Abstract:
Time optimal problems with two-sided boundary controls for the wave equation are considered in classes of strong generalized solutions. Various combinations of boundary conditions of the first, second, and third kinds are admitted in the statement. A noise-immune algorithm is proposed for the approximate calculation of the optimal time and the corresponding boundary controls. The approximate solutions are shown to converge under asymptotic refinement of the parameters of finite-dimensional approximation and a decrease in the error level in the definition of target functions.
Citation:
D. A. Ivanov, M. M. Potapov, “Approximate solution to a time optimal boundary control problem for the wave equation”, Optimal control, Collected papers. In commemoration of the 105th anniversary of Academician Lev Semenovich Pontryagin, Trudy Mat. Inst. Steklova, 291, MAIK Nauka/Interperiodica, Moscow, 2015, 112–127; Proc. Steklov Inst. Math., 291 (2015), 102–117
\Bibitem{IvaPot15}
\by D.~A.~Ivanov, M.~M.~Potapov
\paper Approximate solution to a time optimal boundary control problem for the wave equation
\inbook Optimal control
\bookinfo Collected papers. In commemoration of the 105th anniversary of Academician Lev Semenovich Pontryagin
\serial Trudy Mat. Inst. Steklova
\yr 2015
\vol 291
\pages 112--127
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/tm3663}
\crossref{https://doi.org/10.1134/S037196851504010X}
\elib{https://elibrary.ru/item.asp?id=24776667}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2015
\vol 291
\pages 102--117
\crossref{https://doi.org/10.1134/S0081543815080106}
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Linking options:
https://www.mathnet.ru/eng/tm3663
https://doi.org/10.1134/S037196851504010X
https://www.mathnet.ru/eng/tm/v291/p112
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