Geodesic
Construction of boundary controls in the problem of oscilation damping of a system from $m$~strings
Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, no. 1 (2012), pp. 60-69

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An elastic system of $m$ strings fixed as a graph–star is considered. Such mathematical objects are a basis of mathematical models of fluctuation processes in antenna designs of various types. A method of finding boundary operating influences consisting of the transfer of the system fluctuation process from the appointed initial condition into the rest one is presented. The spectral technics (Fourier analysis) is used allowing rather easily to overcome the complexities generated by the graphgeometry. The main result of the research is presented in the form of the ready formulas defining required boundary controls as the function of time.
Keywords: a boundary problem on the graph, boundary control, transfer of system from the initial condition into the rest one. 
@article{VSPUI_2012_1_a7,
     author = {V. V. Provotorov},
     title = {Construction of boundary controls in the problem of oscilation damping of a system from $m$~strings},
     journal = {Vestnik Sankt-Peterburgskogo universiteta. Prikladna\^a matematika, informatika, processy upravleni\^a},
     pages = {60--69},
     publisher = {mathdoc},
     number = {1},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSPUI_2012_1_a7/}
}
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V. V. Provotorov. Construction of boundary controls in the problem of oscilation damping of a system from $m$~strings. Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, no. 1 (2012), pp. 60-69. http://geodesic.mathdoc.fr/item/VSPUI_2012_1_a7/