Double-Integrator Leader-Follower Networks: Sufficient Conditions for Connectivity Maintenance

Abstract: In this thesis, a set of sufficient conditions that guarantee consensus towards a pre-specified target state in double-integrator leader-follower networks are derived. Since only the leader agents are aware of the global objective and proximity based communication between all agents is considered, the follower agents must not lose contact to the leaders. In a first step, it is shown that such consensus seeking networks converge to the leader induced target state, as long as the interconnection graph is connected. A connectivity analysis framework is then established to make statements on the interconnection of any two initially connected agents during evolution of the system. This framework is subsequently used to state conditions which ensure preservation of all inter-agent links – and thus keeping the graph connected. These sufficient conditions put constraints on the magnitude of the goal attraction force experienced by the leaders as well as on the ratio of leader and follower agents in the network. Various different network topologies are examined, starting from an initially complete graph structure and extending to incomplete graphs. The theoretical results are illustrated by numerous computer simulations highlighting the relevance and effectiveness of the presented conditions.