A non-linear <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$SoC$</tex-math></inline-formula> -adaptive management and control scheme is applied to DC microgrids (MGs) supplied by energy storage systems (ESSs) and connected to the grid. The management and control strategy are performed via decentralized methodologies, allowing power sharing between the battery banks with or without a low-speed communication link, while their limits of operation for charging and discharging are not exceeded. Additionally, the aforementioned technique is based on the sigmoidal function where the solution shows two degrees of freedom as the DC-link voltage error and the state-of-charge <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$(SoC)$</tex-math></inline-formula> in the outer loop (DC-link voltage control), and classical proportional-integral <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$(PI)$</tex-math></inline-formula> controllers regulating the current flow through the DC/DC power converters in the inner loop. To analyze the system stability, the DC MG model was calculated to evaluate the poles movement, frequency and step responses at different scenarios. Finally, the authors rely on a set of results in the Typhoon <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$^{\text{\text{®}}}$</tex-math></inline-formula> 602+ hardware to demonstrate the effectiveness of the proposed solution as well as, a comparison between it and the classical droop controller.