Networked Dynamic Systems: Identification, Controllability, and Randomness

Abstract

The presented dissertation aims to develop a graph-centric framework for the analysis and synthesis of networked dynamic systems (NDS) consisting of multiple dynamic units that interact via an interconnection topology. We examined three categories of network problems, namely, identification, controllability, and randomness. In network identification, as a sub-class of inverse problems, we made an explicit relation between the input-output behavior of an NDS and the underlying interacting network. In network controllability, we provided structural and algebraic insights into features of the network that enable external signal(s) to control the state of the nodes in the network for certain classes of interconnections, namely, path, circulant, and Cartesian networks. We also examined the relation between network controllability and the symmetry structure of the graph. Motivated by the analysis results for the controllability and observability of deterministic networks, a natural question is whether randomness in the network layer or in the layer of inputs and outputs generically leads to favorable system theoretic properties. In this direction, we examined system theoretic properties of random networks including controllability, observability, and performance of optimal feedback controllers and estimators. We explored some of the ramifications of such an analysis framework in opinion dynamics over social networks and sensor networks in estimating the real-time position of a Seaglider from experimental data.