Linear State-Space Identification of Interconnected Systems: A structured approach

Abstract

In this thesis, three novel state-space identification algorithms for linear interconnected systems are proposed. The computational complexity and the topology reconstruction of the interconnected system are addressed. Possible applications of this theory can be found in Biology, Economics, Transportation, Electrical and Mechanical Engineering. The ?rst method estimates the parameters of a large string of interconnected systems in line. Every subsystem is parameterized in state-space form and can be different from each other (a heterogeneous one-dimensional string is considered). The main feature of the proposed method is that both the amount of memory and the number of operations used during the estimation process increase linearly with respect to the number of subsystems. In the second method, an extension of the Past Output Multivariable Output-Error State-sPace (PO-MOESP) identification algorithm for Directed Acyclic Graph (DAGs) is proposed. In this case, the interconnection structure (topology) of the graph is assumed to be unknown. The method proposed in this thesis is able to reconstruct the exact topology of the class of Almost Complete DAGs using input-output data of every node only. Finally, the third methodology extends the classical PO-MOESP identification approach to Hierarchical DAG topologies. It is also assumed that the interconnection structure of the graph is unknown. Exact topology reconstruction is achieved together with consistent estimates of the state-space model for every node.