Geodesic
The problem of boundary control of string vibrations by displacement of the left end when the right end is fixed with the given values of the deflection function at intermediate times
Vestnik rossijskih universitetov. Matematika, Tome 25 (2020) no. 130, pp. 131-146

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We consider the boundary control problem for the homogeneous string vibration equation with given the classical boundary (initial and final) conditions and with given values of the deflection function at intermediate times. The control is performed by displacement of the left end of the string when the right end is fixed. The problem is reduced to the control problem with zero boundary conditions. We propose the constructive method for constructing the boundary control of the process of string vibrations with given values of the deflection function at intermediate times.We present the results of numerical experiments and the corresponding graphs confirm the validity of the results.
Keywords: string vibrations, vibration control, boundary control, intermediate state control, separation of variables. 
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     author = {V. R. Barseghyan and S. V. Solodusha},
     title = {The problem of boundary control of string vibrations by displacement of the left end when the right end is fixed with the given values of the deflection function at intermediate times},
     journal = {Vestnik rossijskih universitetov. Matematika},
     pages = {131--146},
     publisher = {mathdoc},
     volume = {25},
     number = {130},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VTAMU_2020_25_130_a2/}
}
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V. R. Barseghyan; S. V. Solodusha. The problem of boundary control of string vibrations by displacement of the left end when the right end is fixed with the given values of the deflection function at intermediate times. Vestnik rossijskih universitetov. Matematika, Tome 25 (2020) no. 130, pp. 131-146. http://geodesic.mathdoc.fr/item/VTAMU_2020_25_130_a2/