Open AccessOn a generalized boundary value problem for a feedback control system with infinite delay
Author(s) -
Maria Afanasova,
Valeri Obukhovskiĭ,
Garik Petrosyan
Publication year - 2021
Publication title -
vestnik udmurtskogo universiteta. matematika, mehanika, kompʹûternye nauki
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.354
H-Index - 8
eISSN - 2076-5959
pISSN - 1994-9197
DOI - 10.35634/vm210201
Subject(s) - mathematics , banach space , separable space , boundary value problem , differential inclusion , mathematical analysis , boundary (topology) , pure mathematics
We consider a non-local boundary value problem for a feedback control system described by a semilinear functional-differential inclusion of fractional order with infinite delay in a separable Banach space. The general principle of existence of solutions to the problem in terms of the difference from zero of the topological degree of the corresponding vector field is given. We prove a concrete example (Theorem 6) of the implementation of this general principle. The existence of an optimal solution to the posed problem is proved, which minimizes the given lower semicontinuous quality functional.