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An Existence Theorem for a Class of Infinite Horizon Optimal Control Problems

  • In this paper, we deal with infinite horizon optimal control problems involving affine-linear dynamics and prove the existence of optimal solutions. The innovation of this paper lies in the special setting of the problem, precisely in the choice of weighted Sobolev and weighted Lebesgue spaces as the state and control spaces, respectively, which turns out to be meaningful for various problems. We apply the generalized Weierstraß theorem to prove the existence result. A lower semicontinuity theorem which is needed for that is shown under weakened assumptions.

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Metadaten
Author: Valeriya Lykina
DOI:https://doi.org/10.1007/s10957-013-0500-8
ISSN:0022-3239
ISSN:1573-2878
Title of the source (English):Journal of Optimization Theory and Applications
Document Type:Scientific journal article peer-reviewed
Language:English
Year of publication:2016
Tag:Existence theorem; Weak lower semicontinuity; Weighted Sobolev and Lebesgue spaces
Volume/Year:169
Issue number:1
First Page:50
Last Page:73
Faculty/Chair:Fakultät 1 MINT - Mathematik, Informatik, Physik, Elektro- und Informationstechnik / FG Mathematik insbesondere Optimierung
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