On the Innocuousness of Deterministic p-type Antithetic Integral Controllers Arising in Integral Rein Control (2201.13375v2)

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 closed-loop system exhibits some structural stability property with respect to the parameters of the controller. The innocuousness property was first emphasized in [Briat, Gupta, and Khammash, Cell Systems, 2016] 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 output-controllability 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. Analogous results are obtained for exponential and logistic integral controllers. Some examples are given for illustration.