# A. Yu. Popov, Integral minimization of the second derivative module of the boundary control of string vibrations with the fixed end

Title: Integral minimization of the second derivative module of the boundary control of string vibrations with the fixed end
Authors: A. Yu. Popov
Journal title: Automation and Remote Control
Year: 2007
Issue: 2
Volume: 68
Pages: 327–336
Citation:

A. Yu. Popov, “Integral minimization of the second derivative module of the boundary control of string vibrations with the fixed end”, Automation and Remote Control, 2007, 68:2, 327–336

Abstract:

A problem of boundary control of string vibrations with the fixed end with a bounded control resource is studied. The integral of the second derivative module of the boundary control is minimized. Estimates of upper and lower bounds are found for the extremum. In the vibration suppression problem, at the time period T" />$T$ formulas of boundary control that is close to the optimal control with large values of the time period T" />$T$ are given.