Abstract:
Recent advances in computing and communication technologies have led to considerable progress in multi-agent networks. A variety of applications ranging from social networks to intelligent transportation systems makes the area promising in the sense that it seeks solutions to crucial questions in all realms of life. Among various issues studied in the context of multi-agent networks, the distributed consensus problem where a group of agents working collectively to achieve a common objective, has been one of the most popular. A multi-agent network utilizing a distributed linear consensus protocol may converge to different final values depending on the structure of the communication topology. The focus of this dissertation is to analyze the convergence properties of such networks where multi-equilibria consensus emerge. The problem is first examined for undirected networks represented by static or time-varying graphs. Joint connectivity and integral/sum connectivity conditions are presented that can be utilized to determine the number of equilibria as the interactions among the agents evolve over time. Subsequently, the analysis is extended to the study of multi-equilibria consensus in directed networks for which novel concepts of primary and secondary layer subgraphs are introduced. It is theoretically shown that the number of consensus equilibria of a network can be expressed as the total number of these subgraphs which can automatically be determined by a computer program. The convergence properties of multi-equilibria consensus in directed networks with bounded time-delays are also investigated and it is shown that communication time-delays do not affect the number of equilibria of a given network.
