Distributed group consensus in time-varying networks

In past decades, the problem of achieving a common value in a distributed network, or in other words, the distributed consensus problem, has drawn significant attention from researchers due to its rapidly increasing application area, such as mobile robots, clock synchronization, orientation and flight formation of unmanned air vehicles, smart power grids, and rendezvous problem. These applications involve the design and analysis of distributed consensus algorithms regarding the stability and convergence properties of the algorithm. Depending on the topology of the network, consensus can be achieved in the sense of all agents achieving a common state, where complete agreement is beheld, which is a well-studied problem in the literature, as well as consensus can be achieved in the sense of agents form clusters, where the full agreement does not happen. However, we may still claim a partial agreement state has been reached in terms of multiple equilibrium states. This thesis analyzes the multi-equilibria consensus problem for multi-agent networks under switching topologies in discrete time. The main contributions of the thesis are to give sufficient conditions for a network to achieve multi-equilibria consensus under dynamically changing topologies and to express the number of equilibria points in terms of the network's topological properties. It is also demonstrated that the proposed definition of the reduced graph and graph reduction method reduces the size of the network while preserving some critical structural and topological properties that are used to determine the number of clusters forming in the steady-state.