Subspace Identification of Distributed Clusters of Homogeneous Systems

This note studies the identification of a network comprised of interconnected clusters of LTI systems. Each cluster consists of homogeneous dynamical systems, and its interconnections with the rest of the network are unmeasurable. A subspace identification method is proposed for identifying a single cluster using only local input and output data. With the topology of the concerned cluster being available, all the LTI systems within the cluster are decoupled by taking a transformation on the state, input and output data. To deal with the unmeasurable interconnections between the concerned cluster and the rest of the network, the Markov parameters of the decoupled LTI systems are identified first by solving a nuclear-norm regularized convex optimization, following the state-space realization of a single LTI system within the cluster by solving another nuclear-norm regularized optimization problem. The effectiveness of the proposed identification method is demonstrated by a simulation example.