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This paper presents a robust natural-frame-based interfacing scheme for grid-connected distributed generation inverters. The control scheme consists of a dead-beat line-voltage sensorless natural-frame current controller, adaptive neural network (NN)-based disturbance estimator, and robust sensorless synchronization loop. The estimated uncertainty dynamics provide the necessary energy shaping in the inverter control voltage to attenuate grid-voltage disturbances and other voltage disturbances caused by interfacing parameter variation. In addition, the predictive nature of the estimator has the necessary phase advance to compensate for system delays. The self-learning feature of the NN adaptation algorithm allows feasible and easy adaptation design at different grid disturbances and operating conditions. The fact that converter synchronization is based on the fundamental grid-voltage facilitates the use of the estimated uncertainty to extract the position of the fundamental grid-voltage vector without using voltage sensors. Theoretical analysis and comparative evaluation results are presented to demonstrate the effectiveness of the proposed control scheme.