The present paper introduces a novel minimal control-effort and control-time, proportional-derivative feedback control theory for second-order dynamical systems on Lie groups. The devised control theory is particularised to achieve time-synchronisation of rotational systems, with special reference to a master-slave pair of quad-rotor drones. Minimal control-effort and control-time regulation is achieved through an empirical algorithm to infer the optimal values of the proportional and derivative gain.

中文翻译：

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基于比例微分控制的最小控制量和时间李群同步设计

本文介绍了一种新的最小控制力和控制时间、比例微分反馈控制理论，用于李群上的二阶动力系统。设计的控制理论专门用于实现旋转系统的时间同步，特别参考了一对主从四旋翼无人机。通过经验算法来推断比例和微分增益的最佳值，从而实现最小的控制努力和控制时间调节。