Analysis of finite-time regulation property of biomolecular PI controller

In practical applications of dynamic DNA nanotechnology,a biomolecular controller is required for maintaining the operation of the molecular actuator at a desired condition based on the information from molecular sensors.By making use of the DNA strand displacement mechanism as a"programming language"in the controller design,a biomolecular PI controller has been proposed.However,this PI control system has been verified only at the simulation level,and a theoretical regulation analysis is still required.Accordingly,in this study,we perform a rigorous regulation analysis of the biomolecular PI control system.Specifically,we theoretically prove that the output signal approaches the target level at a quasi-steady state.To this end,we apply the concept of finite-time regulation property to the biomolecular PI control system.