Abstract:
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.
Keywords:
feedback control system, optimal solution, fractional differential inclusion, infinite delay, measure of noncompactness, condensing operator, fixed point, topological degree.
The work of the first and second authors is supported by the State contract of the Russian
Ministry of Education as part of the state task (contract FZGF-2020-0009). The work of the third author
is supported by RFBR according to the research project no. 19-31-60011.
Citation:
M. S. Afanasova, V. V. Obukhovskii, G. G. Petrosyan, “On a generalized boundary value problem for a feedback control system with infinite delay”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 31:2 (2021), 167–185
\Bibitem{AfaObuPet21}
\by M.~S.~Afanasova, V.~V.~Obukhovskii, G.~G.~Petrosyan
\paper On a generalized boundary value problem for a feedback control system with infinite delay
\jour Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki
\yr 2021
\vol 31
\issue 2
\pages 167--185
\mathnet{http://mi.mathnet.ru/vuu762}
\crossref{https://doi.org/10.35634/vm210201}
Linking options:
https://www.mathnet.ru/eng/vuu762
https://www.mathnet.ru/eng/vuu/v31/i2/p167
This publication is cited in the following 1 articles:
V. V. Obukhovskii, G. Petrosyan, M. Soroka, “On an Initial Value Problem for Nonconvex-Valued Fractional Differential
Inclusions in a Banach Space”, Math. Notes, 115:3 (2024), 358–370
Citation in format AMSBIB
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