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Optimal feedback control in first-passage resetting
Journal of Physics A: Mathematical and Theoretical ( IF 2.0 ) Pub Date : 2020-10-15 , DOI: 10.1088/1751-8121/abbc7c
Davin Lunz

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.



中文翻译:

首段复位中的最优反馈控制

我们研究了在可控漂移的影响下有限间隔上的扩散过程,其中粒子在到达右侧时重置到左侧。为靠近右手边分配回报,但对到达右手边进行惩罚,会导致内在的权衡。我们寻求最大化长期回报的漂移反馈。通过将问题简化为一个受约束的变分问题,我们推断,对于一大类问题,最优反馈定律非常简单:低于阈值状态产生最大漂移;超过阈值施加最小漂移。

更新日期:2020-10-15
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