  In this work, we design a type of controller that consists of adding a
specific set of reactions to an existing mass-action chemical reaction network
in order to control a target species. This set of reactions is effective for
both deterministic and stochastic networks, in the latter case controlling the
mean as well as the variance of the target species. We employ a type of network
property called absolute concentration robustness (ACR). We provide
applications to the control of a multisite phosphorylation model as well as a
receptor-ligand signaling system. For this framework, we use the so-called
deficiency zero theorem from chemical reaction network theory as well as
multiscaling model reduction methods. We show that the target species has
approximately Poisson distribution with the desired mean. We further show that
ACR controllers can bring robust perfect adaptation to a target species and are
complementary to a recently introduced antithetic feedback controller used for
stochastic chemical reactions.
