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Necessary Conditions in Infinite-Horizon Control Problems that Need no Asymptotic Assumptions

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Abstract

We consider an infinite-horizon optimal control problem with an asymptotic terminal constraint. For the weakly overtaking criterion and the overtaking criterion, necessary boundary conditions on co-state arcs are deduced, these conditions need no assumptions about the asymptotic behavior of the motion, co-state arc, cost functional, and its derivatives. In the absence of an asymptotic terminal constraint, these boundary conditions with the Pontryagin Maximum Principle allow raising the co-state arcs, corresponding to some asymptotic subdifferentials of the cost functional (fixing the optimal control) at infinity. If this set is a singleton, these conditions coincide with the co-state arc representation proposed by Aseev and Kryazhimskii. These results are illustrated by several examples.

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Acknowledgements

I would like to express my gratitude to Boris Mordukhovich and Alexander Kruger for a valuable discussion in during the writing this article.

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  1. Krasovskii Institute of Mathematics and Mechanics, 16 S.Kovalevskaja St., Yekaterinburg, Russia

    Dmitry Khlopin

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Khlopin, D. Necessary Conditions in Infinite-Horizon Control Problems that Need no Asymptotic Assumptions. Set-Valued Var. Anal 31, 8 (2023). https://doi.org/10.1007/s11228-023-00672-5

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