Geodesic
Optimal boundary control of oscillations of a string with given intermediate values of the speed for minimizing boundary energy
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the 6th International Conference "Dynamic Systems and Computer Science: Theory and Applications" (DYSC 2024). Irkutsk, September 16-20, 2024. Part 3, Tome 240 (2025), pp. 3-18

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For the equation of oscillation of a string with given initial and terminal conditions, we consider optimal boundary control problems with given intermediate conditions on the values of the speed with criteria for the qualities of the integrals of the boundary energies. The control is perform by displacements of ends of the string. Boundary energy integrals are considered over the entire time interval. We propose a constructive approach to constructing optimal boundary controls for oscillations based on the methods of separation of variables and moment problems. A computational experiment was carried out and the results obtained were analysed.
Keywords: boundary control, optimal vibration control, intermediate conditions, boundary energy integral, separation of variables 
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     title = {Optimal boundary control of oscillations of a string with given intermediate values of the speed for minimizing boundary energy},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
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     url = {http://geodesic.mathdoc.fr/item/INTO_2025_240_a0/}
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V. R. Barseghyan; S. V. Solodusha; E. V. Markova. Optimal boundary control of oscillations of a string with given intermediate values of the speed for minimizing boundary energy. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the 6th International Conference "Dynamic Systems and Computer Science: Theory and Applications" (DYSC 2024). Irkutsk, September 16-20, 2024. Part 3, Tome 240 (2025), pp. 3-18. http://geodesic.mathdoc.fr/item/INTO_2025_240_a0/