Extremum seeking via continuation techniques for optimizing biogas production in the chemostat

TL;DR

This paper introduces a novel control strategy for optimizing biogas production in a chemostat by combining extremum seeking with continuation techniques, enabling steady-state optimization without knowing the growth rate.

Contribution

It proposes a separation of extremum seeking and feedback control problems, allowing flexible optimization algorithms to maximize biogas output in chemostats.

Findings

Method handles non-monotonic growth functions

Demonstrates effectiveness with continuation and golden-section methods

Achieves steady-state optimization without growth rate knowledge

Abstract

We consider the chemostat model with the substrate concentration as the single measurement. We propose a control strategy that drives the system at a steady state maximizing the gas production without the knowledge of the specific growth rate. Our approach separates the extremum seeking problem from the feedback control problem such that each of the two subproblems can be solved with relatively simple algorithms. We are then free to choose any numerical optimization algorithm. We give a demonstration for two choices: one is based on slow-fast dynamics and numerical continuation, the other is a combination of golden-section and Newton iteration. The method copes with non-monotonic growth functions.