On damping a control system of arbitrary order with global aftereffect on a tree

Fuente: arXiv
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Autor principal: Buterin, Sergey
Formato: Preprint
Publicado: 2023
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author Buterin, Sergey
author_facet Buterin, Sergey
contents We study a problem of damping a control system described by functional-differential equations of natural order $n$ and neutral type with non-smooth complex coefficients on an arbitrary tree with global delay. The latter means that the delay propagates through internal vertices of the tree. Minimization of the energy functional of the system leads to a variational problem. We establish its equivalence to a certain self-adjoint boundary value problem on the tree for equations of order $2n$ with nonlocal quasi-derivatives and multidirectional shifts of the argument, as well as Kirchhoff-type conditions emerging at the internal vertices. The unique solvability of both problems is proved.
format Preprint
id arxiv_https___arxiv_org_abs_2312_17592
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle On damping a control system of arbitrary order with global aftereffect on a tree
Buterin, Sergey
Optimization and Control
34K35, 34K10, 93C23, 49K21
We study a problem of damping a control system described by functional-differential equations of natural order $n$ and neutral type with non-smooth complex coefficients on an arbitrary tree with global delay. The latter means that the delay propagates through internal vertices of the tree. Minimization of the energy functional of the system leads to a variational problem. We establish its equivalence to a certain self-adjoint boundary value problem on the tree for equations of order $2n$ with nonlocal quasi-derivatives and multidirectional shifts of the argument, as well as Kirchhoff-type conditions emerging at the internal vertices. The unique solvability of both problems is proved.
title On damping a control system of arbitrary order with global aftereffect on a tree
topic Optimization and Control
34K35, 34K10, 93C23, 49K21
url https://arxiv.org/abs/2312.17592