Complex Networked Systems: Convergence Analysis, Dynamic Behaviour, and Security.

Complex networked systems are a modern reference framework through which very dierent systems from far disciplines, such as biology, computer science, physics, social science, and engineering, can be described. They arise in the great majority of modern technological applications. Examples of real complex networked systems include embedded systems, biological networks, large-scale systems such as power generation grids, transportation networks, water distribution systems, and social network. In the recent years, scientists and engineers have developed a variety of techniques, approaches, and models to better understand and predict the behaviour of these systems, even though several research and industrial challenges are still open. This thesis addresses the study of dierent properties of complex networked systems and their applications. The main contribution of the work can be considered as threefold: the study of interaction among agents and the relative data clustering in small groups, the analysis of convergence conditions towards a common or multiple agreements, and the investigation of security aspects concerning the detection of perturbations that can propagate across network components and subnetworks. Firstly, a novel approach to solve data clustering problems within wireless sensor networks is proposed, including additional constraints on the distance among cluster centroids. A key feature of the presented algorithm is its ability to partition the original raw dataset into a suboptimal set of clusters, without the requirement of a priori specication of the desired cluster number. Secondly, after introducing a mathematical framework describing the dynamic model of a complex network, a set of centralised and distributed conditions are determined, allowing the detection of the connectedness of the network's underlying topological structure, its convergence to a steady state, and even to an agreement. To this purpose, the so-called Hegselmann-Krause opinion dynamics model is adopted, which describes the way agents of a community dynamically in uence with each other. Thirdly, the problem of optimal sensor location within a class of networked systems, which requires the detection of unknown input disturbance, is addressed. To this aim, a measure simultaneously based on the properties of controllability and observability of the network is used, which allows dierent sensor locations to be evaluated with respect to the location of the signal to be detected. These results inform the design of robust networks, and they suggest that sensor location methods based on the network topology alone may lead to poor detection performance.