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© Inria / Photo C. Morel
Quantitative biology: numbers and fluorescent cells. InBio team (Inria/Institut Pasteur)
Publication : Journal of Physics A: Mathematical and Theoretical

Optimal feedback control in first-passage resetting

Scientific Fields
Diseases
Organisms
Applications
Technique

Published in Journal of Physics A: Mathematical and Theoretical - 13 Oct 2020

Lunz D

J. Phys. A: Math. Theor. 2020; 53:44LT01

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.