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arXiv · 1910.12092

Necessary Conditions In Infinite-Horizon Control Problem That Need No Asymptotic Assumptions

Dmitry V. Khlopin
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Abstract

We consider an infinite-horizon optimal control problem with an asymptotic terminal constraint. For the 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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Dmitry V. Khlopin. 2019-10-26. Necessary Conditions In Infinite-Horizon Control Problem That Need No Asymptotic Assumptions. https://doi.org/10.1007/s11228-023-00672-5

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