Integral population control of a quadratic dimerization process

TL;DR

This paper presents a novel integral control approach for stabilizing the average dimer population in a quadratic reaction network without moment closure, providing explicit bounds and demonstrating effectiveness through stochastic simulations.

Contribution

It introduces a moment control method that avoids moment closure techniques and guarantees convergence for quadratic dimerization processes.

Findings

Local stabilization and convergence achieved

Explicit bounds on controller gain provided

Variance of monomer species bounded explicitly

Abstract

Moment control of a simple quadratic reaction network describing a dimerization process is addressed. It is shown that the moment closure problem can be circumvented without invoking any moment closure technique. Local stabilization and convergence of the average dimer population to any desired reference value is ensured using a pure integral control law. Explicit bounds on the controller gain are provided and shown to be valid for any reference value. As a byproduct, an explicit upper-bound of the variance of the monomer species, acting on the system as unknown input due to the moment openness, is obtained. The obtained results are illustrated by an example relying on the simulation of a cell population using stochastic simulation algorithms.