Jahandari, Sina2023-03-272023-03-272022-05https://hdl.handle.net/11299/253421University of Minnesota Ph.D. dissertation. May 2022. Major: Electrical/Computer Engineering. Advisor: Donatello Materassi. 1 computer file (PDF); xiii, 177 pages.In this dissertation we take a graph-theoretic approach to address different aspects of identification of dynamic networks.We consider a class of networks where each node is assumed to be a stochastic process whose output is influenced by an independent stochastic forcing input and outputs of other nodes. The links (or edges), which represent the influence of other nodes, are assumed to be causal transfer functions. The first contribution of this work is to develop a technique to consistently identify a single transfer function in a network of dynamic systems using only observational data. It is assumed that the topology is partially known, the forcing inputs are not measured, and that only a subset of the nodes outputs is accessible. The developed technique is applicable to scenarios encompassing confounding variables and feedback loops, which are complicating factors potentially introducing bias in the estimate of the transfer function. The results are based on the prediction of the output node using the input node along with a set of additional auxiliary variables which are selected only from the observed nodes. As in other related prediction error methods, the role of the auxiliary variables is to guarantee that the transfer function from the input node to the output node is consistently identified. However, similar prediction error methods provide only sufficient conditions for the appropriate choice of auxiliary variables and assume a priori information about the location of strictly causal operators in the network. In this dissertation, such an a priori knowledge is not required. Indeed, another contribution of this work is algorithms to determine if a transfer function in a dynamic network is strictly causal or not.A most remarkable feature of our approach is that the conditions for the selection of the auxiliary variables are purely graphical. Furthermore, within single-output prediction methods such conditions are proven to be necessary and sufficient to consistently identify all networks with a given topology. A fundamental consequence of this characterization is to enable the search of a set of auxiliary variables minimizing a suitable cost function for single-output prediction error identification. In particular, assuming that the observations have positive additive costs, we develop a systematic algorithm to select a set of auxiliary measurements in order to consistently identify certain transfer functions while minimizing an appropriate cost function.It is shown that sufficient and necessary conditions for consistent identification of a single transfer function are equivalent to the notion of minimum cut in an augmented graph resulted from systematically manipulating the graphical representation of the network. Then, the optimal set of auxiliary measurements minimizing the cost could be found using different approaches such as algorithms from graph theory (i.e. Ford-Fulkerson), distributed algorithms (i.e. push-relabel algorithm), or purely optimization based procedures (i.e. linear programming). The results are also extended to the more challenging scenario where the objective is simultaneously identifying multiple transfer functions. It is shown that the optimal set of observations in this case could be determined via an optimal multi-commodity flow problem with additional commodity specific constraints. Finally, we consider the problem of designing controllers for networked systems in presence of topological uncertainties.We show that, in some cases, our results in identification of networked systems can be used to model the system by a deterministic term and an uncertain term. Using properties of power spectral density, different bounds for the uncertain term of the model are found in different scenarios. Consequently, standard robust control methods are directly applicable to design a stabilizer for the closed loop system. However, because of the discrete nature of uncertainties in the structure of the network, more specialized methods might lead to a larger set of controllers.enThesis or Dissertation