Abstract
The generalized solution u(x, t) of the wave equation u tt (x, t) − u xx (x, t) = 0 admitting the existence of finite energy at every time instant t is used to find among all W 12 [0,T]-functions with a long time interval T the optimal boundary control for a string with a free endpoint that takes the vibration process from a given arbitrary state to a given final state.
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References
V. A. Il’in, “Boundary control of the vibration process at two endpoints in terms of the finite-energy generalized solution of the wave equation,” Different. Uravn., 36,No. 11, 1513–1528 (2000).
V. A. Il’in, “Boundary control of the vibration process at one endpoint when the second endpoint is fixed in terms of the finite-energy generalized solution of the wave equation,” Different. Uravn., 36,No. 12, 1670–186 (2000).
P. A. Revo and G. D. Chabakauri, “Boundary control of the vibration process at one endpoint when the second endpoint is free in terms of the finite-energy generalized solution of the wave equation,” Different. Uravn., 37,No. 8, 1082–1095 (2001).
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Translated from Nelineinaya Dinamika i Upravlenie, No. 4, pp. 23–36, 2004.
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Il’in, V.A., Moiseev, E.I. Optimal boundary control of vibrations at one endpoint of a string when the second endpoint is free. Comput Math Model 18, 332–343 (2007). https://doi.org/10.1007/s10598-007-0029-5
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DOI: https://doi.org/10.1007/s10598-007-0029-5