Markovian description of a wide class of feedback-controlled systems: Application to the feedback flashing ratchet
arXiv:2404.04195 · doi:10.1088/1742-5468/ad64bb
Abstract
In feedback-controlled systems, an external agent -- the feedback controller -- measures the state of the system and modifies its subsequent dynamics depending on the outcome of the measurement. In this paper, we build a Markovian description for the joint stochastic process that comprises both the system and the controller variables. This Markovian description is valid for a wide class of feedback-controlled systems, allowing for the inclusion of errors in the measurement. The general framework is motivated and illustrated with the paradigmatic example of the feedback flashing ratchet.
arXiv comment42 pages, 9 figures; major revision with respect to v1, accepted for publication in JSTAT
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