In this work, we deal with a double control task for a group of interacting agents having a second-order dynamics. Adopting the leader-follower paradigm, the given multi-agent system is required to maintain a desired formation and to collectively track a velocity reference provided by an external source only to a single agent at time, called the 'leader'. We prove that it is possible to optimize the group performance by persistently selecting online the leader among the agents. To do this, we first define a suitable error metric able to capture the tracking performance of the multi-agent group while maintaining a desired formation through a (even time-varying) communication-graph topology. Then we show that this depends on the algebraic connectivity and on the maximum eigenvalue of the Laplacian matrix of a special directed graph depending on the selected leader. By exploiting these theoretical results, we finally design a fully-distributed adaptive procedure able to periodically select online the optimum leader among the neighbors of the current one. The effectiveness of the proposed solution against other possible strategies is confirmed by numerical simulations.