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

Fabbri, Giorgio and Gozzi, Fausto and Swiech, Andrzej (2007): Verification theorem and construction of epsilon-optimal controls for control of abstract evolution equations.

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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.

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