In this study, we consider a regulation problem for molecular robotics realized by DNA reactions. The control objective is to regulate the concentration of a target DNA strand to a desired level using practical DNA circuits. This is a challenging problem as regards to the architecture of the molecular robot, because of the corresponding positiveness, modularity, and finiteness problems. A DNA comparator-based controller with DNA amplifiers is proposed, and it is shown to successfully achieve the control objective. The properties and the stability of the system are evaluated in terms of both retroactivity and the Lyapunov stability theory for a positive second-order system. To the best of our knowledge, this is the first study to realize a regulator in a practical DNA reaction system for molecular robotics.
