Efficient mitigation of power amplifier (PA) nonlinear distortion in hybrid precoding based broadband mmWave systems is an open research problem. In this article, we first carry out detailed signal and distortion modeling in broadband multi-user hybrid MIMO systems with a bank of nonlinear PAs in each subarray. Building on the derived models, we then propose a novel digital predistortion (DPD) solution that requires only a single DPD unit per transmit chain or subarray. The proposed DPD system makes use of a closed-loop learning architecture and combined feedback observation receivers that merge the individual PA output signals within each subarray for DPD parameter learning purposes. Such combined feedback signals reflect the true received signals at the intended users, from the nonlinear distortion point of view.