Optimization of the boundary control of string vibrations at one string end with a given mode at the other end

DOI10.1134/S1064562412040047zbMath1263.93102OpenAlexW2136463764MaRDI QIDQ1761051

E. I. Moiseev, A. A. Kholomeeva

Publication date: 15 November 2012

Published in: Doklady Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s1064562412040047

zbMATH Keywords

boundary controlstring vibrationsone-dimensional elastic string

Mathematics Subject Classification ID

Applications of optimal control and differential games (49N90) Vibrations in dynamical problems in solid mechanics (74H45) Control of mechanical systems (70Q05) Control/observation systems governed by ordinary differential equations (93C15) Strings (74K05)

Cites Work

• On the nonlinear dependence of the optimal boundary control on the initial and terminal conditions
• Solvability of mixed problems for the string oscillation equation in the space \(W_{p}^{1}\), with \(p \geq 1\)
• Optimal boundary displacement control of string vibrations with a nonlocal evenness condition of the second kind
• Optimal boundary control of string vibrations with a model nonlocal boundary condition of one of two types
• Optimal boundary control by an elastic force at one end of a string with the other end being free for an arbitrary sufficiently large time interval
• Optimal boundary control by the displacement of one endpoint of the string with the other endpoint being free in an arbitrarily large time interval
• Optimal boundary control by a displacement in \(W'p\) of a string with free end
• Minimization of the \(L_{p}\)-norm with arbitrary \(p \geq 1\) of the derivative of a boundary displacement control on an arbitrary sufficiently large time interval t
• Optimization of the boundary control of string vibrations by an elastic force on an arbitrary sufficiently large time interval
• Optimization of boundary controls of string vibrations
• Two-endpoint boundary control of vibrations described by a finite-energy generalized solution of the wave equation

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