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Control and Cybernetics

Tytuł artykułu

Dirichlet control problems in smooth and nonsmooth convex plain domains

Autorzy Casas, E.  Mateos, M. 
Treść / Zawartość
Warianty tytułu
Języki publikacji EN
EN In this paper we collect some results about boundary Dirichlet control problems governed by linear partial differential equations. Some differences are found between problems posed on polygonal domains or smooth domains. In polygonal domains some difficulties arise in the corners, where the optimal control is forced to take a value which is independent of the data of the problem. The use of some Sobolev norm of the control in the cost functional, as suggested in the specialized literature as an alternative to the L2norm, allows to avoid this strange behavior. Here, we propose a new method to avoid this undesirable behavior of the optimal control, consisting in considering a discrete perturbation of the cost functional by using a finite number of controls concentrated around the corners. In curved domains, the numerical approximation of the problem requires the approximation of the domain Ω typically by a polygonal domain Ωh, this introduces some difficulties in comparing the continuous and the discrete controls because of their definition on different domains Γ and Γh, respectively. We complete the existing recent analysis of these problems by proving the error estimates for a full discretization of the control problem. Finally, some numerical results are provided to compare the different alternatives and to confirm the theoretical predictions.
Słowa kluczowe
EN optimal control   boundary control   Dirichlet control  
Wydawca Systems Research Institute, Polish Academy of Sciences
Czasopismo Control and Cybernetics
Rocznik 2011
Tom Vol. 40, no 4
Strony 931--955
Opis fizyczny Bibliogr. 19 poz.
autor Casas, E.
autor Mateos, M.
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