The problem of boundary control of vibrations of a string by displacements at two ends with given states at intermediate time moments

V. R. Barseghyan^ab, S. V. Solodusha<sup>cd

a</sup> Institute of Mechanics, National Academy of Sciences of Armenia
^b Yerevan State University
^c Irkutsk State University
^d L. A. Melentiev Energy Systems Institute, Siberian Branch of the Russian Academy of Sciences, Irkutsk

Abstract: The boundary control problem is considered for the equation of string vibration with given initial and final conditions, with given values of the deflection function and velocities of points at different intermediate times. The control is carried out by displacement at the two string ends. We propose a constructive approach for constructing boundary control of string vibrations by displacement at two ends with given initial and final conditions and values of the deflection function and velocities of points given at different intermediate times. A computational experiment was carried out with the construction of the corresponding graphs and their comparative analysis, which confirmed the results obtained.

Keywords: vibrations control, boundary control, multipoint intermediate states, variable separation.

UDC: 517.977, 534.112

MSC: 93C10, 93C95, 70Q05

DOI: 10.36535/0233-6723-2022-212-30-42