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

Details Verification theorem and construction of $ε$-optimal controls for control of abstract evolution equations Verification theorem and construction of $ε$-optimal controls for control of abstract evolution equations

2007-06-10

arxiv.org/abs/0706.1339v1

Mathematics

Optimization and Control

28 pages

Scientific paper

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.

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