Local stabilizability implies global controllability in catalytically-controlled reaction networks

Controlling complex reaction networks is a fundamental challenge in the fields of physics, chemistry, biology, and systems engineering. However, theories for the controllability of such nonlinear systems are yet under development. Here, we prove a general principle for catalytically-controlled reaction systems with kinetics where the reaction order and the stoichiometric coefficient match: the local stabilizability of a given state implies global controllability within its stoichiometric compatibility class. In other words, if a target state can be maintained against small perturbations by a catalytic control, the system can be catalytically controlled from any initial condition to that state. This result highlights a tight link between the local and global dynamics of nonlinear chemical reaction systems, and a clear relationship between controllability and thermodynamic consistency of the reaction systems. The findings illuminate the robustness of biochemical systems and offer a way to control catalytic reaction systems in a generic framework. Development of theories for controllability of complex biochemical reaction networks is essential for understanding nonequilibrium processes and living systems. The authors demonstrate for a wide variety of catalytically controlled reaction networks that local stabilizable states are globally controllable from arbitrary states.