Optimal feedback control in first-passage resetting

Davin Lunz (1, 2)

1 InBio - InBio - Méthodes Expérimentales et Computationnelles pour la Modélisation des Processus Cellulaires / Experimental and Computational Methods for Modeling Cellular Processes
2 COMMANDS - Controle, Optimisation, modèles, Méthodes et Applications pour les Systèmes Dynamiques non linéaires

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]

Davin Lunz. Optimal feedback control in first-passage resetting. Journal of Physics A: Mathematical and Theoretical, 2020, 53 (44), pp.44LT01. ⟨10.1088/1751-8121/abbc7c⟩. ⟨hal-03287816⟩