Verification theorem and construction of epsilon-optimal controls for control of abstract evolution equations

Giorgio Fabbri (), Fausto Gozzi and Andrzej Swiech

MPRA Paper from University Library of Munich, Germany

Abstract: 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 give an explicit construction of $\epsilon$-optimal controls.

Keywords: optimal control of PDE; verification theorem; dynamic programming; $\epsilon$-optimal controls; Hamilton-Jacobi-Bellman equations (search for similar items in EconPapers)
JEL-codes: C61 (search for similar items in EconPapers)
Date: 2007-05
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