A method for the reconstruction of unknown non-monotonic growth functions in the chemostat

TL;DR

This paper introduces an adaptive control method to reconstruct unknown non-monotonic growth functions in chemostats, enabling identification of unstable steady states and graph tracing without prior knowledge of the growth function.

Contribution

The paper presents a novel adaptive control law for reconstructing non-monotonic growth functions in chemostats, including methods for continuous and step-wise graph tracing.

Findings

The control law successfully identifies unstable steady states.

Both continuous and step-wise tracing approaches are effective.

Feedback control enhances identifiability even in multi-species competition scenarios.

Abstract

We propose an adaptive control law that allows one to identify unstable steady states of the open-loop system in the single-species chemostat model without the knowledge of the growth function. We then show how one can use this control law to trace out (reconstruct) the whole graph of the growth function. The process of tracing out the graph can be performed either continuously or step-wise. We present and compare both approaches. Even in the case of two species in competition, which is not directly accessible with our approach due to lack of controllability, feedback control improves identifiability of the non-dominant growth rate.