Optimal feedback control in first-passage resetting
Résumé
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.
Domaines
Mathématiques générales [math.GM]Origine | Fichiers produits par l'(les) auteur(s) |
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