In this paper, a converter-based multi-bus DC microgrid (MG) in series is studied, in which the trade-off between voltage recovery and current equalization has been a hot topic of interest. To solve this problem, a distributed learning-based high-order fully actuated (DL-HOFA) secondary control is proposed in this paper, and the simple structure of this control technique facilitates its application in various modern DC MGs with different configurations. Before designing the secondary control protocol, this paper provides a comprehensive description of DC MGs in advance. In the suggested control strategy, the controller design is tightly related to the underlying physical characteristics of the MG, and this prominent feature represents a significant improvement in its adaptability. In addition, the DL-HOFA control obtains fast dynamic and accurate current sharing performance by virtue of the high-order fully actuated DC MG model. The effectiveness of the proposed control method is verified on a real photovoltaic- and battery-based hardware system with maximum power point tracking (MPPT) controller.