On leader election in multi-agent control systems

In this contribution, we discuss the election of an optimal leader out of a network of agents described by first integrator dynamics and running a consensus algorithm. The network of agents may be a group of autonomous robots or more generally communicating vehicles, and the target is, for instance, to move the formation to a new location. A leader is said to be optimal if it leads to a controllable network, and minimizes a quadratic cost of reaching a target for all the other agents of the network. In the first part, controllability conditions and a decentralized way of checking them are discussed. We then study the correlation between the value of a quadratic cost function measuring the leader performance and the network properties. Strong correlation is found between closeness and degree centrality indices of the agents and the cost of achieving the assigned tasks. This allows us to run the optimal leader election process without a central authority and without the nodes having full knowledge of the network topology.