Data-Driven Modeling, Estimation and Control for Networked LTI Systems

This Ph.D. thesis addresses the study of networked systems, with a particular focus on estimation and control problems. Networked systems frequently exhibit highly complex behaviors influenced by numerous factors, making it challenging to accurately model their dynamics. On the other hand, recent advances in computing capabilities of modern devices have enabled the collection and processing of large volumes of data, thus opening a new line of research aimed at using these data as an alternative description of a system, without the need for an explicit model. This has led to the rapid growth of data-driven techniques across numerous research and engineering fields. Networked systems, however, introduce an additional layer of complexity. Owing to their distributed nature, the data collected from these systems are not only partial but also local and agent-specific, and thus require integration. A common approach is the use of consensus strategies, in which each agent shares its knowledge with neighboring agents while respecting the structural constraints imposed by the network topology and connectivity. The thesis is structured into three parts. The first part addresses the state estimation problem in the presence of unknown inputs or disturbances, starting from the centralized scenario and then moving to the distributed one. In each of the considered problems, model-based solutions are first recalled, before formulating their corresponding data-driven counterparts. In the second part of the thesis, we focus on a particular class of networked systems, namely Boolean control networks. Despite the simplifying "on/off" ("active/inactive", "high/low") logic at the basis of Boolean control networks, the size and complexity of the physical systems they model (e.g., gene regulatory networks) make it difficult to derive an accurate model of the network, as well as to obtain it by means of identification techniques. Therefore, we investigate how the data-driven methodologies developed for traditional dynamical systems can be adapted and employed to solve control problems for Boolean control networks. In particular, we consider the safe control and the output regulation problems, and we derive data-based necessary and sufficient conditions for their solvability, as well as simple algorithms to obtain the solutions. Finally, in its third and last part, the thesis explores a specific application to opinion dynamics, namely the evolution of opinions in social networks. From its origins, research on opinion dynamics has struggled to find models that are accurate enough to realistically describe the phenomenon, yet simple enough to be analytically tractable for prediction and control purposes. In this thesis, we propose a modification of the well-known Friedkin-Johnsen model that is based on an intertwined evolution of opinion dynamics and appraisal dynamics, in accordance to the homophily principle, reflecting the tendency of individuals to associate with others who hold similar opinions.