PO-MOESP subspace identification of Directed Acyclic Graphs with unknown topology

In this paper, a PO-MOESP subspace identification algorithm for Directed Acyclic Graphs (DAG) is presented. The state of every node and the structure of the graph are assumed to be unknown. The method estimates the column space of the observability matrix of every node by projecting away the input-output data from the rest of the graph. A past input-output instrumental variable (IV) approach is adopted to deal with the noise. The topology of the network is revealed by using dedicated projection matrices. Moreover, we provide a characterization of the class of graphs whose topology can be fully reconstructed by using this method. Finally, two simulation examples are provided to show the effectiveness of the proposed methodology.