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/}
}
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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/