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

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Abstract

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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Acknowledgements

The author would like to express her gratitude to anonymous referees for very helpful comments.

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Authors and Affiliations

  1. Chair of Optimization, Brandenburg University of Technology Cottbus-Senftenberg, P.O.B. 10 13 44, 03013, Cottbus, Germany

    Valeriya Lykina

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  1. Valeriya Lykina
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Correspondence to Valeriya Lykina.

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Communicated by Hans Josef Pesch.

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Lykina, V. An Existence Theorem for a Class of Infinite Horizon Optimal Control Problems. J Optim Theory Appl 169, 50–73 (2016). https://doi.org/10.1007/s10957-013-0500-8

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