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, Università 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 Università 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
[ Fulltext-pdf (254 KB)] for subscribers only.