Hybrid Control of a Bioreactor with Quantized Measurements: Extended Version

TL;DR

This paper presents a control strategy for stabilizing an unstable bioreactor model using quantized measurements, ensuring convergence despite measurement discretization and uncertainties.

Contribution

It introduces a novel quantized control approach for bioreactors, analyzing stability and transition dynamics with both perfect and uncertain measurements.

Findings

Quantized control can achieve global stabilization under certain conditions.

Transitions between measurement regions guide trajectories toward equilibrium.

Sliding modes may occur when assumptions are violated.

Abstract

We consider the problem of global stabilization of an unstable bioreactor model (e.g. for anaerobic digestion), when the measurements are discrete and in finite number ("quantized"), with control of the dilution rate. The model is a differential system with two variables, and the output is the biomass growth. The measurements define regions in the state space, and they can be perfect or uncertain (i.e. without or with overlaps). We show that, under appropriate assumptions, a quantized control may lead to global stabilization: trajectories have to follow some transitions between the regions, until the final region where they converge toward the reference equilibrium. On the boundary between regions, the solutions are defined as a Filippov differential inclusion. If the assumptions are not fulfilled, sliding modes may appear, and the transition graphs are not deterministic.