Leader selection in networks under switching topologies with antagonistic interactions

In leader–follower networks, leader selection is an important issue, and efficient schemes of selecting a group of leaders are sought to guarantee the desired coordination performance. In this paper, we study the leader selection problem under switching topologies, and aim to minimize the number of leaders to ensure the consensus of high-order multiagent systems with antagonistic interactions, which are usually represented by negative edge weights on a communication graph. First, as the basis of leader selection, sufficient conditions including average dwell time bounds for each possible topology and a mild network connectivity assumption are derived for followers to reach the expected property. Second, by applying the derived consensus criterion, metrics for identifying leaders are established via the submodular optimization method, and the supermodularity of the metrics is proved in the digraph case. Third, by utilizing the established metrics, a leader selection scheme with two polynomial-time algorithms is presented to determine leaders dynamically, and the optimality of the returned solution has a provable guarantee. Finally, the performance of the proposed leader selection scheme is demonstrated by numerical examples.