Modeling and Control of Networked Kinetic Systems with Delayed Interconnections

The modeling and control of networks of kinetic systems, also called chemical reaction networks (CRNs), containing distributed delays are considered in this paper. The nodes in the network are sub-CRNs with nonnegative nonlinear dynamics, while the interconnections are modeled as linear connecting CRNs. Distributed delays appearing in the system are described as physically motivated connecting sub-CRNs with asymptotically stable linear compartmental dynamics. A control model is given for the studied system class, where the manipulable inputs are selected inlet concentrations, and the control goal is to achieve global stability by ensuring the complex balanced property of the closed loop system. Besides stabilization, the tracking of prescribed setpoints is also solved using a suitable decentralized feedforward-feedback combination. The operation of the proposed method is illustrated through a network containing three sub-CRNs and several linear interconnections.