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On a control problem governed by a linear partial differential equation with a smooth functional
Author(s) -
CriadoAldeanueva F.,
Criado F.,
Odishelidze N.,
Sanchez J. M.
Publication year - 2010
Publication title -
optimal control applications and methods
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.458
H-Index - 44
eISSN - 1099-1514
pISSN - 0143-2087
DOI - 10.1002/oca.911
Subject(s) - mathematics , optimal control , partial differential equation , boundary (topology) , maximum principle , boundary value problem , helmholtz equation , first order partial differential equation , control (management) , free boundary problem , mathematical analysis , type (biology) , mathematical optimization , computer science , ecology , artificial intelligence , biology
In this paper, the optimal control problem for the Helmholtz equation with non‐local boundary conditions is considered. The necessary and sufficient conditions of optimality in a maximum principle form have been obtained. We note that this problem is basically different from classical‐type problems because it is impossible to use Green's formula and we cannot rewrite it in the variational form widely used in the literature. So it is impossible to use all the theory that has been developed for optimal control problems with classical boundary conditions. Copyright © 2009 John Wiley & Sons, Ltd.