Complex networks: analysis and control

The introduction provides an overview on complex networks, trying to investigate what apparently different kinds of networks have in common. Some statistical properties are illustrated and a simulation tool for the analysis of complex networks is presented. A weighted directed random graph is used as network model. The graph contains a fixed number N of nodes and a variable number of edges: in particular, each edge is present with probability p. Some statistical properties (such as strong connection, global and local efficiency, cost, etc) are computed and their reliance on probability p is studied. Some probability distributions (such as shortest path, edge/node load) are also drawn and, by using the method of stages, the best fitting curves are computed. The way as parameters characterizing such curves change when p varies is also investigated. The general structure of the proposed fitting technique allows to model several aspects of complex networks and makes possible its use in many different fields. Finally, the tracking control problem of linear time invariant (LTI) systems when the plant and the controller belong to the same network is considered. Time delays can degrade significantly the performance of a networked control system, eventually leading to instability. The problem characterized by constant and known network delays is analytically examined, showing how to construct a plant state predictor in order to compensate the time delays between the plant and the controller, so to allow the tracking of a reference signal. Computer simulations illustrate the effectiveness of the proposed technique, also when time delays slightly vary around a mean value.