On Damping a Control System of Arbitrary Order with Global Aftereffect on a Tree

IF 0.6 4区数学 Q3 MATHEMATICS

Mathematical Notes Pub Date : 2024-07-15 DOI:10.1134/s0001434624050249

S. A. Buterin

引用次数: 0

Abstract

We study a problem of damping a control system described by functional-differential equations of natural order \(n\) and neutral type with nonsmooth 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.

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论阻尼树上具有全局效应的任意阶控制系统

摘要我们研究了一个控制系统的阻尼问题，该控制系统由具有非光滑复系数的自然阶（n\）和中性型函数微分方程描述，在任意树上具有全局延迟。后者意味着延迟通过树的内部顶点传播。系统能量函数的最小化会导致一个变分问题。我们将其等同于树上的某个自交边界值问题，该问题的方程阶数为\(2n\)，具有非局部准衍生物、参数的多向移动以及在内部顶点出现的基尔霍夫型条件。证明了这两个问题的唯一可解性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Mathematical Notes 数学-数学

CiteScore

0.90

自引率

16.70%

发文量

179

审稿时长

24 months

期刊介绍： Mathematical Notes is a journal that publishes research papers and review articles in modern algebra, geometry and number theory, functional analysis, logic, set and measure theory, topology, probability and stochastics, differential and noncommutative geometry, operator and group theory, asymptotic and approximation methods, mathematical finance, linear and nonlinear equations, ergodic and spectral theory, operator algebras, and other related theoretical fields. It also presents rigorous results in mathematical physics.