Distributed Design of Strong Structurally Controllable and Maximally Robust Networks

The design of multiagent networks with certain properties is in general a difficult problem. From a network control perspective, controllability and robustness are two important but opposing properties. In this dissertation, we address the problem of designing networks that are both structurally controllable and maximally robust. To achieve this objective, we propose several network constructions that are strong structurally controllable, for given network parameters the number of nodes N , leaders NL, and diameter D. To measure controllability, we employ the zero-forcing process, and subsequently, maximize the number of edges in the networks. We also evaluate network robustness using Kirchhoff index. To validate our approach, we compare our network constructions with optimal clique chains and perform numerical evaluations. Furthermore, we present a set of graph grammars that enable the distributed construction of these networks. Our work not only exploits the trade-off between controllability and robustness but also provides an optimal graph structure under specific conditions, and a near-optimal one for most cases.