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The wide use of communication layers in DC microgrids to transmit voltage and current measurements of each distributed generator unit (DGU) increases the possibility of exposure to cyber-attacks. Cyber-attackers can manipulate the measured data to distort the control system of microgrids, which may lead to a shutdown. This paper proposes distributed mitigation layers for the false data injection attacks (FDIA) on voltages and currents of DGUs in meshed DC microgrids. The proposed control strategy is based on integrating two layers for cyber-attack detection and mitigation to immune the primary and the secondary control loops of each DGU. The first layer is assigned to mitigate FDIAs on the voltage measurements needed for the voltage regulation task of the primary control loop. The second layer is devoted to the mitigation of FDIAs on the DGU current measurements, which are crucial for the secondary control level to guarantee the proper current sharing of each DGU. Artificial neural networks (ANNs) are employed to support these layers by estimating the authenticated measurements. Different simulation and experimental case studies are provided to demonstrate the proposed mitigation layers' effectiveness in detecting and mitigating cyber-attacks on voltage and current measurements. The simulation and experimental results are provided to evaluate the dynamic performance of the suggested control approach and to ensure the accurate operation of DC microgrids despite the existence of cyber-attacks on the measurements employed in the control strategy. Moreover, the control strategy succeeds to keep the maximum voltage error and the maximum error in current sharing within tolerance. [ABSTRACT FROM AUTHOR]