Abstract
For a problem of optimal control for a parabolic equation, in the case of bounded control, we construct and justify an approximate averaged control in the form of feedback.
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REFERENCES
A. I. Egorov, Optimal Control of Heat and Diffusion Processes [in Russian], Nauka, Moscow (1978).
J.-L. Lions, Controle Optimal de Systemes Gouvernes par des Equations aux Derivees Partielles, Gauthier-Villars, Paris (1968).
O. A. Kapustyan, “Approximate synthesis of an optimal bounded control for a parabolic boundary-value problem,” Ukr. Mat. Zh., 54, No.12, 1704–1709 (2002).
E. A. Kapustyan and A. G. Nakonechnyi, “Synthesis of an optimal bounded control for a parabolic boundary-value problem with rapidly oscillating coefficients,” Probl. Upravl. Inform., No. 6, 44–57 (1999).
R. Temam, Infinite-Dimensional Dynamical Systems in Mechanics and Physics, Springer, New York (1997).
V. V. Zhikov, S. M. Kozlov, and O. A. Oleinik, Averaging of Differential Operators [in Russian], Fizmatlit, Moscow (1993).
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 56, No. 10, pp. 1384–1394, October, 2004.
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Sukretna, A.V., Kapustyan, O.A. Approximate Averaged Synthesis of the Problem of Optimal Control for a Parabolic Equation. Ukr Math J 56, 1653–1664 (2004). https://doi.org/10.1007/s11253-005-0141-7
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DOI: https://doi.org/10.1007/s11253-005-0141-7