On the Innocuousness of Deterministic p-type Antithetic Integral Controllers Arising in Integral Rein Control

Abstract

The innocuousness property of a controller is that property that makes the closed-loop system stable regardless the values of the controller parameters. In other words, the closedloop system exhibits some structural stability property with respect to the parameters of the controller. The innocuousness property was first emphasized in [1] where it was shown that for stochastic unimolecular networks, the Antithetic Integral Controller (AIC) is innocuous under very mild conditions on the controlled network; namely the ergodicity and the outputcontrollability of the open-loop network, and the admissibility of the set-point value. We show here that the class of p-type AIC controllers arising in the use of Antithetic Integral Rein Controllers (AIRC) also exhibit such a property. It is shown in the unimolecular reaction network case that the closed-loop network is structurally stable with respect to the controller parameters provided that the open-loop dynamics is stable and that the set-point is admissible. Those results are then extended to the case of so-called output unstable linear systems and to stable nonlinear networks. Some examples are given for illustration.

Cascaded Antithetic Integral Feedback for Enhanced Stability and Performance

“…to enhance the dynamic performance [12], [24]- [27]. Recent works have also studied the stabilization of this controller when controlling certain plants [28]- [34]. Suggested stabilizing approaches hitherto include exploiting the controller constant degradation/dilution, molecular buffering [32], lowgain actuation, and the rein mechanism [30].…”