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Journal of Convex Analysis 17 (2010), No. 2, 611--642
Copyright Heldermann Verlag 2010



Verification Theorem and Construction of ε-Optimal Controls for Control of Abstract Evolution Equations

Giorgio Fabbri
Dip. di Studi Economici, UniversitÓ di Napoli
and: School of Mathematics and Statistics, University of New South Wales, Sydney, Australia
giorgio.fabbri@uniparthenope.it

Fausto Gozzi
Dip. di Scienze Economiche ed Aziendali, Libera UniversitÓ Internazionale degli Studi Sociali, Viale Pola 12, 00198 Roma, Italy
fgozzi@luiss.it

Andrzej Swiech
School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332, U.S.A.
swiech@math.gatech.edu



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.

Keywords: Optimal control of PDE, verification theorem, dynamic programming, epsilon-optimal controls, Hamilton-Jacobi-Bellman equations.

MSC: 35R15, 49L20, 49L25, 49K20

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