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This paper presents an adaptive robust predictive current control (RPCC) for grid-connected three-phase inverters that exhibit zero steady-state current error. The error correction is achieved by means of an adaptive strategy that works in parallel with the deadbeat algorithm, therefore preserving the typical fast response of the predictive law. The resulting control adapts to any particular L or LCL filter by estimation of the resistive part of the filter. As a variety of the RPCC class of control, it offers the best tradeoff between robustness and speed.