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Optimal feedback control in first-passage resetting

Davin Lunz 1, 2, *
* Corresponding author
2 COMMANDS - Controle, Optimisation, modèles, Méthodes et Applications pour les Systèmes Dynamiques non linéaires
CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique, Inria Saclay - Ile de France
Abstract : We study a diffusion process on a finite interval under the influence of a controllable drift where the particle resets to the left-hand side upon reaching the right-hand side. Assigning a pay-off for being nearer the right-hand side, but a penalty for reaching it, induces an inherent trade-off. We seek the drift feedback that maximises the long-term reward. By reducing the problem to a constrained variational problem we deduce that, for a wide class of problems, the optimal feedback law is remarkably straightforward: below a threshold state exert maximum drift; beyond the threshold exert minimum drift.
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Submitted on : Thursday, July 15, 2021 - 8:47:26 PM
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Davin Lunz. Optimal feedback control in first-passage resetting. Journal of Physics A: Mathematical and Theoretical, IOP Publishing, 2020, 53 (44), pp.44LT01. ⟨10.1088/1751-8121/abbc7c⟩. ⟨hal-03287816⟩



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