a formula for calculating the radius of the support ball are found. The areas of application of the studied structures in the theory of control of dynamic systems are indicated. An illustrative example is given in which a procedure for analytical calculating the Chebyshev layer of a non-convex set with discontinuous curvature of its boundary is proposed.

Publisher

Tambov State University - G.R. Derzhavin

Reference16 articles.

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