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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.

Minimal control effort and time Lie-group synchronisation design based on proportional-derivative control