Relative time-averaged gain array (RTAGA) for distributed control-oriented network decomposition

Input-output partitioning for decentralized control has been studied extensively using various methods, including those based on relative gains and those based on relative degrees and sensitivities. These two concepts are characterizations of long-time and short-time input-output response, respectively. A unifying new input-output interaction measure, called relative time-averaged gain, which characterizes the input-output interactions during a time scale of interest for linear time-invariant systems is proposed. This measure is used as a basis for community detection in the input-output bipartite graph of a process network to produce subnetworks whose responses are weakly coupled in the time scale of interest. As such, the resulting decomposition accounts for both response characteristics and the network topology, and can be used efficiently for distributed control architecture design. In a case study, the proposed decomposition is applied to the distributed model predictive control of a reactor-separator benchmark process.