A hierarchical control for an integrated voltage regulator may include a voltage regulator circuit with a plurality of parallel voltage cells, with each of the cells having a plurality of phases of interleaved voltage converters, and a feedback control associated with the cells to set identical current references for the phases. A multi-rail embodiment has a plurality of parallel voltage regulator circuits each with a plurality of parallel voltage cells, with each of the cells having a plurality of phases of interleaved voltage converters, and a feedback control associated with the circuits to sense parameters of the circuits and set identical parameter references for the phases.