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Discrete repetitive processes (DRPs) operate iteratively on a fixed-length time window or trial, with the feature that the state and output on each trial are driven by the output of the previous trial. This class of systems includes the case of iterative learning control (ILC). Typical control algorithms in ILC and DRP produce N-th order closed-loop systems, where N is the trial length. Here we marry three existing results to demonstrate a DRP control algorithm that (1) uses the internal model principle to track iteration-varying signals (robust servomechanism); (2) produces a reduced-order closed-loop system; and (3) adaptively converges in the absence of plant knowledge.