Characterization of Sets of Driver Nodes of Complex Networks with Actuators Saturation

Abstract

A complex network system is defined as a network consisting of several nodes which interact with each other to share information. The controllability study- how to drive network to desired state- of complex networks is of paramount importance as perturbations to one node can affect other nodes, potentially causing the entire network to change behavior or fail. A network is said to be controllable if it can be driven from any initial state to the desired final state in finite time using a set of driver nodes. There are several networks for which set of driver nodes is not unique. This raises an important question, how to select driver node(s) when there are multiple options available. This thesis proposes a theory and algorithms to characterize the sets of driver (control) nodes of unstable complex networks. The proposed algorithms identifies a right set of driver nodes when there are multiple sets of driver nodes qualify for driver nodes set. The proposed method is based on maximization of stability regions. A realistic situation where driver node has limited actuating capability is considered. The proposed control law considers actuator saturation a priori and also ensures a specified convergence rate of states. A new method based on the degree distributions of the sets of driver nodes is proposed to identify the right set of driver nodes. This method maximizes the stability region and ensures a specified convergence rate of states for directed cyclic networks. The proposed theoretical developments are verified through simulation of numerical examples and illustrated through a robotic network application.