Optimality conditions for state-constrained PDE control problems with time-dependent controls

• Autorzy: Los Reyes J. C. de , Merino P. , Rehberg F. , Troltzsch F.
• Języki publikacji: EN

Abstrakty

EN

The paper deals with optimal control problems for semilinear elliptic and parabolic PDEs subject to pointwise state constraints. The main issue is that the controls are taken from a restricted control space. In the parabolic case, they are Rm -vector-valued functions of time, while they are vectors of Rm in elliptic problems. Under natural assumptions, first- and second-order sufficient optimality conditions are derived. The main result is the extension of second-order sufficient conditions to semilinear parabolic equations in domains of arbitrary dimension. In the elliptic case, the problems can be handled by known results of semi-infinite optimization. Here, different examples are discussed that exhibit different forms of active sets and where second-order sufficient conditions are satisfied at the optimal solution.

Słowa kluczowe

EN

parabolic equation; elliptic equation; optimal control; pointwise state constraints; sufficient optimality conditions; restricted control class

PL

równanie paraboliczne; równanie eliptyczne; sterowanie optymalne

• Wydawca: Systems Research Institute, Polish Academy of Sciences
• Czasopismo: Control and Cybernetics
• Rocznik: 2008
• Tom: Vol. 37, no 1
• Strony: 5--38
• Opis fizyczny: Bibliogr. 33 poz.

Twórcy

autor

Los Reyes J. C. de

autor

Merino P.

autor

Rehberg F.

autor

Troltzsch F.

• Department of Mathematics, EPN Quito, Ecuador

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