In this paper, we deal with a double control task for a group of interacting agents that have second-order dynamics. Adopting the leader–follower paradigm, the given multiagent 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 that is able to capture the tracking performance of the multiagent 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 that is 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.

中文翻译：

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集体跟踪和编队控制的在线领导者选择：二阶案例

在本文中，我们处理具有二阶动力学的一组交互代理的双重控制任务。采用领导者跟随者范式，给定的多主体系统需要维持所需的编队并共同跟踪外部源仅一次向单个主体提供的速度参考，称为“领导者”。我们证明，可以通过在线不断地从座席中选择领导者来优化团队绩效。为此，我们首先定义一个合适的错误度量，该度量能够捕获多代理组的跟踪性能，同时通过（甚至随时间变化）通信图拓扑保持所需的形式。然后，我们表明，这取决于代数连通性以及取决于所选前导的特殊有向图的拉普拉斯矩阵的最大特征值。通过利用这些理论结果，我们最终设计了一种完全分布式的自适应过程，该过程能够在当前的邻居中周期性地在线选择最佳领导者。数值模拟证实了所提出的解决方案相对于其他可能策略的有效性。