Volume 40, pp. 249-267, 2013.

Adaptive regularization and discretization of bang-bang optimal control problems

Daniel Wachsmuth

Abstract

In this article, Tikhonov regularization of control-constrained optimal control problems is investigated. Typically the solutions of such problems exhibit a so-called bang-bang structure. We develop a parameter choice rule that adaptively selects the Tikhonov regularization parameter depending on a posteriori computable quantities. We prove that this choice leads to optimal convergence rates with respect to the discretization parameter. The article is complemented by numerical results.

Full Text (PDF) [228 KB]

Key words

optimal control, bang-bang control, Tikhonov regularization, parameter choice rule

AMS subject classifications

49K20, 49N45, 65K15

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