Geodesic
Verification Theorem and Construction of ε-Optimal Controls for Control of Abstract Evolution Equations
Journal of convex analysis, Tome 17 (2010) no. 2, pp. 611-642

Voir la notice de l'article provenant de la source Heldermann Verlag

We study several aspects of the dynamic programming approach to optimal control of abstract evolution equations, including a class of semilinear partial differential equations. We introduce and prove a verification theorem which provides a sufficient condition for optimality. Moreover we prove sub- and superoptimality principles of dynamic programming and present an explicit construction of ε-optimal controls.
Classification : 35R15, 49L20, 49L25, 49K20
Mots-clés : Optimal control of PDE, verification theorem, dynamic programming, epsilon-optimal controls, Hamilton-Jacobi-Bellman equations 
@article{JCA_2010_17_2_JCA_2010_17_2_a15,
     author = {G. Fabbri and F. Gozzi and A. Swiech},
     title = {Verification {Theorem} and {Construction} of {\ensuremath{\varepsilon}-Optimal} {Controls} for {Control} of {Abstract} {Evolution} {Equations}},
     journal = {Journal of convex analysis},
     pages = {611--642},
     publisher = {mathdoc},
     volume = {17},
     number = {2},
     year = {2010},
     url = {http://geodesic.mathdoc.fr/item/JCA_2010_17_2_JCA_2010_17_2_a15/}
}
TY  - JOUR
AU  - G. Fabbri
AU  - F. Gozzi
AU  - A. Swiech
TI  - Verification Theorem and Construction of ε-Optimal Controls for Control of Abstract Evolution Equations
JO  - Journal of convex analysis
PY  - 2010
SP  - 611
EP  - 642
VL  - 17
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/JCA_2010_17_2_JCA_2010_17_2_a15/
ID  - JCA_2010_17_2_JCA_2010_17_2_a15
ER  - 
%0 Journal Article
%A G. Fabbri
%A F. Gozzi
%A A. Swiech
%T Verification Theorem and Construction of ε-Optimal Controls for Control of Abstract Evolution Equations
%J Journal of convex analysis
%D 2010
%P 611-642
%V 17
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/JCA_2010_17_2_JCA_2010_17_2_a15/
%F JCA_2010_17_2_JCA_2010_17_2_a15
G. Fabbri; F. Gozzi; A. Swiech. Verification Theorem and Construction of ε-Optimal Controls for Control of Abstract Evolution Equations. Journal of convex analysis, Tome 17 (2010) no. 2, pp. 611-642. http://geodesic.mathdoc.fr/item/JCA_2010_17_2_JCA_2010_17_2_a15/