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

Giorgio Fabbri; Fausto Gozzi; Andrzej Swiech

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 present an explicit construction of ε-optimal controls.

Author information

Contact details are reproduced from the original publication and may be historical.

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

Keywords

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

Mathematics Subject Classification

35R15, 49L20, 49L25, 49K20

Suggested citation

G. Fabbri, F. Gozzi, A. Swiech. “Verification Theorem and Construction of ε-Optimal Controls for Control of Abstract Evolution Equations.” Journal of Convex Analysis 17 (2010), No. 2, 611–642.